SPINNING RESERVE ASSESSMENTIN

INTERCONNECTEDGENERATION SYSTEMS

A Thesis

Submitted to the College of Graduate Studies and Research

in Partial Fulfillment of the Requirements

for the Degree of

Doctor of Philosophyin the

Department of Electrical Engineering

Univ rsity of Saskatchewan

by

NURUL AMIN CHOWDHURY

Saskatoon, Saskatchewan

February 1989

The author claims copyright. Use shall not be made of the material con­

tained herein without proper acknowledgement, as indicated on the copyrightpage.

COPYRIGHT

The author has agreed that the Library, University of Saskatchewan,

may make this thesis freely available for inspection. Moreover, the author

has agreed that permission for extensive copying of this thesis for scholarly

purposes may be granted by the Professor who supervised the thesis work

recorded herein or, in his absence, by the Head of the Department or the

Dean of the College in which the thesis work was done. It is understood

that due recognition will be given to the author of this thesis and to the

University of Saskatchewan in any use of the material in this thesis. Copy­

ing or publication or any other use of this thesis for financial gain without

approval by the University of Saskatchewan and the author's written permis­

sion is prohibited.

Requests for perrmssion to copy or to make any other use of the

material in this thesis in whole or in part should be addressed to:

Head of the Department of Electrical EngineeringUniversity of Saskatchewan

Saskatoon, Canada S7N OWO.

11

ACKNOWLEDGEMENTS

The author would like to express his heartfelt gratitude and apprecia­

tion to Dr. R. Billinton for his guidance and consistent encouragement

throughout the course of this work. His advice and assistance in the

preparation of this thesis is thankfully acknowledged.

The author takes this opportunity to acknowledge the patience and un­

derstanding of his wife Rina, his sons Arif and Ariq.

Financial assistance provided by the Natural Science and Engineering

Research Council of Canada and the Saskatchewan Power Corporation in the

form of a Graduate Scholarship is thankfully acknowledged.

The author thankfully acknowledges the study leave granted by the

Bangladesh University of Engineering and Technology, Dhaka.

III

UNIVERSITY OF SASKATCHEWAN

Electrical Engineering Abstract 88A3Ul

SPINNING RESERVE ASSESSMENTIN INTERCONNECTED

GENERATION SYSTEMS

Student: Nurul Amin Chowdhury Supervisor: Dr. Roy Billinton

Ph. D. Thesis Presented to the

College of Graduate Studies and Research

February 1989

ABSTRACT

Most utilities use deterministic techniques to evaluate unit commitment

and spinning reserve requirements. Deterministic approaches do not specifi­cally take into account the stochastic behaviour of system components in the

determination of spinning reserve requirements. A probabilistic techniquedesignated as the 'Two Risks Concept' which considers the stochastic be­

haviour of system components as an integral element has been developed to

assess spinning reserve requirements in interconnected systems. The tech­

nique provides a rational basis for spinning reserve allocation amongst each

individual system within an interconnected configuration. The technique and

its fundamental features are illustrated in this thesis. The effect on the re­

quired spinning reserve of related system parameters, generating unit failure

probabilities and tie-line capacity are also illustrated. The technique incor­

porates the essential factors in interconnected systems which directly or in­

directly influence system spinning reserve requirements.

The spinning reserve requirements in an interconnected configuration in­

volve the recognition of contracted agreements such as export/import con­

ditions between systems. The development of export/import models and a

corresponding spinning reserve assessment process are presented in this thesis.

The availability of rapid start and hot reserve units and interruptible loads

can reduce the unit commitment risk for a given set of generation and load

conditions. Rapid start and hot reserve units have been included in the

lV

time dependent risk calculation using the Area Risk Technique. The effect

of load interruption on required spinning reserve has been studied in detail.

A technique to determine the maximum allowable time delay for load inter­

ruption is reported in this thesis. A generating system can carry an ad­

ditional load/interruptible load on top of its firm load due to the discrete

size of the generating units without having to commit any additional units

than those required to carry the firm load. A technique to determine the

additional load/interruptible load carrying capability of isolated and intercon­

nected systems is presented in this thesis.

A unit commitment technique for continually changing loads in inter­

connected systems has been developed based on the 'Two Risks Concept'.The unit commitment during a specified scheduling period is constrained byrisk criteria and economic factors. The unit commitment technique in the

presence of contracted export/import and load forecast uncertainty is

described in this thesis. A risk constrained unit loading technique for inter­

connected systems is also been presented in this thesis which utilises a least

costly deviation from economic load dispatch to satisfy the risk criteria.

Two reliability test systems have been utilised to conduct studies based on

the 'Two Risks Concept' and the results are presented in this thesis.

v

Table of Contents

COPYRIGHT. ACKNOWLEDGEMENTS 11

ABSTRACT ill

TABLE OF CONTENTS v

LIST OF FIGURES viiiLIST OF TABLES x

LIST OF PRINCIPAL SYMBOLS XIV

1. INTRODUCTION 1

2. BASIC MODELS AND SYSTEM CONCEPTS 8

2.1. Introduction 8

2.2. Basic Modelling Concepts 11

2.3. Markov Process 12

2.4. Generating Unit Models 13

2.4.1. Two-state model 13

2.4.2. Multi-state model 15

2.5. Matrix Multiplication Method 172.6. Capacity Outage Probability Table 21

2.7. Assessment of Spinning Reserve in a Single System 222.8. Unit Commitment in a Single System 25

2.9. Summary 27

3. SPINNING RESERVE EVALUATION IN INTERCON- 28

NECTED SYSTEMS

3.1. Introduction 28

3.2. Two Risks Concept 29

3.2.1. Equal and Unequal Single System Risk 35

3.3. Effect of Tie-line Capacity 373.4. Effect of a Load Change in One System on The Other System 40

3.5. Effect of Unit Failure Rates on Spinning Reserve 43

3.6. Rapid Start and Hot Reserve Units 46

3.6.1. Rapid start and hot reserve unit models 50

3.6.1.1. Rapid start units 50

3.6.1.2. Hot reserve units 51

3.7. Effect of Load Forecast Error 55

3.8. Summary 63

VI

4. SPINNING RESERVE WITH EXPORT/IMPORT 64

4.1. Introduction 64

4.2. Export/Import Agreements 65

4.3. Firm Purchase Backed Up by the Complete System 65

4.3.1. Tie-line constrained import model 66

4.3.2. Export/import constrained tie-line model 684.3.3. Tie-line failure neglected 70

4.4. Firm Purchase Backed Up by a Specific Unit 704.4.1. Export model 714.4.2. Tie-line constrained import model 724.4.3. Export/import constrained tie-line model 734.4.4. Remainder of the exporting generating unit 734.4.5. Tie-line failures neglected 74

4.5. Interconnected System Risk 75

4.6. Numerical Examples 76

4.6.1. Firm purchase backed up by the entire system 764.6.2. Firm purchase backed up by a specific unit 80

4.7. Effect of Export/Import on the Level of Assistance 86

4.8. Summary 88

5. INTERRUPTIBLE LOAD CONSIDERATIONS 90

5.1. Introduction 90

5.2. Interruptible Loads in a Single System 91

5.3. Additional Load/Interruptible Load Carrying Capability of a 99

System5.4. Additional Load/Interruptible Load Carrying Capability for Dif- 104

ferent System Lead Times5.5. Effect of Firm Load Variation on the Additional 107

Load/Interruptible Load Carrying Capability5.6. Daily Additional Load/Interruptible Load Carrying Capability of 108

a Generation System5.7. Interruptible Loads in an Interconnected System5.8. Interruptible Load Carrying Capability of Interconnected

tems

5.9. Summary6. UNIT COMMITMENT

6.1. Introduction6.2. Loading Order6;3. Start-Up Cost6.4. Dynamic Programming6.5. Scheduling Using the 'Two Risks Concept'6.6. Summary

7. LOCATION OF SPINNING RESERVE7 .1. Introduction7.2. Response Risk7.3. Numerical Example

118

Sys- 123

124

127

127

129130

131

133136

141

141

142144

Vll

7.4. Load Dispatch Using the 'Two Risks Concept'7.4.1. Least costly adjustments

7.5. Summary8. APPLICATION TO RELIABILITY TEST SYSTEMS

8.1. Introduction8.2. Application to the Roy Billinton Test System (RBTS)8.3. Application to the IEEE-RTS8.4. Summary

9. CONCLUSIONS

REFERENCES

147148153

161

161

162172192

193

199

Appendix A. Equivalent Capacity Model 203

A.l. A Recursive Algorithm for Capacity Model Building 203

Appendix B. Determination of Interruptible Load Carrying 205

Capability of an Interconnected Generation SystemB.l. Computational Algorithm 205

Figure 2.1:

Figure 2.2:

Figure 2.3:

Figure 2.4:

Figure 2.5:

Figure 2.6:

Figure 2. '1 :

Figure 2.8:

Figure 3.1:

Figure 3.2:

Figure 3.3:

Figure 3.4:

Figure 3.5:

Figure 3.6:

Figure 3. '1 :

Figure 5.1:

Figure 5.2:

Figure 5.3:

Figure 5.4:

Figure 5.5:

Figure 5.6:

Figure 5. 'T :

Figure 5.8:

viii

List of Figures

Subdivision of System Reliability. 8

Hierarchical Levels in Power System. 10Model for Hierarchical Level I. 10Two-state Model of a Generating Unit. 13

Three-state Model of a Generating Unit. 16

Three-state Model of a Generating Unit With No 17

Repair.Three-state Model of a Generating Unit For Spin- 18

ning Reserve Study.Three-state Model of a Power System Component. 19

Interconnected Systems. 31Area Risk Curve of a System. 46Area Risk Curves of an Interconnected System. 49

Four-state Model for Rapid Start Units. 50Five-state Model For Hot Reserve Units. 52

Seven-step Approximation of the Normal Distribu- 57tion.

Three-step Approximation of the Normal Distribu- 61tion.Area Risk Curve. 94

Equivalent Load Approach For Load Interruption. 95

Equivalent Unit Approach For Load Interruption. 95

Area Risk Curves For Two Loads. 96

Interruptible Load Carrying Capability at the Firm 104Load of 1850 MW .

Additional Load Carrying Capability at a Load 106Level of 1750MW.Additional Load Carrying Capability at a Load 107Level of 1900MWEffect of Firm Load Variation on Additional Load 109

Carrying Capability.Figure 5.9: Effect of Firm Load Variation on Additional Load 110

Carrying Capability.Figure 5.10: Hourly Peak Load Variation of One Week ill the 112

Winter of the IEEE - RTS Load Model.Figure 5.11: Daily Additional Interruptible Load Carrying 115

Capability of System A.

IX

Figure 5.12: Area Risk Curves for Isolated and Interconnected 119

System Operation.Figure 5.13: Additional Interruptible Load Carrying Capability 125

In System B.

Figure 8.1: Additional Load Carrying Capability of RBTS-2. 170

•

Table 2.1:Table 2.2:Table 2.3:Table 2.4:Table 3.1:Table 3.2:

Table 3.3:Table 3.4:Table 3.5:Table 3.6:Table 3.1:Table 3.8:Table 3.9:

Table 3.10:

Table 3.11:Table 3.12:Table 3.13:

Table 3.14:

Table 3.15:

Table 3.16:Table 3.11:

Table 4.1:Table 4.2:Table 4.3:Table 4.4:Table 4.5:Table 4.6:Table 4.1:

Table 4.8:

x

List of Tables

On-line Generating Units of System X. 24

Capacity Outage Probability Table of System X. 24Unit Commitment and Risk in System X. 25Unit Commitment and Spinning Reserve in System X. 26Assistance Equivalent Unit of System X. 28Available Generating Units in System A and System 33B.Tie Lines. 33Unit Commitment in the Interconnected System. 34Unit Commitment With Unequal Single System Risk. 36Unit Commitment With Equal Single System Risk. 38

Effect of Tie-line Capacity. 39Effect of Tie-line Capacity. 40Effect of Load Changes On Unit Commitment (Tie 42

capacity = 2x40 MW).Effect of Load Changes On Unit Commitment (Tie 44

capacity = 2x90 MW).Unit Commitment With Equal Unit Failure Rates. 45

Unit Commitment With Unequal Unit Failure Rates. 45

Transition Rate of Hot Reserve and Rapid Start 53Units.Unit Commitment With Rapid Start and Hot 55

Reserve Units.

Unit Commitment With Load Forecast Uncertainty 58

(Seven-step approximation of the load distribution).Unit Commitment With Zero Load Forecast Uncertaint)60Unit Commitment With Load Forecast Uncertainty 62

(Three-step approximation of the load distribution).Tie-Line Model. 77Tie Constrained Import Model of System A. 77

Export/Import Constrained Tie-Line Model. 78Tie-Line Model. 79Tie Constrained Import Model of System B. 79

Export/Import Constrained Tie-Line Model. 80Unit Commitments (Export is backed up by the en- 81tire exporting system).Export Model of System B. 82

Table 4.9:Table 4.10:

Table 4.11:Table 4.12:Table 4.13:Table 4.14:

Table 4.15:Table 4.16:Table 4.17:Table 4.18:

Table 4.19:

Table 4.20:

Table 5.1:

Table 5.2:Table 5.3:Table 5.4:

Table 5.5:

Table 5.6:Table 5.7:Table 5.8:

Table 6.1:

Table 6.2:Table 6.3:

Table 6.4:

Table 6.5:

Table 7.1:Table 7.2:Table 7.3:Table 7.4:Table 7.5:

Table 7.6:Table 7.7:Table 7.8:Table 7.9:Table 7.10:Table 7.11:Table 7.12:

Xl

Tie Constrained Import Model of System A. 82

Export/Import Constrained Tie-Line Model. 83

Tie Constrained Import Model of System A. 83

Export/Import Constrained Tie-Line. 84

Export Model of System A. 84

Tie Constrained Import Model of System B. 85

Export/Import Constrained Tie-Line Model. 85

Tie Constrained Import Model of System B. 85

Export/Import Constrained Tie-Line Model. 86

Unit Commitments (Export IS backed. up by a 87

specific unit).Unit Commitment With Export (Export backed up 88

by the entire exporting system).Unit Commitment With Export (Export backed up 89

by a specific unit in the exporting system).Spinning Capacity, Reserve and Unit Commitment 92

Risk.Unit Commitment and Corresponding Risk. 92

Typical Unit Commitment Situations. 98

Allowable Additional Load/Interruptible Loads and 102

Lead Times.One Week In The Winter Of The IEEE - RTS Load 114

Model.Additional Unit Requirements. 117

Additional Unit Requirements. 117Unit Commitment with Interruptible Load. 122

Cost Parameters of the Generating Units in System 135

A and B.Peak Load Variations in a 24 Hour Period. 136

Unit Commitment in System A and B. 137

Unit Commitment in System A and B With Load 138

Forecast Uncertainty.Unit Commitment in System A and B With 139

Export/Import.Failure Probability and Response Rate. 144

Load Dispatch in System X. 145

Response Risk. 145

Tie-Line Model. 145

Tie-Line Constrained Response Assistance (Assistance 146

to X provided by Y).Equivalent 5 Minute Response of System X. 146

Response Rate of Generating Units. 150

Load Dispatch During the First Hour. 151

Running Cost During the First Hour. 152

Operating Cost During the 24 Hour Period. 152

Economic Load Dispatch in System A. 154

Economic Load Dispatch in System B. 155

Table 7.13:

Table 7.14:

Table 7.15:

Table 7.16:

Table 8.1:Table 8.2:

Table 8.3:

Table 8.4:

Table 8.5:

Table 8.6:

Table 8.7:

Table 8.8:Table 8.9:

Table 8.10:

Table 8.11:

Table 8.12:

Table 8.13:Table 8.14:Table 8.15:Table 8.16:

Table 8.17:

Table 8.18:

Table 8.19:

Table 8.20:

xu

Risk Constrained Economic Load Dispatch in Sys- 156

tern A (Reloading step = 1 MW).Risk Constrained Economic Load Dispatch in Sys- 157tern B (Reloading step = 1 MW).Risk Constrained Economic Load Dispatch in Sys- 158

tem A (Reloading step = 5 MW).Risk Constrained Economic Load Dispatch in Sys- 159

tem B (Reloading step = 5 MW).RBTS Generating Units and Cost Data. 163

Unit Commitment in the RBTS. 164Unit Commitment in the RBTS With Load Forecast 165

Uncertainty (Seven-step approximation of the load

distribution) .

Unit Commitment in the RBTS With Load Forecast 166

Uncertainty (Three-step approximation of the loaddistribution) .

Unit Commitment in the RBTS With Export/Import 167

(Export is backed up by the entire exporting system).Unit Commitment in the RBTS With Export/Import 167

(Export is backed up by a Specific Unit).Unit Commitment in the RBTS With Interruptible 169

Load.Peak Load Variations of RBTS in a 24 Hour Period. 171

Unit Commitment in the RBTS (24 hours scheduling 172

period).Unit Commitment in the RBTS Without Intercon- 173nection (24 hours scheduling period).Risk Constrained Economic Load Dispatch in the 174

RBTS-l (Reloading step = 5 MW).Risk Constrained Economic Load Dispatch m the 175RBTS-2 (Reloading step = 5 MW).Generating Units in the IEEE-RTS. 176IEEE-RTS Cost Data. 177Unit Commitment in the IEEE-RTS. 179

Unit Commitment in the IEEE-RTS With Load 180

Forecast Uncertainty (Seven-step approximation ofthe load distribution).Unit Commitment in the IEEE-RTS With Load 181

Forecast Uncertainty (Three-step approximation ofthe load distribution).Unit Commitment in the IEEE-RTS With 182

Export/Import (Export IS backed up by the entire

exporting system).Unit Commitment in the IEEE-RTS With 182

Export/Import (Export IS backed up by a specificunit).Unit Commitment in the IEEE-RTS with Interrupt- 183

ible Load.

Table 8.21: Peak Load Variations of IEEE-RTS m a 24 Hour 185

Period.Unit Commitment m the IEEE-RTS (24 hour 186scheduling period) .

Unit Commitment in the IEEE-RTS Without Inter- 187

connection (24 hour scheduling period).Economic Load Dispatch in the IEEE-RTS-l. 188

Economic Load Dispatch in the IEEE-RTS-2. 189Risk Constrained Economic Load Dispatch m the 190

IEEE-RTS-l (Reloading step = 5 MW).Risk Constrained Economic Load Dispatch in the 191

IEEE-RTS-2 (Reloading step = 5 MW).Probability of Failure of Units in System X. 203

Capacity Outage Probability Table of System X. 204

Table 8.22:

Table 8.23:

Table 8.24:Table 8.25:Table 8.26:

Table 8.27:

Table A.1:Table A.2:

Xlll

xiv

LIST OF PRINCIPAL SYMBOLS

Export of System i to System j

F(R) Risk function

[ ..

tJ Import of System i from System j

Failure rate

Total load in System A

Firm load in System A

s:t Interruptible load

Interruptible load in System A

,\ ..

'JTransition rate from state i to state j

Repair rate

R, Specified single system risk

R·t Specified interconnected system risk

Actual single system risk in System A

Actual interconnected system risk in System A

s(t) Unit start-up fuel cost at time t

Unit cold start-up cost

xv

T Lead time

t:.t Discrete time step

SSR Single system risk

ISR Interconnected system risk

SSRR Single system response risk

ISRR Interconnected system response risk

Lead time for the additional thermal units

Time to start hot reserve units

Time to start rapid start units

u·l

Minimum output of unit i in MW

Maximum output of unit i in MW

x·t Output of unit i in MW

1

1. INTRODUCTION

Modern power systems have experienced a tremendous growth In the

last few decades. Almost all aspects of daily life in a modern society dependon the use of electrical energy and the performance of a power utility can be

measured in terms of the quality and reliability of the supply. Electric

power utilities supply power to customers with diverse needs. The require­

ments of different customers in regard to the quality and reliability of power

supply vary widely depending on the nature of usage. Careful planning,

operation and pre-assessment of system performance are required in order to

satisfy the wide variety of customers found in a modern power system.

Operation of a power system is a vast and complex task which involves

forecasting daily load demand, utilisation of available resources under certain

constraints, understanding electro-mechanical behaviour of various system

components including generating units and most importantly the economics of

operation. The economic aspects of generation system operation deals with

the commitment and dispatch of a selected set of available generating units

under certain operating constraints in order to minimise the overall produc­tion cost. Reliability evaluation of power supply involves the recognition of

both quality and continuity of supply. The need for reliable operation of

power systems has been recognised for many years. Reliability and

economics of power system operation can not be considered as two separate

problems. The unit commitment and load dispatch in a system should be

such that economic considerations as well as predefined risk criteria are

satisfied under normal system conditions.

2

Under normal conditions, the generating capacity in operation in a

power system is greater than the actual load demand. Additional generating

capacity above that necessary to meet the load demand is required to make

the system capable of handling unforeseen load changes and possible outages

of generation or other facilities. This extra generating capacity or spinning

capacity held in reserve must be capable of responding within an allowable

margin time to ensure reliable system operation. Two types of margin time

are important; (1) time to satisfy system frequency and dynamic stabilityand (2) time to satisfy loss of generation or other facilities [1, 2]. These

margin times are normally of the order of one minute and five minutes.

The actual magnitude of these time periods can, however, vary from system

to system. In practice, all power system components have some likelihood of

failure. This likelihood can be reduced significantly by proper design and

good maintenance practices, but it can never be reduced to zero. Any sys­

tem, therefore, operates with a likelihood of not fulfilling the operational re­

quirements. Deterministic approaches recognise this fact but do not use it to

consistently assess system performance or spinning reserve requirements.

A number of different methods are presently used to establish the spm­

ning reserve requirement in a power system. These techniques can be

generally grouped into two broad categories; namely, (1) deterministic ap­

proaches and (2) probabilistic approaches. Deterministic assessment of the

spinning reserve requirement can be done using

1. percentage of system load or operating capacity,

2. fixed capacity margin,

3. largest contingency, or

4. any combination of the above methods.

Different utilities have their own rationale for selecting a particularmethod. Deterministic approaches do not specifically take into account the

3

likelihood of component failure, i.e. the probability of failure of generating

units, transmission lines, etc., in the assessment of spinning reserve. A

probabilistic approach can be used to recognise the stochastic nature of sys­

tem components and to incorporate them in a consistent evaluation of the

spmnmg reserve requirement. The actual magnitude and even the type of

spmnmg reserve is therefore determined on the basis of system risk. This

risk can be defined as the probability that the system will fail to meet the

load or just be able to meet the load for a specified time period. The time

dependent risk can be expressed mathematically as

m

i=lwhere

R(t) system risk at time t

probability that the system is in state z at time t

QJt) probability that the system in state i at time t will fail to

meet the quality, continuity or other performance criteria

m total number of system states.

The selection of a suitable risk level is somewhat arbitrary as there is

no simple direct relationship between risk and corresponding worth and suf­

ficient operating experience is required before arriving at a particular risk

level. The operating risk, however, can be decreased by providing more

spinning reserve, i.e. scheduling more generating units. Decreasing the risk

level will result in increased operational costs. The selection of an allowable

risk level is, therefore, a management decision.

The realisation that interconnection between two or more neighbouring

power systems can be beneficial to the utilities concerned IS well

established [3, 4, 5]. The resulting benefits apply to both system adequacy

4

and system security. The participating members of an interconnected poolcan export/import energy, exchange economic energy or assist each other

with operating reserve. The reliable operation of an interconnected power

system when considered on a 'multi-area' basis requires that each system

should have adequate capacity. to meet its own area demand [6, 7].Moreover, each individual system should have adequate capacity to meet its

export/import commitment and regulating margin. In an interconnected sys­

tem considered on a 'single-area' basis, load changes are allocated for

economy dispatch to the next-in-line unit irrespective of its location [6, 7].Economy interchanges between individual members of the pool occur whenever

in achieving system economy, one system modifies its generation for a load

change in another area. Adequate operating reserve must be maintained,

however, for proper coordination and reliable operation of the interconnected

system.

Multi-area unit commitment techniques do not normally involve

probabilistic risk assessment. 'Operating reserve requirements are usuallybased on deterministic approaches in which the reserve is specified as either

a fixed margin or some combination of the capacities of the units in opera­

tion and the system load.;

The emphasis when using a deterministic ap­

proach to unit commitment and spinning reserve assessment is to minimise

the total operating cost [8, 9, 10, 11, 12, 13, 14, 15, 16] and in doing so a

system faces different degrees of risk throughout the day. The set of

generating units in different systems of an interconnected pool are usuallydifferent. The operating units in different systems usually differ in their size,

unavailability, response rate etc.. Deterministic approaches do not take these

factors into consideration in a consistent manner during the allocation of

spinning reserves between the pool members. There exists therefore, a pos­

sibility that a system whose generating units are more likely to fail than the

units of its neighbour is neither maintaining an adequate spinning reserve

nor buying it from others. A system whose units are less likely to fail than

the units of its neighbour, however, may carry more than its share of spin-

5

rung reserve due to the same reason. The fact may not be obvious to the

pool members due to the very nature of the deterministic approach used.

The assessment of spinning reserve IS an integral part of the problem of

unit commitment. Most of the methods previously developed for unit com­

mitment ignore the probabilistic aspects of system components. The units in

some of these methods are scheduled in a way that results in minimum run­

ning cost [8, 9, 10, 11, 12, 13, 14, 15, 16]. Some published techniques recog­

nise the random behaviour of system components but fail to use this infor­

mation in a consistent manner [17, 18]. Spinning reserve assessment in an

isolated system using probabilistic methods have been published [3]. Most

power utilities today operate in interconnected configurations. There has

been relatively little published material on spinning reserve requirements in

interconnected systems which recognises the random nature of the system

components. The basic objective in using a probabilistic technique is to

maintain the unit commitment risk equal to or less than a specified value

throughout the day. A new probabilistic technique has been developed to

assess the spinnmg reserve requirements in interconnected systems. This

thesis presents this new approach and describes the related theoretical and

computational basis of the technique. / This research work concentrates on

the spinning reserves required to satisfy the system load requirement and

does not include the system dynamics associated with the initial or instan­

taneous response of the system to a._�����Il :per�ll.r?���?'_!l./ The principle

strength of the technique presented in this thesis lies in its ability to include

standard operating practices and those factors which directly or indirectly in­

fluence the system reliability in the assessment of spinning reserve. The

power system component models required to support the computational and

analytical work reported in this thesis have been previously published [3] and

are generally accepted by utilities in North America.

The step by step development and basis of the new probabilistic tech­

nique to assess spinning reserve in interconnected systems is designated as

6

the 'Two Risks Concept' and is presented in Chapter 3. The basic ideas of

the 'Two Risks Concepts' are developed using two interconnected power sys­

tems for the sake of simplicity and clarity. The technique, however, is ap­

plicable to higher order interconnected systems. The effects of tie-capacityvariation on spinning reserve and corresponding risk are illustrated in

Chapter 3. Area risk curves have been used to include rapid start and hot

reserve units in the spinning reserve evaluation process in interconnected sys­

tems. With interconnections, the spinning reserve requirements of one system

are affected by the load variations and unit commitments of the neighbouringsystems. This interdependence of interconnected systems with respect to

spmnmg reserve is also illustrated in Chapter 3. A technique to consider load

forecast uncertainty m the spmnmg reserve assessment usmg the

'Two Risks Concept' is presented. A simplified load probability model to

represent the load forecast uncertainty is shown in Chapter 3. New risk in­

dices are defined as necessary elements of the proposed probabilistic tech­

mque.

Most interconnected systems have scheduled export/import from/to their

neighbouring systems. The 'Two Risks Concept' has been used to assess

spinning reserve in interconnected systems with export/import constraints.

The development of the basic export/import models under different agree­

ments are illustrated in Chapter 4.

In the absence of alternative capacity adjustments, system load can be

curtailed to reduce the system operating risk. The determination of the

magnitude of the load which should be curtailed and the corresponding max­

imum allowable time delay to interrupt it to maintain the risk equal to or

less than a specified value is illustrated in Chapter 5. The basic methods

regarding the allowable load interruption and the interruptible load carrying

capability are first developed for a single system. Interruptible load con­

siderations for interconnected systems are derived usmg the

'Two Risks Concept' and the basic techniques applied in a single system.

7

Daily unit commitment schedules based on the basic ideas illustrated in

Chapter 3 are presented in Chapter 6. A process of allocating spinningreserve among the operating units of an interconnected system is presentedin Chapter 7. This approach takes into consideration the responding

capabilities of the operating units and satisfies response risk criteria. The

proposed allocation process evaluates the risk associated with the responding

capability of an interconnected system and determines a loading schedule to

satisfy an acceptable risk with the least costly deviation from the economic

load dispatch. The technique is suitable for both small and large intercon­

nected systems.

The techniques developed and presented in this thesis have been ap­

plied to two reliability test systems. The results from studies which il­

lustrate unit commitment, spinning reserve, load interruption and risk con­

strained economic load dispatch etc. for the two reliability test systems are

presented in Chapter 8.

In summary, this thesis presents a new probabilistic technique for spm-.

nmg reserve assessment in interconnected generation systems. The proposed

technique incorporates the essential stochastic parameters of all the par­

ticipating generation systems and the associated system interconnecting tie

lines. The introduction of the two risk indices, at the isolated system level

and at the interconnected system level, provides consistent operating criteria

in regard to unit commitment and load dispatch. The developments

presented in this thesis advance spinning reserve assessment methodologiesand provide a viable alternative to the deterministic approaches used for

unit commitment in interconnected generation systems.

8

2. BASIC MODELSAND SYSTEM CONCEPTS

2.1. Introduction

The basic objective of a power system is to generate and supply electri­

cal energy to its customers as economically as possible with an acceptable

degree of reliability and quality. In general, the ability of the system to

provide an adequate supply of electrical energy is designated by the term

reliability. The concept of power system reliability covers numerous aspectsof power system performance with respect to satisfying the wide variety of

customer demands.

Due to the wide ranging implications of the term reliability, it is neces­

sary to subdivide it into more specific segments. Figure 2.1 shows the basic

subdivision of power system reliability into system adequacy and system

security [19]. These designations represent two different aspects of power

system performance.

SYSTEM RELIABILITY

SYSTEM SECURITY SYSTEM ADEQUACY

Figure 2.1: Subdivision of System Reliability.

9

System adequacy relates to the existence of sufficient generation, trans­

mission and distribution facilities within the system to satisfy the load

demand. Adequacy evaluation does not take system disturbances into ac­

count. Security evaluation deals with the responding capability of a system

to perturbations arising within the system. The perturbations in the domain

of security analysis include system disturbances such as loss of generation

and transmission facilities. The evaluation of loss of load· expectation

(LOLE) and loss of energy expectation (LOEE) reside in the area of system

adequacy. Assessment of spinning reserve and transient stability are as­

sociated with system security. The work reported in this thesis is in the

system security domain.

A power system can be divided into three functional zones; generation,

transmission and distribution [19]. System planning, operation and reliability

studies can be performed on these three functional zones individually. One

or more of these functional zones can be combined to form hierarchical levels

as shown in Figure 2.2. Hierarchical level I (HL I) represents the generation

facilities. Generation and transmission facilities together form the hierarchical

level II (HL II). The combination of all three functional zones form hierar­

chical level III (HL III). The quantification of spinning reserve in HL I re­

lates to the responding capability of the total spinning capacity (generation

synchronised to the bus) in the event of a perturbation and/or generation

loss. The transmission and the distribution facilities during the assessment

of spinning reserve at HL I are assumed to be fully reliable. The research,

work reported in this thesis is restricted to the assessment of spmnmg

reserve of interconnected systems at HL I. At HL I, all the generation and

load in the system can be grouped to create a hypothetical system with one

generating source supplying a single load. Figure 2.3 shows such a system

representation for spinning reserve assessment at HL I. The HL I represen­

tation of an interconnected system contains an equivalent tie-line in addition

to the single generating unit feeding a solitary load.

10

r---------------,I r------------, II r-----------, I I

I I I I

I I I I

I I !IIi I HIERARCHICAL LEVEL I

I I I

I I II

L _JII II .., HIERARCHICAL LEVEL III JI II II I

L _ _ _..J I. HIERARCHICAL LEVEL III

JIIfIII

L---- .J

GENERATIONFACILITIES

----- -----

TRANSMISSIONFACILITIES

- - -- 1---- -

DISTRIBUTIONFACILITIES

Figure 2.2: Hierarchical Levels in Power System.

TOTAL SYSTEMGENERATION

TOTAL SYSTEMLOAD

Figure 2.3: Model for Hierarchical Level I.

11

2.2. Basic Modelling Concepts

Proper representation of power system components IS an important re­

quirement of all power system reliability studies. A power system com­

ponent can be represented in a reliability study by a model which can be

quite simple or exhaustive, or something in between. How elaborate a model

should be depends on the component itself and the type of the study in

which the model is used. In some reliability studies, the simplest model of a

particular component is quite adequate, whereas for other studies a more

elaborate model is required. A detailed component model will portray the

component behaviour more closely than a simple model of the same com­

ponent. Exhaustive modelling of system components are required for greater

accuracy, but can increase the reliability computation time considerably

above that required with relatively simpler models. Simple models of system

components do not always retain the essential performance characteristics

needed in some reliability studies. A system component should be represented

by a model which is reasonably simple yet retains all the required perfor­

mance features. The essential performance features that a model must

provide will vary from study to study.

Modelling of system components directly depends on the ability and

scope of the data collection system. New techniques in reliability sometimes

demand new system component models. The requirements of these new

models can place changing and sometimes increasing burdens on traditional

power utility data collection schemes. •

This chapter reviews some of the generating unit models and related

spinning reserve concepts which form the basic elements of the research work

described in this thesis on spinning reserve assessment in interconnected sys­

tems.

12

2.3. Markov Process

Many power system component models used in reliability studies are

based on Markov processes. A Markov process can be defined as a stochas­

tic process whose future IS independent of the past for a known

present [20, 21, 22]. The fundamental characteristic of a Markov process IS,

therefore, that the process is memoryless. The future random behaviour of

the process only depends on where it is at present. The process neither

depends on the states occupied in the past nor does it depend on how it ar­

rived at its present position. A Markov process is also homogeneous. This

means that the behaviour of a system is the same at all points of time ir­

respective of the point of time considered [23]. A Markov process as utilised

in reliability studies has two random variables, state and time. The state

and time may either be discrete or continuous. In the work described in

this thesis the system components are modelled by discrete states in a con­

tinuous time domain.

In this thesis, a Markov process with discrete states in the continuous

time domain is called a 'continuous Markov process' and a Markov process

with discrete states in discrete time steps is called a 'discrete Markov

process'. A component modelled as a continuous Markov process will have

constant transition rates from one state to another. All power system com­

ponents included in this thesis are assumed to have constant transition rates

i.e., constant failure and repair rates etc. and therefore exponentially dis­

tributed residence times in the different states.

13

2.4. Generating Unit Models

2.4.1. Two-state model

Generating units should be represented by appropriate models for

probabilistic assessment of static or operating capacity requirements. A two­

state representation of a generating unit is the simplest form. The generat­

ing unit is considered to be either operating at full capacity or failed.

Figure 2.4 shows a two state model for a typical generating unit.

UP DOWN

p.

Figure 2.4: Two-state Model of a Generating Unit.

The unit changes its states from the operating state (up) to the failed

(down) state with a constant transition rate of A, commonly known as the

failure rate. The unit is repaired and put back into the operating state at a

rate /1, known as the repair rate. It is assumed that the residence times of

the generating unit in either of these states are exponentially distributed.

Both transition rates shown in Figure 2.4 are, therefore, time independent.The failure and repair rate of a generating unit can be determined from its

operating history.

number of failures in the given period of time

total period of time the unit was operating

/1number of repairs in the given period of time

total period of time the unit was being repaired

Sufficient operating history IS required to develop a reasonably accurate

14

model of a generating unit. The time dependent state probabilities of a

generating unit represented by the two-state model [3] are shown in Equa­tions (2.1) and (2.2) assuming that the unit is in operating state at t = O .

.Ae-(.A+Jl)t.A+Jl

.Ae-(.A+Jl)t.A+Jl

(2.1)

(2.2)

where

probability that the generating unit is in operating state at

time t

probability that the unit IS In failed state at time t.

Steady state probabilities are used for static capacity evaluation. The

steady state probability is the limiting state probability when t -+ 00. The

limiting state probabilities Po and PI are as follows

Po Po(t=oo)Jl

--

.A+Jl

P1(t=00).A

PI .A+Jl

The fundamental difference between static and operating capacityevaluation is in the time period considered. Static capacity evaluation is

done for long term system requirements, whereas, operating capacity evalua­

tion is done for short term capacity assessment to meet a load demand.

The time period used in an operating capacity evaluation IS generally rela­

tively small and therefore it is possible to neglect generating unit repairs.

Using Equation (2.2) the probability of finding a two-state unit in the failed

state at a time T is grven In Equation (2.3).

P( down) (2.3)

15

If the repair process IS neglected during the time period T, then Equation

(2.3) becomes [3]

P( down) = 1 � e-AT . (2.4)

The time period T is designated in a spmnmg reserve study as the lead

time [3, 24]. This is the time period for which no additional units can be

brought into service. For short lead times of up to several hours, AT« 1

for all practical purposes. The probability that a unit fails and is not

repaired during the lead time T, therefore, IS

P( down ) � AT. (2.5)

The parameter AT is known as the outage replacement rate (ORR) which is

a time-dependent quantity.

2.4.2. Multi-state model

The operating performance of a generating unit is lumped into two

states in a two-state model. Large generating units usually have many

auxiliary equipments. These units, therefore, frequently experience deratingdue to equipment failures. A multi-state model can be used to realistically

represent such a generating unit. A generating unit model with many

derated states, however,· will increase the computational burden and com­

plexity in power system .reliability studies. It is not feasible to consider a

large number of derated states. These derated states can be reduced to a

limited number by using some appropriate weighting techniques [25].

A large generating unit can be represented by a three-state model con­

taining a full capacity output state, a derated capacity state and a failed

state. The derated capacity output states of a generating unit are pooledinto a single derated state in a three-state model of a generating unit.

Figure 2.5 shows such a three-state model [3]. The three-state model shown

in Figure 2.5 includes all possible transition rates. Some of these transition

rates may not exist in practice, in which case these transitions are simply

16

OPERATING

DOWNDERATED

Figure 2.5: Three-state Model of a Generating Unit.

omitted from the model. The transition rate J.t3 shown in Figure 2.5 may

not exist in practice. The repair process will probably put the unit into the

full output state after it is repaired. The time dependent state probabilitiescan be found by the matrix multiplication method [3] instead of solving the

actual differential equations. The steady state probabilities of the three-state

model can be evaluated by the frequency balance approach or by the matrix

multiplication method.

If the repair process 1S neglected in the short lead time then the three­

state model in Figure 2.5 1S reduced to that shown in Figure 2.6 [3]. If the

probability of more than one transition is negligible during the short lead

time then the full three-state model of a generating unit can further be

reduced to that shown in Figure 2.7 [3]. If the unit is considered to be in

the full output state at t=O and the state residence times are assumed to be

exponentially distributed and assuming that AIT« 1 and A2T« 1, where

T is the lead time in hours, it follows from Equation (2.5) that

17

OPERATING

DERATED DOWN

Figure 2.6: Three-state Model of a Generating Unit With No

Repair.

(2.6)

P{ derated) � AIT (2.7)

P{ operating) � 1 (2.8)

The basic models and the state probabilities for other power system com­

ponents can be evaluated using similar techniques.

2.5. Matrix Multiplication Method

The evaluation of time dependent or transient probabilities becomes

tedious when the number of states in which the component can reside are

more than two. The matrix multiplication method is specially useful in

determining the transient probabilities using a digital computer. The for­

mulation of the problem of determining the transient probability of a certain

18

OPERATING

DERATED DOWN

Figure 2.7: Three-state Model of a Generating Unit For Spin­ning Reserve Study.

state of a component using the matrix multiplication method is systematicand straightforward [23]. The matrix multiplication method is equallysuitable for discrete and continuous Markov processes.

In order to apply the matrix multiplication method, it is necessary to

obtain the stochastic transitional probability matrix of the process which

fully represents the operating behaviour of the component concerned. The

elements of the stochastic transitional probability matrix are the probabilitiesof making a transition from one state to another in a single step or in a

single time interval. Figure 2.8 shows a general three-state model for the

component whose operating. behaviour can be described in the continuous

time domain with the transition rates shown. The stochastic transitional

probability matrix for the model of Figure 2.8 is

[PH P12 P13]P= P21 P22 P23P31 P32 P33

19

Figure 2.8: Three-state Model of a Power System Component.

1 2 3

1 [ 1-(A12+Au)A! ).12At AnA! 12 ).21At 1-().21+).23)At ).23At3 ).31At ).32At 1-().31+).32)At

In a discrete Markov process,

Pij = probability of making a transition to the jth state after a

single step, given that it was in state i at the beginning ofthe step.

In a continuous Markov process,

p .. =

ZJ probability of making a transition to the jth state after a

time interval of At, given that it was in state i at the

beginning of the time interval.

20

In a discrete Markov process the p·.'s are given explicitly. In the case'J

of a continuous Markov process the transitional probabilities are expressed in

terms of transition rates and the time interval. The time interval ll.t is suf­

ficiently small that the probability of more than one transition in the inter­

val is negligible.

The time-dependent state probabilities for a continuous Markov process

are [3J

[P(t)J [P(O)] [PJn , (2.9)

where

[P(t)Ji vector of state probabilities at time t

[P(o)Ji vector of initial probabilities

[Pj stochastic transitional probability matrix

n number of time steps used In the discretisation process.

The value of ll.t determines the number of time steps, n. A small

value of ll.t will require large value of n; and a large value of ll.t will result

in a small value of n. The term ll.t should be made sufficiently small that

the errors introduced in the values of the state probabilities become negli­

gible .

•

The transient probabilities for a discrete Markov process are given

by [3]

[P(n)1 [P(O)] [p]n , (2.10)

where

[P(n)] vector of state probabilities after n time intervals.

21

2.6. Capacity Outage Probability Table

The system generation in both adequacy and security analysis at HL I

IS represented by a single equivalent generating source. The equivalent

generating source may have many different capacity output states dependingon the capacity outage states and the corresponding probabilities of the in­

dividual generating units. A capacity outage probability table [3] is a sys­

tematic representation of this equivalent source. In adequacy assessment,

limiting state probabilities of corresponding capacity outage states of m­

dividual units are used to derive the capacity outage probability table. In

spinning reserve assessment, time dependent probabilities of the corresponding

outage states of individual generating units are used to derive the equivalentmodel. The generating units are combined using basic probability concepts.

The capacity model in the form of a capacity outage probability table can be

created using Equation (2.11).

n

(2.11)i=l

where

c·l capacity outage of state i for the unit being added

probability that the ith state of the unit exists

n number of capacity outage states of the generating unit

cumulative probability of the capacity outage state ofX MW before the unit is added

P(X) cumulative probability of the capacity outage state ofX MW after the unit is added.

The capacity outage probability table incorporates all possible genera­

tion states. The table can be truncated by neglecting all capacity states in

the table whose cumulative probabilities are less than a specified value. A

22

capacity outage probability table has discrete capacity outage states with cor­

responding discrete probabilities.

2.7. Assessment of Spinning Reserve in a Single System

Probabilistic techniques have been applied to evaluate the unit commit­

ment and spinning reserve requirements in a power system [3}. The main

purpose of a probabilistic technique is to keep the unit commitment risk

equal to or less than a specified value throughout the day. A probabilistic

approach recognises the random behaviour of system components and incor­

porates them in a consistent evaluation of the spinning reserve requirements.The unit commitment risk can be decreased by providing more spmnmg

reserve, i.e. committing more generation capacity for the same load demand.

The selection of an allowable risk level depends on the desired degree of

reliability, the corresponding cost and the optimum benefit. The unit com­

mitment risk can be expressed as

N

U(t)=L Pi(t)Qi(t) , (2.12)i=l

where

U(t) system risk at time t

probability that the system is in state i at time t

probability that the system load will be equal to or greaterthan the generation in state i at time t

N total number of system states.

In the case of an operating or spinning reserve study Q i becomes either

zero or unity.

o

1

when

when

L<C·,

L>C·- l

23

where

L system load

c·,

total spinning capacity of the system at the ith state.

The capacity outage probability table of the generation system can be

arranged such that

i=1,2,3, . N-1 ,

where N is the total number of states III the generation system. Equation

(2.12) can be modified as

U(t) (2.13)t=n

where n is an integer such that (L-Cn) � ° and (L-Cn_1) < 0, i.e.

Cn-l > L � Cn. Therefore, U( t) is the cumulative probability of the genera­

tion state n at time t. If Rs is the allowable unit commitment risk for a

time period of (O,t) then the unit commitment in a system should be such

that

U(t) < Rs . (2.14)

The unit commitment and the associated unit commitment risk are

based on the

certain period of time designated as the The risk

is considered to be the probability of just carrying or failing to carry the

system load [24]. The unit commitment basically depends on system load,

generating unit failure rates, system lead time and the acceptable unit com­

mitment risk level. One of the most important parameters in unit commit­

ment and spinning reserve evaluation is the system lead time. The basic

spinning reserve evaluation technique in a single system can be illustrated by

considering a simple example. Consider a hypothetical generation system

(System X) with the on-line units as shown in Table 2.1. The unit commit­

ment order is from the top down.

24

Table 2.1: On-line Generating Units of System X.

Unit Failure Rate

3 x 40 MW3 x 20 MW4 x 10 MW

4 flyr3 flyr3 flyr

The failures and repairs of the generating units are considered to be ex­

ponentially distributed. The probability of finding a two-state unit on out­

age at a time equal to the system lead time can be evaluated using the

techniques explained in Section 2.4.1. A generation model in the form of a

capacity outage probability table can be constructed once the capacity state

probabilities of the individual units for a period equal to the system lead

time are known. The unit commitment risk can be found from the capacity

outage probability table given the load is known. The capacity outage prob­

ability table of System X for a lead time of two hours is shown in Table 2.2

Table 2.2: Capacity Outage Probability Table of System X.

Capacity In Capacity Out Cumulative

(MW) (MW) Probability

220 0 1.00000000210 10 0.00750879200 20 0.00478778190 30 0.00274422180 40 0.00273863170 50 0.00001559160 60 0.00000812150 70 0.00000252140 80 0.00000250

If the acceptable unit commitment risk is 0.003 it can be seen from

Table 2.2 that the system can carry a load of 190 MW with a spmmng

reserve of 30 MW. In the same generating situation, the load carrying

25

capability of System X decreases to 170 MW with a spmnmg reserve of

50 MW if the acceptable unit commitment risk is selected as 0.001. In both

cases, the total spinning capacity is 220 MW. Due to the discrete nature of

the capacity outage probability table, there IS no change in risk for load

levels between two available capacity steps.

2.8. Unit Commitment in a Single System

A probabilistic approach to unit commitment in a single system re­

quires that the unit commitment risk should be less than or equal to a

specified risk level for all forecast load levels. In practice, an operator would

use the probabilistic risk assessment method by adding (committing) one unit

at a time from the merit order table until the unit commitment risk given

by the generation model becomes equal to or less than the acceptable level

for the expected load. One of the most important parameters in the assess­

ment of unit commi�r.r!�!lj_ risJLis_.ihe.j;im� .. ��1C3:Y.. 2!: l�a<l ,t_jill�_,,�ft�r. ,,!�!,<:�._t_��."-------�.-.-"'---�'�'-.-.. -"-'-

additional thermal generation will be aVi!-il�!>J�,

It is assumed that the additional thermal generation in System X has a

time delay of 2 hours and the specified risk level is 0.001. The unit com­

mitment and corresponding risk for a load of 140 MW in System X is shown

in Table 2.3.

Table 2.3: Unit Commitment and Risk m System X.

No. of Units Total Spinning Spinning Unit CommitmentCommitted Capacity (MW) Reserve (MW) Risk

4 140 0 1.000000005 160 20 0.004102866 180 40 0.002738627 190 50 0.00000999

System X has no spinning reserve for a load of 140 MW with 4 committed

units as shown in Table 2.3. System X, therefore, is unable to meet any

generation loss or unforeseen load increase by committing only 4 units when

26

the load is 140 MW. The unit commitment risk of System X in this situa­

tion is unity. As more than 4 units are committed for the same load of

140 MW, the spmnmg reserve increases and the corresponding unit commit­

ment risk decreases. System X must commit 7 units to carry a load of

140 MW if the specified unit commitment risk is 0.001. If the load m

System X increases to 170 MW, System X must keep more spinnmg reserve

than that required at the 140 MW load level for the same specified unit

commitment risk. Table 2.4 shows the unit commitment and corresponding

spinning reserve in System X for a load level of 170·MW and a specifiedunit commitment risk of 0.001.

Table 2.4: Unit Commitment and Spinning Reserve m SystemX.

No. of Units Total Spinning Spinning Unit CommitmentCommitted Capacity (MW) Reserve (MW) Risk

7 190 0 1.000000008 200 20 0.002741429 210 40 0.00273863

10 220 50 0.00001559

There is no straightforward relationship between required spmnmg

reserve, specified unit commitment risk and load. The required spmnmg

reserve is a complex function of unit size, unit failure rate, lead time and

specified risk level. The spinning reserve requirement of a system, however,can be reduced by decreasing the lead time of additional generation providedother variables remain the same. This can be achieved by bringing more

rapid start units into the system. The lead time associated with a hot

reserve thermal unit is considerably less than the lead time of the same unit

in a cold reserve status. Due to unit cycling within a 24 hour scheduling

period, some of the thermal units may be in a hot reserve status at some

parts of the day. The commitment of hot reserve and rapid start units can

alleviate the spinning reserve requirement. The inclusion of hot reserve and

rapid start units in the assessment of unit commitment and spinning reserve

can be done using the area risk technique [3].

27

2.9. Summary

This chapter discusses the various functional zones of a power system

and illustrates the concept of adequacy and security. Some basic modelling

aspects including generation models in the form of capacity outage probabil­

ity tables are also briefly discussed. The essential steps in the matrix mul­

tiplication technique to determine state probabilities are also presented.Determination of time dependent probabilities using the matrix multiplicationmethod is a very practical technique in reliability studies. Assessment of

spinning reserve and unit commitment risk in a single system is explained in

this chapter with a simple numerical example.

28

3. SPINNING RESERVE EVALUATIONIN INTERCONNECTED SYSTEMS

3.1. Introduction

System interconnections permit the participating companies to export or

import energy for mutual benefit. In addition, the participating systems can

benefit in terms of reduced overall required spinning reserves. This can be

illustrated by an example using System X given in Section 2.7. The total

on-line spinning capacity in System X is 220 MW as shown in Table 2.2. If

the load in System X is 170 MW, System X can potentially help an inter­

connected system (System Y) to reduce its spinning reserve. System Y in

its turn can also help to reduce System X's reserve requirements. The assis­

tance available from System X with a load of 170 MW up to the point of

load loss in X can be modelled using the capacity outage probability table

shown in Table 2.2. The resulting equivalent assistance model is shown in

Table 3.1.

Table 3.1: Assistance Equivalent Unit of System X.

Capacity In Capacity Out Cumulative

(MW) (MW) Probability

50 0 1.0000000040 10 0.0075087930 20 0.0047877820 30 0.0027442210 40 0.002738630 50 0.00001559

If an interconnection exists between System X and System Y, the

29

equivalent assistance unit of System X can be considered as an additional

generating unit available to System Y at no extra cost as far as the spinning

reserve is concerned. If the load in System Y remains constant prior to and

after considering the assistance from System X, then the corresponding

operating risk of System Y will decrease after interconnection in comparison

to the isolated system level. The recognition of these two different risks

leads to the idea that there should be two different risk criteria; one at the

isolated system level and another at the interconnection level.

3.2. Two Risks Concept

The magnitude of the operating reserve requirement is dependent on

the selection of the basic unit commitment risk provided that the other sys-

tem variables remain fixed. For a specified unit commitment risk, the

operating reserve depends on the generating unit failure rates, load level etc ..

In a multi-area interconnected system, each individual system has to carry

its own load and should be capable of assisting its neighbour such that the

operating risks of the individual systems meet a specified risk index. The

problem is basically one of determining the set of generating units to be

committed in each individual system to meet the specified risk at the inter­

connection level. One possible way to solve this problem is to commit one

generating unit at a time in one system while keeping the generation fixed in

the other systems and then to determine the interconnected system risk.

The system showing the highest interconnected system risk would then be

considered for a further unit commitment. The process would continue until

all systems meet the interconnected system risk. This method, however, does

not provide any insight into the benefits of interconnection and can require a

long computational time [26]. Since the interconnected system risk of a sys­

tem depends on the assistance provided by its neighbours and on its own

commitment; a system may be able to meet the interconnected system risk

without altering its own commitment even when its load increases from one

level to another. In this method, therefore, the assistance provided by an

individual system to its neighbours is not based on any set procedure and

30

hence could lead to an unfair sharing practice with respect to spmmng

reserves.

The problem can, however, be approached by adopting a 'Two Risks

Concept' in which two risk indices are chosen; namely a Single System Risk

and an Interconnected System Risk [26]. An individual system is required to

meet its Single System Risk (SSR) without considering any assistance from

its neighbour. In addition, the individual system is also required to meet its

Interconnected System Risk (ISR) when assistance from its neighbours are

considered. In this technique, the generating units are selected in each in­

dividual system such that it meets the SSR criterion and then the assistance

to each other IS considered to determine the ISR. The system more

removed from meeting its ISR is required to commit an additional unit and

the analysis continues until all the systems meet the ISR. If all participat­

mg systems are equally removed from meeting the ISR, they are all asked to

commit an additional generating unit individually. Each individual system

and the pool could, however, make its own priority list for unit commitment

based on some economic and/or operational considerations. The use of a

SSR criterion prior to considering the ISR provides a consistent starting

point for interconnected system evaluation. The computational time requiredto arrive at an interconnected unit commitment schedule is approximately30% lower using the two risk approach rather than a single ISR

criterion [26].

Assume that two hypothetical power systems with no export/importagreement are interconnected radially as shown in Figure 3.1.

A is the capacity model of System A in the form of a

capacity outage probability table, which satisfies the SSR

(Rsa) of System A for the load of La'

p number of generating units which should be committed m

System A to meet its SSR

31

e'1') .. -'::

I I Tab I IA B

Figure 3.1: Interconnected Systems.

B is the capacity model of System B in the form of a

capacity outage probability table, which satisfies the SSR

(Rsb) of System B for the load of Lb'

Q number of generating units which should be committed In

System B to meet its SSR

A-La

where Ab IS the tie line constrained assistance unit from

System A available to System B.

where Ba

is the tie line constrained assistance unit from

System B available to System A.

where Ae is the equivalent capacity model - of System A

after considering the assistance.

where Be is the equivalent capacity model of System B

after considering the assistance.

The ISR in each system are

Ria risk (Ae La)Rib risk (Be Lb)

32

If both Ria and Rib' are less than or equal to the specified Intercon­

nected System Risk, Ri then the number of generating units committed in

System A and System B are considered to be adequate; i.e., Ria-Ri � 0 and

Rib-Ri � o. Otherwise, if (Ria-Ri) > (Rib-Ri) then A is modified by adding

the (P+ 1) th generating unit.

A -+ A + (P+l)th unitP P+l

On the contrary, if (Ria-Ri) < (Rib-Ri) then B IS modified by adding the

(Q+l)th unit.

B -+ B + (Q+l)th unit

Q -+ Q+l

The computational process is continued to modify the capacity model of

System A or System B or both until the ISR criterion is satisfied. A com­

puter program has been developed based on the 'Two Risks Concept' to

determine an individual system's share of the overall required spinning

reserve when the systems operate as a multi-area interconnected system.

Two radially interconnected hypothetical systems are used to provide numeri­

cal examples. The generating units in each system and the tie lines are

described in Tables 3.2 and 3.3 using the models given in Figures 2.7 and

2.4. The available generating units in both systems are considered to be

identical so that both systems can be compared to each other with respect

to their spinning reserve requirements and the essential features of the 'Two

Risks Concept' can be established. The priority order of unit commitment is

from the top down in Table 3.2 and the lead time in both systems is con­

sidered to be 4 hours. Load forecasting error at this point, is assumed to be

zero in both systems. The load in both systems is assumed to be constant

over the study period. Time varying loads can be considered by dividing

the study period into a number of subintervals during which the load is con­

sidered to be constant.

33

Table 3.2: Available Generating Units m System A and SystemB.

No. of Output Capacity Transition Rate UnitUnits (MW) (Occ./hr) Type

Full Derated ).1 ).2

1 200 0.0003 hydro2 180 0.0003 hydro1 200 160 0.0005 0.0003 thermal3 150 120 0.0005 0.001 thermal3 150 120 0.0002 0.0009 thermal2 100 0.0005 thermal1 120 100 0.0001 0.0007 thermal3 100 0.0006 thermal

Table 3.3: Tie Lines.

Number ofTie Lines

Maxm. Power Transfer

Capability of Each Line

(MW)

Failure Rate

(Occ/hour)

2 100 0.000114155

Table 3.4 shows the number of generating units which must be com­

mitted in System A and System B for a specified ISR of 0.0001. The SSR

is varied from 0.05 to 0.001 in discrete steps. The last two columns

(column 13 and 14) of Table 3.4 show the actual ISR of System A and

System B. The actual magnitude of the spinning reserve can be found by

subtracting load from total spmnmg capacity. Similar results can be ob­

tained for other load levels.

Table 3.4: Unit Commitment in the Interconnected System.

Single System Interconnected System

SSR Load No. of Capacity No. of Capacity ISR

(MW) Units (MW) Units (MW)

A B A B A B A B A B A B A B

0.050 0.050 1800 1650 12 10 1860 1660 13 12 1980 1860 0.00007370 0.00002883

0.050 0.020 1800 1650 12 12 1860 1860 13 12 1980 1860 0.00007370 0.00002883

0.050 0.010 1800 1650 12 12 1860 1860 13 12 1980 1860 0.00007370 0.00002883

0.050 0.005 1800 1650 12 12 1860 1860 13 12 1980 1860 0.00007370 0.00002883

0.050 0.001 1800 1650 12 12 1860 1860 13 12 1980 1860 0.00007370 0.00002883

0.020 0.020 1800 1650 13 12 1980 1860 13 12 1980 1860 0.00007370 0.00002883

0.020 0.010 1800 1650 13 12 1980 1860 13 12 1980 1860 0.00007370 0.00002883

0.020 0.005 1800 1650 13 12 1980 1860 13 12 1980 1860 0.00007370 0.00002883

0.020 0.001 1800 1650 13 12 1980 1860 13 12 1980 1860 0.00007370 0.00002883

0.010 0.010 1800 1650 13 12 1980 1860 13 12 1980 1860 0.00007370 0.00002883

0.010 0.005 1800 1650 13 12 1980 1860 13 12 1980 1860 0.00007370 0.00002883

0.010 0.001 1800 1650 13 12 1980 1860 13 12 1980 1860 0.00007370 0.00002883

0.005 0.005 1800 1650 14 12 2080 1860 14 12 2080 1860 0.00000846 0.00001024

0.005 0.001 1800 1650 14 12 2080 1860 14 12 2080 1860 0.00000846 0.00001024

0.001 0.001 1800 1650 14 12 2080 1860 14 12 2080 1860 0.00000846 0.00001024

c;..:I>f.>.

35

3.2.1. Equal and Unequal Single System Risk

For each Interconnected System Risk there could be three significantlydifferent situations in terms of Single System Risk. The SSR are such that

the systems after interconnection, with the generating units committed by

each individual system to satisfy their respective SSR, (a) just satisfy the

ISR; or, (b) show the ISR lower than the specified ISR; or, (c) show the

ISR higher than the specified ISR. In situations (a) and (b) the number of

generating units to be committed is dictated by the SSR. The system witha lower SSR than that of its neighbour , therefore, will provide more assis­

tance to its neighbour. This means that for two identical systems with iden­

tical sets of. generating units, the system with a smaller SSR has to spin

more generating capacity than the system with higher SSR for identical load

in the two systems. Despite being identical in regard to generating units

and load, one system has to keep more spinning reserve than its neighbourbecause of its decision to select a lower SSR than its neighbour.

Table 3.5 shows the effect of unequal SSR levels. Results for equal

load of 1460 MW in System A and System B with unequal SSR are

presented. The specified ISR is 0.0001. Rows 4, 5, 8, 9, 11 and 12 of

Table 3.5 show that System B needs to commit more generating units than

System A because of the lower SSR of System B than System A for equal

load in both systems. Rows 1, 6, 10, 13 and 15 show that both systems

need an equal number [i.e., identical in this case) of on-line generating units

i.e., equal spinning reserve for equal load when the SSR of both the systems

are equal. There are other situations in Table 3.5 where equal spinning

reserve is required for unequal SSR. Due to discrete capacity outage and

probability entries in the capacity model of a system in the form of a

capacity outage probability table, the unit commitment of a system to satisfy

its single system risk criterion can remain unaltered for a limited range

(dead zone) of SSR variation. For the same reason, the unit commitment of

two identical systems with identical load can be identical at the single sys­

tem level though their SSRs are different. In addition to that, if the SSR

Table 3.5: Unit Commitment With Unequal Single System Risk.

Single System Interconnected System

SSR Load No. of Capacity No. of Capacity IISR(MW) Units (MW) Units (MW)

A B A B A B A B A B A B A B

0.050 0.050 1460 1460 9 9 1510 1510 10 10 1660 1660 0.00004829 0.00004829

0.050 0.020 1460 1460 9 10 1510 1660 10 10 1660 1660 0.00004829 0.00004829

0.050 0.010 1460 1460 9 10 1510 1660 10 10 1660 1660 0.00004829 0.00004829

0.050 0.005 1460 1460 9 11 1510 1760 10 11 1660 1760 0.00001588 0.00000732

0.050 0.001 1460 1460 9 11 1510 1760 10 11 1660 1760 0.00001588 0.00000732

0.020 0.020 1460 1460 10 10 1660 1660 10 10 1660 1660 0.00004829 0.00004829

0.020 0.010 1460 1460 10 10 1660 1660 10 10 1660 1660 0.00004829 0.00004829

0.020 0.005 1460 1460 10 11 1660 1760 10 11 1660 1760 0.00001588 0.00000732

0.020 0.001 1460 1460 10 11 1660 1760 10 11 1660 1760 0.00001588 0.00000732

0.010 0.010 1460 1460 10 10 1660 1660 10 10 1660 1660 0.00004829 0.00004829

0.010 0.005 1460 1460 10 11 1660 1760 10 11 1660 1760 0.00001588 0.00000732

0.010 0.001 1460 1460 10 11 1660 1760 10 11 1660 1760 0.00001588 0.00000732

0.005 0.005 1460 1460 11 11 1760 1760 11 11 1760 1760 0.00000184 0.00000184

0.005 0.001 1460 1460 11 11 1760 1760 11 11 1760 1760 0.00000184 0.00000184

0.001 0.001 1460 1460 11 11 1760 1760 11 11 1760 1760 0.00000184 0.00000184

w0)

37

satisfies one of the two situations of (a) and (b) the unit commitment at the

interconnection level is dictated by the unit commitment at the single system

level. Moreover, if the ISR is dominant, equal spinning reserve is requiredfor equal load in two identical systems while operating at unequal SSR.

In situation (c), generating unit commitment in each individual system

is dictated by the specified ISR index. Considering all the aspects, it is

therefore, appropriate to have a single SSR for the pool members. Three

different SSR values which correspond to the situations noted as (a), (b) and

(c) are difficult to determine. They are complex functions of unit size, unit

failure rate, system load, tie capacity, ISR, etc.. Trial indices can, however

be selected for computational purposes until a desired index is found. Table

3.6 shows the units which must be committed in System A and System B

for a specified ISR of 0.0001. The SSR for both systems IS 0.01. Load in

System B is varied from 1300 MW to 2000 MW in steps of 50 MW while

the load in System A is held at 1800 MW.

3.3. Effect of Tie-line Capacity

The assistance provided by a system to its neighbour depends on the

tie-line capacity and the tie-line failure rate. If the tie-capacity is smaller

than the available assistance then the level of assistance becomes constrained

by the tie-capacity. If the tie-capacity is larger than the available assistance,

then the interconnected system can utilise all the assistance provided by its

neighbour to reduce its ISR. In both cases, however, the original assistance

model will be modified by the tie-line failure probability. Two intercon­

nected systems can behave like a single system with respect to unit commit­

ment and spinning reserve if the tie lines are flexible and capable of transfer­

mg any amount of power as required by the systems. The actual tie­

capacity in practice, is determined by economic and other operational con­

siderations.

Tables 3.7 and 3.8 show the effect of tie-line capacity on the unit COID-

Table 3.6: Unit Commitment With Equal Single System Risk .

•

Single System Interconnected System

SSR Load No. of Capacity No. of Capacity ISR

(MW) Units (MW) Units (MW)

A B A B A B A B A B A B A B

O.OlD O.OlD 1800 1300 13 9 1980 1510 13 9 1980 15lD 0.00006854 0.00001896

0.010 O.OlD 1800 1350 13 9 1980 15lD 14 9 2080 1510 0.00001668 0.00003599

O.OlD 0.010 1800 1400 13 io 1980 1660 13 io 1980 1660 0.00004069 0.00001618

O.OlD 0.010 1800 1450 13 10 1980 1660 13 10 1980 1660 0.00007126 0.00002358

O.OlD 0.010 1800 1500 13 10 1980 1660 14 io 2080 1660 0.00001827 0.00004044

O.OlD 0.010 1800 1550 13 11 1980 1760 13 11 1980 1760 0.00007247 0.00002620

0.010 0.010 1800 1600 13 11 1980 1760 14 11 2080 1760 0.00001854 0.00004178

O.OlD 0.010 1800 1650 13 12 1980 1860 13 12 1980 1860 0.00007370 0.00002883

O.OlD O.OlD 1800 1700 13 12 1980 1860 14 12 2080 1860 0.00001881 0.00004315

O.OlD O.OlD 1800 1750 13 13 1980 1980 13 13 1980 1980 0.00004690 0.00002396

0.010 0.010 1800 1800 13 13 1980 1980 14 14 2080 2080 0.00000283 0.00000283

O.OlD 0.010 1800 1850 13 14 1980 2080 13 14 1980 2080 0.00004791 0.00002545

O.OlD 0.010 1800 1900 13 14 1980 2080 13 15 1980 2180 0.00003638 0.00001173

0.010 O.OlD 1800 1950 13 15 1980 2180 13 15 1980 2180 0.00004892 0.00002695

O.OlD 0.010 1800 2000 13 15 1980 2180 13 16 1980 2280 0.00003657 0.00001199

--.,

Variations (oscillations) in unit commitment in System A is due to the fact that starting from single system unit

commitments, the system with the highest ISR at any instance is responsible for committing the next unit until the

ISRcriterion is met.

w00

39

mitment and corresponding ISR in System A and System B. The specifiedSSR and ISR is 0.01 and 0.0001 respectively. Tie capacity was varied from

2 x 40 MW to 2 x 200 MW in discrete steps to observe the effect of tie

capacity on the level of assistance provided by one system to another.

Table 3.1: Effect of Tie-line Capacity.

La = 1750 MW c, = 2000 MW SSR 0.01 ISR 0.0001

Tie Capacity Units ISR

(MW) A B A B

2x40 14 16 0.00000584 0.000029692x50 14 16 0.00000505 0.000027102x60 14 16 0.00000466 0.00001421

2x70 13 16 0.00002624 0.000009082x80 13 16 0.00001326 0.000007642x90 13 15 0.00002495 0.000053462x100 13 15 0.00002494 0.000051072x125 13 15 0.00002479 0.000032272x150 13 15 0.00002479 0.000032262x175 13 15 0.00002477 0.000032112x200 13 15 0.00002477 0.00003211

The results shown in Table 3.7 have been derived for a load of 1750 MW in

System A and 2000 MW in System B. System A and System B are re­

quired to commit 13 and 15 units respectively to satisfy their SSR criteria.

Both systems must commit one more unit in addition to their single system

commitment to satisfy the ISR when the tie capacity is 2x40 MW. As the

tie capacity is increased from 2x40 MW to 2x60 MW the unit commitment

of both system remain unaltered at 14 units in System A and 16 units in

System B with the ISR's decreasing with increments in tie capacity. When

the tie capacity is 2 x 90 MW, both System A and System B can satisfy their

ISR criteria without committing any additional capacity than their single sys­

tem commitment. The tie capacity of 2x40 MW is, therefore, inadequate for

the potential assistance that systems A and B are capable of providing to

each other at a load level of 1750 MW in A and 2000 MW in B.

40

Table 3.8: Effect of Tie-line Capacity.

La = 1800 MW Lb = 1400 MW SSR 0.01 ISR 0.0001

Tie Capacity Units ISR

(MW) A B A B

2x40 14 11 0.00002715 0.000003422x50 14 10 0.00002554 0.000023732x60 14 10 0.00001277 0.000021882x70 14 10 0.00000681 0.000009072x80 14 10 0.00000567 0.000004422x90 13 10 0.00004283 0.000016292x100 13 10 0.00004069 0.000016182x125 13 10 0.00002198 0.000016172x150 13 10 . 0.00002172 0.000016172x175 13 10 0.00002157 0.000016172x200 13 10 0.00002157 0.00001617

Increments of tie capacity above 2x90 MW do not alter the unit com­

mitment III System A and System B from the unit commitment at the tie

capacity of 2x90 MW. The ISR of System A and System B, however,

decreases as the tie capacity is increased from 2x90 MW to 2x125 MW.

The spinning reserve assistance that System A and System B can provide to

each other tends to saturate as the tie capacity IS increased beyond2 x 125 MW. Similar effects can be seen from Table 3.8 when the load III

System A is 1800 MW and in System B is 1400 MW. The tie capacity at

which the assistance benefit will tend to saturate depends on the set of

generating units and the load levels in the interconnected systems.

3.4. Effect of a Load Change in One System on The

Other System

In an interconnected system, the assistance available from one system

to its neighbour is determined by the capacity outage probability table, the

system load and the tie-line capacity. The neighbouring system sees this as-

41

sistance as an additional generating unit. The capacity model of the system

is therefore modified by the tie-line constrained equivalent assistance unit

from the other system. The ISR is thus influenced by the equivalent assis­

tance unit of the neighbouring system.

If the SSR values satisfy conditions (a) and (b) as noted in Section

3.2.1 despite an increase in load in one system, then the other system will

not be affected in terms of its unit commitment plan. This is virtually the

same as considering the two interconnected member systems to be independ­ent of each other although they are interconnected. This independence

depends on the set of generation units, unit failure rates, tie line capacity,

system load, SSR, ISR, etc. Anyone of these factors can change the equi­

librium, and hence the independence IS an unstable state as far as this

aspect of operation is concerned. A near independence situation can be ach­

ieved by restricting the tie line capacity, which may contradict the basic

philosophy of interconnection. Therefore, in practical power systems it is dif­

ficult to maintain the state of independence with variable load. This situa­

tion can, however, be achieved by lowering the SSR significantly such that

the condition (b) (the systems after interconnection show the ISR SIg­

nificantly lower than the specified ISR) is satisfied for a wide range of load

changes while keeping the ISR fixed. This would, however, realise less

benefit from the interconnection than would be achieved in the state of

dependence.

Table 3.9 shows the effect of load changes in one system on another

system using the data given in Table 3.2 and a tie capacity of 2x40 MW.

The SSR and the ISR is 0.01 and 0.0001 respectively. In these studies, the

load in System A was held constant at 1800 MW and the load in System B

was varied from 1300 MW to 2000 MW in steps of 50 MW. The number

of units to be committed in System A is constant at 14 and the actual ISR

in A changes slightly with the subsequent changes in the load level in

System B.

Table 3.9: Effect of Load Changes On Unit Commitment (Tiecapacity = 2x40 MW).

Single System Interconnected System

Load No. of Capacity No. of Capacity ISR

(MW) . Units (MW) Units (MW)

A B A B A B A B A B A B

1800 1300 13 9 1980 1510 14 10 2080 1660 0.00002715 0.00000315

1800 1350 13 9 1980 1510 14 10 2080 1660 0.00002723 0.00000823

1800 1400 13 10 1980 1660 14 11 2080 1760 0.00002715 0.00000342

1800 1450 13 10 1980 1660 14 11 2080 1760 0.00002724 0.00000902

1800 1500 13 10 1980 1660 14 12 2080 1860 0.00002715 0.00000370

1800 1550 13 11 1980 1760 14 12 2080 1860 0.00002725 0.00000983

1800 1600 13 11 1980 1760 14 13 2080 1980 0.00002710 0.00000255

1800 1650 13 12 1980 1860 14 13 2080 1980 0.00002720 0.00000534

1800 1700 13 12 1980 1860 14 13 2080 1980 0.00002731 0.00002615

1800 1750 13 13 1980 1980 14 " 14 2080 2080 0.00002721 0.00000583

1800 1800 13 13 1980 1980 14 14 2080 2080 0.00002733 0.00002733

1800 1850 13 14 1980 2080 14 15 2080 2180 0.00002721 0.00000632

1800 1900 13 14 1980 2080 14 15 2080 2180 0.00002735 0.00002856

1800 1950 13 15 1980 2180 14 16 2080 2280 0.00002721 0.00000681

1800 2000 13 15 1980 2180 14 16 2080 2280 0.00002737 0.00002983

�N

43

Table 3.10 shows the units that must be committed in System A and

System B for similar operating conditions considered in the case of Table 3.9

but with a change in the tie capacity. The tie capacity in the case of Table

3.10 is 2x90 MW. Using this tie capacity, the unit commitment in

System A changes with variation of load level in System B, although the

load in System A is held constant.

A change in load in one system also changes the level of assistance

that this system can provide to its neighbour. A system experiences the ef­

fect of load change in its neighbouring system through the tie lines intercon­

necting them. A system IS, therefore, less affected by load changes in its

neighbouring system if the tie capacity is far less than that which is requiredfor unconstrained power flow. This is one of the principle reasons why the

load changes in System B shown in Table 3.9 do not influence the unit com­

mitment of System A when the tie capacity is 2x40 MW. On the other­

hand, the unit commitment in System A for similar conditions is affected as

shown in Table 3.10 by the load changes in System B when the tie capacity

is increased to 2 x 90 MW.

3.S. Effect of Unit Failure Rates on Spinning Reserve

Generating unit failure rates are important parameters in unit commit­

ment and spinning reserve assessment. The probabilities of the capacity out­

age states in the capacity model of a system directly depend on the generat­

mg unit failure rates. A system whose units fail more frequently than its

neighbour is likely to commit more units [i.e, more spinning reserve) than its

neighbour provided other variables are identical. The effect of unit failure

rate, however, will differ depending upon the selection of the specified SSR

and ISR as far as the spinning reserve and the unit commitment are con­

cerned.

Table 3.11 shows the unit commitment in System A and System B

when all parameters including the unit failure rates in both systems are iden-

Table 3.10: Effect of Load Changes On Unit Commitment (Tiecapacity = 2x90 MW).

Single System Interconnected System

Load No. of Capacity No. of Capacity ISR

(MW) Units (MW) Units (MW)

A B A a A B A B A B A B

1800 1300 13 9 1980 1510 13 9 1980 1510 0.00007067 0.00001909

1800 1350 13 9 1980 1510 14 10 2080 1660 0.00000290 0.00000176

1800 1400 13 10 1980 1660 13 10 1980 1660 0.00004283 0.00001629

1800 1450 13 10 1980 1660 13 10 1980 1660 0.00007338 0.00002377

1800 1500 13 10 1980 1660 14 11 2080 1760 0.00000381 0.00000467

1800 1550 13 11 1980 1760 13 11 1980 1760 0.00007459 0.00002639

1800 1600 13 11 1980 1760 14 12 2080 1860 0.00000384 0.00000497

1800 1650 13 12 1980 1860 13 12 1980 1860 0.00007581 0.00002903

1800 1700 13 12 1980 1860 14 13 2080 1980 0.00000314 0.00000307

1800 1750 13 13 1980 1980 13 13 1980 1980 0.00004903 0.00002397

1800 1800 13 13 1980 1980 14 14 2080 2080 0.00000316 0.00000316

1800 1850 13 14 1980 2080 13 14 1980 2080 0.00005003 0.00002546

1800 1900 13 14 1980 2080 13 15 1980 2180 0.00003850 0.00001173

1800 1950 13 15 1980 2180 13 15 1980 2180 0.00005103 0.00002696

1800 2000 13 15 1980 2180 13 16 1980 2280 0.00003868 0.00001199

-

Variations (oscillations) in unit commitment in System A is due to the fact that starting from single system unit

commitments, the system with the highest ISR at any instance is responsible for committing the next unit until the

ISRcriterion is met.

.c:..

.c:..

45

tical. The unit commitments are identical for equal load in both systems as

expected. In order to study the effect of unit failure rate on unit commit­

ment and spinning reserve, all the transition rates of the on-line generating

Table 3.11: Unit Commitment With Equal Unit Failure Rates.

Specified SSR = 0.001 Specified ISR = 0.00001

Spinning ISR

Load (MW) Units Capacity (MW)A B A B A B A B

1650 1650 13 13 1980 1980 0.00000051 0.00000051

1750 1750 14 14 2080 2080 0.00000053 0.00000053

1850 1850 15 15 2180 2180 0.00000054 0.00000054

1950 1950 16 16 2280 2280 0.00000055 0.00000055

2050 2050 17 17 2355 2355 0.00000077 0.00000077

units of System A have been changed to 1.5 times that of the transition

rates of the on-line generating units of System B. The units that must be

committed in System A and System B are shown in Table 3.12. For all

cases, Sy�em A requires one more unit to be committed than in System BII

for equal! load in each system. The spinning reserve requirement in

System A is, therefore, higher than that in System B due to the simple

reason that the units in System A are more likely to fail than those in

System B.

Table 3.12: Unit Commitment With Unequal Unit FailureRates.

Specified SSR = 0.001 Specified ISR 0.00001

Spinning ISR

Load (MW) Units Capacity (MW)A B A B A B A B

1650 1650 13 12 1980 1860 0.00000430 0.00000641

1750 1750 14 13 2080 1980 0.00000287 0.00000566

1850 1850 15 14 2180 2080 0.00000305 0.00000621

1950 1950 16 15 2280 2180 0.00000323 0.00000678

2050 2050 17 16 2355 2280 0.00000540 0.00000873

46

3.6. Rapid Start and Hot Reserve Units

In a practical system, generating units are committed for a specified. time period during which additional generation can be made available after a

time delay. The actual time delay depends on the type of additional genera­

tion and many other factors of which the type of additional generation is the

most important. The delay time associated with a thermal generating unit

can be several hours while hydro and gas turbine units can be started very

quickly. The delay times associated with starting, synchronising, and loading

of hydro and gas turbine units are relatively short. The loading characteris­

tics of these rapid units are quite different from the loading characteristics of

conventional thermal units although the lead time of the thermal units can

be reduced considerably by keeping the boilers in a hot state.

The concept of area risk curves [3] can be used to include rapid start

and hot reserve units in the assessment of operating risk. This concept can

be extended to interconnected system operation. A typical area risk curve

for a system with gas turbine and thermal hot reserve units is shown in

Figure 3.2 [3].

F (R)I�- Har RESERVE UNITS IN

---- �---I� ADDITIONAL

__- __ ta L-.___:::UNITS IN

TIME

Figure 3.2: Area Risk Curve of a System.

47

In Figure 3.2, F(R) is the risk function and

t;

= the time to start rapid start gas turbine units

t h the time to start hot reserve units

ta

the lead time for the remaining thermal units.

At time tr the gas turbine units become available and the risk con­

tribution decreases. The risk contribution decreases further at time th when

the hot reserve thermal units become available. At time ta' additional ther­

mal units become available and the risk contribution is reduced significantly.

The ordinate of the risk curve can be considered to be zero for all practical

purposes after a lead time tao The risk level for the entire lead time for

this case IS

R (3.1)

where:

risk level calculated for the operating capacity alone for the

time interval 0 to tr,

risk level calculated for the operating capacity plus the gas

turbine units for the time interval t;

to th,

pa F(R )dtt 3h

risk level calculated for the operating capacity plus the gas•

turbine and hot reserve units for the time interval t h to ta.

The areas under the curve are calculated directly for computational purposes

and the actual integral equations are not used [3]. The total area under the

curve represents the probability that all the present on-line generating units

plus all the back up units in the system will be unable to or just able to

meet the system load demand. The SSR of the system should be equal to

or less than R.

48

In any interconnected system, participating member systems may have

different numbers and types of rapid start and hot reserve units. The lead

time associated with these units may also be quite different for different sys­

tems. In an interconnected system study, the area risk curve of one system

is modified by the area risk curve(s) of its neighbour(s). The modified area

risk curves are shown in Figure 3.3.

F(RAB) is the risk function of System A with assistance from

System B

is the risk function of System B with assistance from

System A

time to start rapid start units m System A

time to start hot reserve units in System A

lead time for the remammg thermal units in System A

time to start rapid start units in System B

time to start hot reserve units in System B

lead time for the remaining thermal units in System B

The ISR of both systems for a total lead time Tare:

itra jtrb jthaRia = F(RAB )dt + F(RAB )dt + F(RAB )dt +o 1 t 2 tb 3

ra r

jthb jtaa jtabF(RAB )dt + F(RAB )dt + F(RAB )dt +t ha

4 t hb5 t

aa6

jT F(RAB )dt (3.2)tab 7

49

.....--thb��------tab

I I

F(�)

T ----.....1 TIME

Figure 3.3: Area Risk Curves of an Interconnected System.

50

where

Ria = ISR of System A

Rib = ISR of System B

3.6.1. Rapid start and hot reserve unit models

3.6.1.1. Rapid start units

The conventional two-state or three-state generating unit models

described in Sections 2.4.1 and 2.4.2 do not contain sufficient detail to ade­

quately represent rapid start units. These units such as gas turbines can be

represented by the four-state model [3] shown in Figure 3.4.

FAILS TO STARr FAILED

READY FOR SERVICE IN SERVICE

Figure 3.4: Four-state Model for Rapid Start Units.

51

The time dependent state probabilities can be evaluated using matrix

multiplication techniques [3]. The stochastic transitional probability matrix P

for the four-state model shown in Figure 3.4 is as follows.

1-(A12+'\14)�t '\12�t 0 '\14�t'\21�t 1-('\21+'\23)�t '\23�t 0

p= 0 '\32�t 1-('\32+'\34)�t '\34�t'\41�t '\42�t 0 1-('\41+'\42)�t

The initial probability vector IS:

where

and

The probability of finding the unit on outage given that a demand has

occurred is given by [3]

P(down)

3.6.1.2. Hot reserve units

A thermal unit when taken out of service can be in one of two states;

hot reserve or cold reserve. In the hot reserve state, the boiler is retained

in an active or semi-active condition. In a cold reserve state, the boiler is

completely shut down. The hot reserve unit, therefore, can be brought back

into service in a shorter time than the cold reserve unit. A hot reserve

thermal unit can be represented by the five-state model [3] shown in Figure3.5.

The initial probability vector for the hot reserve unit is:

52

FAIL TO TAKE

UP LOAD FAIlED

Bar RESERVE IN SERVICE

Figure 3.5: Five-state Model For Hot Reserve Units.

[ P(0) 1 = [P10 0 0 P40 01

where

P40 = )..23/ ()..21 +)..23)PlO = I-P40 .

The time dependent state probabilities can be evaluated usmg similar

techniques to those utilised for a rapid start unit [3].

A computer program has been- written usmg the area risk concept to

53

include rapid start and hot reserve units in a spmnmg reserve study for an

interconnected system configuration. Assume that both System A and Sys­

tem B has one rapid start and one hot reserve unit in addition to those

units in Table 3.2. The corresponding transition rates per hour of the rapidstart and hot reserve unit are shown in Table 3.13.

Table 3.13: Transition Rate of Hot Reserve and Rapid StartUnits.

Rapid start unit:

Capacity = 25 MW Lead time 5 minutes

All=O.OOA21 =0.0033

A31=0.0A41=0.015

A12=0.005A22=0.0A32=0.0A42=0.025

A13=0.0A23=0.0008A33=0.0A43=0.0

A14=0.03A24=O.OA34=0.025A44=0.0

Hot reserve unit:

Capacity 50 MW Lead time = 60 minutes

Al1=O.OA21=0.02A31=0.0A41=0.035A51=0.003A15=0.0A25=0.0

A12=0.024A22=0.0A32=0.0A42=0.0A52=0.0025A35=0.0A45=0.025

A13=0.0A23=0.00002A33=0.0A43=0.0A53=0.0A55=0.0

A14=0.008A24=O.OA34=0.03A44=0.0A54=0.0

Table 3.14 shows the computational results when rapid start and hot

reserve units are added to both systems. The SSR and ISR is considered to

be 0.01 and 0.0001 respectively. The load in System B is varied while the

load in System A is held constant. The actual magnitude of the operatingreserve of each system can be found by subtracting the system load from the

total committed capacity shown in columns 11 and 12 in Table 3.14.

Table 3.14: Unit Commitment With Rapid Start and Hot

Reserve Units.

Single System Interconnected System

Load No. of Capacity No. of Capacity ISR

(MW) Units (MW) Units (MW)I

A B A B A B A B A B A B

1800 1300 13 9 1980 1510 13 9 1980 1510 0.00000581 0.00000317

1800 1350 13 9 1980 1510 13 9 1980 1510 0.00001278 0.00001219

1800 1400 . 13 10 1980 1660 13 10 1980 1660 0.00000412 0.00000076

1800 1450 13 10 1980 1660 13 10 1980 1660 0.00000599 0.00000403

1800 1500 13 10 1980 1660 13 10 1980 1660 0.00001360 0.00001478

1800 1550 13 11 1980 1760 13 11 1980 1760 0.00000603 0.00000411

1800 1600 13 11 1980 1760 13 11 1980 1760 0.00001370 0.00001530

1800 1650 13 12 1980 1860 13 12 1980 1860 0.00000607 0.00000420

1800 1700 13 12 1980 1860 13 12 1980 1860 0.00001379 0.00001583

1800 1750 13 13 1980 1980 13 13 1980 1980 0.00000484 0.00000224

1800 1800 13 13 1980 1980 13 13 1980 1980 0.00000905 0.00000905

1800 1850 13 13 1980 1980 13 13 1980 1980 0.00002350 0.00003907

1800 1900 13 14 1980 2080 13 14 1980 2080 0.00000912 0.00000936

1800 1950 13 14 1980 2080 13 14 1980 2080 0.00002375 0.00004027

1800 2000 13 15 1980 2180 13 15 1980 2180 0.00000919 0.00000967

CJl.1:0.

55

3.7. Effect of Load Forecast Error

Unit commitment and spinning reserve assessment In a power system IS

normally based on an advance estimate of hourly load variation within a

short period of time, typically 24 hrs. The prediction of future load is nor­

mally done on the basis of past data and weather forecasts. A certain de­

gree of error exists between the forecast and the actual load [27] due to the

random nature of system loads, the non-linear relationship between load and

weather changes and inaccuracies in weather forecasting. Load forecast un­

certainty can be reasonably approximated by a normal distribution [�:]. The

mean of the distribution is the forecast load. The normal distribution can

be discretised into several class intervals for computational simplicity [3]. The

probability associated with a class interval can be assigned to the load

representing the class interval mid-point.

Assume that the load forecast uncertainty in System A and System B

can be approximated by discretizing the normal distribution of loads in

System A and System B with nand m steps respectively. For one load

step in System A there are m possible risk indices in System A due to the

m load steps in System R The ISR of System A due to the kth load step

In System A is

m

L Ra(k,j)PbU)j=1

(3.4)

where

ISR of System A due to a load of La(k) in System. A and

LbU) in System B,

ISR of System A due to the kth load step in System A and

all the load steps in System B,

kth load step of the load distribution In System A,

Jth load step of the load distribution In System B,

56

probability of the load step LbU) m System B.

The ISR of System A can be expressed as the weighted summation of

the risk contributions due to the n load steps in System A.

n

L R'ia{k)Pa(k)k=l

(3.5)

where

ISR of System A,

probability of the load step La (k) in System A.

Combining Equations (3.4) and (3.5), the ISR in System A can be expressedas

n m

Ria(k) = L {L Ra(k,i)PbU)}Pa(k)k=l j=l

(3.6)

A similar expression can be written for the corresponding ISR in System B.

Based on Equation (3.6) a computer program has been developed to assess

spmnmg reserve and unit commitment in interconnected systems in the

presence of load forecast uncertainty. Equation (3.6) indicates that rn x n in­

dividual ISR computations are required to determine the unit commitment

risk in System A and System B. The computation time required to assess

spinning reserve and unit commitment with load forecast uncertainty is con-•

siderably higher than that required with zero load forecast uncertainty due to

this m x n individual risk computations. The computation time in the

presence of load forecast uncertainty, however, can be kept in reasonable

limits by approximating the load distributions with a comparatively small

number of load steps.

A normally distributed load can be approximated by seven or three

load steps depending on the degree of accuracy required. Figure 3.6 shows

57

PROBABILITY GIVEN BY INDICATED AREA

-3 -2 -1 0

NO. OF STANDARD DEVIATIONSFROM THE MEAN

+1 +2 +3

MEAN FORECAST LOAD(MW)

Figure 3.6: Seven-step Approximation of the Normal Distribu­tion.

the seven-step approximation of a normal distribution. In the seven-step ap­

proximation to normal curve, the distribution beyond ± 3.5 standard devia­

tion (SD) is neglected. It IS assumed that the respective area be­

tween +2.5 SD to +3.5 SD and between -2.5 SD to -3.5 SD is 0.006. As­

sume that the load forecast uncertainty in System A and System B can be

approximated by the seven-step load distribution shown in Figure 3.€;. Table

3.15 shows the unit commitment and corresponding risk In System A and

System B. A standard deviation of 2% of the forecast load is assumed in

both systems. The load in System B is varied from 1300 MW to 2000 MW

in steps of 50 MW while the load in System A is held constant at

Table 3.15: Unit Commitment With Load Forecast Uncertainty(Seven-step approximation of the load distribution).

Single System Interconnected System

Load No. of Capacity No. of Capacity ISR

(MW) Units (MW) Units (MW)

A B A B A B A B A B A B

1800 1300 14 9 2080 1510 14 9 2080 1510 0.00000931 0.00001211

1800 1350 14 10 2080 1660 14 10 2080 1660 0.00000332 0.00000139

1800 1400 14 10 2080 1660 14 10 2080 1660 0.00000508 0.00000464

1800 1450 14 10 2080 1660 14 10 2080 1660 0.00001000 0.00001519

1800 1500 14 11 2080 1760 14 11 2080 1760 0.00000521 0.00000541

1800 1550 14 11 2080 1760 14 11 2080 1760 0.00001015 0.00002664

1800 1600 14 12 2080 1860 14 12 2080 1860 0.00000529 0.00000566

1800 1650 14 12 2080 1860 14 12 2080 1860 0.00001050 0.00002760

1800 1700 14 13 2080 1980 14 13 2080 1980 0.00000448 0.00000433

1800 1750 14 13 2080 1980 14 13 2080 1980 0.00000833 0.00001457

1800 1800 14 14 2080 2080 14 14 2080 2080 0.00000453 0.00000453

1800 1850 14 14 2080 2080 14 14 2080 2080 0.00000866 0.00001589

1800 1900 14 15 2080 2180 14 15 2080 2180 0.00000480 0.00000497

1800 1950 14 15 2080 2180 14 15 2080 2180 0.00000894 0.00001714

1800 2000 14 16 2080 2280 14 16 2080 2280 0.00000490 0.00000585

CJ100

59

1800 MW. Table 3.16 shows the unit commitment and corresponding risk

for the same forecast load levels as shown in Table 3.15 but with zero load

forecast error. It can be seen by comparing the Tables 3.15 and 3.16 that

at some load levels, System A or System B must commit more generatingunits in the presence of load forecast uncertainty than that with zero forecast

uncertainty. The computation time required to determine the unit commit­

ment shown in Table 3.15 is 46 mins. and 12.81 sees, CPU (VAX 8650).The computation time to determine the unit commitments for the load levels

shown in Table 3.16 with zero load forecast uncertainty is 1 min. and 37.33

sees,

A three-step approximation to the normal distribution for the loads in

System A and System B can also be used for unit commitment and spinning

reserve assessment with a small loss of accuracy compared to the seven-step

approximation. A three-step approximation will considerably reduce the com­

putation time from that required with a seven-step approximation. The

saving in computation time should be judged against the potential loss of ac­

curacy. Figure 3.7 shows a three-step approximation to the normal distribu­

tion. In this three-step approximation the distribution beyond ± 3 SD is

neglected. It has been assumed that the respective area between + 1 SD to

+3 SD and between -1 SD to -3 SD is 0.1587 instead of 0.1574. Table 3.17

shows the unit commitments and corresponding risk in System A and

System B with the identical forecast loads shown in Table 3.15. The normal

distribution of load in the case of Table 3.17, however, is approximated by a

three-step approximation with a standard deviation of 2% of the forecast

load in both systems. The unit commitments in System A and System B

are identical with seven-step and three-step approximations to the normal

distribution except when the load is 1800 MW in System A and 1350 MW

in System B. The computation time is 8 mins. and 46.42 sees. with the

three-step approximation for an identical set of forecast load as used in the

seven-step approximation case.

Table 3.16: Unit Commitment With Zero Load Forecast Uncertainty,

Single System Interconnected System

Load No. of Capacity No. of Capacity ISR

(MW) Units (MW) Units (MW)

A B A B A B A B A B A B

1800 1300 13 9 1980 1510 13 9 1980 1510 0.00006854 0.00001896

1800 1350 13 9 1980 1510 14 9 2080 1510 0.00001668 0.00003599

1800 1400 13 10 1980 1660 13 10 1980 1660 0.00004069 0.00001618

1800 1450 13 10 1980 1660 13 10 1980 1660 0.00007126 0.00002358

1800 1500 13 10 1980 1660 14 10 2080 1660 0.00001827 0.00004044

1800 1550 13 11 1980 1760 13 11 1980 1760 0.00007247 0.00002620

1800 1600 13 11 1980 1760 14 11 2080 1760 0.00001854 0.00004178

1800 1650 13 12 1980 1860 13 12 1980 1860 0.00007370 0.00002883

1800 1700 13 12 1980 1860 14 12 2080 1860 0.00001881 0.00004315

1800 1750 13 13 1980 1980 13 13 1980 1980 0.00004690 0.00002396

1800 1800 13 13 1980 1980 14 14 2080 2080 0.00000283 0.00000283

1800 1850 13 14 1980 2080 13 14 1980 2080 0.00004791 0.00002545

1800 1900 13 14 1980 2080 13 15 1980 2180 0.00003638 0.00001173

1800 1950 13 15 1980 2180 13 15 1980 2180 0.00004892 0.00002695

1800 2000 13 15 1980 2180 13 16 1980 2280 0.00003657 0.00001199

�

8

61

PROBABILITY GIVEN BY INDICATED AREA

0.6826

-3 -2 -1 o +1 +2 +3

NO. OF STANDARD DEVIATIONSFROM THE MEAN

MEAN = FORECAST LOAD(MW)

Figure 3.1: Three-step Approximation of the Normal Distribu­tion.

T8ble 3.17: Unit Commitment With Load Forecast Uncertainty(Three-step approximation of the load distribution).

Single System Interconnected System

Load No. of Capacity No. of Capacity ISR

(MW) Units (MW) Units (MW)

A B A B A B A B A B A B

1800 1300 14 9 2080 1510 14 9 2080 1510 0.00000973 0.00001242

1800 1350 14 9 2080 1510 14 9 2080 1510 0.00002264 0.00007230

1800 1400 14 10 2080 1660 14 10 2080 1660 0.00000519 0.00000454

1800 1450 14 10 2080 1660 14 10 2080 1660 0.00001049 0.00001500

1800 1500 14 11 2080 1760 14 11 2080 1760 0.00000544 0.00000606

1800 1550 14 11 2080 1760 14 11 2080 1760 0.00001066 0.00003494

1800 1600 14 12 2080 1860 14 12 2080 1860 0.00000545 0.00000629

1800 1650 14 12 2080 1860 14 12 2080 1860 0.00001074 0.00003555

1800 1700 14 13 2080 1980 14 13 2080 1980 0.00000465 0.00000451

1800 1750 14 13 2080 1980 14 13 2080 1980 0.00000855 0.00001480

1800 1800 14 14 2080 2080 14 14 2080 2080 0.00000468 0.00000468

1800 1850 14 14 2080 2080 14 14 2080 2080 0.00000866 0.00001536

1800 1900 14 15 2080 2180 14 15 2080 2180 0.00000472 0.00000487

1800 1950 14 15 2080 2180 14 15 2080 2180 0.00000885 0.00001630

1800 2000 14 16 2080 2280 14 16 2080 2280 0.00000498 0.00000679

0)t-.j

63

3.8. Summary

The theoretical and computational features of a new spinning reserve

assessment technique for interconnected systems are introduced in this chap­

ter. The technique designated as the 'Two Risks Concept' uses the stochas­

tic nature of the system components during the spinning reserve evaluation.

The 'Two Risks Concept' proposes that two risk levels are to be satisfied by

each individual interconnected system for a fair sharing of spinning reserve

among the pool members. The 'Two Risks Concept' has the capability to

incorporate the essential system parameters which directly or indirectly in­

fluence the system reliability. The inclusion of hot reserve and rapid start

units in the unit commitment process is illustrated in this chapter. This

chapter also discusses spinning reserve assessment in interconnected systems

with load forecast uncertainty. The results of some typical spinning reserve

situations and the corresponding unit commitment risks are also presented.

64

4. SPINNING RESERVEWITH EXPORT/IMPORT

4.1. Introduction

Chapter 3 presents the basic aspects of the 'Two Risks Concept' and il­

lustrates this technique for spinning reserve assessment in an interconnected

generating system assuming that there is no contracted export/import.Energy flow occurs between the interconnected systems if one system suffers

a sudden generation loss. The system with the lost generation is, however,

required to adjust its generation within an allowable time limit agreed by the

pool members. Inadvertent energy flow between systems also occurs due to

electrical disturbances and inaccuracies in the tie line control. These inter­

changes are unscheduled and utilities interconnected by tie lines make pay­

ments to each other for these interchanges in accordance with some

agreements [27, 28]. In a practical multi-area system, contracted

export/import between different areas IS a common operating condition. A

probabilistic assessment of the spinning reserve requirement in different areas

of a multi-area interconnected system with export/import can be performedbased on the 'Two Risks Concept'. In the following sections, a

technique [29] for spinning reserve assessment in a multi-area system with

export/import agreements is illustrated.

65

4.2. Export/Import Agreements

There could be many different agreements regarding contracted

export/import of energy between the interconnected utilities in a power pool.The export/import agreements between utilities not only control' the tie line

flow but also influence the unit commitment in the interconnected systems.

The amount of power flow through the tie lines affects the level of assistance

with respect to the spinning reserve that a system can provide to its neigh­

bours. The probabilistic models for export/import will depend greatly on the

type of agreements between utilities. It is not practical to develop methods

to assess spinning reserve for all possible export/import agreements. Two

basic agreements are considered in this thesis. These agreements are (1)firm purchase by one system is backed up by the complete system of the ex­

porting utility and, (2) firm purchase is tied to a specific unit in the export­

ing system.

4.3. Firm Purchase Backed Up by the Complete System

In this form of agreement, the availability of a certain capacity

(import) is guaranteed by the entire exporting system. The import can be

modelled as an equivalent generating unit with an effective zero forced out­

age rate as far as the importing system is concerned. The export, on the

other hand, can be modelled as an additional load as far as the exporting

system is concerned. The guarantee of the exporting system is limited by

the reliability of its generating units. An exporting system would require In­

finite generation capacity to maintain a finite export capacity with 100�

reliability. If the export capacity is considerably less than the load of the

exporting system, then for all practical purposes the reliability of the export­

ing capacity can be considered as 100%. If the export capacity, on the

other hand, is relatively large in comparison to the load of the exporting sys­

tem, then the export commitment cannot be considered to be 100% reliable

and the actual risk associated with the export should be considered for com­

putational and contractual purposes.

,66

Assume that

Li load of System i,

Iij import of System i from System j,

Eij export of System i to System j,

Tii tie capacity between System i and System j.

In the case where export is backed up by the entire exporting system

and L Eij< Li, all export can be modelled as additional load to the ex­

porter. Therefore, the effective load of System i, Lei becomes

(4.1)

If all the imports �f System i are completely backed up by the respective ex­

porters and the tie lines are 100% reliable, the generation model of System i

will be modified by the additional generating unit of capacity equal to the

sum of all imports of System i with forced outage rates of zero. It is as­

sumed that all tie-line capacities are greater than the proposed import

through them. If a specific tie capacity, Tij is less than the proposed im­

port, Iii through it, then the import of System i from System j becomes Til

In most situations, tie lines are assumed to be 100% reliable and the

development of export and import models are relatively straightforward.These models have to be modified, however, to recognise tie line constraints

if it is considered that tie-line failures cannot be neglected. Under these

conditions, the import in concern cannot be modelled as a 100% reliable

generating unit.

4.3.1. Tie-line constrained import model

The tie-line flow depends on the system states at the two ends of the

tie line. The tie-line flow IS constrained by its maximum power transfer

capability. For the sake of simplicity it is assumed that the tie-capacity is

constant during the time period equal to the system lead time. In the case

where tie-capacity varies during the study period, the study period is sub-

67

divided into several intervals and tie-capacity IS assumed to be constant

within each of these intervals.

Assume that

kth capacity state of the tie line between System i and

System j at time t ,

�/t) probability that the kth state of the tie line,· Tii exists at

time t,

total no. of capacity states in the tie-line model,

kth capacity state of the import model for the import of Iiiat time t,

�it) probability that the kth state of the import model for the

import of Iii exists at time t,

R�J-:-l(t) > Rk ( ). ii

t

and

total no. of capacity states in the import model.

If Q:j(t) > Iii the import model becomes

68

1I· .Ri/t) t)

n

1

L P:/t)S .. (t)I)

k=l

R�/t) =

Q�;:n-l(t)}S� .(t) = Pc_ .(t)

k

I) tJ

2, 3, 4, ... , (nt-n+l)

where n is an integer such that Q�.(t) > I .. > Q��l(t).tJ- lJ IJ

If Q�/t):::; Iij i.e., the tie capacity IS less than or equal to the import,

the import model is

1, 2, 3 ... , nt

The tie-line constrained import model can be considered for computa­

tional purposes as an additional on-line generating unit to the importing sys­

tem.

4.8.2. Export/import constrained tie-line model

The available capacity of the tie-line model with respect to the assis-1

tance of additional spinning reserve reduces to zero when Qi/t):::; Iij and the

entire tie-line model can only transfer the export/import capacity, with or

without capacity constraints on the imported power. The tie lines can,

69

however, assist the connecting systems with spinning reserve if at least

Ql iit) > Iij. The export/import constrained tie-line model can be derived

using the following relationships.

Assume that

if. .(t) =

Z)kth capacity state of the tie line between System i and

System j after fulfilling the export/import commitment at

time t,

0. .(t) =

Z)

\

Then

r.1/t)

probability that the kth capacity state of the tie line be­

tween System i and System j exists after fulfilling the

export/import commitment at time t,

total number of capacity states in the tie-line model after

fulfilling export/import commitments.

kQ .. (t)t)

-

I.J.Z)

k 1, 2, 3, ... , n

0. .(t) = P'. .(t)Z) ')

where n is an integer such that Q�.(t) > I;). > Q�:l(t)f) •

-

t)

nt

L P:/t)k=n+l

and it = n + 1

The export/import constrained tie-line model is used to determine the

tie-line constrained assistance equivalent unit of each system for risk and

spinning reserve assessment.

70

4.3.3. Tie-line failure neglected

If the tie lines are assumed to be 100% reliable then the import model

also becomes 100% reliable.

1I· . T··Ri/t) I· . <

'J IJ IJ

T·· , Iij > T··'J IJ

1

Si}t) 1

and

mt - 1

The export/import constrained tie-line model with a 100% reliable tie line IS

as follows.

1T.. - I· . T··Ui/t) > I· .

t) ZJ ZJ Z)

0 , Tij < I· .

'J

�}t) 1

and

It 1

4.4. Firm Purchase Backed Up by a Specific ..

Unit

In this agreement the export is tied to a specific generating unit of the

exporting system. The export therefore cannot be modelled as a generatingunit with zero forced outage rate. The export model will have outage

parameters which are based on the unit guaranteeing the export. The ex­

porting unit must be committed as long as it is available for operation. The

capacity remaining above the export commitment can, however, be used bythe exporting system to assist its neighbours with spinning reserve.

71

4.4.1. Export model

Assume that

kth capacity state of the exporting unit of System i at time

k-l kt and Ai (t) > Ai (t),

n:(t) probability that the kth capacity state of the exporting unit

of System i exists at time t,

total number of capacity states in the exporting unit,

kth capacity state of the export model for export from

System i to System j at time t, and C:; l(t) > C:/t),

D�,.(t) probability that the kth capacity state of the export model

for export from System i to System j exists at time t and

total number of capacity states in the export model.

If A�(t) > Eji i.e., unit size IS larger than the export commitment, the

export model is as follows

1E··Cji(t) J'

n

k

L B�(t)Dji(t)1.=1

k

A�+n-'(t}C .. (t)Jt

2, 3, 4, ... , (ne -n+l)k B�+n-l(t)D .. (t)Jt J

and

me = ne-n+l

n( . n+l( )where n IS an integer such that Aj t) 2: Eji > A

jt

72

If A�(t) � Eji i.e., unit size is equal to or less than export commitment,

the export model becomes

and

Other export models can be developed III a similar manner if the sys­

tem has more than one export commitment.

4.4.2. Tie-line constrained import model

There can be as many as nt possible capacity states III the tie-line con­

strained import model for each capacity state C��t) in the export model,

where nt is the total number of capacity states in the tie-line model. The

import model is

R�/t) = C7/t) ,C7/t) s Q�/t)

Q�/t) C�(t) > Q:/t)k

S .. (t)tJ D�.( t) J!. .(t)lJ tJ

where

m =e

total number of capacity states in the export model for the

export of System i to System j,

n 1, 2, ... , me .

73

There may be many identical capacity states and the states may not be

m order out of all the possible nt·me capacity states m the tie-line con-

strained import model. The identical capacity states can be grouped

together and the model arrangedk-l k

{ )such that R.. (t) > R. t .

tJ tJ

4.4.3. Export /import constrained tie-line model

There could be as many as nt possible states in the export/import con­

strained tie-line model for each capacity state C�.(t) in the export model.'J

r1;(t) k- C:J{t)

k

C:/t)Q .. (t) Q .. (t) >tJ ZJ

k C�.(t)0 , Qdt) <ZJ

V;;(t) .I. .(t) D�.(t)ZJ ZJ

where

k nt(n-1)+1, nt(n-l)+2, ... , nt·n

n 1, 2, 3, ... , me

The states can be rearranged as discussed in the previous section. The

export/import constrained tie-line model is used to determine the tie-line con­

strained assistance equivalent unit of each system for risk and spinningreserve assessment.

4.4.4. Remainder of the exporting generating unit

In many cases, the exporting unit capacity is larger than the export

commitment. This additional capacity of the exporting unit can be used bythe exporting system as committed capacity after it has fulfilled its export

commitment.

74

Assume that

kth capacity state of the remainder of the exporting unit of

System i at time t and G�-l(t) > G�(t),

probability that the kth capacity state of the remainder of

the exporting unit of System i exists at time t,

total number of states in the remainder of the exportingunit,

total number of states in the exporting unit.

The additional capacity of the exporting unit can be modelled as

1, 2, 3, ... , n

ne

L B�(t)k=n+l

n + 1

where,: is an integer such that A�(t) > Eij > A�+l(t).

4.4.5. Tie-line failures neglected

If the tie lines are assumed to be 100% reliable, then the tie-line con­

strained import model can be determined as follows.

75

T·· ,��.(t) > T··tJ lJ lJ

k kT· .Ci;(t) , C .. (t) <

lJ lJ

k= D .. (t)lJ

where k = 1, 2, 3,

The export/import constrained tie-line model becomes

cI.(t) k .

, Tij >

d,P)T·· - C .. (t)IJ tJ IJ

k = 1, 2, 3, ... , n

V:/t) D�J�t)

U�:l(t) - 0

me

�/l(t) L kD .. (t)IJ

k=n+l

It n + 1·

where n IS an integer such that C�.(t) > T··> C�:\t).lJ IJ -

1J

4.5. Interconnected System Risk

Given the load and the SSR of a system, the assistance model of that

system can be developed. This assistance model depends on the set of

generating units required to be committed to satisfy the load, export/importand the SSR. The assistance of one system to the other can be realised

through the export/import constrained tie capacity. The tie-line constrained

assistance equivalent model can be developed as described earlier. The tie­

line constrained assistance model of one system can be viewed as an extra

generating unit available to the neighbouring system. When this extra unit

is added to the generation capacity committed on the basis of system load,

76

export/import and SSR; the unit commitment risk is modified. This

modified unit commitment risk is the Interconnected System Risk. If the

ISR criterion IS not satisfied, generating units are added to the intercon­

nected systems as described in Reference [26] until the ISR criterion is

satisfied by the participating systems.

4.6. Numerical Examples

Two systems interconnected by two tie lines are considered for numeri­

cal examples. The method as described in this chapter, however, can be ap­

plied to interconnected configurations with more than two systems. A com­

puter program has been developed to assess the spinning reserve requirements

in interconnected systems with export/import constraints. Table 3.2 shows

the generating units in System A and System B. Table 3.3 shows the tie

lines interconnecting the two systems. The lead time for both systems is

considered to be 120 mins. The Interconnected System Risk and the Single

System Risk for both systems are 0.0001 and 0.01 respectively.

4.6.1. Firm purchase backed up by the entire system

A system must commit an adequate number of generating units to

satisfy its SSR for a particular load. In addition to the firm load, a system

may export/import some power to/from its neighbouring system. The effec­

tive load seen by a system is modified by the export/import.Case 1

Assume that

La 1450 MW Eab = 0 MW , lab = 60 MW

Lb 1210 MW Eba = 60 MW , lba = 0 MW

and the export of System B is backed by the entire system.

The effective loads become

77

1390 MW

1270 MW.

The export/import of each system is considered to be 100% reliable for

the purpose of calculating SSR. This reduces the computational complexityand although the individual system must first satisfy its SSR, the same sys­

tem is required to satisfy its ISR criterion as the final goal. During the ISR

assessment, therefore, the appropriate unavailability of the export/import due

to the tie-line constraints are considered. In order to satisfy the SSR

criterion, System A and System B are required to commit 10 and 9 units

respectively in the merit order shown in Table 3.2. The tie-line model for a

period of 120 minutes is shown in Table 4.1.

Table 4.1: Tie-Line Model.

Cap. Out

(MW)Cap. In

(MW)Cumulative

Probability

o100200

200

100

o

1.000000000.00045657

0.00000005

The tie-line constrained import model for the import of 60 MW by

System A from System B is shown in Table 4.2.

Table 4.2: Tie Constrained Import Model of System A.

Cap. Out

(MW)Cap. In

(MW)Cumulative

Probability

o60

60

o

1.000000000.00000005

The tie-line model as shown m Table 4.1 IS modified due to the

export/import commitment. The export/ import constrained tie-line model is

shown in Table 4.3.

78

Table 4.3: Export/Import Constrained Tie-Line Model.

Cap. Out Cap. In Cumulative

(MW) (MW) Probability

0 140 1.00000000100 40 0.00045657140 0 0.00000005

The export/import constrained tie-line model as shown in Table 4.3 is

used to assess the level of assistance, with respect to the spinning reserve,

that System A and System B can provide each other. In order to satisfy

the ISR criterion, System A is required to commit 10 and System B is re­

quired to commit 9 generating units from their respective merit order tables.

The actual ISRs of System A and System B at this point are 0.00000067

and 0.00000480 respectively.

If tie-line failures are neglected, the tie-line model is equivalent to a

100% reliable tie-line with a maximum power transfer capability of 200 MW.

The unit commitment required to satisfy the SSR remains unchanged. The

tie-line constrained import model for the import of 60 MW by System A

from System B becomes 100% reliable. The export/import constrained tie­

line model again becomes equivalent to a 100% reliable line with a maximum

power transfer capability of 140 MW. The· unit commitments required to

satisfy the ISR criterion for Systems A and B also remain unchanged. The

actual ISRs of System A and System B become 0.00000065 and 0.00000476

respectively.

Case 2

Consider another situation where the lead time for both systems IS 120

minutes and

79

La 1510 MW , Eab= 70 MW , lab = 0 MW

1430 MW , Eba o MW , Iba = 70 MW

and the export of System A is backed by the entire system. The specifiedSSR and ISR are 0.01 and 0.0001 respectively. The effective loads of

System A and System Bare

1580 MW

and Leb 1360 MW.

The corresponding tie-line model, tie-line constrained import model of

System B and export/import constrained tie-line model are shown in Tables

4.4, 4.5 and 4.6 respectively.

Table 4.4: Tie-Line Model.

Cap. Out Cap. In Cumulative

(MW) (MW) Probability

0 200 1.00000000

100 100 0.00045657

200 0 0.00000005

Table 4.5: Tie Constrained Import Model of System B.

Cap. Out

(MW)Cap. In

(MW)Cumulative

Probability

o70

70

o

1.000000000.00000005

System A and System B must commit 11 and 10 units respectively to satisfy

the SSR and ISR criteria. The corresponding actual ISR of System A is

0.00004874 and of System B is 0.00000135.

80

Table 4.6: Export/Import Constrained Tie-Line Model.

Cap. Out Cap. In Cumulative

(MW) (MW) Probability

0 130 1.00000000100 30 0.00045657130 0 0.00000005

The tie constrained import model of System B is equivalent to a 100%

reliable unit of 70 MW if tie-line failures are neglected. With this ap­

proximation, the export/import constrained tie-line model becomes a 100%

reliable line whose maximum power transfer capability is 130 MW. The unit

commitments of both the systems required to satisfy the SSR and the ISR,

when tie-line failures are neglected, remain the same as that when tie-line

failures are considered. The actual ISR with 100% reliable tie lines,

however, becomes 0.00004870 for System A and 0.00000133 for System B.

Some typical unit commitment results with and without considering tie-line

failures are summarised in Table 4.7. It is obvious from Table 4.7 that tie­

line failures do not have a significant impact on the unit commitment

schedule. Tie-line failures, therefore, can be neglected in a practical system

study.

4.6.2. Firm purchase backed up by a specific unit

'I'he availability of the export is tied to the availability of a specificunit when the export IS designated as being backed up by that unit. The

probability that the export/import commitment will be fulfilled by the

respective system is taken as unity during the unit commitment in order to

satisfy the SSR. Recognition of the appropriate failures in the export/importmodel, however, is considered during the assessment of the ISR. The

specified SSR and specified ISR are 0.01 and 0.0001 respectively in the fol­

lowing numerical examples.

Table 4.7: Unit Commitments (Export is backed up by the en­

tire exporting system).

Tie failures Considered Tie Failures Neglected

Load Export Import No. of ISR No. of ISR

(MW) (MW) (MW) Units Units

A B A B A B A B A B A B A B

14501210 0 0 0 0 10 9 0.00000067 0.00000036 10 9 0.00000065 0.00000036

14501210 0 60 60 0 10 9 0.00000067 0.00000480 10 9 0.00000065 0.00000476

13701530 0 0 0 0 10 11 0.00000042 0.00000069 10 11 0.00000042 0.00000067

13701530 70 0 0 70 10 10 0.00003545 0.00004918 10 10 0.00003542 0.00004915

17501770 0 0 0 0 13 13 0.00000254 0.00000263 13 13 0.00000252 0.00000261

17501770 0 80 80 0 12 14 0.00004983 0.00003659 12 14 0.00004978 0.00003653

15101540 0 0 0 0 11 11 0.00000139 0.00000142 11 11 0.00000137 0.00000139

15101540 100 0 0 100 12 10 0.00003501 0.00004826 12 10 0.00003496 0.00004823

00.....

82

Case 1

Consider that the load, export and import in System A and System B

are identical to those shown in Case 1 of Subsection 4.6.1. The effective

loads for the purpose of unit commitment in the individual systems are

1390 MW

and Leb 1270 MW.

The tie-line model for a system lead time of 120 minutes is identical to

that shown in Table 4.4. Usually the unit which backs up the export is

committed before any other unit commitment. In this example, unit #1 of

System B backs up the export of 60 MW. The export model of System B

for the export of 60 MW from System B is shown in Table 4.8.

Table 4.8: Export Model of System B.

Cap. Out

(MW)Cap. In

(MW)Cumulative

Probability

o

6060

o

1.000000000.00060005

The tie-line constrained import model of System A for the import of 60 MW

from System B to System A is shown in Table 4.9.

Table 4.9: Tie Constrained Import Model of System A.

Cap. Out

(MW)Cap. In

(MW)Cumulative

Probability

o

60

60o

1.000000000.00060005

The export/import constrained tie-line model IS shown ill Table 4.10.

83

Table 4.10: Export/Import Constrained Tie-Line Model.

Cap. Out Cap. In Cumulative

(MW) (MW) Probability

0 200 1.00000000

60 140 0.99940027

100 100 0.00045657

160 40 0.00045629

200 0 0.00000005

Unit #1 in System B has a capacity of 200 MW. This unit has ad­

ditional capacity of 140 MW beyond the export commitment. This ad­

ditional capacity is used for the purpose of spinning reserve and risk assess­

ment. System A requires 10 units and System B requires 9 units to satisfy

the SSR of 0.01. In order to satisfy the ISR criterion, System A and

System B are again required to commit 10 and 9 units respectively from

their respective merit order tables. The actual ISR of System A is

0.00000066 and of System B is 0.00000286.

The tie lines can be represented as a 200 MW line with 100%

reliability if the tie-line failures are neglected. The tie-line constrained im­

port model and the export/import constrained tie line with 100% reliable

lines are shown in Table 4.11 and 4.12 respectively.

Table 4.11: Tie Constrained Import Model of System A.

Cap. Out

(MW)Cap. In

(MW)Cumulative

Probability

o60

60

o

1.000000000.00060005

The unit commitments of both the systems with tie-line failures

84

Table 4.12: Export/Import Constrained Tie-Line.

Cap. Out

(MW)Cap. In

(MW)Cumulative

Probability

o60

200

140

1.000000000.99940000

neglected are the same as those with the tie-line failures considered. The ac­

tual ISR, however, becomes 0.00000064 for System A and 0.00000283 for

System B when tie-line failures are neglected.

Case 2

Consider that the load, export and import of System A and System B

are identical to those shown in Case 2 of Subsection 4.6.1. The effective

loads for the purpose of unit commitment in the individual systems are

1580 MW

and Leb 1360 MW.

The export model, the tie-line constrained import model and the

export/import constrained tie-line model are shown in Tables 4.13, 4.14 and

4.15 respectively.

Table 4.13: Export Model of System A.

Cap. Out

(MW)Cap. In

(MW)Cumulative

Probability

o70

70o

1.000000000.00060000

System A requires 11 units and System B requires 10 units to satisfy

85

Table 4.14: Tie Constrained Import Model of System B.

Cap. Out

(MW)Cap. In

(MW)Cumulative

Probability

o70

70o

1.00000000

0.00060005

the SSR and the ISR criterion. The actual ISR of System A IS 0.00004195

and of System B is 0.00000132.

Table 4.15: Export/Import Constrained Tie-Line Model.

Cap. Out Cap. In Cumulative

(MW) (MW) Probability

0 200 1.0000000070 130 0.99940027

100 100 0.00045657

170 30 0.00045629

200 0 0.00000005

The tie-line constrained import model and the export/import con­

strained tie line with tie-line failures neglected are shown in Tables 4.16 and

4.17 respectively.

Table 4.16: Tie Constrained Import Model of System B.

Cap. Out

(MW)Cap. In

(MW)Cumulative

Probability

o70

70o

1.000000000.00060000

The unit commitment in both the systems neglecting tie-line failures

remains the same as it is when tie-line failures are considered. The actual

ISRs when tie-line failures are neglected, however, become 0.00004191 for

86

Table 4.17: Export/Import Constrained Tie-Line Model.

Cap. Out

(MW)Cap. In

(MW)Cumulative

Probability

o70

200

130

1.000000000.99940000

System A and 0.00000129 for System B. Some unit commitment results

with and without considering the tie-line failures are summarised in Table

4.18. It is obvious from Table 4.18 that the tie-line failure have no sig­

nificant impact on the unit commitment schedule of System A and

System B. In a practical interconnected system study, the tie-line failures

normally can be neglected. It may be necessary, however, to perform an ex­

ploratory study to determine the impact of this approximation on system risk

and unit commitment schedule.

4.7. Effect of Export/Import on the Level of Assistance

The ISR of an interconnected system is influenced by the tie-line con­

strained import model and the export/import constrained tie-line model. The

tie-line capacity for the purpose of unit commitment is considered to be fixed

at an average value during a particular time period. The same tie-line

capacity is shared by the export/import and the additional assistance with

respect to the spinning reserve. The tie-capacity left after fulfilling the

scheduled export/import can be used to transfer assistance in the case of a

sudden generation loss or a capacity deficiency due to a sudden load rise in

an interconnected system. The level of assistance that an interconnected sys­

tem can provide to its neighbour without committing a breach of

export/import schedule depends on the tie capacity and the scheduled

export/import. Table 4.19 shows the unit commitment and correspondingrisk in System A and System B for a specified SSR of 0.01 and a specifiedISR of 0.0001 and a load level of 1750 MW in both systems. The export of

System A to System B was varied from 80 MW to 180 MW in steps of

Table 4.18: Unit Commitments (Export is backed up by a

specific unit).

Tie failures Considered Tie Failures Neglected

Load Export Import No. of ISR No. of ISR

(MW) (MW) (MW) Units Units

A B A B A B A B A B A B A B

14501210 0 0 0 0 10 9 0.00000067 0.00000036 10 9 0.00000065 0.00000036

14501210 0 60 60 0 10 9 0.00000066 0.00000286 10 9 0.00000064 0.00000283

13701530 0 0 0 0 10 11 0.00000042 0.00000069 10 11 0.00000042 0.00000067

13701530 70 0 0 70 10 10 0.00002692 0.00004921 10 10 0.00002688 0.00004918

17501770 0 0 0 0 13 13 0.00000254 0.00000263 13 13 0.00000252 0.00000261

17501770 0 80 80 0 12 14 0.00004987 0.00002805 12 14 0.00004982 0.00002799

15101540 0 0 0 0 11 11 0.00000139 0.00000142 11 11 0.00000137 0.00000139

15101540 100 0 0 100 12 10 0.00002637 0.00004825 12 10 0.00002632 0.00004822

00'1

88

Table 4.19: Unit Commitment With Export (Export hacked up

by the entire exporting system).

Export Units to Units to ISR

(MW) Satisfy SSR Satisfy ISR

Eab A B A B A B

80 14 12 14 12 0.00000726 0.00004962

100 14 12 14 12 0.00004969 0.00004918

120 14 12 15 12 0.00000234 0.00004826

140 14 12 15 12 0.00003503 0.00004826

160 14 11 15 12 0.00005228 0.00004826180 15 11 16 12 0.00000565 0.00004825

20 MW. The export was backed by the entire system of A. For an export

of 80 MW, the unit commitments in both systems required to satisfy the

ISR are identical to the respective unit commitments to satisfy the SSR. As

the export increases to 160 MW, both systems need one more unit than

their single system commitment to satisfy the ISR criterion. This is due to

the fact that as the export/import through the tie line increases, the level of

potential assistance with respect to the spinning reserve that the tie line can

carry decreases provided that the tie capacity remains constant. A system,

therefore, must commit more capacity than its previous commitment to

satisfy the ISR criterion with an assistance less than that during the pre­

vious commitment. Similar results are also shown in Table 4.20. Results in

Table 4.20 were computed for similar conditions to those used in the case of

Table 4.19 other than the designation of export. The export in the case of

Table 4.20 is backed by unit # 1 of System A.

4.8. Summary

The procedure described in this chapter can be used to assess the spin­

ning reserve requirements of a multi-area interconnected system configurationwith export/import constraints. The necessary steps required to evaluate the

tie constrained export/import model and the export/import constrained tie­

line model are. discussed in detail. The probability of tie line failure can

89

Table 4.20: Unit Commitment With Export (Export backed up

by a specific unit in the exporting system).

Export Units to Units to ISR

(MW) Satisfy SSR Satisfy ISR

Eab A B A B A B

80 14 12 14 12 0.00000524 0.00004961100 14 12 14 12 0.00004104 0.00004921120 14 12 15 12 0.00000104 0.00004983140 14 12 15 12 0.00002636 0.00005056160 14 11 15 12 0.00004278 0.00005725180 15 11 16 12 0.00000361 0.00005725

generally be neglected in the computational process. This should be checked,

however, and may not be valid for all systems. The procedure described in

this chapter utilises a probabilistic risk assessment framework which permitsthe inclusion of those factors that influence the system reliability.

90

5. INTERRUPTIBLE LOADCONSIDERATIONS

5.1. Introduction

A probabilistic assessment of spmnmg reserve and unit commitment

normally utilises the criterion that the unit commitment risk should be less

than or equal to a specified level. In addition to other capacity adjustments,it is also possible to utilise load interruption to maintain the system fre­

quency and integrity. During peak load hours it may be necessary to inter­

rupt some load in order to keep the unit commitment risk within limit. A

sudden loss of generation can also cause some load to be interrupted on

short notice. The cost associated with interruption may be lower for some

loads than that of other loads, and the consumer may be willing to have

his/her load interrupted, if necessary, provided that there is some economic

benefit. Some power utilities actually consider curtailable load as part of

their spinning/operating reserve [30]. It is generally recognised that selected

load curtailment can be used to reduce system risk. The utilisation of

probabilistic risk assessment techniques can be used to quantitatively assess

the impact of such load curtailment on unit commitment risk [31]. The

magnitude of curtailable load and the corresponding maximum allowable time

delay before which the load should be curtailed to maintain the system risk

level less than or equal to a specified level, can be determined using

probabilistic techniques. Load curtailment should only be considered in the

absence of other possible capacity adjustments.

A certain number of generating units are committed at any time in the

hourly operation of a power system to satisfy the system load at a unit

91

commitment risk equal to or lower than the specified level. Because of the

discrete nature of the generating unit capacity, a system can usually carry

additional load on top of the firm load without committing any more units

than is required to carry the firm load without exceeding the specified risk

level [32]. The additional load capability provides the ability within the sys­

tem to respond to unexpected load variations without materially affecting the

unit commitment and the corresponding risk.

5.2. Interruptible Loads in a Single System

The generating capacity that is spinning, synchronised to the bus and

ready to take up load is generally known as spinning reserve. The required

spinning reserve is dependent on the system load, generating unit failure

rates, lead time and allowable risk level. One of the most important

parameters in spinning reserve evaluation is lead time [3, 24], which is the

time period for which no additional capacity can be brought into service. A

generation model in the form of a Capacity Outage Probability Table [3] can

be constructed given that the probabilities associated with the different states

of the generating units for a period equal to the lead time are known. The

unit commitment risk can be found from the Capacity Outage ProbabilityTable given that the load is known [3].

In practice, an operator can use the probabilistic risk assessment

method by adding (committing) one unit at a time from a merit order table

until the unit commitment r�k given by the generation model becomes equalto or less than the acceptable value for the expected load. Consider SystemA with the available generating units shown in Table 3.2. The commitment

order is from the top down and the lead time is considered to be 2 hours.

The specified unit commitment risk in an isolated system is assumed to

be 0.001 for the studies in this section. Table 5.1 illustrates the unit commit­

ment and corresponding risk in System A for a load of 1850 MW.

92

Table 5.1: Spinning Capacity, Reserve and Unit Commitment

Risk.

No. of Units Total Spinning Spinning Unit Commitment

Committed Capacity (MW) Reserve (MW) Risk

12 1860 10 0.02217724

13 1980 130 0.01511939

14 2080 230 0.00018157

With 11 committed units the system is unable to meet the load. If

the acceptable risk is 0.001 then the system requires 14 units to carry a load

of 1850 MW and the corresponding spmnmg reserve is 230 MW. Assume

that the load in System A is 2250 MW at a particular time of the day.

Table 5.2 shows the unit commitment and corresponding risk under this con­

dition. The commitment of all 18 on-line units does not satisfy the risk

criterion for a load level of 2250 MW at an acceptable risk of 0.001. The

risk in this situation can be alleviated by: 1) bringing in additional generat­

mg units before the lead time of ta or 2) curtailing some load if required.

Table 5.2: Unit Commitment and Corresponding Risk.

No. of Units Total Spinning Spinning Unit Commitment

Committed Capacity (MW) Reserve (MW) Risk

16 2280 30 0.0270572017 2355 105 0.01652324

18 2415 165 0.00401203

In a practical system, generating units are committed for a specifiedtime period during which additional generation can be made available after a

time delay. The actual time delay depends on many factors of which the

type of additional generation is the most important. The delay time as­

sociated with a thermal generating unit may be in the order of several hours

while the delay times associated with the starting, synchronising and loading

of hydro and gas turbine units are relatively short. The loading characteris-

93

tics of these rapid start units are also quite different from those of conven­

tional thermal units although the lead time of thermal units can be reduced

considerably by keeping the boilers in a hot reserve state [2]. Rapid start

and hot reserve units can be utilised to reduce the unit commitment risk.

The concept of area risk curves [3] can be used to include rapid start and

hot reserve units in the risk assessment process. The concept of area risk

curves and the models for hot reserve and rapid start units are discussed in

Chapter 3.

The availability of rapid start and hot reserve units can alleviate the

system unit commitment risk. It is also possible that the system load could

be such that the unit commitment risk criterion cannot be met even after in­

cluding all available rapid start and hot reserve units. In this situation, a

suitable segment of the system load can be considered for possible interrup­tion to reduce the unit commitment risk. Load curtailment, however, should

only be considered when other economic capacity adjustments can not be

achieved during the lead time. In this regard, interruptible loads can be

considered as part of the operating reserve. During peak load hours it may

be necessary to interrupt some load in order to keep the unit commitment

risk within limits. A sudden loss of generation may also cause some load to

be interrupted at short notice. The cost associated with interruption may be

lower for some loads than that of other loads, and a consumer may be will­

ing to suffer load interruption if necessary, provided there is an economic

benefit. Risk assessment in the presence of interruptible loads can be il­

lustrated using the area risk technique [3( Assume that M generating units

are operating and the system load is L MW. A typical area risk curve for

a system with interruptible load is shown in Figure 5.1. At time ti,

Ali MW of load is interrupted and the risk contribution decreases. The risk

level for the entire lead time in this case can be evaluated using similar

techniques to those utilised for rapid start and hot reserve units. In order

to simplify the problem, all M units are considered to be on-line units. In­

terruptible load can be considered for computational purposes as a load

94

F(R)

......LOAD INTERRUPTION

(�li MW)

ADDITIONAL___.

UNITS IN

o t·1 TIME

Figure 5.1: Area Risk Curve.

variation or as an equivalent generating unit with a failure rate equal to

zero. Figure 5.2 shows the system load and total spinning capacity when

the interruptible load is considered in the computational technique as a load

variation. Figure 5.3 shows the system load and total spinning capacity

when the same interruptible load is considered as an equivalent generatingunit. Both approaches provide identical results.

A generation system may interrupt some of the designated load if the

unit commitment risk for the period of the lead time is greater than the

specified risk, Rs' Figure 5.4 shows two risk functions for two different loads.

The shaded area in Figure 5.4 represents the reduction of unit commitment

risk due to a load interruption at time ti.Assume that

L is the system load,�li is the interruptible load,F(R1) IS the risk function for a load of (L-�li) MW with M units,

F(R2) is the risk function for a load of L MW with M units.

95

LI--------

SPINNING CAPACITY

MWJl

C�--------------------------------

LOAD .L-.6ol· - -- - - -'------------11

I

I

o-

t TIMEa

Figure 5.2: Equivalent Load Approach For Load Interruption.

I

I. �

-

0 t. t TIME]. a

MWJ•SPINNING CAPACITYC+.6oI· -----------------

1

C ......------

LOADL �----------------------------��

Figure 5.3: Equivalent Unit Approach For Load Interruption.

F(R)

96

t·1

o TIME

Figure 5.4: Area Risk Curves For Two Loads.

Unit commitment risk can be expressed as

when load L .MW and

when load L-Al· .MWt

If Rf > R8' load curtailment is necessary in the absence of other

capacity adjustments. Once it has been decided to interrupt some load, it is•

important to determine the magnitude of the interruptible load and the time

of interruption. In practice, a utility has prior knowledge regarding the

various loads that can be interrupted with minimum penalty. The load with

the least penalty for interruption should be considered first. The time of in­

terruption, ti can be determined by solving Equation (5.1) where ti is the

maximum allowable time delay for curtailment of Ali MW. Curtailment of

Ali MW load after time ti will not reduce the unit commitment risk to a

value equal to or lower than the specified risk.

97

(5.1)

or

(5.2)

For computational purposes, Equation (5.1) is solved by an iterative

method with the help of the following sequence.

t . = t·n-1 - nf:l.tt t

where

and

Dot discrete time step.

A course time step can be used as a starting point to roughly identify

the zone where f(t) crosses the time axis in Equation (5.2). A smaller time

step can then be used to finally solve for t i: Solutions for other interrupt­

ible loads can be achieved in the same manner. In order to reduce the unit

commitment risk, however, a system must interrupt a minimum amount of

load. This minimum interruptible load at any point varies with the operat­

ing variables prevailing at that point of time. An interruptible load which is

at least equal to or greater than the minimum bound at an operating situa­

tion, should satisfy the following relationship.

where

98

Dolm - mmimum load that has to be interrupted.

Consider a load of 2090 MW and a lead time of 120 mins. The com­

mitment of all 16 units in System A will result in a unit commitment risk

of 0.00279073, which is higher than the allowable risk of 0.001. The min­

imum load Dolm, that must be interrupted almost instantaneously to bring

the unit commitment risk below the allowable risk is approximately 11 MW.

A load of 50 MW should be interrupted within 36 minutes in order to keepthe unit commitment risk equal to the allowable risk of 0.001.

Table 5.3 shows some typical unit commitment situations in System A

when interruptible loads are considered as part of the operating reserve.

The system load is again 2090 MW and the allowable risk is 0.001 with a

lead time of 120 mins.

Table 5.3: Typical Unit Commitment Situations.

No. of Spinning Operating Interruption UnitUnits Reserve Reserve Load Time Commitment

Committed (MW) (MW) (MW) (Minutes) Risk

16 190 190 0.0027907316 190 240 50 36 0.00098528

16 190 270 80 39 0.0009937816 190 300 110 40 0.00099580

In Table 5.3, the operating reserve includes spinning reserve and interruptible

load. The 4th row of Table 5.3 shows that System A can carry a load of

2090 MW with a unit commitment risk of 0.00099580 provided that the sys­

tem has the option to interrupt 110 MW load within 40 minutes, if neces-

sary.

99

5.3. Additional Load/Interruptible Load CarryingCapability of a System

A generation system can carry additional load on top of the firm load

without committing any additional units than is required to carry the firm

load, if the actual unit commitment risk at the firm load condition is less

than the specified risk, Rs' The shaded area in Figure 5.4 represents the

reduction in risk due to a load interruption at time ti"Assume that

L f is the firm load,6.1

ais the additional load,

F(R1) IS the risk function for a load of Lf MW withM units,

F(R2) is the risk function for a load of L f+6.1a MW with M units.

Based on these assumptions, unit commitment risk can be expressed as

when L=L f and

Rf< Rs' additional load is added in suitable steps. The additional load

can be increased up to the point at which Ra=Rs' If the additional load IS

increased further then Ra > Rs' i.e., the unit commitment risk criterion IS

violated. The unit commitment risk can be reduced even with this increased

additional load if the additional load is capable of being interrupted prior to

tao The time of interruption, ti can be determined by solving Equation

(5.3).

{tiF(R2)dt + {ta F(Rl)dt s n,io itiLoad interruption should only be considered as an operating strategy if other

(5.3)

economic adjustments cannot be done within the system lead time and if

load interruption is permissible.

100

A power system commits a designated number of generating units using

a specified system lead time to satisfy a forecast load at a unit commitment

risk less than or equal to a specified risk. Due to the discrete size of the

generating units, the capacity outage probability table may have some room

for additional load on top of the firm load of the system; without requiring

any additional units to be committed other than those required to satisfy the

firm load. This additional load must not cause the actual unit commitment

risk to exceed the specified risk. The allowable additional load depends on

the firm load of the system, the set of generating units and the specifiedunit commitment risk of the system. The window between the capacity out­

age probability table and the firm load of the system may be wide enoughto carry a certain additional load for a period equal to the system lead time,

or the window could be just enough to carry the additional load for a periodless than the system lead time without violating the risk criterion. The ad­

ditional load which the system can carryon top of its firm load for a periodless than the system lead time is designated as the allowable interruptibleload. Interruptible load can be added to the system on top of the firm load

without committing any additional generation other than that required to

meet the firm load until the actual unit commitment risk becomes equal to

the specified unit commitment risk. It is of interest to determine the mag­

nitude of additional load/interruptible load carrying capability of a system.

This is not a constant value and will vary with the system firm load and

the generating units in operation. The additional load/interruptible load

does not involve any additional unit commitment costs and is serviced at the

production cost. The generating system shown in Table 3.2 is used to il­

lustrate this concept. The unit commitment order is from the top down.

In order to determine the additional load carrying capability of the sys­

tem, a sufficient number of generating units are first committed to carry the

firm load at an unit commitment risk lower or equal to the specified risk.

If the actual unit commitment risk is equal to the specified risk no further

evaluation is done. In this case, the system will not be able to carry any

101

additional load/interruptible load on top of its firm load at that time. If

the actual risk is less than the specified risk, certain additional load is added

to the firm load and the unit commitment risk is re-evaluated. If the newly

calculated unit commitment risk is less than the specified risk then the sys­

tem is able to carry the corresponding additional load on top of the firm

load without adding any additional units. The additional load is increased

gradually until a point is reached where the actual risk becomes equal to the

specified risk. The magnitude of the additional load could be increased fur­

ther but the system would not be able to carry that additional load without

committing additional unit(s). The system may be able to carry the same

additional load without requiring additional generation if the time required to

remove the additional load is less than the system lead time. In order to

consider this variable, the magnitude of the additional load IS gradually in­

creased and the time period, before which the additional load should be

removed in order to keep the actual risk from exceeding its limit is deter­

mined from Equation (5.3). This procedure results in a set of additional

load/interruptible loads and corresponding times which are dependent on the

set of generating units, firm load of the system and the specified risk. The

time period for which the additional load/interruptible load can be carried

by the system, before the system unit commitment risk exceeds its limit, is

called the lead time of the additional load/interruptible load. A set of ad­

ditional load/interruptible loads for the generation system shown in Table 3.2

is given in Table 5.4.

Table 5.4 was derived for a firm load of 1850 MW with a system lead

time of 120 minutes and a unit commitment risk of 0.001. The system re­

quires 14 committed generating units to carry the firm load of 1850 MW.

The actual unit commitment risk at this point is 0.00018157 and the spin­

ning capacity is 2080 MW. The first column of Table 5.4 shows the ad­

ditional load/interruptible load that the system is able to carryon top of the

firm load of 1850 MW. The second column shows the lead time of the ad­

ditional load/interruptible load in minutes for which the corresponding ad-

102

Table 5.4: Allowable Additional Load/Interruptible Loads andLead Times.

Total spinning capacity = 2080 MW

Int.load(MW) Lead time(mins) Risk

5 120 0.00018157

10 120 0.0001876715 120 0.00018767

20 120 0.00019266

25 120 0.0001926630 37 0.00097904

35 37 0.00097904

40 37 0.0009801145 37 0.00098011

50 25 0.0009722555 25 0.00097225

60 25 0.0009723565 25 0.00097235

70 25 0.0009724175 25 0.0009724180 6 0.00094090

85 6 0.00094090

90 6 0.0009409095 6 0.00094090

100 6 0.00094094105 6 0.00094094

110 5 0.00087274

115 5 0.00087274

120 5 0.00087274125 5 0.00087274130 4 0.00084117135 4 0.00084117

140 4 0.00084117

145 4 0.00084117

150 4 0.00084117

155 4 0.00084117160 4 0.00084118

165 4 0.00084118

170 4 0.00084118

175 4 0.00084118

180 4 0.00084118

185 4 0.00084118

190 4 0.00087449

103

Table 6.4: (continued)

Int.load(MW) Lead time(mins) Risk

195 4 0.00087449

200 3 0.00080628

205 3 0.00080628

210 3 0.00081128

215 3 0.00081128

220 3 0.00081128225 3 0.00081128

ditional load or interruptible load in the first column or an additional

load/interruptible load of magnitude less than that shown in the first column

can be carried by the system, without committing any additional generation

than that committed to carry the firm load of 1850 MW and without violat­

ing the unit commitment risk. The third column shows the actual unit com­

mitment risk for the system. When the lead time associated with the inter­

ruptible load becomes equal to the system lead time, the load (interruptible)becomes the additional load which the system should be able to carry with­

out being required to interrupt it. Table 5.4 shows that the generation sys­

tem given in Table 3.2 can carry an additional load of 25 MW on top of

the firm load of 1850 MW with an actual unit commitment risk of

0.00019266. Figure 5.5 is a pictorial representation of Table 5.4. The sys­

tem can carry the additional load/interruptible load shown by the symbols in

Figure 5.5 and all other. additional load/interruptible loads vertically below

the individual symbols. In Figure 5.5, all symbols are connected to show

the trend in the variation of the lead time associated with different ad­

ditional load/interruptible loads. A point on the curve other than the sym­

bols is not a valid point unless it lies vertically below a symbol. If the

coordinate of a symbol is (ti ' �li) then the rectangle formed by the points

(0 , 0), (0 , �li)' (ti ' 0) and «. ' �li) represents a valid operating zone as

far as the unit commitment risk is concerned. This condition applies to all

similar figures in this thesis.

Different sets of additional load/interruptible loads exist for different

104

300�-----------------------------------.

3t:E 200.5"'Ca

_gs..: 100-

.s

fIRM LOAD - 1850 MWSPECIfIED RISK - 0.001TOTAL NO. Of UNITS SPINNING - 14TOTAL SPIN. CAPACITY - 2080 MW

O�----..------�----..----�----�----...

o 20 40 60 80

Lead Time in mins.100 120

Figure 5.5: Interruptible Load Carrying Capability at the FirmLoad of 1850 MW.

firm loads. It is difficult to determine a general relationship between the ad­

ditional load that a system is able to carry without crossing the risk line

and the different parameters of the generation system. It can be seen from

Figure 5.5 that as the interruptible load magnitude is increased, its lead time

is decreased, i.e. the higher the interruptible load is, the shorter the allow­

able time period would be before which the load has to be curtailed in order

to keep the unit commitment risk from growing larger than the specified unit

commitment risk.

5.4. Additional Load/Interruptible Load CarryingCapability for Different System Lead Times

The required spinning reserve is a function of generation, system load,

system lead time and operating risk. A part of this spinning reserve can be

used to carry additional load or additional interruptible load on top of the

firm load without adding any additional units and without violating the risk

criterion. In general the magnitude of the required spinning reserve mcreases

with an increase in system lead time. A generation system with a longer

105

lead time than that of another generation system, therefore, 1S likely to carry

more spinning reserve than the other system, provided the system load and

other parameters are identical in both systems. Theoretically, a generation

system in which the standby capacity can respond without any delay ir­

respective of any contingency, does not require spinning reserve. A practical

system can not achieve this responding capability. A system can, however,

have many rapid start units which can be synchronised in a relatively short

time compared to conventional thermal units. A system whose standby

response capability is much faster than that of another system will have

smaller room for additional load or additional interruptible load than its

counterpart provided that they have equal risk criteria.

As the system lead time decreases from 240 minutes to 15 minutes, the

unit commitment mayor may not change for a given system load. Figure5.6 shows the additional load/interruptible load carrying capability of genera­

tion System A when the load is 1750 MW and the specified risk is 0.001.

The unit commitment of System A at this load level remained unchanged at

13 units for all values of lead time of 240, 120, 60, 30 and 15 minutes. The

additional load carrying capability of A at a load of 1750 MW with 13 com­

mitted units is 25 MW for lead time of 240, 120 and 60 minutes. The ad­

ditional load carrying capability increases to 75 MW for lead times of 30 and

15 minutes. If the unit commitment required to carry the load of 1750 MW

remains unchanged at 13 units the unit commitment risk decreases from

0.00064776 to 0.00000258 as the lead time decreases from 240 minutes to 15"

minutes. This reduction in risk level is reflected as increased additional load

carrying capability for lead times of 30 and 15 minutes. The system at the

same generation and loading condition can, however, carry additional inter­

ruptible load of 80 MW for 2 minutes when the system lead time is 240

minutes. The interruption of the 80 MW load can be delayed up to 6

minutes for a system lead time of 120 minutes and 7 minutes for system

lead times of 30 and 15 minutes.

106

250�------------------------------------�----------.,

c-

e

4

100 - I �

fIRM LOAD - 1750 MWSPECIfIED RISK - 0.001

.E

200- ,�

150 -

II'

I

LEAD TIME(mi.ns)240120603015

NO. Of UNITS

1313131313

Legend• �_1q_!!,j._'1�.:__

C 120 mLns.

• 60 mi.ns.

o 30 ,!i.ns ':._

A � �ns-=-

·�ifl!50 -

ilt 1:n,-------1---------------------------"-------.�O�--A---&----��.--------._--.U------P_--------�------�-�I , , I

o 50 100 150 200

Lead TIme in mins.250

Figure 5.6: Additional Load Carrying CapabilityLevel of 1750 MW.

at a Load

Figure 5.7 shows the additional load/interruptible load carrying

capability of System A when the firm load is 1900 MW. System A must

commit 15 units for lead times of 240, 120 and 60 minutes and 14 units for

lead times of 30 and 15 minutes to satisfy the specified unit commitment

risk of 0.001. The additional load carrying capability is 75 MW for lead

times of 240, 120 and 60 minutes but reduces to 25 MW for lead times of

30 and 15 minutes. System A can carry an additional interruptible load of

80 MW for 23, 40 and 44 minutes for system lead times of 240, 120 and 60

minutes respectively. The system can not carry any additional load or inter­

ruptible load beyond 25 MW when the system lead time is 30 minutes. If

the system lead time is reduced to 15 minutes for the same unit commit­

ment and firm load then the actual risk is much less. In this case the sys­

tem can carry additional interruptible load of 80 MW with a delay time of 3

minutes.

107

300�----------------------------------------�----------�

.5"0o

..9150

LEAD TIME(m�ns)240120603015

NO. OF' UN ITS

15151514H

Legend• .?.1.q_!'.!-_I!!.:__

[J 120 m�ns.

• 60 m�ns.

o 30 m�ns'!._t:. � �ns�

�-

.5 100

.".-,:;::ItI ! 11I • :�----�".r--�".....�--�--�--�-�-----------------------------------T� I I !

50 I .1 9 io� ! a i i

:o 50 100 150 200 250

Lead Time in mins.

F'IRM LOAD - 1900 MWSPECIF'IED RISK - 0.001

250

� 200:2

Figure 5.7: Additional Load Carrying CapabilityLevel of 1900 MW.

at a Load

5.5. Effect of Firm Load Variation on the Additional

Load/Interruptible Load Carrying Capability

A system will commit a designated number of generating units to carry

a forecast firm load at an actual unit commitment risk equal to or lower

than the specified unit commitment risk. The same system capacity may

also be able to carry some additional load on top of the firm load without

the actual risk exceeding the specified risk. As the additional load increases,

the difference between the actual and specified unit commitment risk

decreases. In the same manner, the system firm load can be increased such

that no further unit addition is required but the actual unit commitment

risk increases to the specified unit commitment risk. As the difference be­

tween the actual and specified unit commitment risk decreases, the additional

•

108

load or the interruptible load carrying capability of the system decreases for

the given set of generating units. Figure 5.8 shows the additional

load/interruptible load carrying capability of System A for a system lead

time of 120 minutes. As the firm load increases from 1850 MW to

1870 MW in steps of 10 MW, the additional load or interruptible load mag­

nitude decreases. When the firm load becomes 1880 MW , the system needs

an additional generating unit above that required for a firm load of 1850 -

1870 MW. The additional load and the interruptible load carrying capability

of System A is increased compared to that which existed at the firm load of

1870 MW. Once the system commences to operate 15 generating units, one

more than that required for a firm load of 1870 MW, the additional load

and interruptible load carrying capability again starts to decrease from its

new value as the firm load increases. This is shown in Figure 5.9, where

the firm load increases from 1870 MW to 1910 MW III steps of 10 MW.

Similar characteristics occur for other system lead times.

5.6. Daily Additional Load/Interruptible Load CarryingCapability of a Generation System

The magnitude of interruptible load and corresponding lead time

depends on the number of operating units, system unit commitment risk,

firm load and system lead time. It IS not possible, therefore, to determine a

unique additional load/interruptible load which the system will be able to

carry at all times. Different results have been obtained using system lead

times of 240, 120 and 60 mins. If the firm load and the on-line units are

such that the actual unit commitment risk is close to the specified unit com­

mitment risk, there is not enough room for additional load/interruptible load.

When the actual unit commitment risk is significantly less than the specified

unit commitment risk, the system may be able to carry some additional

load/interruptible load with different combinations of magnitude and lead

time. The hourly load in a day varies from the low load to the peak load.

The additional load/interruptible load carrying capability of the system with­

out committing any additional generation will change in different portions of

300

I � I Legend I

250-

�200-

::Ec.-

"'00 150-

.9c-

.£100-

50-

I-'o<0

I

,.?�·�1��?•

to- --...PJ:

Ii.--------------- .¢--------m.-- ..-�---.

.---------. 0

Q----A.r.tt .------------------------------------------------- •

�----------------------------�tt----------•

o0 20 40 60 80 100 120

Lead Time in mins.

• JJ!�Q_!!.lLl'_J�t!l1.�o 18§!Lll!L 14J!N ITS

tt 187'1 MW_14 �NIT�o �8CLMW_!5 �ITI

TOTAL SPIN. CAP. - 2080 MW (14 UNITS)TOTAL SPIN. CAP. - 2180 MW (15 UNITS)

16-

-1----- __- �------

I

J

Figure 5.8: Effect of Firm Load Variation on Additional Load

Carrying Capability.

�200

�e.-

"'013 150

.3..:-

.E100

300��----------------------------------------------P-------------�

250

......

......o

TOTAL SPIN. CAP. - 2080 MW (14 UNITS)TOTAL SPIN. CAP. - 2180 MW (15 UNITS)

Legend• J_8.zQ_nli_H__lJ�11.�[J 18!!QJ:!!L15_!!NITS• 189Q MW)5 lJNIT�o 190Q_MW_l5 _!!N ITS

A 1910 MW 15 UNITS

III

·...,--------i:.__

...-----

.cr - - -

IA . -_

--1-Ii .-__ .

� c?-- -

.

-------------------,----------

• A .----------_

T.

�---------------•

.--------------- .IIII

.---------.•.

.------------------------------------------------------------------------.o

0 20 40 60 80 100 120

Lead Time in mins.

50

Figure 5.9: Effect of Firm Load Variation on Additional Load

Carrying Capability.

111

the day. The IEEE - RTS [33] load model has been used to illustrate the

variability of the additional load/interruptible load carrying capability in a

day. One week in the winter was taken from the IEEE - RTS load model.

The hourly peak load variations for the week are shown in Figures 5.10.

The number of generating units, spinning capacity and the set of additional

load/interruptible loads was determined in each day for three distinct load

zones for the generating System A.

The weakly peak load is assumed to be 1920 MW. The hourly peak

load variation for the 7 day period shows a common characteristic of two

peaks and one valley in each day. The peaks and valley for the 7 day

period are shown in Table 5.5. The additional load/interruptible load car­

rying capabilities were determined for a system lead time of 120 minutes.

•

The two peaks and one valley from the load model in a day were con­

sidered for unit commitment. During the intervals when load varies from

one peak to another peak or peak to valley, generating units are either

gradually committed to service or taken out of service. Within these inter­

vals, a system can handle the additional load simply by committing some

units earlier than the planned schedule when the firm load is increasing, or

by keeping some units on line for a greater period than they were planned

for as long as the unit commitment risk criterion is met. During these in­

tervals, additional load can be handled by adjusting the- unit commitments,

and therefore do not jeopardise the system's ability to carry additional load .

Unit commitments during the peaks and valleys can therefore be considered

in order to evaluate the additional load/interruptible load carrying capability

of the system. It is assumed that other capacity adjustments cannot be

done before the time period equal to the system lead time. The additional

load/interruptible load carrying capability of the system varies from peak to

peak and from peak to valley in a given day. The minimum additional

load/interruptible load carrying capability for the two peaks and one valley

situation is considered to be the additional load/interruptible load carrying

'XCJ

l"'"::siu

-I

100 I. . . .

I· . . .

· . . .

· . . .

· . . .

· . . .

i-' ! i •••,!90 -f•••••••••••••••, ···········'···7·.. ···•·• ••..••.....••..

i /. 1•• ••• l\

· . . ..: : : :

�· . . .

· . . .

10 -f•••••••••••••••,•••••••.•.•••••••••.•••••••••••••••••••••••••••••••••••••••••

! I �ONOA� j.70 -f••.••.•••••••••,.... • ••.•••4••••••••••••••••••••••••••••••4••••••\••••••

I;..· I I 1·\• i i j !&0 .;.t...,.···· ..···i.. ·· ...········.. ·i·······....······i······· .. ·······i····· .. ·····

•.•• j. ! ! i

. . .

50: ! : :

o

100 : : : •• :

�::: . '\:

oX 1 •••••• l I •CJ :: .:\e 90 .••.•........••, .•.•.•••.t , I!' ,••.•••••...••

Cl. ! iii� .•... \....

.....

::si 1 Ii: i.e 80 , .•.•.••+

\.

-I � WEDNESDAY !l; 70 i··Z·-:········i

i i �\.

· ." . '.

� . : : : :'-' " ! ! ! !" ..: : : : .

.sDI.

r······.·i! ···_··-:--········T-·······..

r···.. ·····

.' . . .

· . . .

· . . .

· . . .

50 iii io 5 ro � �

TIme in hrs.

-o

�.........

"CJ

.s

5 10 �

TIme in hrs.

2520 25

roo • • ••••.· . . ,.

� i •••••• i I •oX ::..:\CJ : I: . :.u 90 , ····,···············:············.. ·t· •••••••••••

0.. ; i 1 ! \>-. i·! i !::si i! iii·i 10 ·····....

·····T···: ····TU·ESO·Ay···..

······r····'··....

-

it··!·o 70 .••• ·.·1· .. • 1 4 ,••

: : : :

� . : : : :

'-' ,,: : : :

" .., i : ! : •

CJ 60 Ii •...........! ! ! .

a.:::

..J:::::. : : :· . . .

50: : : :

o

loai ! ! !

�.. .....

..x ::: ,:

CJ ! •••••• ! I •

e 90 ·····•· ..

······,··········7··t···· • • ···········t�·············

0.. !!: i."'" !!! t ! \- .•..

, .

�. '" . .

., 10 · .......•······i··.·····,······j············..·i··.. · .. ··.·····i···· •........

! ! / T�URSD�Y I \o 70 •.••••.••••••••1••

1.. · 4 ,••••••••••••·.·,·•••• ••• .

: : : :

\. ::::!S, • : : : :

· . . .

-0' , : : : :

CJ 60· ...•: ..•.... !.. . ! ! ! .

.9 I· -r iii I50 iii io 5 ro � �

TIme in hrs.

.....

.....�

255 10 �

TIme in hrs.20 25

Figure 5.10: Hourly Peak Load Variation of One Week in the

Winter of the IEEE - RTS Load Model.

�D

�>..

::xI)

�'0�.....,

"CJD

..9

100 . • •

�i • • ••• !· . .. ,.

904···············1···········••••••.i .. ·/.···.····· •..·.··.·······

: /:.. :\

: : : :.· . . .

\: : ! :10 4 · ······,········.·.. ··, ·· ·,·.. ····.. · .. · .. ,···· .

j I �RIDA� I·70 4 · ···,· .. · � " 1 � "

i / iii .\. : : : :· . . .

60 .-:..'.........1··· ····.. ··· ..�··.. ·······....�........·······i···.. · .... ·

•.: : : :

•••• l 1 !· . . .

· .. . .

50: : : :

o

10 : : : :

'i j SATURDAY r-;II :.. , : ••Q.. 70 ! ! ! ·· .. ·· .. l·.. ·

\..

� i· •••' ! •� . /! . .

\... ....· . . .

!. 1 ! ! ! •W'

• • • • • •

3t 60 -I.• • .. ·•.. ·· .. :.. · ......

7····l .. · ...... · .. ···!· .. ·· ..··....·-!·.. • .. · .. · ....

\.. . .

.. . . .

: : : :.. . . .

· . . .

'.. ! /. i i· i••••

• •

504···· .. · .. ·· .' •........! : ! ..

. . .

· . . .· . . .

! � i j40

: : : :

o 5 W � �

TIme in hrs.

'0�.._.,

'8...9

5 20 Z52510 �

TIme in hrs.

10

j i j !: 1 : •• :

1 : 1 /. •

701: : .: 1:. .. ..

: :.:.:.>- ::. - :, : \

::x !.. Ii. ! •I) : I: . : \.,. ::::.... . . . .

.� 10 I ' : : :•••••••••••••••:............ •

'. ! / SUNDAY !'. ! ,.: : i

"CJ 50 • ':"i •·.. ·· .. ·l ' r

· .. · l·

a -:::

..9::::· .. . .

· . . .

: i : :40

.

: : : :

o

�D

�I-'......w

'0�.......

·

5I

20 25

Figure 5.10:

I I

10 �

TIme in hrs.

(continued) Hourly Peak Load Variation of One Week m

the Winter of the IEEE - RTS Load Model.

114

Table 5.5: One Week In The Winter Of The IEEE - RTS LoadModel.

MondayTuesdayWednesdayThursdayFridaySaturdaySunday

Valley (MW) Peak 1 (MW) Peak 2 (MW)

1056 1728 1786

1152 1862 1920

1131 1824 1882

1114 1786 1843

1075 1728 1824

960 1344 1496

960 1306 1440

capability of the day. Figure 5.11 shows the additional load/interruptibleload that System A is able to carry on a day without having to commit any

additional unit(s) than those required to satisfy the firm load and without

violating the system unit commitment Tisk criterion. It should be noted that

the actual unit commitment 'risk, corresponding to the points denoted by the

symbols shown in Figure 5.11 and all points vertically below the symbols, is

either equal to or less than the specified unit commitment risk.

The mmimum additional load/interruptible load carrying capability

resulting from 14 peaks and 7 valleys in the 7 day period can be considered

as the additional load/interruptible load carrying capability of the system on

a weekly basis. It is important for the system manager to know what an

additional load/interruptible load will cost the system in terms of capacity

cost, or more simply whether such load should be supported by an ad­

ditional operating unit. Table S.6 and Table 5.7 show whether additional

generation is required to carry a given interruptible load on top of the firm

load for a specified lead time.

Table 5.6 shows that if the interruptible load is 60 MW with 30

minutes lead time then additional units would have to be committed 6 times

for the 21 load zones. Table 5.7 shows this requirement would drop to 4

times if the interruptible load is 40 MW. If the additional interruptible load

�:2 200.5

s..9� 100

£

�:2 200.5

-g..9c 100...

..5

300------�----�----�----�----�----�

•I

•

� i . . . ... , � + : � + .

• l l l l :

� I 'I MONDAY I I,! ! ! i i

.. •=.......;.... ·······�·········· .. i····· .. ·····f·············�···· .. ··· ...

: I: : : :: .__. : : :

� . : : :

: ::: �: : i i •• f'"

0: :::,o 20 40 60 80 100 120

TIme in mins.

3..

!.: : :

· . .

I: : : I •..., ······i············t············t·· .. ·········i············t······ .. ·····

-' . . . .

: l WEDNESDAY I. . .

.. . . . .• • • • f

I• • • • •• • • • I

....• ·····i···· .. ··· .. ··�···· .. ······j·· .. · .. ·····i· .. ·· .. ··· ..-t··· .

• I • • • •

---1--. i ! i i: I: : : :

� .-;. iiil l. ::.•• •• I

o:: ::

'"o 20 40 60 80 100 120

TIme in mins.

3••

I"

"I... ..... .,... "

,. ... .... ..., '".... ..... • I., ...., ..... "... "... ..

•••........ J � : -!. ..

I ., ••.. "

....:: ::_... ....

: I:

TUESDAY: II. . . . •.... •• • f· .. ••••• .. · .. ··-:-···· • .. •·• .. t .. •• .. ••••• ·f •• ? .

I' . . . .

.: : : : :· . . .. .• • • • I

.�.: : : :

l Iii i 1: .---+. : : :

I: :.

. : :•o iii I I I

o 20 40 60 80 100 120

TIme in mins.

:=� 200.�"tJ"

..9c 100...

..5

3.. .

.

.

. I. . . , . .

I : : : : :

.: : : : :· . . . .

.- : .:. � : � .

T : : : : :. : . . . :

• l THURSDAY 1I • • • I •

• • • I • •· , . . .

_. • I • •

.. ··J········i .. ···········,.;.·········· .. ·.············i·· -t •..•••.•••••.---i-.: : : :

: I : : : :

i •__ .' i i !: . . . .

.! •

o:

'"o 20 40 60 80 100 120

TIme in mins.

I-'I-'�

:=:2 200.5

-g..9� 100-

..5

Figure 5.11: Daily Additional Interruptible Load CarryingCapability of System A.

300, .

� I• i ii i :.

I: : : :

�

1.iii i i;;> _ I 0 • • ,

. . . . . .::::::Ii! 200 ' •........ � .:. 01 •••••••••••• :•••••••••••• .:. .

C.: : : : :

.- .: : : : :

�! ! PRIDAY ! I•: : 0 : :

· . . . .

•• • • I •· . . . .

100-4".�•.......j. •••••••••••• j •••••••••••• .j .j. ••••••••••••: I: : : :: .__. : : :

i • : : :

: :: : �: :! :.· .. ..

o: :: :,

o 20 .0 60 eo 100 120

TIme in mins.

�

1i • • •

::::::IE 200 ......•...... ; : ; : .

C I: : : :

.- •• l : : l

-� 1 SUNDAY 1.' : : : :

. . . .

100 -4 ...........•. j i ; i .

.' : : : :. . . .

I : : : :

.: : : :••

•

: : I : :i i .: :.: : : :.---1

10 20 30 .0 50

."a

.9cC

."a

.s..:+-

J:

300,_----��----�------�----�------,

o_o

TIme in mins.

300 , ,

•� I, • i>- ... : : : • i

:2 200 ·····':.····i············+············f············�···· + ..

C I' , , . ,. . , . .

.- .:. . . :

� +! SATURDAY !.9 •: . . . :

. . . . ,

,: :.: : :

100 .....•� + i · ·� + ..

: I: : : :

i --+. i � i: :. :

. .

.iii Ii: :: .

o' "

IIIo 20 .0 60 eo 100 120

TIme in mins.

�

....

....0)

Figure 5,11: (continued) Daily Additional Interruptible Load CarryingCapability of System A.

117

Table 5.6: Additional Unit Requirements.

System lead time = 120 mins.Intr. load = 60 MW, lead time = 30 mins.

Valley Peak 1 Peak 2

Monday No No No

Tuesday Yes Yes No

Wednesday Yes No No

Thursday No No Yes

Friday No No No

Saturday No No No

Sunday No Yes Yes

Table 5.7: Additional Unit Requirements.

System lead time = 120 mins.Intr. load = 40 MW, lead time = 30 mins.

Valley Peak 1 Peak 2

Monday No No No

Tuesday Yes Yes No

Wednesday No No No

Thursday No No No

Friday No No No

Saturday No No No

Sunday No Yes Yes

IS 20 MW with a lead time of 42 minutes then no additional units are re­

quired to be committed during the weekly period. In this example the ad­

ditional load/interruptible load carrying capability on Sunday is the lowest

during the week and, therefore, determines the maximum additional

load/interruptible load carrying capability of the period.

118

5.7. Interruptible Loads in an Interconnected System

Unit commitment and spinning reserve assessment in interconnected sys­

tems using the 'Two Risks Concept' is discussed in detail in Chapter 3 and

in Reference [26]. Unit commitment risk of a system can be reduced if part

of the system load is interruptible. Risk evaluation in an interconnected sys­

tem with load interruption capability can be illustrated using the area risk

curve technique [3]. Consider Systems A and B as interconnected throughtwo tie lines and that each tie line has 100 MW of power transfer capabilityand a failure rate of one failure per year. The system lead time of both the

systems is assumed to be 120 minutes. Typical area risk curves for isolated

and interconnected system operation are shown in Figure 5.12

Hot reserve and rapid starting units are not included for the sake of

simplicity in the example shown in Figure 5.12. The area risk curve of the

interconnected system shows that the risk function is subdivided into several

time intervals based on the instant of load interruption in System A and

System B and the system lead time of System A and System B. In situa-"

tions where rapid starting and hot reserve units are available, the number of

subinterval will increase. The risk can be calculated using a similar tech­

nique to that used in the isolated system. The risk calculated from the risk

function as shown in Figure 5.12 will depend on the magnitude and instant

of load interruption. The ISR of System A and System B with load inter­

ruption can be expressed as following:

(5.4)

F(A)

F(B)r---_

119

(Alia MW)

ADDITIONAL _.UNITS IN

o taa TIME

�- LOAD INTERRUPTION (Alib MW)

o TIME

o

Figure 5.12: Area Risk Curves for Isolated and Interconnected

System Operation.

120

Similarly

(5.5)

In order to satisfy the ISR criterion, both Ria and Rib should be equalto or less than the specified ISR, Ri. Equations (5.4) and (5.5) can be

satisfied by adjusting the four variables Lia, Lib' tia and tib. This will

produce an infinite number of solutions. The magnitude and maximum al­

lowable time delay of load interruption in one system can be derived if the

magnitude and maximum allowable time delay of load interruption in

another system is known. This will give a suitable starting point for a trial

solution leading to a desirable solution.

The levels of SSR and ISR largely influence the unit commitment in an

interconnected system. The levels of SSR and ISR could be such that the

unit commitment which just satisfies the SSR is also capable of satisfyingthe ISR for a range of loads as discussed in Section 3.2.1 of Chapter 3. In

this situation, the SSR is dominant over the ISR as far as spinning reserve

and unit commitment is concerned. Depending upon the level of SSR and

ISR, ISR can be dominant over SSR for a range of system loads. With

dominant SSR the objective of load interruption is to satisfy the specifiedSSR i.e., to satisfy the risk criterion in an isolated system. Once the SSR

criterion is satisfied, the corresponding ISR criterion will also be satisfied in

the case of a dominant SSR. Load interruption in an isolated system is al­

ready explained in the previous sections of this chapter. With dominant

ISR, however, the objective of load interruption is to satisfy the ISR

criterion provided the SSR criterion is already satisfied.

121

Consider System A and System B each with identical generating units

as shown in Table 3.2 in Chapter 3. The SSR for both systems is 0.01 and

the specified ISR is 0.00001. System A must commit 16 units and System B

15 units for a load of 2100 MW in A and 1950 MW in B. The intercon­

nected unit commitment risks in A and B for this operating condition are

0.00000915 and 0.00000360 respectively. The interconnected unit commitment

risk of System A becomes 0.00002320 with 16 committed units and the cor­

responding unit commitment risk of System B becomes 0.00001958 with 15

committed units if the load in System B increases to 1980 MW with the

load in System A remaining at 2100 MW. System A is unable to satisfy its

ISR criterion and it has a higher ISR than System B even after committing

all the available 16 units. System A is therefore responsible for committing

additional unit(s). In the absence of any additional unit(s) System A can

consider curtailment of its interruptible load in order to satisfy the ISR

criterion. The magnitude and the corresponding maximum allowable time

delay of load interruption in System A can be determined using a similar

approach to that used in the case of an isolated system. In the case of in­

terconnected systems, however, the assistance from neighbours is included In

the risk assessment process. A computer program has been developed to

compute the magnitude and the corresponding maximum allowable time delay

for load interruption in interconnected systems, if such interruption is neces­

sary. System A can satisfy the ISR criterion for a load of 2100 MW by

committing all 16 available units provided it can interrupt 25 MW of load

within 67 minutes. System B IS required to commit 15 generating units to

satisfy its load of 1980 MW. The corresponding ISR of System A and B

are 0.00000955 and 0.00000987 respectively.

Interruptible loads can be included in the unit commitment process in

interconnected systems using the area risk technique. Table 5.8 shows the

units that must be committed in System A and System B when both sys­

tems are capable of interrupting 30 MW load within 20 minutes. The

specified SSR is 0.01 and the ISR is 0.00001.

..-----------------------------------------------�-------- __ -

Tsble 5.8: Unit Commitment with Interruptible Load.

Single System Interconnected System

Load No. of Capacity No. of Capacity ISR

(MW) Units (MW) Units (MW)

A B A B A B A B A B A B

1800 1300 13 9 1980 1510 13 9 1980 1510 0.00000260 0.00000158

1800 1350 13 9 1980 1510 13 10 1980 1660 0.00000093 0.00000012

1800 1400 13 10 1980 1660 13 10 1980 1660 0.00000156 0.00000093

1800 1450 13 10 1980 1660 13 10 1980 1660 0.00000280 0.00000210

1800 1500 13 10 1980 1660 13 11 1980 1760 0.00000156 0.00000094

1800 1550 13 11 1980 1760 13 11 1980 1760 0.00000284 0.00000221

1760 13 0.00000157I-'

1800 1600 13 11 1980 12 1980 1860 0.00000095 �l�

1800 1650 13 12 1980 1860 13 12 1980 1860 0.00000287 0.00000232

1800 1700 13 12 1980 1860 13 13 1980 1980 0.00000106 0.00000031

1800 1750 13 13 1980 1980 13 13 1980 1980 0.00000193 0.00000145

1800 1800 13 13 1980 1980 13 13 1980 1980 0.00000357 0.00000357

1800 1850 13 13 1980 1980 13 14 1980 2080 0.00000194 0.00000147

1800 1900 13 14 1980 2080 13 14 1980 2080 0.00000363 0.00000376

1800 1950 13 14 1980 2080 13 15 1980 2180 0.00000195 0.00000150

1800 2000 13 15 1980 2180 13 15 1980 2180 0.00000369 0.00000396

123

5.8. Interruptible Load Carrying Capability of

Interconnected Systems

If the actual ISR of an interconnected power system is less than the

specified ISR, the system can carry some additional load/interruptible load

on top of the firm load without committing any additional unit(s) other than

those required to carry the firm load. The factors which affect the ad­

ditional load/ interruptible load carrying capability of an isolated system also

affect the additional load/interruptible load carrying capability of an intercon­

nected system. In addition, the additional load/interruptible load carrying

capability of an interconnected system also depends on the assistance from

neighbouring systems. In the determination of the additional

load/interruptible load carrying capability of an interconnected system, the

unit commitments required to carry the firm loads of all the systems inter­

connected together are not modified until the firm loads change. A set of

additional load/interruptible load and the corresponding lead time of an in­

terconnected system can be derived using a similar method to that employed

for isolated systems given that the firm load and additional load/interruptibleload of the neighbouring systems are known. Any change in the additional

load/ interruptible load of the neighbouring systems will change the ad­

ditional load/interruptible load carrying capability of an interconnected sys­

tem. There could therefore be many solution sets depending upon the ad­

ditional load/ interruptible load conditions within the neighbouring systems.

The solution technique is discussed in detail in Appendix A.

A computer program has been developed to evaluate the additional

load/interruptible load carrying capability of an interconnected system. The

interconnected systems A and B noted earlier have been used to illustrate

the application. Figure 5.13 shows the additional load/interruptible load car­

rying capability of System B when the firm load of System B is 1640 MW

and the firm load of System A is 1870 MW. The SSR and ISR are con­

sidered to be 0.01 and 0.00001 respectively. Additional load/interruptibleloads of System B are plotted for additional load/interruptible loads of 15,

124

35 and 65 MW with interruption times of 50, 30 and 15 minutes respectively

in System A. Figure 5.13 also showi a base curve with no additional

load/interruptible load in System A. The system lead time for both systems

is 120 minutes. The additional load/interruptible load that an interconnected

system can carry does not require any additional committed capacity other

than that required to satisfy the firm load. This additional

load/interruptible load, however, affects the actual ISR of the interconnected

system and the ISR of its neighbours. The ability of an interconnected sys­

tem to carry an additional load/interruptible load can extend up to the

point where its actual ISR becomes equal to the ISR of anyone of its neigh­

bours. The overall additional load/interruptible load carrying capability of

all the member systems of an interconnected pool can give the system

planner/operator an appreciation of the additional interruptible load that the

pool can carry at all time or at a specific operating point without having to

commit any additional capacity.

5.9. Summary

Probabilistic techniques to include load curtailment ill the operating

reserve assessment of isolated and interconnected systems are discussed in

this chapter. Interruptible loads can be included in a system probabilisticrisk assessment using the area risk technique. Probabilistic methods can be

used to provide a consistent approach to evaluating load interruptibility and

its effects on the unit commitment risk of both isolated and interconnected

system. These techniques are used in this chapter to evaluate the magnitude

and corresponding maximum allowable time delay for load interruption re­

quired to reduce the unit commitment risk in the absence of other capacity

adjustments. Load interruptions, however, should be considered in conjunc­

tion with other economic adjustments.

A generation system can carry an additional load or an additional in­

terruptible load on top of its firm load without committing any additional

generation above that required to carry its firm load. This capability

250,-------------------------------------�---------------

. -----------... ----------------.

.-------.

Io

•

o 20 40 60 80 100 120

Lead Time in mins.

·200-

�� 150-c

......

"'C0

.s. 100-L.

-+-C

50-

•

i. _-

..

11._.

L�._-

..

�r.-=-0__••I

�= _..

.

o.; th.::.:-::.:'0-------.

-.-

fIRM LOAD IN SYSTEM A - 1870 MWfIRM LOAD IN SYSTEM B - 1640 MW

Legend• 9__���__q_T�_�!: __L_�_� _

o 15___!j!iz._§Q_mL�:....Ln J!• 35 _1'!!iz..._;!��_'2!.:..__

Ln J:t•o § � !.§ �ns.!.-LI}_A

Figure 5.13: Additional Interruptible Load Carrying Capabilityin System B .

..

i-'t>.:)�l

126

depends on the operating set of generating units, the firm load and the

specified unit commitment risk. In addition to these factors, the additional

load/additional interruptible load carrying capability of an interconnected sys­

tem also depends upon related conditions within the neighbouring systems.

A probabilistic technique which can be used to evaluate the inherent inter­

ruptible load carrying capability of isolated and interconnected generating

systems without having to commit any extra unit(s) other than those re­

quired to carry the firm load is also presented in this chapter.

The additional load/interruptible load that an isolated or an intercon­

nected system can carry in addition to a given firm load, without violating

the specified risk, is not a unique quantity. There IS at any moment,

however, a unique set of additional load/interruptible loads and associated

lead times. This set will change for different generating unit combinations

even if the firm load and specified unit commitment risk remain unchanged.

127

6. UNIT COMMITMENT

6.1. Introduction

The load in a practical power system changes continuously and it is

not economical to run all the units required to satisfy the peak load during

the low loads. Depending upon the load levels, some units are put into ser­

vice at one time and may be removed. from service at another time of the

day. The units in the various segments of a scheduling period should be

committed in such a way that the operating cost is minimised with a satis­

factory level of reliability. There are many generating unit factors which af­

fect the unit commitment. They are in general, fuel price, heat rate curve,

start up cost, unit failure rate and the time delay associated with starting,

synchronising and loading.

Assessment of spinning reserve is an integral part of unit commitment.

The unit commitment should be such that the unit commitment risk is less

than or equal to a specified level. In an interconnected system, the unit

commitment should satisfy two risk levels, namely single system risk (SSR)and interconnected system risk (ISR) as discussed in the previous chapters.

Once the unit commitment risk levels are satisfied, the spinning capacity in

excess of the system load is the spinning reserve available at that point of

time. The unit commitment technique in interconnected systems at a con­

stant load level has been explained in Chapter 3. The inclusion of hot

reserve units, rapid start units and interruptible load to reduce unit commit­

ment risk has also been discussed in Chapters 3 and 5. The application of

the 'Two Risks Concept' to unit commitment for a continually changing load

is considered in this chapter.

128

A number of methods for unit commitment have been published. The

majority of these methods deal with economic optimisation of unit

scheduling [6, 8, 9, 10, 11, 15, 16]. Economic starting and stopping of

generating units has been considered in Reference [91. Some of the published

material utilises mathematical programming in order to minimise running

cost [8, 12, 14, 34]. The use of a unit priority list has also been

suggested [9]. Relatively little work has been done on the application of

quantitative reliability concepts to unit commitment [4, 17, 24, 26, 35]. The

reliability methods presented are basically for isolated systems and become

impractical with a large number of operating units with back up units

having variable start-up times [17, 35].

This chapter presents a probabilistic technique which applies quantita­tive reliability assessment to unit commitment and spinning reserve evalua­

tion. The proposed method suggests that the unit commitment of an inter­

connected system in each scheduling period should be such that two different

risk levels; SSR at the isolated system level and ISR at the interconnected

system level are satisfied. If an interconnected system is unable to satisfy its

SSR or ISR during a scheduling period, it should bring more generation into

service or it should buy energy from its neighbours.

Generating units used in a previous scheduling period can still be in a

hot reserve state and can be brought into service in a relatively short period

of time depending upon the length of time these units are out of service.

Hydro and rapid start gas turbine units can be started and put into service

in the order of 5 to 10 minutes. In the absence of other potential capacity

adjustments, the presence of interruptible loads can reduce the unit commit­

ment risk. These aspects can be included in the assessment of unit commit­

ment risk and are discussed in Chapters 3 and 5. It has been assumed in

the following sections for the sake of simplicity that the thermal units once

taken out of service are not maintained in a hot reserve state.

129

6.2. Loading Order

A priority unit loading order can be prepared based on economic and

system operating factors. The priority list approach to unit commitment is

used by many utilities. The principle advantages of this technique are that

it is simple, straightforward and can be applied to systems with a large

number of units. As the load increases, individual units are committed ac­

cording to a pre-determined priority order. Units are removed from service

as the load decreases using the reverse priority order. Different utilities use

different approaches to prepare their priority order of unit commitment. The

approach used by the Texas Electric Service Company to prepare the unit

commitment priority list is presented in Reference [6] and utilises Equation

(6.1).

c·• (6.1)

where

Ci relative operating cost of unit I at the point of maximum

efficiency - $ /MWH

Hi most efficient heat rate of unit t - BTU /MWH

Fi = fuel cost of unit i - $/BTU

PG i= generation of unit i at the point of maximum efficiency

- MW

• minimum expected run time of unit l before cycling - hours

Si start up cost of unit z - $

A priority unit order list should in general reflect the long term

economic objectives of the utility in question.

The operating cost of hydro units are usually far lower than the

operating cost of thermal units and hydro units are generally considered first

130

for commitment where there is sufficient water. Limited storage hydro units,

however, are often used for peak shaving purposes. The time delays as­

sociated with starting, synchronising and loading hydro units are in the order

of 5 to 10 minutes and therefore some hydro units are retained as standby

units. Run of the river hydro units which can not be operated due to low

water conditions do not serve any standby generation purpose.

The area frequency and tie line regulation requirements of a system

must be satisfied. Hydro, gas turbine and gas engines can respond to load

changes at a faster rate than conventional thermal units. Some of these fast

acting units should be committed to satisfy local area constraints if the

responding capability of the operating thermal and/or nuclear units are not

satisfactory. The available hydro, gas turbine and gas engines not com­

mitted during a particular period act as ready reserve for that period.

6.3. Start-Up Cost

There is a cost associated with starting a thermal unit. The cost

depends on the duration of time since the unit last operated. The start-up

cost of a thermal unit can be expressed as 19]

where

s(t) = unit start-up fuel cost at time t,"

So = unit cold start-up cost,

a cooling rate of the unit,

T shut down hour of the unit.

The shut down time of all units are usually recorded. The unit start­

up cost over a scheduling period can be calculated knowing the cold start-up

cost and the cooling rate of the units. The start-up costs of hydro units are

131

negligible compared to those of thermal units and can be considered to be

zero for all practical purposes.

6.4. Dynamic Programming

Optimisation of non-linear functions with n decision variables can be

achieved using dynamic programming [36, 37, 38]. A dynamic programmmg

method applied to unit commitment was presented in 1966 [8]. The method

replaces the problem of finding optimum outputs of the various units for a

given load with the problem of finding optimum outputs of the various units

for all load levels between minimum and maximum output of the units. The

optimum way of operating N units can be found once the optimum way of

operating N-l units is known.

The dynamic programmmg starts with a single unit. The input-output

curves of all the units must be known. With only one unit available, the

input in dollars per hour as a function of output in megawatts can be deter­

mined from the input-output curve of the unit. The curve is defined from

the minimum to the maximum output of the unit. With two units avail­

able, a curve of input in dollars per hour as a function of output in

megawatts can be obtained from the input-output curves of these units. The

combined input-output curve will be defined from the minimum to the max­

imum output of the two units. At each load level between the mmunum

and maximum output of the two units, the load will be shared by each unit

in such a way that the input in dollars per hour becomes minimum. Based

on the combined input-output curve of two units a combined input-output

curve of three units can be obtained. Similarly the procedure is extended to

obtain the combined cost curve for all the available units.

Assume that

minimum running cost of carrying z MW load on N

generating units,

132

cost of carrying xi MW load on the ith unit.

The output of an individual unit is constrained by its mmimum and

maximum output as follows:

U· < z . < v·t t - t

where

Ui = minimum output of unit i in MW,

Vi = maximum output of unit i in MW.

The total output z is constrained as

where

gN = Min{u1 ,u2 ' ... ,uN}N

hN = LVii=1

The mmimum runmng cost for a total output of z MW IS:

subject to the following conditions .

•

gN < z-/ < hN-1-1 -

where

N-l

i=l

The maximum output of a unit can be the rated capacity of that

133

unit. The minimum output of a unit can be considered to be some value

or zero whichever is applicable.

6.5. Scheduling Using the 'Two Risks Concept'

The reliability constraints are first satisfied in this approach. The

number of units required to be committed in an interconnected system are

determined first from a table of loading order priorities for the respective

systems. The unit commitment should be such that it satisfies the SSR and

ISR criteria. Hot reserve and rapid start units are included in the unit

commitment process using the area risk technique. The number of units re­

quired in each interconnected system is determined in this manner for each

commitment period.

After the reliability constraints are satisfied, a tentative unit loading

schedule in each commitment period is prepared using dynamic programming

to assess the hourly running cost. The cost curve Yi In dollars per hour as

a function of the output xi in' MW for thermal units is approximated by a

second order function as shown below.

Yo = a 0 + b .z 0 + c ox2 0

t Z 1 t Z 1

where ai' bi and c/s are cost coefficients, which can be estimated from ac­

tual input-output unit data.

For the sake of simplicity all hydro units in this thesis are considered

to be run of the river generating units without any energy constraints and

whose input-output is given by

The last step of this commitment method is to check whether delaying

or advancing the starting and stopping of a certain unit results in a saving

In the running cost [9]. If a saving is possible, the commitment schedule is

134

altered and another tentative loading schedule IS prepared usmg the

previously established input-output curves obtained by dynamic programming.The checking for readjustments of starting and stopping times of units con­

tinues until no further savings are achieved. A normalised cooling rate of

0.25 is considered for all thermal units in this thesis.

Identical generation systems A and B with generating units shown in

Table 3.2 are considered for unit commitment over a period of 24 hours.

System A and. System B are interconnected with the 2x100 MW tie lines

described in Table 3.3. Assume that both System A and B have one

25 MW rapid start hydro unit and one 25 MW rapid start gas turbine unit

available in addition to the units in Table 3.2. These rapid start units have

a lead time of 5 minutes. The rapid start hydro unit has a failure rate of

0.0002 per hour with a negligible starting failure rate. The transition rates

of the rapid start gas turbine unit are given in Table 3.13. The commence­

ment of the scheduling period is arbitrary. In this chapter the scheduling

period commences from the moment of the daily peak and it is assumed that

the peak loads in both systems occur at the same time. These assumptionshave no influence on the basic method of unit commitment.

The coefficients of the running cost vs. output in MW curves and the

cold start-up cost of the generating units in both System A and B are given

in Table 6.1. Table 6.2 shows the hourly peak load variation in System A

and System B in a 24 hour commitment period. Table 6.3 shows the unit

commitment in System A and System B for the hourly peak load variation

shown in Table 6.2 with zero load forecast uncertainty. The specified SSR

of 0.01 and ISR of 0.0001 are used in obtaining the unit commitment

schedule for System A and System B. The lead times of additional thermal

generation in both systems are considered to be 2 hours.

The unit commitment in System A and System B with 4 % load

forecast uncertainty is shown in Table 6.4. The mean values of the daily

135

Table 6.1: Cost Parameters of the Generating Units In SystemA and B.

Unit # a· b· c· Cold Start-Up Typet t t

z Cost($)

1 0 0.2643 0.0 0 hydro2 0 0.2750 0.0 0 hydro3 0 0.2750 0.0 0 hydro4 60 1.1954 0.00127 70 thermal5 52 1.2136 0.00148 92 thermal6 52 1.2136 0.00148 95 thermal7 52 1.2241 0.00148 97 thermal8 45 1.2458 0.00212 100 thermal9 45 1.2458 0.00234 100 thermal

10 46 1.2532 0.00212 100 thermal-11 40 1.6966 0.00382 65 thermal

12 40 1.6966 0.00382 65 thermal13 29 1.8015 0.00212 110 thermal14 32 1.7522 0.00401 70 thermal15 32 1.8518 0.00393 70 thermal16 32 1.8518 0.00393 70 thermal17 0 0.25 0.0 0 hydro18 65 2.2271 0.00415 150 rapid start

peak load variation are shown in Table 6.2. The load forecast uncertainty

in this case has been modelled using the three-step approximation to the

normal distribution discussed in Section 3.7. The magnitude of overall spin­

ning reserve requirement with load forecast uncertainty is higher than that

without load forecast uncertainty as seen from Tables 6.3 and 6.4

Unit commitment in System A and B with export/import is shown in

Table 6.5 for the hourly peak load variations shown in Table 6.2. System A

exports 60 MW to System B and the export is backed by the entire system

of A. The total spinning capacity in System A includes the load in A, ex­

port commitment to B and the spinning reserve. The spinning reserve In

System A with a contracted export to System B is

Spinning Reserve = Total spinning capacity - Load - Export

136

Table 6.2: Peak Load Variations in a 24 Hour Period.

Hour

1

2

34

5

678

910111213

141516

1718192021222324

The spinning reserve m

IS

Spinning Reserve

6.6. Summary

A new reliability

La(MW) Lb(MW)

1900 1920

1880 19001840 18501820 18201800 1800

1750 17001770 16501740 16001700 15501600 15001500 14801400 14201310 1320

1200 12101150 11501100 11001150 10601250 1100

1400 13001550 14001650 16501730 17501820 18501900 1920

System B with a contracted import from System A

Total spinning capacity - Load + Import

constrained unit commitment method for intercon­

nected systems is discussed in this chapter. The unit commitment must

satisfy two risk levels; one at the isolated system level and another in the

interconnection level. The method uses a priority loading order for the units

to be committed during the period of increasing generation requirements.

137

Table 6.3: Unit Commitment in System A and B.

Hour System A System B

La No. of . Spinning Lb No.of Spinning(MW) Units Reserve{MW) (MW) Units Reserve{MW)

1 1900 14 180 1920 14 1602 1880 14 200 1900 14 180

3 1840 13 140 1850 13 130

4 1820 13 160 1820 13 160

5 1800 13 180 1800 13 180

6 1750 12 110 1700 12 1607 1770 13 210 1650 11 no

8 1740 12 120 1600 11 1609 1700 12 160 1550 10 no

10 1600 11 160 1500 10 160

11 1500 10 160 1480 10 18012 1400 9 110 1420 10 240

13 1310 9 200 1320 9 190

14 1200 8 160 1210 8 150

15 1150 8 210 1150 8 210

16 1100 7 110 1100 7 110

17 1150 8 210 1060 7 15018 1250 8 110 1100 7 110

19 1400 9 110 1300 9 21020 1550 11 210 1400 9 11021 1650 12 210 1650 12 21022 1730 12 130 1750 13 23023 1820 13 160 1850 13 130

24 1900 14 180 1920 14 160

138

Table 6.4: Unit Commitment in System A and B With LoadForecast Uncertainty.

Hour System A System B

La No. of Spinning Lb No.of Spinning(MW) Units Reserve{MW) (MW) Units Reserve{MW)

1 1900 14 180 1920 15 260

2 1880 14 200 1900 15 280

3 1840 14 240 1850 14 230

4 1820 14 260 1820 14 260

5 1800 14 280 1800 14 280

6 1750 13 230 1700 12 160

7 1770 13 210 1650 12 210

8 1740 13 240 1600 11 160

9 1700 12 160 1550 11 210

10 1600 12 260 1500 10 160

11 1500 11 260 1480 10 180

12 1400 10 260 1420 10 240

13 1310 9 200 1320 9 190

14 1200 8 160 1210 8 150

15 1150 8 210 1150 8 210

16 1100 8 260 1100 8 260

17 1150 8 210 1050 7 160

18 1250 9 260 1100 7 110

19 1400 10 260 1300 9 210

20 1550 11 210 1400 10 260

21 1650 12 210 1650 12 210

22 1730 13 250 1750 13 230

23 1820 14 260 1850 14 230

24 1900 14 180 1920 15 260

139

Table 6.5: Unit Commitment In System A and B With

Export/Import.

Hour System A System B

La No. of Spinning Lb No.of Spinning(MW) Units Reserve(MW) (MW) Units Reserve(MW)

1 1900 15 220 1920 13 120

2 1880 14 140 1900 13 1403 1840 14 180 1850 13 1904 1820 14 200 1820 13 2205 1800 14 220 1800 12 120

6 1750 13 170 1700 11 1207 1770 13 150 1650 11 1708 1740 13 180 1600 10 120

9 1700 13 220 1550 10 17010 1600 12 200 1500 10 220

11 1500 11 200 1480 10 24012 1400 10 200 1420 9 15013 1310 9 140 1320 9 25014 1200 9 250 1210 8 210

15 1150 8 150 1150 7 12016 1100 8 200 1100 7 17017 1150 8 150 1060 7 21018 1250 9 200 1100 7 17019 1400 10 200 1300 8 120

20 1550 11 150 1400 9 17021 1650 12 150 1650 11 17022 1730 13 190 1750 12 17023 1820 14 200 1850 13 19024 1900 15 220 1920 13 120

140

The starting and stopping times of different units are adjusted to achieve

savings in the running cost.

141

7. LOCATION OF SPINNING RESERVE

7.1. Introduction

Reliable power system operation requires that the system generation

must respond to sudden changes in generation due to generation outages or

to unforeseen changes in system load or to any other contingency which

results in a generation loss. Hydro units can pick up load in the order of 1

to 5 minutes and, therefore, can respond to the generation or load changes

very quickly. Hydro units held as spinning reserve can be utilised to satisfythe system frequency and dynamic stability. The running costs of hydro

units are far lower than those of thermal units. Substantial economic

savings can be achieved by loading hydro units to their maximum output

level. Some sort of compromise between response requirements and economic

savings must be made when loading the hydro units.

Economic load dispatch methods consider allocation of load into dif­

ferent operating units III order to achieve mmimum running

cost [13, 14, 39, 40]. Part of the spinning reserve must be available within

a certain margin time [41] to protect system frequency and tie line regula-_.

tion. Two types of margin time are important; (1) time to satisfy system

frequency and dynamic stability and (2) time to satisfy loss of generation or

other facilities. These margin times are normally of the order of one minute

and five minutes. The actual magnitude of these time periods can, however,

vary from system to system. A system may have a large amount of spin­

ning reserve with a particular generation/load condition but the actual

responding capability can be quite inadequate for reliable system operation.

142

A method for spinning reserve allocation m interconnected systems

which satisfies specified risk criteria is presented in this chapter. Algorithms

are developed for two interconnected systems. Spinning reserve location in

multi-interconnected power systems can be considered using the multi-area

techniques given in references [5] and [42J.

7.2. Response Risk

Assessment of spinning reserve and unit commitment as developed in

the preVIOUS chapter do not suggest the manner in which the individual com­

mitted units should be loaded. The units held as spinning reserve should be

capable of picking up load within the specified margin time in the case of a

sudden generation loss or an increase in the load. The ability of a unit to

respond to sudden changes and pick up load, if required, depends on the

unit type. Hydro units can pick up load of up to 30% of their full output

capacity in one minute. These units therefore play a dominant role in satis­

fying system frequency and tie-line regulation. Typical thermal units can

pick up 1-3% of their full output capacity in one minute. The response rate

of thermal units depends on the loading point. Gas turbine and some gas

engines can pick up load in a relatively short period of time. The time

delay associated with starting, synchronising and loading these gas turbine

and gas engines could be in the order of three to five minutes.

The allocation of spmmng reserve amongst the committed units can be

done by selecting a suitable risk level. The load dispatch should be such

that the system should. have adequate responding capability. The probability

of meeting the regulating margin within the specified margin time, known as

response risk, ��?1l1� l:>�._�q'!�LtQ ... <?l" .1E!s§ . th�Jt, <L �P�c!t1�<lleyel. The assess­

ment of response risk can be done using the I1:!(il"gi�.. E�e and failure andt::--_ _�_._.. �_�__

w--·----'''''··-· ""- ,.,� .. ,'"_ �.�=.,-,.."",�"�." .. �._...•. �." ,,.,,�.,,,, "" .. �",- .. _.,,,...,_,-�.. '-.�-'.. ""'.'

response rate of the units held in reserve. The response risk evaluation tech-'---_ _--- ,.",

"."." " __._-----,_,,, .. __ _,, ,. ,' "

- .. ,..'

, .. , .. , _"

"'

.

nique is similar to the technique for unit commitment risk evaluation., The

\,-�I!it c�P�<:Jt.y�J!l- �i�§p.Q!l.se··risk ey�_l_'!<Lti()..I! ... i� .. !�e t()t(iLE��P()_n_� output of the- .. --.'� -.". -""---�-��,,"'. ,,- .. _-,,' '''-'''�'-' ._"-_'-" •..... , .�.�.,-.

unit at the end ()Lth.�,_IIta,l"giI]. tip:l,e. The O!1ta,_geJ�I>J<L�ement rate (ORRLip.-

. -

,- -----. ---�----.-...• - ... __ .---- --

.. '. � -.- ....•

--�.-.��-�-�.--.".� .. -,,- ...•. - ....... ��-----�.-- .....•.--

143

the case of response risk evaluation is the probability that th�__ll.I!!t.JClU§ and�

. __ • __�'�__ .'.�....__ " .. .• �._ ,_�.' ' � -.,_"._",� ··_.r = __ .� ••. __ �_ ,,""._�� •• ,,�,� ........_._ ,�.'/"'''''' '__ -_.--._. ----.----�--."' -�-

is not replaced within the margin time. The response risk evaluation tech-

nique for a single system is discussed in detail in Reference [3].

In the case of an interconnected system, the response capacity IS

modified by assistance from neighbouring systems. All tie line constrained

response assistance can be considered as responding units available to the

system of concern. The technique of developing an equivalent response

capacity model is similar to that of developing an equivalent transient

capacity model as explained in Chapter 3.

The time delays associated with hot reserve units are such that the

units can not be included in the response capacity model. Hydro, rapid

start gas turbine and gas engines can be included in the risk assessment

using the area risk technique explained in Chapter 3. Interruptible loads

with the maximum allowable time delay of up to 5 minutes can be included

in the response risk assessment using the area risk technique. Chapter 5 ex­

plains in detail the inclusion of interruptible load in the risk assessment

process. In the case of response risk assessment, the lead time of additional

response capacity is equal to the margin time. It is assumed that after the

margin time there will be enough responding capacity available to the system

that the risk will become zero for all practical purposes.

An interconnected system must meet two risk levels for both the

regulating margin requirements. The committed units in a system should be

dispatched in a way that the response risk designated as single system

response risk (SSRR) should be less than or equal to a specified level. Once

the response risk criteria at the single system level are satisfied in each sys­

tem, all response assistances are considered at the interconnection level. All

response assistances to a given system in the interconnected configuration are

added to form an equivalent response model and the response risk designated

as the interconnected system response risk (ISRR) must satisfy a specified

144

risk level. The system most removed from meeting its ISRR criterion is re­

quired to modify its dispatch in order to achieve greater response. The ac­

tual ISRR of an interconnected system can be improved by having more

rapid start units available to the system.

7.3. Numerical Example

A numerical example to illustrate the assessment of response risk in an

interconnected system is shown in this section. Consider the generation

System X in Table 2.1 in Chapter 2. Assume that the specified unit com­

mitment risk of System X at the single system level is 0.001. System X

must commit all 10 of its available units in order to carry a load of

170 MW if the lead time of additional thermal generation is two hours. The

equivalent generation model for 10 committed units with a lead time of two

hours in the form of a capacity outage probability table is shown in Table

2.2 of Chapter 2. The probability of unit failure assuming a 5 minute mar-

gm time is shown in Table 7.1.

Table '1.1: Failure Probability and Response Rate.

Unit Failure Probability ResponseSize Rate of Failure Rate

(MW) (fjyr) in 5 mins. (MWjmin)

40 4 0.00003805 1

20 3 0.00002854 1

10 3 0.00002854 1

Table 7.2 shows a possible load dispatch (not necessarily economic) of 10

operating units in system X when the load is 170 MW. The 5 minute

response risk is shown in Table 7.3 for the load dispatch in Table 7.2. If

the 5 minute regulating margin requirement of System X is assumed to be

25 MW, then the SSRR of X is 0.00017123 for the dispatch shown in Table

7.2.

145

Table 7.2: Load Dispatch ill System X.

Unit 1 2 3 4 5 6 7 8 9 10

G 40 40 40 20 20 20 10 10 10 10

L 40 40 40 10 10 10 10 5 5 0

R 0 0 0 5 5 5 0 5 5 5'

G is available generating capacity in MWL is individual unit loading in MWR is the 5 minute response in MW

Table 7.3: Response Risk.

Response(MW)

Individual

ProbabilityCumulative

Probability(risk)

3025

0.999828770.00017123

1.000000000.00017123

Assume that System X is interconnected to a neighbouring system

(System Y) through a tie line which has a maximum power transfer

capability of 27 MW and a failure rate of 1 failure/year. Table 7.4 shows

the tie-line model for the 5 minute margin time.

Table 7.4: Tie-Line Model.

Cap. In Cap. out Individual Cumulative

(MW) (MW) Probability Probability

27 0 0.99999049 1.00000000

0 27 0.00000951 0.00000951

The available generation, load and load dispatch in System Y is assumed to

146

be identical to that in System X and therefore the response reserve of

System Y will be identical to that shown in Table 7.3. The tie-line con­

strained response assistance to System X provided by System Y is shown in

Table 7.5.

Table 1.5: Tie-Line Constrained Response(Assistance to X provided by Y).

Assistance

Response Individual Cumulative

(MW) Probability Probability

27 0.99981926 1.00000000

25 0.00017123 0.00018074

0 0.00000951 0.00000951

The 5 minute response of System X will be modified by the tie-line

constrained response assistance it can receive from System Y. The equiv­

alent 5 minute response of System X is shown in Table 7.6.

Table 1.6: Equivalent 5 Minute Response of System X.

Response Individual Cumulative

(MW) Probability Probability( risk)

57 0.99964806 1.00000000

55 0.00017120 0.00035194

52 0.00017120 0.00018074

50 0.00000003 0.00000954

30 0.00000951 0.00000951

The 5 minute response risk of System X at the interconnection level can be

found from Table 7.6 given the 5 minute regulating margin of System X. If

the 5 minute regulating margin of System X is 30 MW then the ISRR of X

is 0.00000951. The equivalent 5 minute response model of System Y can be

developed in a similar manner. The equivalent 5 minute response model of

147

System X will change if the load dispatch in System X or in System Y or

both are changed. The one minute response risk can be evaluated using a

similar approach.

7.4. Load Dispatch Using the 'Two Risks Concept'

The load dispatch in an interconnected system should be such that the

one minute and 5 minute response requirements meet two risk levels; one at

the single system level and another at the interconnected system level.

Response risk changes with load dispatch. A particular economic load dis­

patch may not meet the reliability criteria. There must be adequate

responding generation to satisfy the one minute and five minute response

reserve requirements. The one minute response reserve requirement can be

assessed by off-line transient and dynamic stability studies of the intercon­

nected systems. The factors which affect the response risk are the loading of

units, unit failure rate, response rate of units, availability of rapid start

standby units etc.. The distribution of responding generation on many units

rather than on a few units for the same amount of responding generation

reduces the response risk. The system operating cost, however, will increase

if the response requirement is increased.

•

The first step of the load dispatch approach usmg the 'Two Risks

Concept' is to prepare an economic loading schedule. The second and final

step of this approach is to make the least costly adjustments of the economic

schedule to meet the risk criteria. The economic loading schedule in each

interconnected system can be prepared using any suitable economic load dis­

patch technique. Once the economic loading schedules for each system are

prepared, the SSRR and ISRR of each system are evaluated. If the SSRR

and ISRR criteria are satisfied m each interconnected system, the economic

loading schedule in each system stands as a reliable loading schedule. In the

event that the risk criteria are not satisfied, the system farthest removed

from meeting the ISRR become responsible for making the necessary change

in its load dispatch provided all the systems satisfy the SSRR criterion.

148

Dynamic programming was used to obtain the economie loading

schedules for System A and System B. Several assumptions have been made

in the application of dynamic programming to obtain economic loading

schedules. Transmission losses in both areas and in the tie-lines have been

neglected. AU hydro generation is considered to be run of the river type

without any energy constraints. Ril?;_orous economic load dispatch

techniques [13, 14, 39, 43] can be applied if necessary to consider the trans­

mission losses and pumped storage hydro if necessary.

7.4.1. Least costly adjustments

The response output of a generating unit depends on response rate,

margin time and the spmnmg reserve held on the unit. The response

capability of a unit is the product of response rate and the margin time as­

suming a constant response rate over the output range of the unit, { In the

case where the spinning reserve held on the unit is less than the response

capability of that unit, the response output IS constrained by the spinning

reserve held on the unit. The first step of the least costly adjustment is to

classify the operating units into three groups according to whether an in­

dividual unit's spinning reserve is higher (Group I) or lower (Group II) than

or equal (Group III) to its response capability. The next step is to identify

the unit in Group II whose incremental running cost at the respective load

point is the highest and the unit in Group I whose incremental running cost

at the respective load point is the lowest. The unit identified this way in

Group I is the acceptor unit and the unit identified in Group II is the donor

unit. If transmission losses are considered when obtaining the economic

loading schedule in the first step, the incremental running cost during the

identification process should include the incremental transmission cost. Once

the donor and acceptor in a system is identified, an incremental load is

taken away from the donor and put into the acceptor unit. The ISRR of all

interconnected systems are re-assessed and the whole process is repeated until

the system in concern satisfies its ISRR criterion. Any constraints regarding

the reloading of the units can be considered during the adjustments.

149

The incremental running cost of the units In Group I and Group II can

be obtained in the following way.'

Assume

(7.1)

where

Y i running cost of unit i in $ /hr,xi = output of unit i in MW.

The running cost of unit i for a load of (x+�x) MW IS

c. + b.(x+�x.) + c.(x+�x.)2I' 1 I t I I t (7.2)

where

� Y i= change in running cost in unit i in $ /hr,

�xi = change in output of unit i in MW.

From Equations (7.1) and (7.2) the change in running cost of unit t

can be expressed as

�Y' = {b. + c.(2x+�x.)}�x.I 1 'I & t(7.3)

In the limiting case, Equation (7.3) can be rearranged as the derivative of

the running cost of unit i at a load point of xi MW.

b. + 2c·x·tIt

A discrete change of �X In output of the donor and the acceptor unit has

been used for computational purposes. A smaller value of �x will require a

longer computation time than that of a larger value of �x for the same

starting loading schedule. �x is positive for the acceptor unit and negative

for the donor unit. Once the discrete reloading between the donor and the

acceptor is done a new pair of donor and acceptor is selected. A discrete

load change of 1 MW and 5 MW was used to obtain the loading schedules

for System A and System B.

150

Table 7.7 shows the response rate of the available generating units in

System A and System B. Response rate of all generating units are assumed

constant over the entire output range of the respective units.

Table 7.7: Response Rate of Generating Units.

Unit #z

Maximum

Output(MW)

ResponseRate

(MWjmin)

Minimum

Output(MW)

Type

1234

5

67

89

101112131415

161718

200180180200

150200150200150150100100120100100

1002525

ooo

70507050705050

303030303030

oo

40.0

30.030.0

3.02.03.0

2.03.02.02.01.51.52.02.0

2.02.05.05.0

hydrohydrohydrothermalthermalthermalthermalthermalthermalthermalthermalthermalthermalthermalthermalthermal

hydrorapid start

The hourly peak load variation and the corresponding unit commitment in

System A and System B as shown in respective Tables 6.2 and 6.3 of Sec­

tion 6.5 are considered for the purpose of load dispatch. The load duringthe first hour of the 24 hour scheduling period is 1900 MW in System A

and 1920 MW in System B. The load dispatch during this hour is shown

in Table 7.8. The running cost during this first hour is $2757.10 in

System A and $2800.08 in System B according to the economic load dis­

patch. The specified SSRR and ISRR is 0.01 and 0.0001 respectively. The

economic load dispatch in both systems during the first hour have been

modified to meet the reliability criteria. The resultant load dispatch requires

151

Table 7.8: Load Dispatch During the First Hour.

Unit # Economic Load Risk Constrained Economic Load Dispatchz Dispatch ..6. x 1 MW ..6. x 5 MW

A B A B A B

1 200 200 200 200 200 2002 180 180 134 154 130 1503 180 180 180 180 180 1804 200 200 185 185 185 1855 150 150 140 140 140 1406 150 150 140 140 140 1407 150 150 140 140 140 1408 150 150 140 140 140 1409 150 150 140 140 140 140

10 150 150 140 140 140 14011 57 61 77 77 87 91

12 57 61 93 93 92 91

13 78 86 110 110 108 10614 48 52 81 81 78 77

The output of all units are in MW

an increased running cost in both the systems. The running cost during the

first hour is $2884.44 in System A and $2889.94 in System B when a reload­

ing stepsize of 1 MW has been used. The computation time required to res­

chedule the economic load dispatch during the first hour to meet the

reliability criteria is 10.68 CPU seconds with a reloading step of 1 MW and

1.89 CPU seconds with a reloading step of 5 MW. The running cost during

the first hour is $2892.47 in System A and $2898.19 in System B when a

reloading stepsize of 5 MW has been used. The running costs for reliabilityconstrained economic load dispatch is summarised in Table 7.9.

The operating cost during the 24 hour period is shown in Table 7.10.

The operating cost in .each system includes the starting cost of generatingunits during the 24 hour scheduling period. The total starting cost during

152

Table '1.9: Running Cost During the First Hour.

EconomicLoad Dispatch

Risk ConstrainedEconomic Load Dispatch

System .6.x = 1 MW .6.x = 5 MW

AB

$2757.10$2800.08

$2884.44$2889.94

$2892.47$2898.19

.6.x = reloading step size in MW

Table '1.10: Operating Cost During the 24 Hour Period.

EconomicLoad Dispatch

Risk ConstrainedEconomic Load Dispatch

System .6.x = 1 MW .6.x = 5 MW

AB

$50,239.93$48,377.10

$52,846.59$50,956.67

$53,031.99$51,119.12

.6.x = reloading step size in MW

this 24 hour period is $525.00 in System A and $513.00 in System B. The

operating cost in both System A and System B has increased with the im­

position of the response risk criteria compared to that with economic load

dispatch. The additional operating cost due to the imposition of response

risk criteria can be considered as the cost of reliability and should be judged

against the worth of reliability. The question of reliability worth is beyondthe scope of this thesis. The computation time required td reschedule the

unit loadings starting from the economic load dispatch to satisfying the risk

criteria depends on the number of units committed during a particular

period, economic load dispatch, SSRR, ISRR, reloading step size etc.. The

computation times required to reload the units in the first hour in order to

153

satisfy the risk criteria starting from the economic schedule, therefore, are

not representative. The computation time to reschedule the unit loadings

during the 24 hour period to obtain a risk constrained economic dispatch

starting from the basic economic dispatch is 3 minutes 22.29 seconds and

56.55 seconds CPU for a reloading step size of 1 MW and 5 MW respec­

tively. The economic and the risk constrained economic load dispatches for

the 24 hour period assuming constant hourly loads as shown in Table 6.2

are presented in Tables 7.11 to 7.16.

The first three units in both Systems A and B are hydro generatingunits. The running cost of these hydro units are much lower than the ther­

mal units in either system. In the economic load dispatch for System A

and System B shown in Tables 7.11 and 7.12, these three hydro units are

dispatched to their maximum output level. The response rates of the first

three hydro units as shown in Table 7.7 are considerably higher than those

of the thermal units in the system. Part of the spinning capacity of some of

these hydro units are held as reserve capacity when the risk constraints are

imposed on the economic load dispatch. This is evident in Tables 7.13 to

7.16. After fulfilling the 5 minute response criterion the one minute response

requirements are considered in a similar manner. Only the on-line generat­

ing units contribute to the one minute response capability of a system. The

loading of the units are further modified if necessary, to meet the one

minute response risk criteria if necessary.

7.S. Summary

A risk constrained spmnmg reserve allocation technique IS presented in

this chapter. Spinning reserve should be allocated among the operationalunits in such a way that the response requirements are satisfied. Each in­

terconnected system must satisfy SSRR and ISRR for 5 minute and one

minute regulating margins. An interconnected system can receive assistance

from its neighbour to meet its response requirements. This assistance is

taken into consideration when meeting the ISRR. Risk constrained economic

154

Table 1.11: Economic Load Dispatch in System A.

Individual Unit Outputs

Hour La . Xl X2 X3 X4 X5 X6 x7 Xs Xg XlO Xu X12 X13 x14

1 1900 200 180 180 200 150 150 150 150 150 150 57 57 78 48

2 1880 200 180 180 200 150 150 150 150 150 150 53 53 71 43

3 1840 200 180 180 200 150 150 150 150 150 150 54 54 72

4 1820 200 180 180 200 150 150 150 150 150 150 49 48 63

5 1800 200 180 180 200 150 150 150 150 150 150 43 43 54

6 1750 200 180 180 200 150 150 150 150 150 150 45 45

7 1770 200 180 180 200 150 150 150 150 150 150 36 35 39

8 1740 200 180 180 200 150 150 150 150 150 150 40 409 1700 200 180 180 200 150 150 150 148 135 147 30 30

10 1600 200 180 180 200 150 150 150 124 113 123 30

11 1500 200 180 180 192 150 150 150 103 94 101

12 1400 200 180 180 193 150 150 150 103 94

13 1310 200 180 180 169 138 138 135 89 81

14 1200 200 180 180 162 132 132 129 85

15 1150 200 180 180 149 122 122 119 7816 1100 200 180 180 157 129 129 12517 1150 200 180 180 149 122 122 119 7818 1250 200 180 180 173 143 143 139 9219 1400 200 180 180 193 150 150 150 103 94

20 1550 200 180 180 199 150 150 150 108 97 106 30

21 1650 200 180 180 200 150 150 150 131 119 130 30 30

22 1730 200 180 180 200 150 150 150 150 150 150 35 35

23 1820 200 180 180 200 150 150 150 150 150 150 49 48 63

24 1900 200 180 180 200 150 150 150 150 150 150 57 57 78 48

La and x/s are in MW

155

Table 7.12: Economic Load Dispatch in System B.

Individual Unit Outputs

Hour t., xl x2 X3 X4 x5 x6 X7 Xs X9 XlO Xu Xl2 X13 xl4

1 1920 200 180 180 200 150 150 150 150 150 150 61 61 86 52

2 1900 200 180 180 200 150 150 150 150 150 150 57 57 78 48

3 1850 200 180 180 200 150 150 150 150 150 150 57 56 77

4 1820 200 180 180 200 150 150 150 150 150 150 49 48 63

5 1800 200 180 180 200 150 150 150 150 150 150 43 43 54

6 1700 200 180 180 200 150 150 150 148 135 147 30 30

7 1650 200 180 180 200 150 150 150 142 128 140 308 1600 200 180 180 200 150 150 150 124 113 123 309 1550 200 180 180 200 150 150 150 118 106 116

10 1500 200 180 180 192 150 150 150 103 94 10111 1480 200 180 180 185 150 150 149 99 90 97

12 1420 200 180 180 173 142 142 138 92 83 9013 1320 200 180 180 171 140 140 137 90 8214 1210 200 180 180 164 135 134 131 8615 1150 200 180 180 149 122 122 119 7816 1100 200 180 180 157 129 129 12517 1060 200 180 180 146 119 119 11618 1100 200 180 180 157 129 129 12519 1300 200 180 180 166 137 137 133 88 7920 1400 200 180 180 193 150 150 150 103 9421 1650 200 180 180 200 150 150 150 131 119 130 30 30

22 1750 200 180 180 200 150 150 150 150 147 150 31 31 31

23 1850 200 180 180 200 150 150 150 150 150 150 57 56 7724 1920 200 180 180 200 150 150 150 150 150 150 61 61 86 52

-

Lb and x/s are in MW

156

Table 7.13: Risk Constrained Economic Load Dispatch ill Sys-tem A (Reloading step = 1 MW).

Individual Unit Outputs

Hour La xl X2 X3 X4 x5 X6 X7 X8 X9 XlO x11 X12 X13 x14

1 1900 200 134 180 185 140 140 140 140 140 140 77 93 110 81

2 1880 200 114 180 185 140 140 140 140 140 140 77 93 110 81

3 1840 200 164 180 185 140 140 140 140 140 140 81 80 110

4 1820 200 144 180 185 140 140 140 140 140 140 81 80 110

5 1800 200 124 180 185 140 140 140 140 140 140 81 80 110

6 1750 200 180 180 188 140 141 140 140 140 140 81 80

7 1770 200 94 180 185 140 140 140 140 140 140 81 80 110

8 1740 200 174 180 185 140 140 140 140 140 140 81 80

9 1700 200 134 180 185 140 140 140 140 135 140 83 83

10 1600 200 127 180 185 140 140 140 140 140 140 68

11 1500 200 119 180 185 140 140 140 128 128 140

12 1400 200 159 180 185 140 140 140 134 122

13 1310 200 69 180 175 140 140 140 140 126

14 1200 200 99 180 185 140 140 140 116

15 1150 200 49 180 185 140 140 140 116

16 1100 200 139 180 165 140 140 13617 1150 200 49 180 185 140 140 140 116

18 1250 200 149 180 185 140 140 140 116

19 1400 200 159 180 185 140 140 140 134 12220 1550 200 77 180 185 140 140 140 140 140 140 68

21 1650 200 84 180 185 140 140 140 131 125 140 93 92

22 1730 200 164 180 185 140 140 140 140 140 140 81 80

23 1820 200 144 180 185 140 140 140 140 140 140 81 80 110

24 1900 200 134 180 185 140 140 140 140 140 140 77 93 110 81

La and Xi's are in MW

157

Table 7.14: Risk Constrained Economic Load Dispatch in Sys-tem B (Reloading step = 1 MW).

Individual Unit Outputs

Hour Lb xl x2 x3 x4 x5 x6 x7 Xg Xg XlO Xu x12 x13 x14

1 1920 200 154 180 185 140 140 140 140 140 140 77 93 110 81

2 1900 200 134 180 185 140 140 140 140 140 140 77 93 110 81

3 1850 200 174 180 185 140 140 140 140 140 140 81 80 110

4 1820 200 144 180 185 140 140 140 140 140 140 81 80 1105 1800 200 124 180 185 140 140 140 140 140 140 81 80 110

6 1700 200 134 180 185 140 140 140 140 135 140 83 83

7 1650 200 177 180 185 140 140 140 140 140 140 688 1600 200 127 180 185 140 140 140 140 140 140 68

9 1550 200 169 180 185 140 140 140 128 128 14010 1500 200 119 180 185 140 140 140 128 128 14011 1480 200 99 180 185 140 140 140 128 128 14012 1420 200 39 180 173 140 140 140 140 128 14013 1320 200 79 180 175 140 140 140 140 12614 1210 200 109 180 185 140 140 140 11615 1150 200 49 180 185 140 140 140 11616 1100 200 139 180 165 140 140 13617 1060 200 99 180 165 140 140 13618 1100 200 139 180 165 140 140 13619 1300 200 59 180 175 140 140 140 140 12620 1400 200 159 180 185 140 140 140 134 12221 1650 200 84 180 185 140 140 140 131 125 140 93 92

22 1750 200 74 180 185 140 140 140 140 140 140 81 80 11023 1850 200 174 180 185 140 140 140 140 140 140 81 80 11024 1920 200 154 180 185 140 140 140 140 140 140 77 93 110 81

Lb and x/s are in MW

158

Table 7.15: Risk Constrained Economic Load Dispatch in Sys-tem A (Reloading step = 5 MW).

Individual Unit Outputs

Hour La xl x2 x3 X4 x5 x6 x7 Xs Xg xlO xll X12 xIS xl4

1 1900 200 130 180 185 140 140 140 140 140 140 87 92 108 78

2 1880 200 110 180 185 140 140 140 140 140 140 88 93 106 78

3 1840 200 160 180 185 140 140 140 140 140 140 84 84 107

4 1820 200 140 180 185 140 140 140 140 140 140 84 83 108

5 1800 200 120 180 185 140 140 140 140 140 140 83 83 109

r,6 1750 200 180 180 185 140 140 140 140 140 140 85 80

7 1770 200 90 180 185 140 140 140 140 140 140 81 85 109

8 1740 200 170 180 185 140 140 140 140 140 140 85 80

9 1700 200 125 180 185 140 140 140 143 135 142 85 85

10 1600 200 125 180 185 140 140 140 139 138 138 75

11 1500 200 115 180 187 140 140 140 138 124 136

12 1400 200 155 180 188 140 140 140 133 12413 1310 200 65 180 184 138 138 140 139 12614 1200 200 95 180 182 137 137 139 130

15 1150 200 45 180 184 137 137 139 128

16 1100 200 135 180 172 139 139 13517 1150 200 45 180 184 137 137 139 128

18 1250 200 140 180 183 143 143 139 122

19 1400 200 155 180 188 140 140 140 133 12420 1550 200 70 180 189 140 140 140 138 137 136 80

21 1650 200 80 180 185 140 140 140 131 139 140 90 85

22 1730 200 160 180 185 140 140 140 140 140 140 85 80

23 1820 200 140 180 185 140 140 140 140 140 140 84 83 108

24 1900 200 130 180 185 140 140 140 140 140 140 87 92 108 78

La and =» are in MW

159

Table 7.16: Risk Constrained Economic Load Dispatch in Sys-tem B (Reloading step = 5 MW).

Individual Unit Outputs

Hour Lb xl X2 X3 X4 x5 X6 X7 Xs Xg XIO Xll Xl2 Xl3 x14

1 1920 200 150 180 185 140 140 140 140 140 140 91 91 106 77

2 1900 200 130 180 185 140 140 140 140 140 140 87 92 108 78

3 1850 200 170 180 185 140 140 140 140 140 140 82 86 1074 1820 200 140 180 185 140 140 140 140 140 140 84 83 108

5 1800 200 120 180 185 140 140 140 140 140 140 83 83 109

6 1700 200 125 180 185 140 140 140 143 135 142 85 85

7 1650 200 175 180 185 140 140 140 142 138 140 70

8 1600 200 125 180 185 140 140 140 139 138 138 75

9 1550 200 165 180 185 140 140 140 138 126 13610 1500 200 115 180 187 140 140 140 138 124 136

11 1480 200 95 180 185 140 140 144 134 125 13712 1420 200 35 180 178 142 142 138 137 128 14013 1320 200 75 180 181 140 140 137 140 12714 1210 200 lOS 180 184 140 139 136 12615 1150 200 45 180 184 137 137 139 12816 1100 200 135 180 172 139 139 135

17 1060 200 9S 180 171 139 139 136

18 1100 200 135 180 172 139 139 13519 1300 200 55 180 181 137 137 138 138 13420 1400 200 155 180 188 140 140 140 133 12421 1650 200 80 180 185 140 140 140 131 139 140 90 85

22 1750 200 70 180 185 140 140 140 140 142 140 86 81 106

23 1850 200 170 180 185 140 140 140 140 140 140 82 86 10724 1920 200 150 180 185 140 140 140 140 140 140 91 91 106 77

Lb and x/s are in MW

160

loading schedules have been developed using reloading steps of 1 MW and 5

MW. In an actual system, other reloading steps should be tried to meet the

specific needs of the system in terms of operating economy and computation

time.

161

8. APPLICATION TO RELIABILITYTEST SYSTEMS

8.1. Introduction

The application of the 'Two Risks Concept' and the related computer

programs developed to assess the spinning reserve and unit commitment in

interconnected systems have been tested using selected reliability test sys­

tems. The IEEE - Reliability Test System has been used extensively to

compare the capabilities of computer programs used in reliability studies.

The IEEE-RTS represents a reasonably large power system. The size of the"

IEEE-RTS makes it difficult to obtain a direct appreciation of the various

steps involved in the computational process and the effectiveness of various

assumptions. A small test system designated as the Roy Billinton Test Sys­

tem (RBTS) [44] has also been used for many years by the Power Systems

Research Group at the University of Saskatchewan to test a wide variety of

computer programs for reliability studies. The IEEE-RTS and RBTS have

been used to assess the spinning reserve and unit commitment requirements

in interconnected systems and the results are presented in this chapter. Nei­

ther reliability test systems contains complete data for conducting spinning

reserve studies in an interconnection mode. The missing data have been as­

sumed wherever required.

..

The specified SSR and ISR have been taken as 0.01 and 0.0001 respec­

tively in all cases. The lead time in each interconnected system is assumed

to be 120 minutes. The results presented in this chapter utilise the main

concepts developed and illustrated in the previous chapters.

162

8.2. Applieation to the Roy Billinton Test System

(RBTS)

The RBTS has 11 generating units of which 7 are hydro units ranging

from 5 MW to 40 MW. The hydro units can be started, synchronised and

loaded up to the full output capacity in 5 minutes. The annual peak load

of the RBTS is 185 MW. The generating units in the RBTS and the cor­

responding running cost data are shown in Table 8.1. It is assumed that

two identical RBTS are interconnected radially through a tie line with a

maximum power transfer capability of 30 MW. The tie line failure is con­

sidered to be one per year. The two RBTS have been designated as

RBTS-1 and RBTS-2-. Table 8.2 shows the units that the two RBTS must

commit to satisfy a SSR of 0.01 and an ISR of 0.0001. The corresponding

spinning reserve can be found by subtracting load in columns 1 and 2 from

the respective total spinning capacity in columns 9 and 10. The load in

RBTS-1 is varied from 110 MW to 185 MW in steps of 5 MW while the

load in RBTS-2 is kept constant at 100 MW. Columns 11 and 12 show the

unit commitment risk at the interconnected level.

Table 8.3 shows the units that must be committed in RBTS-1 and

RBTS-2 when the forecast load has an uncertainty of 4% of the forecast

mean. The load in each system has been assumed to be normally dis­

tributed and the distribution has been approximated by seven discrete steps

as noted in Section 3.7 of Chapter 3. Table 8.4 shows the units that must

be committed in each RBTS when the load forecast uncertainty is 4% of the

forecast mean but the load distribution has been approximated by three dis­

crete steps as noted in Section 3.7 of Chapter 3.

The level of potential assistance with respect to spinning reserve

decreases when part of the tie-capacity is set aside for export/import. Table

8.5 shows the unit commitment in RBTS-1 and RBTS-2 with export/importwhen the export IS backed up by the entire system of the exporting utility.

Table 8.5 shows that the RBTS-1 and RBTS-2 must commit 6 and 7 units

Table 8.1: RBTS Generating Units and Cost Data.

Unit Unit Priority Failure Running Cost Cold Maximum Minimum ResponseSize Type Loading Rate Parameter Start-up Output Output Rate

(MW) Order (f/yr) a· b. c· Cost($) (MW) (MW) (MW/min)1 1 1

40 hydro 1 3.0 0 0.50 0.0 0 40 0 8

20 hydro 2 2.4 0 0.50 0.0 0 20 0 4

20 hydro 3 2.4 0 0.50 0.0 0 20 0 4

40 thermal 4 6.0 26 12.00 0.01 70 40 10 2

40 thermal 5 6.0 28 12.00 0.01 75 40 10 2

20 thermal 6 5.0 16 12.25 0.02 36 20 5 1

10 thermal 7 4.0 14 12.50 0.02 30 10 3 1

20 hydro 8 2.4 0 0.50 0.0 0 20 0 4

20 hydro 9 2.4 0 0.50 0.0 0 20 0 4t-'0)w

5 hydro 10 2.0 0 0.50 0.0 0 5 0 1

5 hydro 11 2.0 0 0.50 0.0 ·0 5 0 1

.J"�

--.- ..... _.

Table 8.2: Unit Commitment in the RBTS.

Single System Interconnected System

Load No. of Capacity No. of Capacity ISR

(MW) Units (MW) Units (MW)

1 2 1 2 1 2 1 2 1 2 1 2

110 100 4 4 120 120 5 4 160 120 0.00000010 0.00000042

115 100 4 4 120 120 5 4 160 120 0.00000010 0.00000042

120 100 5 4 160 120 5 4 160 120 0.00000060 0.00000059

125 100 5 4 160 120 5 4 160 120 0.00000060 0.00000059

130 100 5 4 160 120 5 4 160 120 0.00000061 0.00000059

135 100 5 4 160 120 5 4 160 120 0.00000061 0.00000059

140 100 5 4 160 120 6, 4 180 120 0.00000071 0.00000065 I-'0)

145 100 5 4 160 120 6 4 180 120 0.00000071 0.00000065�

150 100 5 '4 160 120 6 4 180 120 0.00000072 0.00000065

155 100 5 4 160 120 6 4 180 120 0.00000073 0.00000065

160 100 6 4 180 120 7 4 190 120 0.00000081 0.00000071

165 100 6 4 180 120 7 4 190 120 0.00000082 0.00000071

170 100 6 4 180 120 8 4 210 120 0.00000157 0.00000069

175 100 6 4 180 120 8 4 210 120 0.00000157 0.00000069

180 100 7 4 190 120 8 4 210 120 0.00000191 0.00000074

185 100 7 4 190 120 8 4 210 120 0.00000212 0.00000074

•

Table 8.3: Unit Commitment in the RBTS With Load Forecast

Uncertainty (Seven-step approximation of the load

distribution) .

Single System Interconnected System

Load No. of Capacity No. of Capacity ISR

(MW) Units (MW) Units (MW)

1 2 1 2 1 2 1 2 1 2 1 2

110 100 4 4 120 120 5 4 160 120 0.00000011 0.00000243

115 100 5 4 160 120 5 4 160 120 0.00000017 0.00000246

120 100 5 4 160 120 5 4 160 120 0.00000086 0.00000264

125 100 5 4 160 120 5 4 160 120 0.00000607 0.00000523

130 100 5 4 160 120 5 4 160 120 0.00003839 0.00002381

135 100 5 4 160 120 6 4 180 120 0.00000029 0.00000249

140 100 5 4 160 120 6 4 180 120 0.00000175 0.00000318

145 100 5 4 160 120 6 4 180 120 0.00001448 0.00001031

150 100 6 4 180 120 6 4 180 120 0.00007212 0.00004404

155 100 6 4 180 120 7 4 190 120 0.00001450 0.00001033

160 100 6 4 180 120 7 4 190 120 0.00007215 0.00004405

165 100 6 4 180 120 8 4 210 120 0.00000104 0.00000262

170 100 7 4 190 120 8 4 210 120 0.00000618 0.00000526

175 100 7 4 190 120 8 4 210 120 0.00002483 0.00001591

180 100 8 4 210 120 8 4 210 120 0.00008561 0.00004915

185 100 8 4 210 120 9 4 230 120 0.00002116 0.00000318

I-'

O'lCon

Table 8.4: Unit Commitment in the RBTS With Load Forecast

Uncertainty (Three-step approximation of the load

distribution) .

Single System Interconnected System

Load No. of Capacity No. of Capacity ISR

(MW) Units (MW) Units (MW),

1 2 1 2 1 2 1 2 1 2 1 2

110 100 4 4 120 120 5 4 160 120 0.00000010 0.00000040

115 100 5 4 160 120 5 4 160 120 0.00000019 0.00000044

120 100 5 4 160 120 5 4 160 120 0.00000050 0.00000052

125 100 5 4 160 120 5 4 160 120 0.00001486 0.00000914

130 100 5 4 160 120 5 4 160 120 0.00007676 0.00004621

135 100 5 4 160 120 6 4 180 120 0.00000021 0.00000045

140 100 5 4 160 120 6 4 180 120 0.00000058 0.00000057

145 100 5 4 160 120 6 4 180 120 0.00001494 0.00000919

150 100 6 4 180 120 6 4 180 120 0.00007690 0.00004626

155 100 6 4 180 120 7 4 190 120 0.00001496 0.00000920

160 100 6 4 180 120 7 4 190 120 0.00007696 0.00004630

165 100 6 4 180 120 8 4 210 120 0.00000045 0.00000047

170 100 7 4 190 120 8 4 210 120 0.00001573 0.00000921

175 100 7 4 190 120 8 4 210 120 0.00001578 0.00000923

180 100 8 4 210 120 8 4 210 120 0.00008724 0.00004635

.......0)0)

167

Table 8.5: Unit Commitment in the RBTS With Export/Import(Export is backed up by the entire exportingsystem).

Load Export Import No. of ISR

(MW) (MW) (MW) Units1 2 1 2 1 2 1 2 1 2

150 160 0 0 0 0 6 7 0.00000096 0.00000097150 160 10 0 0 10 7 6 0.00000183 0.00000175160 160 0 0 0 0 7 7 0.00000097 0.00000097160 160 15 0 0 15 8 6 0.00006148 0.00000152170 160 0 0 0 0 8 7 0.00000133 0.00000075170 160 0 10 10 0 7 8 0.00000162 0.00000181180 160 0 0 0 0 8 6 0.00000217 0.00000217180 160 0 15 15 0 8 8 0.00000150 0.00006148

respectively to carry a load of 150 MW in RBTS-l and 160 MW in RBTS-2

with zero export/import. The units that must be committed in each RBTS

changes to 7 units for RBTS-l and 6 units for RBTS-2 for an export of

10 MW by RBTS-l to RBTS-2. Table 8.6 shows the unit commitment when

the export is backed up by the first unit in the exporting system. The unit

backing up the export is a 40 MW thermal unit. This unit has a must run

status as long as it is available for service.

Table 8.6: Unit Commitment in the RBTS With Export/Import(Export is backed up by a Specific Unit).

Load Export Import No. of ISR

(MW) (MW) (MW) Units1 2 1 2 1 2 1 2 1 2

150 160 0 0 0 0 6 7 0.00000096 0.00000097150 160 10 0 0 10 7 6 0.00000137 0.00000181160 160 0 0 0 0 7 7 0.00000097 0.00000097160 160 15 0 0 15 8 6 0.00003167 0.00000152170 160 0 0 0 0 8 7 0.00000133 0.00000075170 160 0 10 10 0 7 8 0.00000169 0.00000158180 160 0 0 0 0 8 6 0.00000217 0.00000211180 160 0 15 15 0 8 8 0.00000166 0.00003168

168

The presence of interruptible loads can reduce the unit commitment

risk for a particular system load level and a given set of generation. The

ability of a system to interrupt load can be considered as the ability to

bring in ready reserve into the system depending upon the allowable time

delay of such load interruption. Table 8.7 shows the units that must be

committed in RBTS-1 and RBTS-2 when both systems have the ability to

interrupt 10 MW of their load within a time delay of 10 minutes. An inter­

connected generation system can carry some additional load/interruptible load

on top of its firm load without having to modify its unit commitment or

that of its neighbours from the commitments required to carry the respectivefirm loads. This capability, however, depends on the firm load and unit

commitment in all the member systems and the available assistance from the

neighbouring systems. In order to carry a load of 150 MW in RBTS-l and

180 MW in RBTS-2, RBTS-l and RBTS-2 must commit 6 and 9 generatingunits respectively from their priority loading order list. The additional

load/interruptible load carrying capability of RBTS-2 on top of its firm load

of 180 MW is shown in Figure 8.1. The corresponding additional load in

RBTS-l is assumed to be zero. The additional load carrying capability of

RBTS-2 will change for a corresponding change In the additional

load/interruptible load in RBTS-l.

Generating units in a system are usually committed on a continuous

basis during a scheduling period depending upon the forecast load and

economic factors. In order to have two different load profiles in the two in-•

terconnected systems, the percentiles of the hourly peak load on Tuesday and

Monday during the week #51 of the IEEE-RTS load model have been used

to provide the load profiles over a 24 hour period in RBTS-l and RBTS-2

respectively. The annual peak load for the RBTS is 185 MW. The hourly

peak load variations in a 24 hour period in both RBTS-l and RBTS-2 are

given in Table 8.8. The unit commitment and spinning reserve in both

RBTS-l and RBTS-2 during this 24 hour scheduling period are shown in

Table 8.9. Table 8.10 shows for comparison purposes, the unit commitment

Table 8.7: Unit Commitment in the RBTS With InterruptibleLoad.

Single System Interconnected System

Load No. of Capacity No. of Capacity ISR

(MW) Units (MW) Units (MW)

1 2 1 2 1 2 1 2 1 2 1 2

110 100 4 4 120 120 5 4 160 120 0.00000010 0.00000029

115 100 4 4 120 120 5 4 160 120 0.00000010 0.00000029

120 100 5 4 160 120 5 4 160 120 0.00000051 0.00000046

125 100 5 4 160 120 5 4 160 120 0.00000051 0.00000046

130 100 5 4 160 120 5 4 160 120 0.00000060 0.00000046

135 100 5 4 160 120 5 4 160 120 0.00000060 0.00000046

140 100 5 4 160 120 6 4 180 120 0.00000062 0.00000052

145 100 5 4 160 120 6 4 180 120 0.00000062 0.00000052

150 100 5 4 160 120 6 4 180 120 0.00000071 0.00000052

155 100 5 4 160 120 6 4 180 120 0.00000071 0.00000052

160 100 6 4 180 120 7 4 190 120 0.00000080 0.00000057

165 100 6 4 180 120 7 4 190 120 0.00000080 0.00000057

170 100 6 4 180 120 8 4 210 120 0.00000078 0.00000055

175 100 6 4 180 120 8 4 210 120 0.00000078 0.00000055

180 100 7 4 190 120 8 4 210 120 0.00000165 0.00000060

185 100 7 4 190 120 8 4 210 120 0.00000165 0.00000060

-

(;r)�

170

40,_------------------------------------------�

r.""

20

fIRM LOAD IN RBTS-] - 150 M�fIRM LOAD IN RBTS-2 - 180 MW

.......................................... -

-_

............................................

ii•

30

10

04---------�--------------------------------�

70 80 90 100 110 120

Lead TIme in mins

Figure 8.1: Additional Load Carrying Capability of RBTS-2.

schedule for both RBTS-1 and RBTS-2 with no interconnection between

them. Both systems are required to satisfy a unit commitment risk of

0.0001 which is equal to the specified ISR. RBTS-1 is unable to satisfy its

unit commitment risk in absence of interconnection during the hours of 17,

18 and 19 after committing all 11 available units. The overall spinning

reserve requirements in both RBTS-1 and RBTS-2 are higher in the case of

no interconnection than those with interconnection.

The conventional economic load dispatch may not provide sufficient

response reserve on the generating units. A reliable load dispatch should be

such that an adequate 1 minute and 5 minute regulating margin exists. The

1 minute regulating reserve requirement can be determined by dynamic and

171

Table 8.8: Peak Load Variations of RBTS in a 24 Hour Period.

Hour Lt(MW) L2(MW)

1 124 1152 117 1093 111 1034 110 1015 110 1016 111 1037 137 1278 159 1489 176 164

10 178 16611 178 16612 176 16413 176 16414 176 16415 172 16016 174 16217 183 17018 185 17219 185 17220 178 16621 168 15622 154 143

23 135 12624 117 109

. transient stability studies. Hydro and rapid start gas turbine and gas en­

gines can be considered as part of the 5 minute response reserve because of

their relatively short lead time (in the order of 5 minutes). Tables 8.11 and

8.12 show the modified economic load dispatch in RBTS-l and RBTS-2. It is

interesting to note that the load dispatch shown in Tables 8.11 and 8.12

satisfy the 5 minute response criterion without any load adjustments. The

SSRR and ISRR are chosen as 0.01 and 0.0001 respectively. Both RBTS

have a significant number of hydro units compared to their thermal units.

Some of these hydro units are left as ready reserve which provides additional

5 minute response reserve on top of the on-line response reserve. The trans­

mission and tie-line losses have been neglected and all hydro units have been

considered as run of the river units without any energy constraints.

172

Table 8.9: Unit Commitment in the RBTS (24 hours schedulingperiod).

Hour RBTS-1 RBTS-2

Ll No. of Spinning L2 No.of Spinning(MW) Units Reserve(MW) (MW) Units Reserve(MW)

1 124 5 36 115 5 45

2 117 5 43 109 4 11

3 111 5 49 103 4 17

4 110 5 50 101 4 19

5 110 5 50 101 4 19

6 111 5 49 103 4 17

7 137 5 23 127 5 33

8 159 6 21 148 6 32

9 176 8 34 164 7 26

10 178 8 32 166 7 24

11 178 8 32 166 7 24

12 176 8 34 164 7 26

13 176 8 34 164 7 26

14 176 8 34 164 7 26

15 172 8 38 160 7 30

16 174 8 36 162 7 28

17 183 8 27 170 7 20

18 185 9 45 172 7 18

19 185 9 45 172 7 18

20 178 8 32 166 7 24

21 168 7 22 156 6 24

22 154 6 26 143 5 17

23 135 5 25 126 5 34

24 117 5 43 109 4 11

8.3. Application to the IEEE-RTS

The IEEE-RTS has 32 generating units rangmg from sizes of 12 MW

to 400 MW. Among the units there are 6 x 50 MW hydro units and

2x400 MW nuclear units. Nuclear units are considered to operate as base

load units and load fluctuations are not taken up by the nuclear units. The

response rate of the nuclear units of the IEEE-RTS within the margin time

of 5 minutes is considered to be zero for all practical purposes. Two iden-

173

Table 8.10: Unit Commitment in the RBTS Without Intercon­nection (24 hours scheduling period).

Hour RBTS-2RBTS-1

No. of SpinningUnits Reserve(MW)

No.of

UnitsSpinning

Reserve(MW)

1

23

4

5

67

89

10

11

121314

1516

1718

19

2021222324

124117111

110

110111137159176178178176176176

172174183185

185178168154

135117

6

5555

5

689

9

9

99999*

*

*

56

434950

50494351

54

52525454

545856**

**

**

115109

103101101103

127148

164166166164164164

160162170172172166156143126109

5

55

5

55

67

8

88

8888

89

9988

7

65

455157

59595753424644

44

46464650

48605858

44

544754

51

9

8865

524256

4543

tical IEEE-RTS have been considered to be interconnected through three tie

lines. Each of the three tie lines can transfer up to 100 MW on average.

The failure rate of each tie line is one failure per year. Two of 6x50 MW

hydro units are placed at the end of the loading order priority list in each

IEEE-RTS. The lead times of all hydro units are considered to be 5

minutes.

Studies similar to those conducted for the RBTS have been done for

the IEEE-RTS. The generating unit data of each IEEE-RTS are shown in

174

Table 8.11: Risk Constrained Economic Load Dispatch in the

RBTS-1 (Reloading step = 5 MW).

Load

(MW)Individual Unit Outputs

(MW)

Hour L1

67

89

10

11

12

13

14

15

1617

18

1920

2122

23

24

1234

124117

2020

20

2020202020

2020

20202020202020

202020202020202020

2219

16

15

1516

29

34

3232

3232

32

3230

313428

2832

3632

28

19

22181515

15152834

32323232323230

313427273236322718

119

10

10999

9

911

77

101110

34

4

3333

343345

202020

2020

20202020202020

20

20

4040

5

111 40 20

110 40 20

110 40 20111 40 20137 40 20159 40 20

176 40 20178 40 20178 40 20

176 40 20

176 40 20

176 40 20172 40 20174 40 20183 40 20

185 40 20

185 40 20178 40 20168 40 20154 40 20135 40 20

117 40 20

Table 8.13. The runnmg cost of each generating unit is estimated by a

second degree polynomial using the heat rates provided [33] at different out­

put levels of the unit. Table 8.14 shows the running cost and the cold

start-up cost of each unit. The two IEEE-RTS have been designated as

IEEE-RTS-1 and IEEE-RTS-2 for the sake of clarity.

Table 8.15 shows the units that must be committed in each IEEE-RTS

for the corresponding loads in columns 1 and 2. The load in IEEE-RTS-2 is

varied from 2100 MW to 2850 MW while the load in IEEE-RTS-l is held

175

Table 8.12: Risk Constrained Economic Load Dispatch ill theRBTS-2 (Reloading step = 5 MW).

Load Individual Unit Outputs(MW) (MW)

Hour 12 xl X2 X3 X4 X5 x6 x1 x8 Xg xlO

1 115 40 20 20 18 172 109 40 20 20 29

3 103· 40 20 20 23

4 101 40 20 20 21

5 101 40 20 20 216 103 40 20 20 237 127 40 20 20 24 238 148 40 20 20 30 30 89 164 40 20 20 34 34 11 5

10 166 40 20 20 35 35 11 5

11 166 40 20 20 35 35 11 512 164 40 20 20 34 34 11 513 164 40 20 20 34 34 11 514 164 40 20 20 34 34 11 515 160 40 20 20 33 33 10 4

16 162 40 20 20 34 34 10 4

17 170 40 20 20 36 36 12 6

18 172 40 20 20 37 37 12 6

19 172 40 20 20 37 37 12 6

20 166 40 20 20 35 35 11 5

21 156 40 20 20 33 33 1022 143 40 20 20 32 3123 126 40 20 20 23 2324 109 40 20 20 29

Table 8.13: Generating Units in the IEEE-RTS.

Unit Unit No. of Priority Failure Maximum Minimum ResponseSize Type Units Loading Rate Output Output Rate

(MW) Order (f/yr) (MW) (MW) (MW/min)

50 hydro 6 1-4,31-32 4.42 50 0 10

400 nuclear 2 5-6 7.96 400 200 �O

350 thermal 1 7 7.62 350 150 9

197 thermal 3 8-10 9.22 197 80 6

155 thermal 4 11-14 9.13 155 60 5

100 thermal 3 15-17 7.30 100 40 3

76 thermal 4 18-21 4.47 76 25 2

12 thermal 5 22-26 2.98 12 5 1

20 thermal 4 27-30 19.47 20 6I-'

4 -1Q)

Table 8.14: IEEE-RTS Cost Data.

Unit Unit No. of Priority Running Cost Cold

Size Type Units Loading Parameter Start-up(MW) Order a· b· c· Cost($)I I I

50 hydro 6 1-4,31-32 0.0 0.5 0.0 0

400 nuclear 2 5-6 216.57585 5.34515 0.00028 800

350 thermal 1 7 388.25027 8.91965 0.00392 300

197 thermal 3 8-10 301.22318 20.02271 0.003 150

155 thermal 4 11-14 206.70340 9.27063 0.00667 100

100 thermal 3 15-17 286.24109 17.92387 0.02203 80

76 thermal 4 18-21 100.43962 12.14489 0.01131 60

12 thermal 5 22-26 30.39611 23.27773 0.13733 15

20 thermal 4 27-30 40.0 37.55452 0.18256 30......-...:t-...:t

178

constant at 2100 MW. The number of units that must be committed in

IEEE-RTS-1 varies between 12 and 13 although its load is at a constant

level. This is due to the reason that the independence of a system from the

operating variations of another system is lost when these systems are inter­

connected with the objective of assisting each other with respect to spinning

reserves. This phenomenon is explained in detail in Section 3.4 of Chapter

3. The unit commitment with load forecast error is shown in Tables 8.16

and 8.17. All the load levels in Table 8.16 have a load forecast uncertainty

of 4% of the forecast mean and the load distribution is approximated by

seven discrete steps. The unit commitment and corresponding risk using the

three-step approximation to the load distribution is shown in Table 8.17.

The unit commitment risks have also been assessed with export/importbetween two interconnected IEEE-RTS. Table 8.18 shows the units that

must be committed in each IEEE-RTS and the corresponding unit commit­

ment risk if the export is backed up by the entire exporting system. The

unit commitment and the corresponding risk with export backed up by a

specific unit in the exporting system is shown in Table 8.19. The unit that

is backing up the export in the IEEE-RTS is a hydro unit of 50 MW size.

This is a must run unit. Any unit can be used to back up the export.

The unit which backs up the export will have a must run status.

The presence of interruptible load can reduce the unit commitment risk

of a system. Load curtailment, however, should only be considered in the

absence of other economic capacity adjustments. Table 8.20 shows the unit

commitment in IEEE-RTS-1 and IEEE-RTS-2 when both IEEE-RTS have an

interruptible load of 70 MW with a lead time of 10 minutes. It can be seen

from Tables 8.15 and 8.20 that the unit commitments in both IEEE-RTS

with the 70 MW interruptible load are identical to those without the inter­

ruptible load except when the load in IEEE-RTS-2 is 2250 and 2750 MW.

The ISR in both IEEE-RTS is reduced in the presence of the 70 MW inter­

ruptible load in both systems for the same load and unit commitment situa-

Table 8.15: Unit Commitment in the. IEEE-RTS.

Single System Interconnected System

Load No. of Capacity No. of Capacity ISR

(MW).

Units (MW) Units (MW)

1 2 1 2 1 2 1 2 1 2 1 2

2100 2100 12 12 2251 2251 13 13 2406 2406 0.00001039 0.00001039

2100 2150 12 12 2251 2251 12 13 2251 2406 0.00007758 0.00003139

2100 2200 12 13 2251 2406 13 13 2406 2406 0.00001111 0.00003717

2100 2250 12 13 2251 2406 12 14 2251 2561 0.00007735 0.00001165

2100 2300 12 13 2251 2406 12 14 2251 2561 0.00007778 0.00003168

2100 2350 12 14 2251 2561 13 14 2406 2561 0.00001117 0.00003742

2100 2400 12 14 2251 2561 12 15 2251 2661 0.00007791 0.00003189

2100 2450 12 14 2251 2561 13 15 2406 2661 0.00001118 0.00003753

2100 2500 12 15 2251 2661 12 16 2251 2761 0.00007805 0.00003211

2100 2550 12 15 2251 2661 13 16 2406 2761 0.00001118 0.00003764

2100 2600 12 16 2251 2761 12 17 2251 2861 0.00007819 0.00003232

2100 2650 12 16 2251 2761 13 17 2406 2861 0.00001118 0.00003775

2100 2700 12 17 2251 2861 13 18 2406 2937 0.00001118 0.00003778

2100 2750 12 17 2251 2861 12 19 2251 3013 0.00007835 0.00003258

2100 2800 12 18 2251 2937 13 19 2406 3013 0.00001118 0.00003789

2100 2850 12 19 2251 3013 13 20 2406 3089 0.00001112 0.00003773

•

....-1<0

Table 8.16: Unit Commitment in the IEEE-RTS With LoadForecast Uncertainty (Seven-step approximation ofthe load distribution).

Single System Interconnected System

Load No. of Capacity No. of Capacity ISR

(MW) Units (MW) Units (MW)

1 2 i 2 1 2 1 2 1 2 1 2

2100 2100 13 13 2406 2406 13 13 2406 2406 0.00003071 0.00003071

2100 2150 13 13 2406 2406 13 13 2406 2406 0.00005779 0.00009311

2100 2200 13 13 2406 2406 13 14 2406 2561 0.00002031 0.00001470

2100 2250 13 14 2406 2561 13 14 2406 2561 0.00003181 0.00003156

2100 2300 13 14 2406 2561 13 14 2406 2561 0.00005796 0.00009179

2100 2350 13 14 2406 2561 13 15 2406 2661 0.00003370 0.00003374

2100 2400 13 15 2406 2661 13 15 2406 2661 0.00006336 0.00009349

2100 2450 13 15 2406 2661 13 16 2406 2761 0.00003393 0.00003404

2100 2500 13 16 2406. 2761 13 17 2406 2861 0.00002740 0.00002130

2100 2550 13 16 2406 2761 13 17 2406 2861 0.00003609 0.00003719

2100 2600 13 17 2406 2861 13 18 2406 2937 0.00003065 0.00003190

2100 2650 13 18 2406 2937 13 18 2406 2937 0.00004721 0.00008073

2100 2700 13 18 2406 2937 13 19 2406 3013 0.00003635 0.00006677

2100 2750 13 19 2406 3013 13 20 2406 3089 0.00003300 0.00003408

2100 2800 13 20 2406 3089 13 20 2406 3089 0.00005616 0.00008965

2100 2850 13 20 2406 3089 13 21 2406 3165 0.00004588 0.00006940

�00o

Table 8.17: Unit Commitment in the IEEE-RTS With Load

Forecast Uncertainty (Three-step approximation ofthe load distribution).

Single System Interconnected System

Load No. of Capacity No. of Capacity ISR

(MW) Units (MW) Units (MW)

1 2 1 2 1 2 1 2 1 2 1 2

2100 2100 13 13 2406 2406 13 13 2406 2406 0.00002935 0.00002935

2100 2150 13 13 2406 2406 13 13 2406 2406 0.00006866 0.00008837

2100 2200 13 13 2406 2406 13 14 2406 2561 0.00002883 0.00002090

2100 2250 13 14 2406 2561 13 14 2406 2561 0.00002962 0.00003069

2100 2300 13 14 2406 2561 13 14 2406 2561 0.00006658 0.00008550

2100 2350 13 14 2406 2561 13 15 2406 2661 0.00002987 0.00003123

2100 2400 13 15 2406 2661 13 15 2406 2661 0.00006696 0.00008689

2100 2450 13 15 2406 2661 13 16 2406 2761 0.00003004 0.00003146

2100 2500 13 16 2406 2761 13 17 2406 2861 0.00002993 0.00002211

2100 2550 13 16 2406 2761 13 17 2406 2861 0.00003148 0.00003299

2100 2600 13 17 2406 2861 13 18 2406 2937 0.00003017 0.00003142

2100 2650 13 18 2406 2937 13 18 2406 2937 0.00005079 0.00007310

2100 2700 13 18 2406 2937 13 19 2406 3013 0.00003174 0.00005902

2100 2750 13 19 2406 3013 13 20 2406 3089 0.00003045 0.00003200

2100 2800 13 20 2406 3089 13 20 2406 3089 0.00005102 0.00007431

2100 2850 13 20 2406 3089 13 21 2406 3165 0.00005087 0.00006421

.....00.....

182

Table 8.18: Unit Commitment III the IEEE-RTS With

Export / Import (Export is backed up by the entire

exporting system).

Load Export Import No. of ISR

(MW) (MW) (MW) Units1 2 1 2 1 2 1 2 1 2

2400 2100 0 0 0 0 15 12 0.00003189 0.000077912400 2100 30 0 0 30 15 12 0.00004157 0.000077872450 2100 0 0 0 0 15 13 0.00003753 0.000011182450 2100 40 0 0 40 16 12 0.00003153 0.000077402500 2100 0 0 0 0 16 12 0.00003211 0.000078052500 2100 0 30 30 0 15 13 0.00006346 0.00003144

2550 2100 0 0 0 0 16 13 0.00003764 0.000011182550 2100 0 40 40 0 16 13 0.00003142 0.00003088

Table 8.19: Unit Commitment in the IEEE-RTS With

Export /Import (Export is backed up by a specificunit).

Load Export Import No. of ISR

(MW) (MW) (MW) Units1 2 1 2 1 2 1 2 1 2

2400 2100 0 0 0 0 15 12 0.00003189 0.000077912400 2100 30 0 0 30 15 12 0.00004159 0.000077902450 2100 0 0 0 0 15 13 0.00003753 0.000011182450 2100 40 0 0 40 16 12 0.00003150 0.000077402500 2100 0 0 0 0 16 12 0.00003211 0.000078052500 2100 0 30 30 0 15 13 0.00006350 0.000031402550 2100 0 0 0 0 16 13 0.00003764 0.000011182550 2100 0 40 40 0 16 13 0.00003145 0.00003085

•

Table 8.20: Unit Commitment in the IEEE-RTS with Interrupt­ible Load.

Single System Interconnected System

Load No. of Capacity No. of Capacity ISR

(MW) Units (MW) Units (MW)

1 2 1 2 1 2 1 2 1 2 1 2

2100 2100 12 12 2251 2251 13 13 2406 2406 0.00000378 0.00000378

2100 2150 12 12 2251 2251 12 13 2251 2406 0.00003722 0.00001112

2100 2200 12 12 2251 2251 13 13 2406 2406 0.00000425 0.00001100

2100 2250 12 13 2251 2406 13 13 2406 2406 0.00000430 0.00001171

2100 2300 12 13 2251 2406 12 14 2251 2561 0.00002528 0.00001130

2100 2350 12 13 2251 2406 13 14 2406 2561 0.00000426 0.00001116

2100 2400 12 14 2251 2561 12 15 2251 2661 0.00002532 0.00001136

2100 2450 12 14 2251 2561 13 15 2406 2661 0.00000426 0.00001122

2100 2500 12 14 2251 2561 12 16 2251 2761 0.00002536 0.00001143

2100 2550 12 15 2251 2661 13 16 2406 2761 0.00000426 0.00001128

2100 2600 12 15 2251 2661 12 17 2251 2861 0.00002540 0.00001149

2100 2650 12 16 2251 2761 13 17 2406 2861 0.00000426 0.00001134

2100 2700 12 16 2251 2761 13 18 2406 2937 0.00000426 0.00001086

2100 2750 12 17 2251 2861 13 18 2406 2937 0.00000439 0.00001194

2100 2800 12 17 2251 2861 13 19 2406 3013 0.00000426 0.00001137

2100 2850 12 18 2251 2937 13 20 2406 3089 0.00000426 0.00001086

�00w

184

tion. It is noted in Chapter 5, that an interconnected system can carry an

additional load/interruptible load on top of its firm load without having to

commit any additional capacity than that required to carry the firm load

and still maintaining the risk criteria. This can de illustrated by an ex­

ample. Consider a firm load of 2040 MW in IEEE-RTS-1 and 2520 MW in

IEEE-RTS-2. IEEE-RTS-1 and IEEE-RTS-2 must commit 12 and 16 units

respectively from their loading order priority" list. If the firm load and unit

commitment in each system is unchanged then IEEE-RTS-2 can carry an ad­

ditional load of up to 50 MW given that the additional load in IEEE-RTS-1

is zero. The additional load carrying capability of IEEE-RTS-2 reduces to a

maximum of 40 MW if IEEE-RTS-1 carries an additional load of 10 MW.

This capability will change with any change in firm load or unit commit­

ment in anyone of the interconnected utilities.

The percentiles of hourly peak load variations in a 24 hour scheduling

period in each IEEE-RTS are identical to those considered for the RBTS.

The annual peak load of the IEEE-RTS is 2850 MW. The hourly peak load

variations in each IEEE-RTS during the specified 24 hour scheduling periodare shown in Table 8.2l. The unit commitment during the same 24 hour

scheduling period is shown in Table 8.22. This table also shows the number

of units that should be committed in each IEEE-RTS and the corresponding

hourly spinning reserve during the 24 hour scheduling period.reserve in IEEE-RTS-1 varies from 145 MW to 455 MW.

reserve in IEEE-RTS-1 during the peak load of 2850 MW IS

The spinningThe spinning

239 MW. The..

spinning reserve in IEEE-RTS-2 varies from 135 MW to 282 MW. Table

8.23 shows for comparison purposes, the unit commitment schedule for both

IEEE-RTS-1 and IEEE-RTS-2 with no interconnection between them. Both

systems are required to satisfy a unit commitment risk of 0.0001 which 1S

equal to the specified ISR. The overall spinning reserve requirements In

both IEEE-RTS-1 and IEEE-RTS-2 are higher in the case of no interconnec­

tion than those of with interconnection.

185

Table 8.21: Peak Load Variations of IEEE-RTS III a 24 HourPeriod.

Hour L1(MW) L2(MW)

1 1910 17762 1796 16703 1710 15904 1682 15645 1682 15646 1710 15907 2109 19618 2451 22799 2708 2518

10 2736 254411 2736 254412 2708 251813 2708 251814 2708 251815 2651 246516 2679 249117 2822 262418 2850 265119 2850 265120 2736 254421 2594 241222 2366 220023 2081 193524 1796 1670

Tables 8.24 and 8.25 show the economic load dispatch in IEEE-RTS-l

and IEEE-RTS-2 respectively for the 24 hour unit commitment shown in

Table 8.22. These economic load dispatches, however, do not satisfy the 5

minute response criterion. Risk constrained economic load dispatch has

been obtained for both IEEE-RTS assuming that all hydro units are run of

the river generating units without any energy constraints. The transmission

and tie-line losses have been neglected III determining the load dispatch. A

reloading step of 5 MW has been used to modify the economic load dispatchinto the risk constrained economic load dispatch. The risk constrained load

dispatch in IEEE-RTS-l is shown in Table 8.26. The corresponding dispatch

186

Table 8.22: Unit Commitment In the IEEE-RTS (24 hour

scheduling period) .

Hour IEEE-RTS-l IEEE-RTS-2

No. of SpinningUnits Reserve(MW)

No.of

UnitsSpinning

Reserve(MW)

1

23

45

678

9

10

11121314

15161718192021

222324

1910

179617101682

16821710210924512708273627362708270827082651267928222850

285027362594

236620811796

1212

1111

11

1113151818

1818181818

18192020

1816141310

1776167015901564

15641590196122792518

25442544251825182518

2465249126242651

265125442412220019351670

10109

999

11141616

1616161615

15171717

16151311

10

165271154

180180154

135282243

217217243

243243196170237

210210217249

206161271

341

455386414

414386297210229

201

201229229229286258

191239239201167195325145

In IEEE-RTS-2 IS shown In Table �.27. Generating units In each of the

IEEE-RTS have been dispatched such that the total spinning capacity In

each system has enough response reserve to satisfy the 5 minute regulating

margin. The running cost of each 50 MW hydro unit in the IEEE-RTS is

the lowest of all units. These hydro units are dispatched to their full out­

put level to obtain greater savings as shown in the economic load dispatchIn Tables 8.24 and 8.25. The response rate of these hydro units IS the

highest among units of the IEEE-RTS. In the risk constrained load dis­

patches shown in Tables 8.26 and 8.27 some of these hydro units are used

187

Table 8.23: Unit Commitment in the IEEE-RTS Without Inter-connection (24 hour scheduling period).

Hour IEEE-RTS-l IEEE-RTS-2

L1 No. of Spinning L2 No.of Spinning(MW) Units Reserve(MW) (MW) Units Reserve(MW)

1 1910 13 496 1776 12 4752 1796 12 455 1670 11 4263 1710 12 541 1590 11 5064 1682 11 414 1564 11 5325 1682 11 414 1564 11 5326 1710 12 541 1590 11 5067 2109 14 452 1961 13 4458 2451 17 410 2279 16 4829 2708 21 457 2518 18 419

10 2736 21 429 2544 19 46911 2736 21 429 2544 19 46912 2708 21 457 2518 18 41913 2708 21 457 2518 18 419

14 2708 21 457 2518 18 41915 2651 21 514 2465 18 47216 2679 21 486 2491 18 44617 2822 26 403 2624 20 46518 2850 28 415 2651 20 43819 2850 28 415 2651 20 43820 2736 21 429 2544 19 46921 2594 19 419 2412 17 44922 2366 17 495 2200 15 46123 2081 14 480 1935 13 47124 1796 12 455 1670 11 426

Table 8.24: Economic Load Dispatch in the IEEE-RTS-i.

Load

(MW)Individual Unit Outputs

(MW)

HourLl xl X2 X3 X4 X5 X6 X7 Xs X9 XlO Xu Xl2 X13 X14 X15 X16 Xl7 XIS X19 X20 X2l

11910 50

21796 50

31710 50

41682 50

51682 50

61710 50

72109 50

82451 50

92708 50

102736 50

112736 50122708 50

132708 50

142708 50

152651 50

162679 50

172822 50

182850 50

192850 50

202736 50212594 50

222366 50

232081 50

50 50

50 50

50 50

50 50

50 50

50 50

50 50

50 50

50 50

50 50

50 50

50 50

50 50

50 50

50 50

50 50

50 5050 50

50 50

50 50

50 50

50 50

50 50

50 400 400 350 84 83 83 155 155

50 400 400 280 80 80 80 138 138

50 400 400. 315 80 80 80 155

50 400 400 295 80 80 80 14750 400 400 295 80 80 80 14750 400 400 315 80 80 80 155

50 400 400 350 98 98 98 155 155 155

50 400 400 350 139 138 138 155 155 155 155 66

50 400 400 350 153 153 152 155 155 155 155 68

50 400 400 350 161 161 161 155 155 155 155 69

50 400 400 350 161 161 161 155 155 155 155 69

50 400 400 350 153 153 152 155 155 155 155 68

50 400 400 350 153 153 152 155 155 155 155 68

50 400 400 350 153 153 152 155 155 155 155 68

50 400 400 350 136 136 135 155 155 155 155 66

50 400 400 350 144 144 144 155 155 155 155. 67

50 400 400 350 164 163 163 155 155 155 155 70

50 400 400 350 150 149 149 155 155 155 155 68

50 400 400 350 150 149 149 155 155 155 155 68

50 400 400 350 161 161 161 155 155 155 155 69

50 400 400 350 161 161 162 155 155 155 155 70

50 400 400 350 132 132 132 155 155 155 155

50 400 400 350 89 89 88 155 155 155

241796 50 50 50 50 400 400 350 149 149 148

6869696868

6866677068

68

6970

68

69696868

6866

677068

68

69

767676767676767676767676

.....0000

767676

7676

Table 8.25: Economic Load Dispatch in the IEEE-RTS-2.

Load

(MW)Individual Unit Outputs

(MW)

HourL2 xl x2 X3 X4 X5 x6 X7 X8 X9 XlO Xu Xu Xl3 x14 Xl5 Xl6 Xl7 xl8 xl9 X20 X21

11776 50 50 50 50 400 400 350 142 142 14221670 50 50 50 50 400 400 350 107 107 10631590 50 50 50

41564 50 50 50

51564 50 50 5061590 50 50 5071961 50 50 50

82279 50 50 50

92518 50 50 50102544 50 50 50112544 50 50 50122518 50 50 50132518 50 50 50

142518 50 50 50152465 50 50 50162491 50 50 50172624 50 50 50182651 50 50 50192651 50 50 50

202544 50 50 50212412 50 50 50222200 50 50 50

231935 50 50 50241670 50 50 50

50 400 400 350 120 12050 400 400 350 107 10750 400 400 350 107 10750 400 400 350 120 12050 400 400 350 152 152 152 15550 400 400 350 103 103 103 155 155 155 15550 400 400 350 139 139 138 155 155 155 155 66 6650 400 400 350 146 146 146 155 155 155 155 68 6850 400 400 350 146 146 146 155 155 155 155 68 6850 400 400 .350 139 139 138 155 155 155 155 66 6650 400 400 350 139 139 138 155 155 155 155 66 6650 400 400 350 139 139 138 155 155 155 155 66 6650 400 400 350 143 143 142 155 155 155 155 6750 400 400 350 151 151 151 155 155 155 155 6850 400 400 350 150 150 150 155 155 155 155 68 68 6850 400 400 350 158 158 158 155 155 155 155 69 69 6950 400 400 350 158 158 158 155 155 155 155 69 69 6950 400 400 350 146 146 146 155 155 155 155 68 6850 400 400 350 126 126 125 155 155 155 155 6550 400 400 350 128 128 129 155 155 15550 400 400 350 144 143 143 15550 400 400 350 107 107 106

I-'00to

Table 8.26: Risk Constrained Economic Load Dispatch in theIEEE-RTS-1 (Reloading step = 5 MW).

Load

(MW)Individual Unit Outputs

(MW)

HourLl xl x2 x3 x4 Xs x6 x7 Xg Xg XIO xll x12 Xu Xu xIS x16 x17 xIS x19 x20 X21

11910 50 40

21796 0 0

31710 20 0

41682 0

51682 0

61710 20

72109 50

82451 50

92708 50

102736 50

112736 50

122708 50

132708 50

142708 50

152651 50

162679 50

172822 50

182850 50

192850 50

202736 50

212594 50

222366 50

o 0

o 0o 0

50 50

50 50

50 50

50 50

50 50

50 50

50 50

50 50

50 50

50 5050 50

50 50

50 50

50 50

50 50

50 50

o 50 400 400 305 84 163 158 130 130

o 20 400 400 280 105 165 160 133 133

o 50 400 400 305 80 165 160 130

40 400 400 295 90 165 160 132

40 400 400 295 90 165 160 132

50 400 400 305 80 165 160 130

50 400 400 310 98 153 153 130 130 135

50 400 400 350 139 138 148 155 155 150 150

50 400 400 350 153 153 152 155 155 155 155

50 400 400 350 161 161 161 155 155 155 155

50 400 400 350 161 161 161 155 155 155 155

50 400 400 350 153 153 152 155 155 155 155

50 400 400 350 153 153 152 155 155 155 155

50 400 400 350 153 153 152 155 155 155 155

50 400 400 350 136 136 150 155 155 130 135

50 400 400 350 144 144 144 155 155 145 15050 400 400 350 164 163 163 155 155 155 155

50 400 400 350 150 149 149 155 155 155 155

50 400 400 350 150 149 149 155 155 155 155

50 400 400 350 161 161 161 155 155 155 155

50 400 400 350 161 161 162 155 155 155 155

50 400 400 350 132 137 137 155 155 150 150

232081 50 50 30 50 400 400 305 89 159 158 130 130 130

241796 50 50 50 50 400 400 350 149 149 148

6668696968

6868

81

6770

6868

6970

686969

68

6868

81827073736970

6869

69686868767770686869

76767676767666

6676767676

I-'

8

76

7171

7676

Table 8.27: Risk Constrained Economic Load Dispatch in the

IEEE-RTS-2 (Reloading step = 5 MW).

Load

(MW)Individual Unit Outputs

(MW)

HourL2 xl X2 x3 X4 x5 x6 x7 Xs X9 xlO Xu X12 Xl3 X14 Xl5 Xl6 Xl7 XIS Xl9 X20 X21

11776 50 50 50

21670 50 50 10

31590 50 50 50

41564 50 50 50

51564 50 50 50

61590 50 50 50

71961 50 50 50

82279 50 50 50

92518 50 50 50

102544 50 50 50

112544 50 50 50

122518 50 50 50

132518 50 50 50

142518 50 50 50

152465 50 50 50

162491 50 50 50

172624 50 50 50

182651 50 50 50

50 400 400 350 142 142 142

50 400 400 305 107 147 151

50 400 400 350 120 120

50 400 400 325 122 11750 400 400 325 122 11750 400 400 350 120 120

50 400 400 350 152 152 152 15550 400 400 350 103 153 148 130 130 130 135

50 400 400 350 139 139 138 155 155 140 145

50 400 400 350 146 146 146 155 155 155 155

50 400 400 350 146 146 146 155 155 155 155

50 400 400 350 139 139 138 155 155 140 145

50 400 400 350 139 139 138 155 155 140 145

50 400 400 350 139 139 138 155 155 140 145

50 400 400 350 143 143 142 155 155 155 155

50 400 400 350 151 151 151 155 155 155 155

50 400 400 350 150 150 150 155 155 150 155

50 400 400 350 158 158 158 155 155 155 155

192651 50 50 50 50 400 400 350 158 158 158 155 155 155 155

202544 50 50 50 50 400 400 350 146 146 146 155 155 155 155

212412 50 50 50 50 400 400 350 126 126 165 155 155 130 135

222200 50 50 50 50 400 400 350 128 138 139 155 145 145

231935 50 50 50 50 400 400 350 144 143 143 155

241670 50 50 10 50 400 400 305 107 147 151

8168

688181816768

686969 6968 6870

7668

68767676

.....

!O.....

7369

68

6969

192

as response reserve unit whenever necessary. The running cost during the 24

hour period is $635,592.69 in IEEE-RTS-1 and $573,102.13 in IEEE-RTS-2

when the units are dispatched economically. The starting cost is $623.21 in

IEEE-RTS-1 and $766.29 in IEEE-RTS-2. During the 24 hour period the

reliability constrained economic dispatch require an addiitonal running cost of

$22,132.69 in IEEE-RTS-1 and $5,492.75 in IEEE-RTS-2 compared to the

respective economic load dispatch. The computation time required to modifythe economic load dispatch into the risk constrained economic load dispatchas shown in Tables 8.26 and 8.27 is 11.44 CPU seconds.

8.4. Summary

The unit commitment and spmnmg reserve assessment techniques based

on the 'Two Risks Concept' have been applied to two different reliability

test systems. The unit commitment and spinning reserves which satisfy the

two risk levels are presented in this chapter. The results of risk constrained

economic load dispatch in interconnected RBTS and IEEE-RTS are also dis­

cussed. The computer programs developed can also assess spinning reserve

and unit commitment risk in interconnected systems using other assumptionsthan those utilised in this chapter.

193

9. CONCLUSIONS

This thesis presents a new probabilistic technique to assess spmnmg

reserve requirements in interconnected systems. The technique is based on

the fulfilment of two specified risk levels in each interconnected system. An

interconnected system must satisfy the single system risk (SSR) at the ISO­

lated level and also the interconnected system risk (ISR) at the intercon­

nected level. The philosophy behind the new technique is designated as the

'Two Risks Concept'. The basic principles of the 'Two Risks Concept' are

developed and discussed in detail in Chapter 3. Spinning reserve assessment

involving the 'Two Risks Concept' utilises the essential stochastic parameters

of the generating units and tie lines which influence the system reliability.

The proposed technique uses conventional generating unit models. Improvedmodels for generating units and tie lines can, however, be readily incor­

porated into the computational process of the new technique. Rapid start

and hot reserve units can be included in the assessment of unit commitment

risk. The area risk curve technique has been extended to include rapid start

and hot reserve units into the spinning reserve and unit commitment risk as­

sessment process. The matrix multiplication technique has been used to

determine the transient probabilities of rapid start and hot reserve units.

In the 'Two Risks Concept', the unit commitment and spinning reserve

In one system is affected by the unit commitment and spinning reserve of

neighbouring system(s). System independence is lost when this system is in­

terconnected with another system where the objective is to provide and/orreceive assistance in regard to spinning reserve. In the case of a dominant

SSR, the unit commitment of an interconnected system is primarily dictated

by the SSR. The system with a smaller SSR, therefore, has to spin more

194

generating capacity than the system with a higher SSR for identical load and

generating sets. Despite being identical in regard to load and generation

sets, a system will have to maintain more spinning reserve than its neigh­bour because of its decision to select a lower SSR. It is, therefore, desirable

to have a single SSR for all participating systems. In the case of a

dominant ISR, the unit commitment and spinning reserve is dictated by the

ISR itself. It is, however, difficult to obtain a dominant ISR level. The

dominance can be shifted from the ISR to the SSR or vice versa with

changes in load level, generation etc.. The level of assistance that an inter­

connected system can provide to its neighbour is dependent on the tie line

capacity. The level of assistance generally increases with an increase in tie

capacity provided other factors remain the same. The assistance , however,saturates when the tie capacity is increased beyond a certain level. The tie

capacity beyond which the available assistance saturates depends on generat­

ing units, unit commitment risk, spinning reserve etc.. The effect of one

single parameter on this level will vary from one set of interconnected sys­

tems to another. These effects should be examined in each case.

Load forecasting in any system involves some degree of uncertainty.The proposed probabilistic technique can include load forecast uncertainty in

the assessment of spinning reserve and unit commitment risk. The probabil­

ity distribution of the forecast load can be represented by a discrete distribu­

tion. The computation time required to determine the spinning reserve re­

quirements in an interconnected system increases with an increase in the

number of steps used in the load distribution. Examples with seven-step

and three-step approximations to a normally distributed load are shown in

Chapter 3.

Interconnected systems export/import energy to/from neighbouring sys­

tems. Usually the export/import between two or more interconnected sys­

tems is governed by agreements between the utilities concerned. The nature

of these agreements vary widely. Two basic export/import agreements have

195

been considered in this thesis. The agreements are: 1) firm purchase by one

system backed up by the complete system of the exporting utility and 2)firm purchase tied to a specific unit in the exporting utility. Methods have

been illustrated in this thesis to assess spinning reserve in interconnected sys­

tems with export/import using risk constraints based on the 'Two Risks

Concept' . The method can easily be extended to accommodate other

export / import agreements.

Interruptible loads can be included in the unit commitment risk assess­

ment of interconnected systems using the area risk technique. Interruptibleloads can be considered to be equivalent to ready reserve depending upon

the allowable time delay associated with the interruptible loads. It is

generally appreciated that interruptible loads can reduce the system risk.

There has been relatively little work done on the development of systematic

quantitative approach to determine the effects of interruptible loads in singleor in interconnected systems. A probabilistic method has been developed to

assess the magnitude of curtailable load and the corresponding maximum al­

lowable time delay before which the load must be interrupted to maintain

the system risk level equal to or less than a specified value. The same

method, with little modification, has also been used to determine the ad­

ditional load/interruptible load carrying capability of a power system. Inter­

ruptible loads can be included in the risk assessment process either by an

equivalent load approach or by an equivalent generating unit approach.Both approaches to incorporating interruptible loads provide identical results.

,

Important probabilistic features of interruptible loads and additional load car-

rying capability have been developed. Based on the principles created for

isolated system applications, techniques have been developed to study the ef­

fects of having interruptible loads in an interconnected system. These

developments are reported in this thesis.

A generation system can carry additional load or additional interrupt­ible load on top of its firm load without committing additional generation

196

above that required to carry the firm load. This capability depends on the

operating set of generating units, the firm load and the specified unit com­

mitment risk. In addition to these factors, the additional load/interruptibleload carrying capability of an interconnected system also depends upon the

operating conditions and unit commitment within the neighbouring system.

The additional load/interruptible load that an isolated or an interconnected

system can carry in addition to the firm load without violating the unit

commitment risk is not a unique quantity. There is at any moment,

however, a unique set of additional loads/interruptible loads and correspond­

ing lead times. This set will change with a change in the operating units

even if the firm load and the specified unit commitment risk remain un­

changed. The minimum additional load/interruptible load carrying capabilityof a system can be determined for a specific scheduling period. These con­

cepts can be used in short and medium term operational planning.

The 'Two Risks Concept' has been used to develop unit commitment

schedules on a continuous basis for a specified period. Units have been com­

mitted according to a predetermined loading order such that a specified SSR

level is satisfied at the isolated system level and a specified ISR level is also

satisfied at the interconnection level. The determination of a priority loadingorder for the generating units in a system is not discussed in detail in this

thesis as this activity IS outside the scope of this research work. Different

utilities use different approaches to determine their priority loading order

based on accepted economic and operating goals. Once the units are

scheduled in each hour of the scheduling period, the stopping and restartingtime of each unit is delayed or advanced if such modification results in ac­

ceptable savings. This advancing or delaying of the stopping and restartingtimes are based on a tentative economic load dispatch and forecast load

during the scheduling period. A method of determining risk constrained unit

commitment on a continuous basis is presented in this thesis. This proce­

dure can easily be implemented in interconnected systems.

197

Economic load dispatch does not normally consider probabilistic aspects

of the response capability of a system. A reliable load dispatch should be

such that an interconnected system must be able to respond with enoughreserve capacity to maintain dynamic stability, loss of generation or un­

foreseen load changes within an allowable margin time. In the terms of the

'Two Risks Concept', each interconnected system must maintain enough

responding reserve for the specified margin times such that a specified SSRR

is satisfied at the isolated system level and a specified ISRR is satisfied at

interconnected level. Chapter 7 presents a technique for obtaining a risk

constrained economic load dispatch starting from an economic load dispatch.The computation time required to modify an economic load dispatch into a

risk constrained economic dispatch is insignificant. The computation time in­

creases with a decrease in the reloading step used to modify the economic

load dispatch. An increase in the reloading step size, however, moves the

risk constrained economic load dispatch further away from the initial

economic point. Each individual pool must use its own judgement in

selecting an appropriate reloading step. Several assumptions have been made

in the development of the risk constrained economic load dispatch technique.The most important assumptions are that the transmission and tie line losses

are negligible and that all hydro units are run of the river type. Transmis­

sion and tie line losses can be included in the reloading process by includingthe change in losses due to the change in reloading a unit. Any appropriatetransmission loss formula can be used for this purpose with a sacrifice in

computation time. The algorithm that modifies the economic load dispatchinto a risk constrained economic load dispatch is simple in concept and can

.

be implemented in interconnected systems with little difficulty.

•

Two reliability test systems are utilised in order to illustrate the tech­

niques presented in this thesis. The results of studies on spmnmg reserve

requirement, unit commitment and reliability constrained load dispatch in in­

terconnected RBTS and interconnected IEEE-RTS are presented in this

thesis. The methods presented can easily be implemented in small or large

power systems.

198

I

The spinning reserve assessment technique presented in this thesis is

based on the stochastic behaviour of the system components. The proposed

technique advances the method of spinning reserve assessment III intercon­

nected systems and provides a framework within which a fair allocation of

spinning reserve among the interconnected utilities can be achieved. The

techniques presented in this thesis are very practical and incorporate impor­tant operating practices.

199

REFERENCES

1. A. V. Jain, R. Billinton, "SpinningPower System", IEEE Paper No.

IEEE/PES Winter Meeting, NewFebruary 2 1973.

Reserve Allocation in a ComplexC 73 097-3 , Presented at the

York, New York, January 28 -I2. Adarsh V. Jain, Operating Reserve Assessment in Multi-Interconnected

Systems, PhD dissertation, University Of Saskatchewan; Saskatoon,Canada, 1972.

3. R. Billinton and R. N. Allan, Reliability Evaluation of Power Systems,Longmans (England) I Plenum Press, New York, 1984.

4. R. Billinton, A. V. Jain, "Interconnected System Spinning ReserveRequirements", IEEE Transactions on Power Apparatus and Systems,Vol. PAS-91, March/April 1972, pp. 517-526.

5. R. Billinton, A. V. Jain, "Power System Spinning Reserve Determina­tion in a Multi System Configuration", IEEE Paper No. T72 �02-6,Presented at the IEEE Summer Power Meeting, San

Francisco,California, July 9-14 1972.

6. . Raymond R. Shoults, Show Kang Chang, Steve Helmick, W. MackGrady, "A Practical Approach to Unit Commitment, Economic Dis­patch and Savings Allocation For Multiple-area Pool Operation WithImport Iexport Constraints", IEEE Transactions on Power Apparatusand Systems, Vol. PAS-99, No.2, MarchiApril 1980, pp. 625-633.

7. Nathan Cohn, "Methods of Controlling Generation on InterconnectedPower System", AlEE Paper 60-846, Presented at AlEE SummerGeneral Meeting, Atlantic City, N. J., June 19-24 1960.

8. P. G. Lowery, "Generating Unit Commitment by DynamicProgramming", IEEE Transactions on Power Apparatus and Systems,Vol. PAS-85, No.5, May 1966, pp. 422-426.

9. R. H. Kerr, J. L. Scheidt, A. J. Fontana, J. K. Wiley, "UnitCommitment", IEEE Transactions on Power Apparatus and Systems,Vol. PAS-85, No.5, May 1966, pp. 417-421.

10. H. H. Happ, R. C. Johnson, ·W. J. Wright, "Large Scale Hydro-

200

Thermal Unit Commitment-Method and Results", IEEE Transactionson Power Apparatus and Systems, Vol. PAS-90, May/June 1971, pp.1373-1382.

11. K. Hara, M. Kimura and N. Honda, "A Method for PlanningEconomic Unit Commitment and Maintenance of Thermal Power

Systems", IEEE Transactions on Power Apparatus and Systems, Vol.

PAS-85, No.5, May 1966, pp. 427-436.

12. John A. Muckstadt and Richard C. Wilson, "An Application of

Mixed-Integer Programming Duality to Scheduling Thermal GeneratingSystems", IEEE Transaction on Power Apparatus and Systems, Vol.

PAS-87, No. 12, Dec. 1968.

13. E. B. Dahlin and D. W. C. Shen, "Optimal Solution to the Hydro­Steam Dispatch Problem for Certain Practical Systems", IEEE Trans­action on Power Apparatus and Systems, Vol. PAS-85, No.5, May1966, pp. 437-458.

14. 1. Hano, Y. Tamura and S. Narita, "An Application of the Maximum

Principle to the Most Economical Operation of Power Systems", IEEETransactions on Power Apparatus and Systems, Vol. PAS-85, No.5,May 1966, pp. 486-494.

15. John J. Shaw, Dimitri P. Bertsekas, "Optimal Scheduling of LargeHydrothermal Power Systems", IEEE Transactions on Power Ap­paratus and Systems, Vol. PAS-_104, No.2, February 1985, pp.286-294.

16. T. N. Saha, S. A. Khaparde, "An Application of a Direct Method to

the Optimal Scheduling of Hydrothermal System", IEEE Transactionson Power Apparatus and Systems, Vol. PAS-97, No.3, May/June1978, pp. 977-983.

17. J. D. Guy, "Security- Constrained Unit Commitment", IEEE Trans­actions on Power Apparatus and Systems, Vol. PAS-90, May/Jun

1971, pp. 1385-1389.

18. Bruce F. Wollenberg, Kenneth A. Fegley, "A Cost Effective SecurityDispatch Methodology", IEEE Transactions on Power Apparatus and

Systems, Vol. PAS-95, No.1, January/February 1976, pp. 401-409.

19. R. Billinton and R. N. Allan, "Power System Reliability m

Perspective", lEE Electronics and Power, Mar 1984, pp. 231-236.

20. M. S. Bartlett, An Introduction to Stochastic Processes With SpecialReference to Methods and Applications, The Syndics of the CambridgeUniversity Press, London, 1966.

21. E. B. Dynkin, translated from the Russian by D. E. Brown, edited byT. Kovary, Theory of Markov Processes, Prentice-Hall Inc., EnglewoodCliffs, N.J./Pergamon Press, London, 1961.

I22.

23.

24.

25.

26.

27.

28.

29.

•

201

E. B. Dynkin, translated from the Russian by J. Fabius,V. Greenberg, A. Maitra, G. Majone, Markov Processes, AcademicPress Inc., Publishers New York, N. Y., Vol. I, 1965.

R. Billinton and R. N. Allan, Reliability Evaluation of EngineeringSystems: Concepts and Techniques, Longmans (England)/ Plenum

Press, New York, 1983.

L .. T. Anstine, R. E. Burke, J. E. Casey, R. Holgate, R. S. John andH. G. Stewart, "Application of Probability Methods to the Determina­tion of Spinning Reserve Requirements for the Pennsylvania-NewJersey-Maryland Interconnection", IEEE Transactions on Power Ap­paratus and Systems, Vol. PAS-821963, pp. 726-735.

Kamal Debnath, Reliability Modelling of Power System ComponentsUsing the CEA-ERIS Data Base, PhD dissertation, University Of Sas­

katchewan, Saskatoon, Canada, June 1988.

R. Billinton, Nurul A. Chowdhury, "Operating Reserve Assessment InInterconnected Generating Systems", IEEE Transactions on Power Ap­paratus and Systems, Vol. PAS-3, No.4, November 1988, pp.1479-1487.

Robert H. Miller, Power System Operation, McGraw-Hill Book Com­

pany, New York, New York, 1970.

Leon K. Kirchmayer, Economic Control of interconnected Systems,John Wiley & Sons, Inc., New York/Chapman & Hall, Ltd., London,1959.

N. Chowdhury, R. Billinton, "Assessment of Spinning Reserve in Inter­connected Generation Systems With Export/Import Constraints", IEEE

Paper No. WP 89-65, Accepted for Presentation at the IEEE/PES1989 Winter Meeting, New York, New York, January 29 - February 31989.

J. 1. Nish, N. A. Millar, "Generating System Operating Reserve As­

sessment Practices Used by Canadian Utilities", Canadian Electrical

Association, Power system Planning and Operation Section, SpringMeeting1984.

31. R. Billinton, N. A. Chowdhury, "Operating Benefits of InterruptibleLoads", Presented at the 1988 Spring Meeting of Canadian Electrical

Association/Power System Planning and Operating Section, Montreal,Quebec, March 16-21 1988.

30.

32. N. Chowdhury, R. Billinton, "Interruptible Load Carrying Capabilityof a Generation System", IEEE Paper No. 88 SM 652-0 , Presentedat the IEEE/PES Summer Meeting, Portland, Oregon, July 24 - 291988.

202

34. James G. Waight, Farrokh Albuyeh, Anjan Bose, "Scheduling of

Generation and Reserve Margin Using Dynamic and Linear

Programming", IEEE Transactions on Power Apparatus and Systems,vei. PAS-100, No.5, May 1981, pp. 2226-2230.

35. A. K. Ayoub, A. D. Patton, "Optimal Thermal Generating Unit

Commitment", IEEE Transactions on Power Apparatus and Systems,Vol. PAS-90, No.4, July/August 1971, pp. 1752-1756.

36. Richard Bellman, Dynamic Programming, Princeton University Press,Princeton, N.J., 1957.

37. Richard E. Bellman, Stuart E. Dreyfus, Applied DynamicProgramming, Princeton University Press, Princeton, N.J., 1962.

38. George L. Nemhauser, Introduction to Dynamic Programming, John

Wiley and Sons Inc., New York, New York, 1966.

39. 1. Megahad, N. Abou-Taleb, M. Iskandrani, A. Moussa, "A ModifiedMethod for Solving the Economic Dispatching Problem", IEEE Trans­actions on Power Apparatus and Systems, Vol. PAS-96, No.1,January/February 1977, pp. 124-132.

40. T. H. Lee, D. H. Thorne, E. F. Hill, "Modified Minimum Cost Flow

Dispatching Method for Power System Application", IEEE Trans­

actions on Power Apparatus and Systems, Vol. PAS-100, No.2,February 1981, pp. 737-744.

41. W. O. Stadlin, "Economic Allocation of Regulating Margin", IEEE

Transactions on Power Apparatus and Systems, Vol. PAS-90, July­August 1971, pp. 1776-1781.

42. Chaw Lam Wee, A Frequency and Duration Approach for GeneratingCapacity Reliability Evaluation, PhD dissertation, University Of Sas­

katchewan, Saskatoon, Canada, 1985.

43. H. H. Happ, "Optimal Power Dispatch", IEEE Transaction on Power

Apparatus and Sy.stems, Vol. PAS-93, No.3, 1974, pp. 820-830.

44. R. Billinton, S. Kumar, N. Chowdhury, K. Chu, K. Debnath, L. Goel,E. Khan, P. Kos, G. Nourbakhsh, J. Oteng-Adjei, "A Reliability Test

System for Educational Purposes - Basic Data", IEEE Paper No. 89

WM 035-7-PWRS, Presented at the IEEE/PES 1989 Winter Meeting,New York, New York, January 29 - February 3 1989.

203

Appendix A

Equivalent Capacity Model

A.I. A Recursive Algorithm for Capacity Model Building

A simple recursive algorithm can be used to create a capacity model of

a generation system [3}. The technique is applicable for multi-state units as

well as for two-state units. Consider System X in Chapter 2 with a lead

time of two hours. Table A.l shows the probability of failure of the units

in System X in 2 hours.

Table A.l: Probability of Failure of Units in System X.

Unit Probability of Failure

3 x 40 MW3 x 20 MW4 x 10 MW

0.000913240.000684930.00068493

The capacity outage probability table IS created sequentially usmg

Equation (2.11) as follows:

Add the first unit

P(O) = (0.99908676)(1.0) + (0.00091324)(1.0) = 1.0

P(40) = (0.99908676)(0) + (0.00091324)(1.0) = 0.00091324

Add the second unit

P(O) = (0.99908676)(1.0) + (0.00091324)(1.0) = 1.0

P(40) = (0.99908676)(0.00091324) + (0.00091324)(1.0) = 0.00182565

P(80) = (0.99908676)(0) + (0.00091324)(0.00091324) = 0.00000083

Add the third unit

P(O) = (0.99908676)(1.0) + (0.00091324)(1.0) 1.0

204

P(40) = (0.99908676)(0.00182565) + (0.00091324)(1.0) = 0.00273722

P(80) = (0.99908676)(0.00000083) + (0.00091324)(0.00182565) = 0.00000250

P(120) = (0.99908676)(0) + (0.00091324)(0.00000083) = 0.00000000

The remaining units -in System X can be added in a similar manner.

The resulting capacity model in the form of a capacity outage probabilitytable after adding all 10 units in System X is shown in Table A.2.

Table A.2: Capacity Outage Probability Table of System X.

Capacity In Capacity Out Cumulative

(MW) (MW) Probability

220 0 1.00000000

210 10 0.00750879

200 20 0.00478778190 30 0.00274422

180 40 0.00273863

170 50 0.00001559

160 60 0.00000812

150 70 0.00000252

140 80 0.00000250

A similar approach is followed in adding an equivalent assistance unit

to the on-line capacity model of a system .

•

Ji

,205

Appendix B

Determination of Interruptible Load

Carrying Capability of an InterconnectedGeneration System

B.I. Computational Algorithm

If the actual ISR of an interconnected power system is less than the

specified ISR, the system may be able to carry some additional load or ad­

ditional interruptible load on top of its firm load without having to modify

its unit commitment from what is required to satisfy the firm load. The ad­

ditional load/interruptible load carrying capability of an interconnected sys­

tem among many things also depends on the firm load and unit commitment

of the neighbouring systems. A set of additional load/interruptible load and

the corresponding lead time of a system can be derived provided the firm

load and additional load/interruptible load of the neighbours are known.

There could be as many sets of solution as the assumptions regarding the

additional load/interruptible load of the neighbouring systems.

Assume that

T = total study period,Rs = specified SSR,

Ri = specified ISR,. Rsa = actual SSR of System A,

Rsb actual SSR of System B,

Ria = actual ISR of System A,

Rib = actual ISR of System B,L fa

= firm load of System A,L fb

= firm load of System B,tmin = minimum allowable time delay for load interruption,

206

additional load of °a

In System A with a lead time of Ta'

additional load of 0b in System B with a lead time of Tb'

set of additional loads in System A for additonal load of

(Ob,Tb) in System B,

set of additional loads III System B for additonal load of

(Oa,Ta) in System A.

For each (Oa,Ta) in System A there will be a corresponding set of ad­

ditional load/interruptible load, Sb(8 ,T) in System B. To start the com-, a a

putation it is assumed that the additional loads can be tolerated for' the en­

tire period of T. To derive all possible sets of additional loads in System A

and B, °a

and 0b can be assumed zero to start with. A set of additional

loads and corresponding lead times in System B can be derived for each ad­

ditional load (0a,Ta) in System A provided the additional load in A satisfies

the SSR criterion. If the additional load in A does not satisfy the SSR

criterion Ta

is modified as

T ...... T -Ata a

where

At is the discrete time step in minutes,

before the computation proceeds any further. After the SSR criterion of

System A is satisfied ()b is updated to ()b+A1, where Al is the discrete incre­

ment in additiotnal load. If all the risk criteria are met, (()b+A/,Tb) becomes

an element of the set Sb(Oa,Ta). In the case where any of the risk criterion

is not met the lead time of the addiitonal load is modified acording to the

following conditions.

If Rsb> R" the lead time Tb IS modified as

207

If R < R R > Rand R > R Tb is modified assb - 8' ia i ib i

T -+ T -Cita a

and the computations for a new set of additional load/interruptible load In

System B begins.

When Tb reches to a value such that Tb � tmin, the additional load

(Oa,Ta) of A is updated to (Oa+Ci1,Ta) and a new set of calculations start to

determine the additional load/interuptible load of B with a starting value of

(O,T). The computation stops when Ta � tmin0

The computation time depends on the selection of Cil,Cit and tmin0 In

this thesis Cil,Cit and t min is taken as 5 MW, 5 minutes and 2 minutes

respectively.