Voltage Stability

1

A

SEMINAR REPORT

ON

“AVOIDING RISK OF VOLTAGE INSTABILITY IN A

POWER SYSTEM THROUGH REACTIVE POWER

RESCHEDULING AND LOAD SHEDDING”

(SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE AWARD

OF THE DEGREE OF)

BACHELOR OF TECHNOLOGY

2010 – 2011

JAIPUR NATIONAL UNIVERSITY, JAIPUR

(A Venture of seedling group of institutions)

BY

MANISH KUMAR SHARMA

2

ABSTRACT

As the use of renewable energy sources (RESs) increases worldwide, there is a rising interest

on their impacts on power system operation and control. The important impacts of a large

penetration of variable generations in area of operation and control can be summarized in the

directions of regional overloading of transmission lines in normal operation as well as in

emergency conditions, reduction of available tie-line capacities due to large load flows,

frequency performance, grid congestions, increasing need for balance power and reserve

capacity, increasing power system losses, increasing reactive power compensation, and

impact on system security and economic issues. The distributed power fluctuation (due to

using of variable generations) negatively contributes to the power imbalance, frequency and

voltage deviations. Significant disturbance can cause under/over frequency/voltage relaying

and disconnect some lines, loads and generations. Under unfavourable conditions, this may

result in a cascading failure and system collapse. Here we describe a procedure for improving

voltage stability condition of a power system by reactive power rescheduling or load

shedding. For this purpose, a voltage stability index and its threshold value is used as the

basis. Sensitivity factors are derived to relate change in voltage stability index for changes in

reactive power at generation buses and changes in load at load buses. Using these sensitivity

factors, a procedure is proposed for avoiding risk of voltage instability in a power system by

applying reactive power rescheduling or load shedding.

3

ACKNOWLEDGEMENT

I would like to convey my sincere thanks to Prof. DEVENDRA DODA (HOD, EE) for

giving us such a wonderful opportunity to enhance our skills through these seminars.

I would like to express my deep sense of gratitude, indebtedness to Mr. DURGESH

NANDAN PATHAK (lecturer, EE, JNU, Jaipur), and all the faculty members for their

guidance, ever inspiring help, affectionate encouragement & motivation .They have been a

great source of inspiration for me. I’ve been receiving valuable suggestions from them.

I am also thankful to Mrs. DEEPIKA CHAUHAN who helped me in my seminar with his

full interest. The uphill task for completing this seminar report would have been impossible

without support of all staff member.

No words are sufficient to express my gratitude to colleagues for their

exemplary patience, understanding, co-operation & for creating congenial environment to

carry out this work.

NAVEEN KUMAR MEENA

4

FIGURE INDEX

TOPICS PAGE NO.

Figure1. Flow chart for reactive power rescheduling or/and load Shedding to improve

voltage stability condition of a power system........................................................................19

Figure1 continued..................................................................................................................20



Figure2. IEEE30 Bus system................................................................................................24

5

CONTENTS

1. Introduction..............................................................................................................7

2. Classification of Instability Mechanisms..................................................................8

2.1 Transient period..................................................................................................8

2.1 Power system stability........................................................................................8

2.2 Voltage stability..................................................................................................8

3. Procedure for Control Action to Avoid Voltage Instability........................................9

3.1 Reactive power rescheduling..............................................................................9

3.1.1 Checking reactive power limit violation...................................................12

3.2 Emergency Load Shedding...............................................................................12

3.2.1 Checking limit violation for loads............................................................16

4. Determination of suitable value of MG, ML and solution procedure...............................17

5. Simulation result and discussion....................................................................................21

5.1 Desired value of I19des= 0.75...............................................................................21

5.2 Desired value of I19des= 0.8.................................................................................23

6. Conclusions....................................................................................................................29

7. Appendices....................................................................................................................30

8. References.....................................................................................................................31

6

INTRODUCTION

The problem related to voltage instability in a power system is a major concern for power system operation and planning. A major factor contributing to voltage instability is the voltage drop that occurs when active and reactive power flow through inductive reactance of the transmission network; this limits the capability of the transmission network for power transfer and voltage support. The power transfer and voltage support are further limited when some of the generators hit their field or armature current time-over load capability limits. Voltage stability is threatened when a disturbance increases the reactive power demand beyond the sustainable capacity of the available reactive power resources. Voltage collapse is characterized by a slow variation in system operating point, due to increase in the loads, in such a way that the voltage magnitude gradually decreases until a sharp accelerated change occurs. It has been observed that voltage magnitudes, in general, do not give a good indication of proximity to voltage stability limit. In recent literature, many voltage stability and voltage collapse prediction methods have been presented. Some of the important ones are:

(1) Voltage collapse index based on a normal load flow solution (L-index);

(2) Voltage collapse index based on closely located power flow solution pairs;

(3) Voltage collapse index based on sensitivity analysis; and

(4) Minimum singular value of Newton-Raphson power flow Jacobian matrix.

These methods assess the closeness to the critical loading by looking in to the voltage stability sensitivity indices or the smallest Eigen value or singular value of load flow Jacobian matrix. Index presented in gives a scalar number to each load bus, called the L-index, to indicate the proximity of voltage collapse for a power system. The index value ranges from 0 to 1. The bus with largest value of L is the most vulnerable bus in the system. In the procedure for calculation of L has been simplified using some acceptable approximations; this reduces the computational burden considerably. A reliable voltage stability index Ii has been proposed, whose threshold value is found to be varying marginally between 0.43 to 0.52 as against the theoretical threshold value of 0.5. The decrements of this index are rapid with respect to load variation as it approaches the proximity of voltage collapse. Therefore, index near to 0.7 is an alarming situation so far as voltage stability of a power system is concerned. For a voltage stability index to be effective and useful, it should possess the following qualities: (1) Indicator/index should be related to the controllable parameters of a power system through a simple function; and (2) some corrective measures could be derived from the indices. The proposed procedure aims at involving only sensitive generation buses and/or load buses for reactive power rescheduling and/or load shedding, respectively, to improve voltage stability condition of a power system. Load shedding option is undertaken when reactive power rescheduling of generation buses cannot improve voltage stability index of a bus to a desired value.

7

2. CLASSIFICATION OF INSTABILITY MECHANISMS

The objective of this section is to relate the above concepts of large disturbance and time scale decomposition to power system phenomena and models. We provide a classification of loss of stability mechanisms relevant to voltage phenomena. State approximation to be used and the overall system instability to be decomposed in several well defined categories. Let us assume a large disturbance and consider the possible unstable system responses that might result.

2.1 Transient Period

In the transient period immediately following the disturbance the slow variables do not respond yet and may be considered constant. The three major instability mechanisms are

T1: loss of equilibrium of the fast dynamics.

T2: lack of attraction towards the stable post-disturbance equilibrium of the fast dynamics.

T3: post-disturbance equilibrium oscillatory unstable. The transient period is the usual time frame of angular stability studies. For instance, the loss of synchronism following too slow a fault clearing is a typical T2 mechanism. This is also the time frame of transient voltage stability, which results from loads trying to restore their power in the transient time frame. Typical examples are induction motor loads and HVDC components. An example of T1 voltage instability is the stalling of an induction motor fed through a long transmission line, after some circuit tripping makes the transmission impedance too large. Motor stalling causes the voltage to collapse. The motor mechanical and electrical torque curves do not intersect any longer, leaving the system without a post-disturbance equilibrium. An example of T2 voltage instability is the stalling of induction motors after a short-circuit. In heavily loaded motor and/or slowly cleared fault conditions, the motor cannot reaccelerate after the fault. The mechanical and electrical torque curves intersect but at fault clearing, the motor slip is larger than the unstable equilibrium value.

2.2 Power System Stability

“Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically the entire system remains intact. ”

2.3 Voltage Stability

“Voltage stability refers to the ability of a power system to maintain steady voltages at all buses in the system after being subjected to a disturbance from a given initial operating condition. ” Characterized by loss of a stable operating point as well as by the deterioration of voltage levels in and around the electrical centre of the region undergoing voltage collapse”

8

3. Procedure for Control Action to Avoid Risk of Voltage Instability

The voltage stability index

indicates the voltage stability condition of ith bus of a power system. This voltage stability index for a bus decreases from 1.0 as the load increases at the bus. It is found that when the value of Ii approaches 0.5, system collapse takes place. Therefore, bus(es) having voltage stability index Ii close to 0.5 are considered to be the most vulnerable bus(es). It is observed that even for the index value from 0.7–0.75, the system is very near to the voltage collapse situation, i.e., margin for additional load is very small and small increase in load at the vulnerable bus(es) may lead to voltage collapse of the system. Therefore, it is required to maintain voltage stability index for all buses higher than a desired value Ii

des (say, 0.7 or more) to avoid the risk of voltage instability of a power system. When the index Ii for a load bus goes below this desired value, the corrective action should be taken to bring back Ii to its desired value. Hence, it is required to reschedule reactive power of generation buses and/or load shedding at load buses to improve the voltage stability index of the most vulnerable load bus to its desired value to avoid possible voltage collapse of the system. The most vulnerable bus of a power system is the bus having the lowest value of the voltage stability index. i.e., Ik = Min {Ii, for i = 1 . . . N} i.e., kth bus has the lowest value of the index.

The required change in index for kth load bus is:

In the next sections, procedures for improving Ik to its desired value Ikdes are presented. The

procedures involve: 1) reactive power rescheduling in selected generation

buses; and 2) emergency load shedding at the target load bus(es).

3.1 Reactive Power Rescheduling

It is accepted that the voltage instability in a power system appears due to lack of reactive power supply to the vulnerable load bus(es). Therefore, it is required to reschedule reactive power of generation buses to improve voltage stability condition of a power system, which is indicated by the index Ik of the most vulnerable kth load bus. Without loss of generality, taking bus 1 as the slack bus, the change in index (∆Ik) with respect to change in bus voltage can be expressed as:

·

9

The change in bus voltage vector [∆V ] with respect to change in reactive power

injection vector [∆Q] can be expressed as:

Substituting [∆V ] in Eq. (2) from Eq. (3), we have

The sensitivity factors [β] relate change in the index value for kth bus with respect to change in reactive power injections at the buses, but reactive power rescheduling can be carried out only in the generation buses, as such, representing Eq. (4) only for generation buses we have

10

A generation bus with low/insignificant sensitivity factor requires considerably higher changes in reactive power for small change in the voltage stability index Ik. Therefore, it is required to select generation buses having higher values of SF for upgrading/improving the index Ik to its desired value Ik

des . For this purpose, SF are ranked and based on the ranks of SFs [βi for i = 1,...,NG], generation buses are selected to take part in the process of upgrading index Ik. To ensure participation of sensitive buses in the process of upgrading the index Ii , a cut-off value for sensitivity factor βcut is selected. The buses with SF below this cut-off value are not included. The value of βcut is determined based on the largest value of SF among all generation buses as follows:

Simulation of a number of systems shows that MF value between 0.5 to 0.6 includes those buses that are sensitive to the index Ik. Assuming MG as the number of participating generation buses in the process of upgrading/improving the index Ik in terms of ranked sensitivity factor, Eq. (5) is represented for participating generation buses as follows:

[β] is a row matrix, therefore, [∆Q] values are to be calculated using pseudo inverse technique i.e.,

Solving the above equation the value of ∆Qi can be written as

11

Thus, the modified contribution from generation buses is as follows:

Now, reactive power at these buses is to be modified to the new value taking them as

PQ buses.

3.1.1 Checking Reactive Power Limit Violation: - As long as the required reactive power

modification satisfy QGi(min) ≤ QGi(old) + Qi ≤ QGi(max) for i = 1,...,MG, there is

no violation of reactive power limits. When violation in reactive power limit(s) of a generator is detected the procedure described below is adopted for assigning a fixed change in reactive power governed by its limit. If rth generator bus violates the reactive power limit, then for that bus change in reactive power injection is calculated as given below:

Now, rth bus would undergo a fixed change in reactive power by the quantity ∆Qr(allowed) and this bus would take the status of a non participating generator bus. Thus, the modified value of ∆I would be

3.2 Emergency Load Shedding:

Emergency load shedding at selected buses (including vulnerable bus) improves the voltage stability index Ik for the kth bus. Under emergency situations when the reactive power rescheduling cannot improve the index value Ik to the desired value Ikdesk , load shedding is to be applied to avoid risk of voltage instability in a power system. The change in index value Ik at kth vulnerable load bus with respect to system state variable vector [∆δ ∆V ] is given as:

12

The Jacobian matrix of NR load flow analysis relates change in real and reactive power injections with respect to change in bus voltage angles and bus voltage magnitudes as follows:-

Substituting [∆δ ∆V ] in Eq. (12) from Eq. (13) we have

13

The above equation can be expressed as:

where [γ ] and [β] are the sensitivity factors (SFs) relating [∆P] and [∆Q] to the change in the index value of kth bus. Assuming load power factors do not change with change in load values, Eq. (15) can be written as:

14

Where αj = γj + tan(φj )βj = sensitivity factor for jth load bus

Inclusion of load buses with low/insignificant sensitivity factors require considerably higher load shedding at the buses for required change in the voltage stability index Ik. Therefore, it is required to select load buses having higher values of SFs for upgrading the index Ik. For this purpose also, SF are ranked and based on the ranks of SFs (αi for i = 1. . N), load buses are selected to take part in the process of upgrading the index Ik. To ensure participation of sensitive load buses, a cut-off value for sensitivity factor αcut is selected. The value of αcut is determined based on the largest value of SF among all load buses as follows:

Simulation of a number of systems shows that MF value between 0.6 to 0.7 includes those buses that are sensitive to index Ik. Assuming ML as the number of participating load buses in the process of upgrading/improving the index Ik in terms of ranked sensitivity factor, Eq. (16) is represented for participating load buses as follows:

Sensitivity factor matrix [α] is a row matrix, therefore, [∆P] values are to be calculated using pseudo inverse technique, i.e.,

Solving the above equation the value of ∆Pi can be written as:

15

Thus, the modified load at these buses is:

Load shedding at a load bus basically makes ∆P positive at that bus; therefore, SF values for load shedding must be positive, i.e., only load buses with αi > 0.0 are selected for load shedding. In case of load shedding modified load at the load buses are as follows:

3.2.1 Checking Limit Violation for Loads: - In order to ensure that essential loads are not shed, limit on load shedding has been fixed at load buses selected for load shedding. As long as this limit on load shedding is not violated, i.e., if PDi(min) ≥ PDi(old)- ∆Pi , for i = 1,...,ML, load shedding is within allowable limit. In case of limit violation, following strategies are adopted. Assuming limit violation at rth load bus, i.e.

Now, the rth bus would under go a fixed change in real power by the quantity ∆Pr(allowed) and this bus would take the status of a non participating load bus. Thus, the modified value of ∆Ik would be

Equation (19) is solved for this new ∆Ik(modified) ith reduced number of load buses (i.e., in this case for i = 1,...,ML − 1). If more than one load buses violate the limits, then the number of participating load bus will be reduced accordingly.

16

3. Determination of Suitable Value of MG, ML, and Solution Procedure:-

The proposed procedure aims at involving sensitive generation buses and/or load buses for reactive power rescheduling and/or load shedding, respectively, to improve the voltage stability condition of a power system. Load shedding option is undertaken when reactive power rescheduling of generation buses cannot improve the voltage stability index of a vulnerable load bus to its desired value. To ensure participation of sensitive generation buses and/or load buses, buses having SF values more than cut off values βcut and αcut are selected for reactive power rescheduling and/or load shedding, respectively. A factor (KM > 1) is included for the purpose of ensuring that sufficient number of buses are included during improvement of the value of Ik and all the rescheduled (reactive power) generators or load shedding buses do no get fixed at their limits. A value of KM ≈ 1.1–1.2 has been found to work well for most of the systems. The procedure adopted for the selection of participating buses is as follows:1. Store the bus number in arrays BRj and BLj for j = 1. . .N according to descending order of the sensitivity factor associated with each bus for reactive power rescheduling and load shedding, respectively (buses having highest sensitivity factor are ranked as one, bus with next highest sensitivity ranked two, and so on) and set MG= 0.2. Set j = 1 and ∆Iach = 0.3. i = BRj .4. If ith bus is not a generation bus; go to step 6.5. If ∆Iach > KM ∆Ik go to 15 MG = MG + 1

∆Iach = ∆Iach + βi ∆Qilimit

6. j = j + 1.

7. If j ≤ N; go to step 3.

8. Set j = 1 and ML = 0.

9. i = BLj .

10. If ith bus is not a load bus; go to 13.

11. If αj < 0 go to step 13.

12. If ∆Iach > KM ∆Ik go to 15.

ML = ML + 1∆Iach = ∆Iach + αi ∆ PDi

limit

13. j = j + 1.

14. If j ≤ N; go to step 9.

15. Stop.

17

Where

The sensitivity factors are determined using linear relation among [∆V], [∆δ], [∆P], and [∆Q] corresponding to a system operating condition. Therefore, change in system operating condition (i.e., due to change in bus injections) leads to change in SF values for the buses. As such, if the estimated change in [∆P] and [∆Q] (for desired change in index value ∆IK) are applied to their respective buses and a load flow analysis is carried out, the desired value of the index Ides k may not be achieved. Therefore, it is required to repeat load flow analysis by assigning ∆Ik = Ides

K – IKk , where IK

k is the index value at Kth iteration of load flow analysis. This results in correction in SF values and ensures improvement of Ik to the desired value. The algorithm of the proposed procedure for reactive power rescheduling or/and load shedding to improve voltage stability condition of a power system is depicted in the flow chart presented in Figure 1. In the flow chart an array [BF] is used to set flags for participating generation and load buses. [BF] is assigned by “1” for all participating buses. When limit violation is detected at a bus, the bus status is modified to a non-participating bus (i.e., if rth bus violates the reactive power or load shedding limit, BFr is reassigned by “0”) as described in Sections 3.1.1 and 3.2.1. An integer variable FV is introduced in the flow chart to indicate limit violation during estimation of reactive power rescheduling and load shedding. FV is set to “0” before checking limit violation for the participating generation buses or loads buses. When limit violation is detected for a generation or a load bus, FV is set to “1,” the bus is demarcated as non-participating bus and required change in the index value is modified as given by Eqs. (11) Or (23) by assigning the bus with the limiting value, as described in Sections 3.1.1 and 3.2.1.

18

19

20

5. Simulations Results and Discussion

To verify the applicability of the proposed procedure, simulations were carried out on IEEE30 bus system shown in Figure 2. To demonstrate the effectiveness of the procedure, both reactive power rescheduling and load shedding were carried out according to the requirements to improve the value of the index Ik of most vulnerable bus to its desired value Ides

k . The system loading is adjusted in such a way that voltage stability indices of a few buses of the system falls below 0.75. Table 1 shows the generations, loads, and voltage conditions at these generation buses. Table 2 presents the loads, voltage condition, and voltage stability index of load buses of the system. It shows the minimum value of voltage stability index is appearing at load bus 19, the value is I19 = 0.718003. From voltage instability point of view, this bus is the most vulnerable bus. Simulations were carried out to improve this index to different desired value with different reactive power limits on the generation buses. Minimum value of load, which cannot be shed at load bus, is taken as 20% of the initial load at the bus. Table 3 presents the two different reactive power limits applied to the generation buses for simulation purpose. Power limits on the generation buses. Minimum value of load, which cannot be shed at load bus, is taken as 20% of the initial load at the bus. Table 3 presents the two different reactive power limits applied to the generation buses for simulation purpose.

5.1. Desired Value of I19des = 0.75

Case-I reactive power limits are applied to the generation buses for improving value of the voltage stability index at bus 19. The results obtained from simulation are presented in Tables 4 and 5.

The simulation results show that the voltage stability index is improved to 0.744932 from 0.718003 through reactive power rescheduling. In this case, load shedding is not required for improvement of the voltage stability index.

21

22

5.2. Desired Value of I19des = 0.8

At first, Case-I reactive power limits are applied to the generation buses for improving value of the voltage stability index at bus 19. The results obtained from simulation are presented in Tables 6 and 7.

23

24

25

The simulation results show that the voltage stability index is improved to 0.796110 from 0.718003 through reactive power rescheduling and load shedding. As the reactive power reserve are saturated, i.e., generators are set to maximum reactive power limits, load shedding has been applied to improve the index to its desired value. Load shedding has been carried out only at bus 19. Again, Case-II reactive power limits are applied to the generation buses for improving value of voltage stability index at bus 19. The results obtained from simulation are presented in Tables 8 and 9. The simulation results show that the voltage stability index is improved to 0.801468 from 0.718003 through reactive power rescheduling only after the limits on reactive power generations are changed from Case-I to Case-II. Therefore, the change in reactive power limits on generation buses affects the load shedding options.

26

27

28

6. CONCLUSION

The proposed procedure for reactive power rescheduling or load shedding aims at improving voltage stability condition of a power system from proximity of voltage collapse. Index Ik, the voltage stability index of the most vulnerable bus of a power system, is used as the basis for the improvement of voltage stability condition of the system. Sensitivity factors are derived to relate change in voltage stability index for change in reactive power at generation buses and change in load at load buses. The sensitivity factors are used to determine the required reactive power rescheduling and/or load shedding to improve voltage stability condition of a power system. The proposed procedure aims at involving only sensitive generation buses and/or load buses for reactive power rescheduling and/or load shedding, respectively, to improve voltage stability condition of a power system. Load shedding option is undertaken when reactive power rescheduling of generation buses cannot improve voltage stability index of a bus to its desired value. The proposed procedure for improving voltage stability condition by reactive power rescheduling or load shedding can provide useful information to power system planner/operator to undertake corrective action to avoid risk of voltage instability in a power system.

29

7. APPENDICES

N Total number of buses in the system

NG Total number of generation buses in the system

NL Number of load buses in the system

Pi Injected active power at ith bus

Qi Injected reactive power at ith bus

QGi(max) Maximum limit of reactive power generation at ith bus

QGi(min) Minimum limit of reactive power generation at ith bus

PDi(min) Limit on load shedding of the ith load bus

Si Pi + jQi

Vi Magnitude of voltage at ith bus

δi Angle of the bus voltage at ith bus

Gi j + jBi j Element of Y -BUS matrix at ith row and j th column

30

8. REFERENCES

1.Kunder, P., Paserda, J., Ajjarapu, V., Anderson, G., Bose, A., Conizares, C., Haliziargyriou, N.,Hill, D., Stamaoric, A., Taylor, C., Cutsen, T. V., and Vittal, V., “Definition and classification of power system stability,” IEEE/CIGRE Joint Task Force on Stability Terms and Definition, IEEE Trans. Power Syst., Vol. 19, No. 2, pp. 1387–1401, May 2004.

2. Kessel, P., and Glavitsch, H., “Estimating the voltage stability of a power system,” IEEE Trans. Power Del., Vol. PWRD-1, No. 3, pp. 346–354, July 1986.

3. Clark, H. K., “New challenges: Voltage stability,” IEEE Power Eng. Rev., pp. 33–37, April 1990.

4. Tamura, Y., Mori, H., and Lwanoto, S., “Relationship between voltage instability and multiple load flow solutions in electrical system,” IEEE Trans., Vol. PAS-102, pp. 1115–1125, May 1983.

5. Crisan, O., and Liu, M., “Voltage collapse prediction using an improved sensitivity approach,” Elec. Power Syst. Res., pp. 181–190, 1984.

6. Lof, P. A., Anderson, G., and Hill, D. J., “Voltage stability indices of stressed power system,” IEEE Trans. PWRS, Vol. 8, No. 1, pp. 326–335, 1993.

7. Tiranuchit, A., and Thomas, R. J., “A posturing strategy against voltage instability in electrical power systems,” IEEE Trans. PWRS, Vol. 3, No. 1, pp. 87–93, 1989.

8. Tuan, T. Q., Fandino, J., Hadjsaid, N., and Sabonnadiere, J. C., “Emergency load shedding to avoid risk of voltage instability using indicators,” IEEE Trans. Power Syst., Vol. 9, No. 1, pp. 341–351, Feb. 1994.

9. Sinha, A. K., and Hazarika, D., “Comparative study of voltage stability indices in a power system,” Int. J. Power Energy Syst., Vol. 22, pp. 589–596, Nov. 2000.

Documents

Voltage Stability