2006 International Conference on Power System Technology

Non-Coherence in Transmission Line Arrangements

Wenyuan Li, IEEE Fellow, Jiaqi Zhou, Kaigui Xie and Xiaofu Xiong

Abstract - Non-coherence in system reliability refers to thefact that absence of a component from the system creates amore reliable system state or provides a higher systemreliability level. This phenomenon may exist in transmissionsystems. Unfortunately, it has not been sufficientlyrecognized in the power industry. This paper explains thebasic concept of non-coherence in transmission systems andprovides a case study where the single transmission linestructure with loop-in connection for supplying loads fromtwo ends is superior to the double transmission line structurewith tap-connection for supplying the same loads not only inan economic sense but also in accordance with the reliabilitylevel. This is contrary to intuition since transmission planningengineers normally make an opposite judgment. The examplegiven in the paper is an actual application in a utility ofCanada. It also has a wider significance because the double-line arrangement with tap-connection is a popular choice intransmission planning practice of utilities across the world. Itis important and beneficial for utilities to recognize andidentify the non-coherence feature that could exist in theirtransmission systems using quantified reliability evaluation.This can help improve system reliability while avoidingunnecessary capital investments in the system planningprocess.

Index Terms - non-coherence, substation, transmission linearrangement, transmission system reliability

I. Introduction

Coherence is an important concept in general engineeringsystem reliability evaluation. This concept states that if acomponent fails or is out-of-service, system reliability neverimproves. Conversely, if a failed component is recovered,system reliability never decreases. The coherence assumptionis widely used in reliability assessment of engineeringsystems including power systems. Conceptually, it is easy tounderstand that the assumption is valid in generation systemreliability evaluation and this has been proved in manystudies [1]. However, it is not always true for a transmissionor composite generation and transmission system. In otherwords, absence of a transmission component may notdeteriorate system reliability. The possible non-coherencefeature in transmission system reliability was presented morethan 10 years ago [2].

Wenyuan Li is an advisory professor at Chongqing University, China andwith British Columbia Transmission Corporation, Vancouver, CanadaJiaqi Zhou, Kaigui Xie and Xiaofu Xiong are with the College of ElectricalEngineering, Chongqing University, China

Unfortunately, very little attention has been paid to thisphenomenon although considerable efforts have beendevoted to transmission reliability in the past decades [1-10].Only a few academic papers have been published fordiscussing the topic. Some methods for transmission systemreliability evaluation are even based on a coherenceassumption [11], which may create large computationalerrors in the assessment. Particularly, electric utilities haveoverlooked the non-coherence feature that may exist in theirsystems for years. Ignorance of possible non-coherence hasresulted in and will continuously result in surplustransmission additions and thus a huge waste of capitalinvestment.

This paper provides a case study for combinative structuresof transmission lines and substation configurations, in whicha double-line structure with tap-connection for supplyingloads from two ends has lower reliability than a single-linestructure with loop-in connection for supplying the sameloads while both arrangements require the same number ofother equipment. It is an interesting example because it issomewhat against intuition. This is an actual application in autility of Canada. Many utilities across the world have beenusing similar double-line structures with tap-connection intheir system planning practice. Transmission planningengineers in utilities basically always believe that a double-line structure should be more reliable. If the non-coherencefeature of a system can be identified through quantifiedreliability evaluation, we can improve system reliability byavoiding a surplus transmission component and at the sametime save the capital investment in system planning.

The paper is organized as follows. The basic concept of non-coherence in transmission systems is explained in Section 2.Two transmission line arrangements are presented in Section3. The failure and repair models of transmission lines andsubstation components in the arrangements for reliabilityevaluation are illustrated in Section 4. Results are given inSection 5 and conclusions in Section 6.

II. Basic Concept of Non-coherence in TransmissionSystems

The concept of non-coherence in transmission systems can beexplained using the 4-bus system shown in Figure 1[3, 12].The two generators at Buses (1) and (4) supply the two loadsat Buses (2) and (3). Each load is 50 MW + 15 MVAR. Line1 and Line 3 have the impedance of 0.008+jO.034 p.u., theimpedance of Line 2 is 0.001+jO.003 p.u. and the impedanceof Line 4 is 0.005+jO.015 p.u. All the lines have a rating of55 MVA. The power flow results show that there is no

1-4244-0111-9/06/$20.00c02006 IEEE.

overload in the normal system state. When Line 4 fails, thepower from G2 is interrupted and both the loads are suppliedby G I (see Figure 2). In this outage state, Line 2 isoverloaded due to the power flow re-distributions imposed bythe Kirchhoff's Laws. In order to eliminate the overloading,some load curtailments at either load bus have to beperformed. However, if we intentionally open Line 3 (seeFigure 3), the overloading problem on Line 2 will disappear.The line flows at the "from bus" side for the three cases aregiven in Table 1. Note that there are losses on the lines sothat the power flows at the two ends of each line aredifferent.

This simple example provides the basic concept of non-coherence, i.e., losing Lines 3 and 4 will create the morereliable system state than just losing Line 4. The non-coherence event is dependent on system states in thisexample. The intentional opening of Line 3 leading to a morereliable system state does not mean that it is surplus andshould be removed permanently. Obviously, Line 3 is neededin the normal and other contingency states to make thesystem more reliable. In the following real example, we willshow a case where non-coherence is associated with thesystem structure but not just with a system state and thereforea line can be permanently removed or avoided to improvereliability. The non-coherence associated with only systemstates provides a possibility for system operators to reducesystem operation risk by changing operation modes or systemconnections [12] whereas the non-coherence associated withsystem structures enables transmission planning engineers toimprove or keep reliability and save capital investments byavoiding a surplus or unnecessary system component in thesystem reinforcement planning process. In either case, areliability evaluation technique that is based on theassumption of coherence cannot be applied in thetransmission system reliability assessment.

Table 1 Line flows corresponding to Figures 1, 2 and 3

Line Bus to Bus Line flow Rating(MVA) (MVA)

Normal state1 (1) to (2) 27.36 552 (1) to (3) 25.30 553 (3) to (2) 25.07 554 (4) to (3) 52.20 55

Line 4 in outage1 (1) to (2) 29.61 552 (1) to (3) 75.11 55 (overload)3 (3) to (2) 22.81 55

Line 4 in outage and Line 3 opened1 (1) to (2) 52.64 552 (1) to (3) 52.25 55

1

(2)

(4)

50+j15

Figure 1 4-bus system (normal state)

t)GI 50-tjlI G2

M') 2 (3) L4 7(4)

(2~ ~ ~ G

50+j15

Figure 2 4-bus system (Line 4 outage)

(1)Q GI 50+j15 G2

(1)7 2 (3) L4 (4)

1\ 3

(2)

50+j15

Figure 3 4-bus system (Line 4 outage andLine 3 intentionally opened)

III. Two Transmission Line Arrangements

In transmission systems below 230 kV, the tappingconnection from a transmission line is a commonly usedarrangement for supplying substations from two ends. Twotransmission line arrangements with substation layouts in themiddle are shown in Figures 4 and 5 respectively. Theswitches at both sides of the breakers or transformers areomitted in the figures. The transmission line is at the 60 kVlevel and the low voltage side is at 12 kV. The twosubstations, which are located at the one-third from each endof the transmission line, have the identical layout and each ofthe four customers has the same amount of load demand. In

other words, the two transmission line arrangements areidentical except that the one is a double-line structure withtap-connection while the other is a single-line structure withloop-in connection. In the single line arrangement, the secondtransmission line is removed and the breakers BK3 and BK4on the two ends of the second line are respectively moved tothe two substations. The two arrangements need the samenumber of breakers and transformers. Intuitively, the double-line structure looks more reliable and it is the choice aplanning engineer normally selects. Is it true that the doublelines in parallel is really reliable than the single line in thiscase? It has been found difficult to make a judgment. This isan actual application in a utility of Canada. However, it has awider significance since similar double-line structures withtap-connection are commonly used in other utilities acrossthe world and they are facing the same question in making aninvestment decision: which one is better?

ABK1 Line 1 BK2

B

transmission line failure is represented using the up-and-down two-state model as shown in Figure 6. Theunavailability, i.e., the probability of the down state iscalculated using Equation (1):

ut = AA +p

(1)

where i and ,u are the failure and repair rates of transmissionlines.

A bus failure is represented using the component groupoutage model as shown in Figure 7. The unavailability, i.e.,the probability of the down state of all components in thegroup is calculated using Equation (2):

2Ub =

Ac +Pc(2)

where )u and p, are the failure and repair rates of buses.

The two-state model n Figure 6 and component group outagemodel in Figure 7 look the same and they have the similarmathematical equations. However, their implications aredifferent. In the component group outage model, a bus failurewill lead to outages of all components that are directlyconnected to it and they can return to service only after thebus is repaired. The group outage model is a model fordependent outage events of multiple components whereas thetwo-state model is only associated with one singlecomponent.

Figure 4 Double-line arrangement with tap-connection

BK1 BK2B

Figure 6 Two state model for transmission lines

All Xc |. All |up state

.4down state

pLcFigure 5 Single- line arrangement with looped-in connection

IV. Models of System Components in ReliabilityEvaluation

The configurations shown in Figures 4 and 5 are combinativestructures of transmission line and substation layouts. Inreliability evaluation of this type networks, different modelsshould be used for different system components. A

Figure 7 Group outage model for buses

A failure of a transformer or breaker is represented using a

three-state model shown in Figure 8. In this model, Xto, Xts, ptrand tsw are the passive (open-circuit) failure rate, active(short-circuit) fault rate, repair rate and switching raterespectively. A switching state refers to the state in which,when there is a short fault on a breaker or transformer,breakers around it are automatically opened by a protectionscheme, resulting in a simultaneous outage of multiple

A

components including the faulted breaker or transformer.After that, the switches at its two sides can be manuallyopened so that the faulted breaker or transformer is isolatedand power supply of partial or all loads may be restored,entering the repairing state where only faulted breaker ortransformer is being repaired. Applying the Markov equationapproach or the frequency balance method [3, 13] to thethree-state model, the following equations for calculating thestate probabilities can be obtained:

PiAto + PIits = P2/trPIito + P3/swJ=P2 tr

PIAts = P3Psw J(3)

where, PI, P2 and P3 are the state probabilities for the up,

repairing and switching states respectively. By combiningEquations (3) with the full probability formula,i.e. P1 + P2 + P3 = 1.0, the probabilities of the three states are

solved to yield

PI = /tr/sw (4)/tr/-sw + iswito + SW its + jttrits

P3/'tr its

P tr ssw + swi to + jUswi/ts + trLts

(5)

(6)

With the state probabilities of all system components, a

Monte Carlo simulation or state enumeration technique can

be used to evaluate reliability of the combinative structures oftransmission line and substation layouts. The evaluationtechniques can be found in Reference 3.

Figure 8 Three state model for transformers and breakers

V. Reliability Evaluation Results

Reliability of the two transmission line arrangements shownin Figures 4 and 5 was evaluated using an enumerationtechnique. The study conditions are as follows:

* The transmission lines, breakers, transformers and busesare represented using the three models given in SectionIV.

* Failures of switches at both side of a transformer orbreaker are neglected since they are manually used onlywhen a transformer or breaker has a fault and there is norecord in the past statistics data showing that they oncerefused to switch. Even if a low probability of theirrefusing to switch was considered, there would not be aneffective impact on results. The time required by manualswitching is assumed to be one hour. If a supervisorycontrol was installed, the switching time could be veryshort.

* The power source points A and B at the two ends of thetransmission line arrangements are assumed to be 100%reliable. Note that the power source points are substationslocated at the two ends but not generators and they havethe same effects for the two transmission linearrangements.

* The failures of the buses (BS5, BS6, BS7 and BS8) towhich the loads are directly connected are not consideredsince their impacts on the reliability level of the twotransmission line arrangements are identical.

* The breakers BK9 and BK1O are normally opened andeach one can be automatically closed when either of thebreakers at its two sides is opened due to the protectionscheme.

The data of the transmission lines, substation componentsand loads are shown in Tables 2 - 4. The length of Lines 1and 2 in the double-line arrangement is 30 km while in thesingle-line arrangement, Line 1 is split into the three sectionsof Lines 1-1, 1-2 and 1-3 by the two breakers with the equallength of 10 km and Line 2 is removed. The failure data arebased on the average historical statistics of transmissionfacilities in the utility. The four customers have the equalload with the same load factor.

The three reliability indices of PLC (Probability of LoadCurtailment), EFLC (Expected Frequency of LoadCurtailment) and EENS (Expected Energy Not Supplied)were evaluated. The results for the two transmission linearrangements are shown in Table 5. These are the totalindices for the four load points. The total PLC or EFLC is theprobability or frequency of load curtailments happening atleast at one load point. Each index is divided into the twoportions. The first one is associated with load curtailments inthe switching states that exist only in a short time. Thesecond one is associated with load curtailments in therepairing states that would last until the end of the repairprocess and corresponds to a relatively long time.

P2 =PSW (Ato + Ats )

Ptr Psw + Psw Ato + Psw Ats + Ptr Ats

Table 2 Data of transmission lines

Line Capacity Length Failure dataFrequency Repair time

(MVA) (km) (f/year) (hrs/f)

Line 1 100 30 0.3612 62.5Line 2 100 30 0.3612 62.5Line 1-1 100 10 0.1204 62.5Line 1-2 100 10 0.1204 62.5Line 1-3 100 10 0.1204 62.5

Table 3 Data of substation components

Component Capacity Failure frequency Repair timeActive Passive

(MVA) (f/year) (f/year) (hrs/f)

Transformer 40 0.0761 0.0026 490.0Breaker 0.0124 0.0012 80.4Bus-bar 0.0912 25.2

Switching time = 1 hour

Table 4 Data of bus loads

Bus Peak load (MW) Load factor

BS5 14 0.7143BS56 14 0.7143BS7 14 0.7143BS8 14 0.7143

Table 5 Reliability indices

Arrangement PLC EFLC EENS(f/year) (MWh/year)

Double lineSwitching states 0.000005748 0.050896 1.0540Repairing states 0.000107392 0.016442 20.7702Total 0.000113140 0.067338 21.8242

Single lineSwitching states 0.000009164 0.081147 1.1851Repairing states 0.000066006 0.008531 11.8343Total 0.000075170 0.089678 13.0194

The following observations can be made:

* The single-line arrangement with loop-in connection hasthe lower probability of load curtailments and the smallerexpected energy not supplied but the higher expectedfrequency of load curtailments compared to the double-line arrangement with tap-connection. By looking at the

composition of the indices, all the PLC, EFLC and EENSindices associated with the repairing states for the single-line arrangement are smaller than those for the double-line arrangement. Although the indices associated withthe switching states for the single-line arrangement arelarger than those for the double-line arrangement, thisportion of indices is only associated with short switchingtime.

* The relatively high frequency of load curtailments in thesingle-line arrangement is due to the failure events thatcan be isolated by switching actions.

* The EFLC indices are dominated by the portion in theswitching states that are associated with the short durationwhile the PLC and EENS indices by the portion in therepairing states that are associated with the long duration.

* Generally, the EENS index carries more information thanthe PLC and EFLC indices since it is a combination of theduration, frequency and consequence (amount of loadcurtailments) of failure states. The total EENS for thesingle-line arrangement is about 60% of that for thedouble-line arrangement.

* Particularly, if automatic switching devices can beinstalled so that failed components can be isolatedinstantly or switching time is so short that switching statescan be effectively ignored, then the indices associatedwith switching states will no longer exist.

It can be concluded from the quantified reliability evaluationthat the single-line arrangement not only enables to save onetransmission line of 30 km but also provides higher powersupply reliability in comparison to the double-linearrangement in this example.

VI. Conclusions

Non-coherence in system reliability refers a fact in whichabsence of a component creates a more reliable system stateor provides a higher system reliability level. Thisphenomenon may exist in transmission systems.Unfortunately, it has not been sufficiently recognized in thepower industry. This paper explains the basic concept of non-coherence in transmission systems and provides a case studywhere the single transmission line arrangement with loop-inconnection for supplying loads from two ends is superior tothe double transmission line arrangement with tap-connectionfor supplying the same loads not only in the economic sensebut also in accordance with the reliability level. This iscontrary to intuition since transmission planning engineersnormally make an opposite judgment. Although the examplegiven in the paper is an actual application in a utility ofCanada, it has a wider significance because the double-linearrangement with tap-connection for supplying loads fromtwo ends is a popular choice in transmission planningpractice of utilities across the world. More investigations maybe needed before we draw a more general conclusion.However, most likely, the loop-in connection in the single-line structure should be more reliable than the tap-connection

in the double-line structure when the loads in the middle aresupplied from two sides of the structure. It is important andbeneficial for utilities to recognize and identify the non-coherence feature that could exist in their transmissionsystems using quantified reliability evaluation. This can helpimprove system reliability while avoiding unnecessarycapital investments in the system planning process.

References

[1] R. Billinton and R.N. Allan, Reliability Evaluation of PowerSystem, Plenum Press, New York and London, 1996

[2] R. Billinton and Wenyuan Li, Reliability Assessment ofElectric Power Systems Using Monte Carlo Methods, PlenumPress, New York, 1994

[3] Wenyuan Li, Risk Assessment of Power Systems: Models,Methods, and Applications, IEEE Press and John Wiley &Sons, USA and Canada, 2005

[4] R.N. Allan, R. Billinton, A.M. Breipohl, C.H. Grigg,"Bibliography on the Application of Probability Methods inPower System Reliability Evaluation: 1992-1996", IEEETransactions on Power Systems, Vol. 14, No. 1, 1999, pp. 51-57.

[5] EPRI Report, Reliability Evaluation for Large Scale BulkTransmission Systems, Report EL5291, 1988

[6] IEEE Tutorial Course Text, Electric Delivery SystemReliability Evaluation, 05TP175, IEEE PES General Meeting,San Francisco, June 2005

[7] CIGRE Task Force 38-03-10 Report, Composite Power SystemReliability Analysis: Application to the New Brunswick PowerCorporation System, CIGRE Symposium on Electric PowerSystem Reliability, Sept. 16-18, 1991, Montreal

[8] R. Billinton and Wenyuan Li, "Hybrid Approach for ReliabilityEvaluation of Composite Generation and TransmissionSystems Using Monte Carlo Simulation and EnumerationTechnique", IEE Proceedings-C, Vol. 138, No. 3, May, 1991,pp233-241

[9] A.M. Leite da Silva, L.A.F. da Fonseca Manso, J.C.O. deOliveira Mello and R. Billinton, "Pseudo-ChronologicalSimulation for Composite Reliability Analysis with TimeVarying Loads", IEEE Transactions on Power Systems, Vol.15, No. 15, February, 2000, pp. 73-80.

[10] Wenyuan Li, Y. Mansour, J.K. Korczynski and B.J. Mills,"Application of Transmission Reliability Assessment inProbabilistic Planning of BC Hydro Vancouver South MetroSystem", IEEE Trans. on PS, Vol. 10, No. 2, May 1995,pp964-970

[11] A. C. G. Melo, M.V.F. Pereira, A.M. Leite da Silva, "AConditional Probability Approach to the Calculation ofFrequency and Duration Indices in Composite ReliabilityEvaluation", 1992 IEEE PES Summer Meeting, Seattle, WA,July 12-16, Paper 92 SM 425-9-PWRS, 1992

[12] Wenyuan Li and J.K. Korczynski, "Risk Evaluation ofTransmission System Operation Modes and Its Application atBritish Columbia Transmission Corporation", IEE ProceedingsGeneration, Transmission & Distribution, Vol. 151, No. 5,September 2004, pp658-664

[13] R. Billinton and R.N. Allan, Reliability Evaluation pfEngineering System: Concepts and Techniques, Plenum Press,New York and London, 1992

Bibliography

Dr. Wenyuan Li (IEEE Fellow): is currently a PrincipalEngineer at the British Columbia Transmission Corporationin Canada, He is the author of the book "Risk Assessment ofPower Systems: Models, Methods, and Applications, IEEEPress and Wiley, USA and Canada, 2005 and the co-authorof the book "Reliability Assessment of Electrical PowerSystems Using Monte Carlo Methods", Plenum Press, NewYork, 1994. He is the winner of the 1996 "OutstandingEngineer" Award by IEEE Canada for contributions in powersystem reliability and probabilistic planning.

Mr. Jiaqi Zhou is currently a full professor at the College ofElectrical Engineering of Chongqing University in China. Hehas been active in power system planning and reliabilityevaluation for about 30 years and published over 100 papersin this area. He won several science and technology awardsin China for his contributions in power system reliabilitymethods and applications in electric power utilities.

Dr. Kaigui Xie is a full professor at the College of ElectricalEngineering of Chongqing University in China. His interestsinclude power system reliability evaluation, system analysisand system planning.

Dr. Xiaofu Xiong is a full professor at the College ofElectrical Engineering of Chongqing University in China.His interests include power system protection andautomation, and reliability evaluation.