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1524 Transactions on Power Systems, No. November 1990

A NEW APPROACH TO DYNAMIC CONTINGENCY SELECTION

ChUg-Liang Chang Y~an-Yih

HSU

Department of Electrical Engineering

National Taiwan University Taipei, Taiwan

ABSTRACT

Contingency selection is important for the security analysis of a large scale power system since it can reduce the required computa- tional effort by ranking the various outage events according t o their severities. Among the three aspects of power system security, i.e., transient security, dynamic security, and steady-state security, contingency selection for dynamic security assessment is of concern in this paper. The proposed method is to use an iterative method to compute the eigenvalues of the system under outage conditions. The initial values for the iterative procedure are the eigenvalues for the normal operating condition (base case eigenvalues). To reduce the computational burden, the eigenvalues of the system under outage conditions from the first iteration are employed for contingency ranking. From the results obtained from the study on Taiwan power system, it is concluded that contingency ranking using the eigenvalues from the first iteration is both accurate and efficient. It is also found that only the eigenvalues for the worst-damped mode must be considered in contingency ranking. To further improve the efficiency of the proposed method, results obtained from the first iteration of the fast decoupled load flow (FDLF) are also used to model the operating conditions after contingencies. Again, it is observed that satisfactory dynamic contingency selection can be achieved by using the first iteration of FDLF with much less computational effort than that required by full AC power flow. It is thus concluded that accurate dynamic contingency selection can be performed efficiently by first computing the operating conditions after contingencies using the first iteration of FDLF and then calculating the eigenvalues for the worst-damped mode by using the first iteration of eigenvalue computations.

Keywords: contingency selection, security analysis, dynamic security assessment

1. INTRODUCTION

To reduce the computational requirements in the security analysis of a large power system, numerous approaches t o steady-state contingency selection have been developed in the past decade [ 1-10]. These works on steady-state contingency selection have been very successful in ranking the severities of various outage events according to steady-state line overloadings and bus voltage violations following a generator trip or a line outage. Computational burden associated with security analysis can thus be alleviated by performing full AC power flow on only those cases on top of the ranking lists.

In addition to steady-state security assessment, dynamic security and transient security assessments are also important security functions in an energy management system. Only dynamic security assessment will be discussed in this paper.

It has been observed that, in a longitudinal power system such as Taiwan power system, dynamic instability may take place on some occasions due to insufficient damping for the electromechanical

T h i s paper w a s sponsored by t h e I E E E Power E n g i n e e r i n g S o c i e t y f o r p r e s e n t a t i o n a t t h e I E E E Power I n d u s t r y Computer A p p l i c a t i o n Conference, S e a t t l e , Washington, May 1

-

5, 1989. Manuscript w a s p u b l i s h e d i n t h e 1989 PICA Conference Record.

mode [ 1 1 - 121

.

Fast dynamic security assessment is thus essential for these cases where undamped low frequency oscillations may impose undesirable limitations on the operation of power systems. This motivates the development of an efficient approach for dynamic contingency selection which can reduce the computational effort in dynamic security assessment t o a great extent.

In contrast to the significant advances in steady-state contingency selection, developments in dynamic contingency selection have been rather limited. Venikov et al. [ 131 estimated system stability using the results from load flow computations. The proposed method was effective only for steady-state stability since it failed to take system dynamics into account. For the purpose of dynamic contingency selection, the sensitivities of system eigenvalues to a contingency can be evaluated using left and right eigenvectors [ 14- 161. The major drawback of such an approach is that considerable effort is needed for eigenvector computations, which must be repeated any time the network topology or operating condition of the system is changed.

In this paper, a novel approach for dynamic contingency selection is developed. The proposed method, which can be regarded as an extension of the work by Albugh, et al. [ 11 on steady-state contingency selection to the dynamic case, utilizes the results from the first iteration of the fast decoupled load flow (FDLF) t o estimate the operating condition following an outage event. Then, the eigen- values from the first iteration of an iterative eigenvalue computation method are used t o approximate system eigenvalues under outage conditions.

To demonstrate the effectiveness of the presented method, outage events on the transmission lines of Taiwan power system are studied. The results from this study indicate that accurate ranking list for dynamic security assessment can be achieved very efficiently by the proposed algorithm.

2. PROPOSED METHOD

Power system dynamic security assessment is aimed at examining the dynamic performance of the system following an outage. In general, two steps are involved for this purpose: the determination of postfault operating condition using load flow analysis and the computation of system eigenvalues following an outage event. This time-consuming process must be repeated for each possible outage event, thus making dynamic security analysis computationally infeasible for on-line use unless certain simplifying algorithm is adopted.

An efficient algorithm using the first iteration of FDLF has been presented for determining system operating conditions [ 1

1.

The method has been shown t o be capable of alleviating the computa- tional burden while maintaining good accuracy. In view of the success in approximating the operating condition by using the results from the first iteration, it is decided t o extend this concept to estimate eigenvalues.

In this paper, an iterative algorithm based on modified AESOPS (Analysis of Essentially Spontaneous Oscillations in Power Systems) program [ 171 is employed t o calculate the eigenvalues for low frequency electromechanical mode oscillations. It is noted that only the electromechanical mode oscillations are considered in dynamic contingency selection since a longitudinal power system such as Taiwan power system is vulnerable t o these oscillations when the trunk lines connecting the various areas of the system are heavily loaded. In fact, as will be shown later, the damping of the worst- damped electromechanical mode will be employed as the performance index for dynamic contingency selection. Thus, the proposed algorithm is very efficient since only the first iteration has t o be 0885-8950/90/1100-1524$01.00 0 1990 IEEE

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First Nuclear plant # 1 First Nuclear plant # 2 Second Nuclear plant # 1 Second Nuclear plant # 2 Shenao # 1 Shenao # 2 Taipei (synchronous condensers) Chinshan Churkung Takuan Talin #1 Hsinta # 1 Hsinta # 2 Nanpn # I & 2 Nanpu #3 Kaohsung performed for only one oscillation mode. It will also be shown later

that the algorithm can yield very accurate contingency ranking lists. In summary, the proposed method employs the first iteration of FDLF t o determine system operating condition and then uses the first iteration of AESOPS to estimate worst-damped eigenvalues. It can be regarded as the “first-iteration method for dynamic contingency selection”. Fig. 1 illustrates the flow charts of both the proposed first-iteration method and the sensitivity method [ 14-16] for purpose of comparison.

nuclear N 582.0 nuclear N 587.0 nuclear N 950.0 nuclear N 853.0 thermal N 38.0 thermal N 85.0 s.c.

I

O.O hydro C 74.1 hydro C 22.0 hydro C 33.0 thermal S 112.0 thermal S 220.0 thermal S 220.0 thermal S 40.0 thermal S 57.0 S.C. s 0.0 ANALYSIS OF BASE CASE

(PREFAULT CONDITION) 0.9900 0.9900 0.9900 0.9900 0,9900 0.9900 0.9993 0.9900 0.9701 0.9892 0.9900 0.9900 0.9900 0.9900 0.9900 0.9976 I 17.0 17.0 17.4 16.7 10.1 9.8 4.4 0.0 -9.3 -10.8 -13.1 -7.3 -7.3 -15.4 -15.3 -18.6 SELECT DEFINED CONTINGENCY I Center

I

129.1

1

3.3%

6 )

OPERATING CONDITION USING FIRST ITERATION METHOD

940 24.8%

ESTIMATE THE WORST- DAMPED EIGENVALUE USING FIRST ITERATION

649 South

(9

USING

16.7% 1450 38.2%

COMPUTE LEFT AND RIGHT EIGENVECTORS I Total

6

CONTINGENCIES 3873.1 100% 3790 100% USING SYSTEM DAMPING

(A) PROPOSED FIRST-ITERATION METHOD

(B) SENSITIVITY METHOD

Fig. 1 A comparison of the proposed first-iteration method and the sensitivity method

3. DESCRIPTION OF THE STUDY SYSTEM

The system studied is the Taiwan power system which consists of 16 generating units including 2 synchronous condensers as shown in Fig. 2. These generating units are geographically located at three different areas on the island of Taiwan, i.e. the northern area, the central area, and the southern area. Under normal operating condition (called base case), the generator bus data and the area generations and load demands are listed in Tables 1 and 2, respectively. The

I

fifteen electromechanical oscillation modes of the system are listed in Table 3, where the blocked entries correspond to those generators with the normalized speeds greater than 0.15. It can be observed from Table 3 that the damping for the oscillation mode with lowest frequency (1.18 1 Hz) is very poor. This is due to the longitudinal structure of Taiwan power system and the great amount of power flows on the EHV transmission lines (see Table 1 and Table 2). Hence, it is important t o examine how the damping for this worst-damped oscillation mode changes as a result of an outage event on one of the 345 trunk lines connecting the three areas of the system. In fact, it is the main objective of this paper t o establish a dynamic contingency ranking list according t o the estimated damping for the worst-damped mode from first iteration results. When the ranking list is established, detailed dynamic stability analyses and eigenvalue computations should be performed on only those outage events on top of the list.

bus number 3 4 9 10 25 27 100 112 116 118 219 237 23 8 257 258 3 00

-

Table 2.

Table 1. Summary of generator bus data reactivt power 95.0 95.6 148.3 137.0 26.8 72.1 -20.0 40.6 10.0 50.0 118.3 115.8 115.4 29.9 39.1 -33.0 roltage voltage magnitude1 angle

Real power generations and load demands in the three areas

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Table 3. Electromechanical oscillation modes for the base case node mmbe 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

-

Ir uency

82)

1.181 1.350 1.388 1.499 1.534 1.673 1.717 1.791 1.824 1.859 1.866 1.929 1.938 2.043 2.989 ~ eigenvalue a+p -0.063837.4191 -3.7616fj8.4815 -3.292338.7223 -1.485239.4 176 -0.344 lfj9.6400 -0.3493310.510! -0.2542+10.7894 -0.156 Zkjl1.251? -0.4937?j11.460? -0.182*j11.682I -2.1951tj11.726C -1.584&j12.1176 -0.165ej12.1784 -0.272Ctkj12.8381 -0.342Ctkj 18.7802 driven generator 1 9 1100 1300 # l l Z # l o $4 # 27 d219 #3 #237 #116 $118 $257 $258 1 2 5

normalized speed eigenvectors bus 3 4 9 10 25 27 100 112 116 118 219 237 238 257 258 300 0:; 0:;

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RESULTS

Using the normal operating condition (base case solution) as the initial guess, the first iteration of fast decoupled load flow is per- formed t o estimate the operating condition after a line outage event. Then the fust iteration of AESOPS is used to estimate the damping of the worst-damped electromechanical mode under each operating condition. Again, base case eigenvalues are chosen as the initial guess for the AESOPS. It is not necessary t o compute all eigenvalues since only mode 1, the worstdamped electromechanical oscillation mode, is of major concern. To excite mode 1, generator #9 (see Table 3 ) is chosen as the driven generator.

In the following discussions, dynamic contingency selection will be performed for single-line-fault contingencies and double-line-fault contingencies on the 345 KV trunk lines.

4.1 Single-line-fault contingency ranking

The real parts of the eigenvalues associated with the worst- damped mode (ao ) and the oscillation frequencies (Po /27r) for the system under various single-line-fault outages are listed in Tables 4 and 5. Table 4 gives the results from the exact method (full AC load flow and exact eigenvalue computations) while Table 5 lists the results from the proposed first-iteration method (first iteration of FDLF and first iteration of AESOPS).

Table 4. Single-line-fault contingency evaluation using the exact method

rankin 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 outaged branch 426-5 1 1 346-416 416-426 1 - 3 6 326-346 511-521 51 1-235 1-7 31 1-326 32-306 306-326 7-311 32-7 1-311

real part of mode 1 (ao)

-0.0062 -0.0196 -0.0474 -0.0539 -0.0575 -0.0582 -0.0585 -0.06 15 -0.0616 -0.0622 -0.0625 -0.0632 -0.0632 -0.0637 frequency (p0/27r) 1.086 1.113 1.150 1.167 1.171 1.177 1.170 1.179 1.178 1.179 1.179 1.180 1.180 1.181

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real part of mode 1 (M) Table 5. Single-line-fault contingency evaluation using

the first-iteration method

frequency @&r) ranking 1 2 3 4 5 6 7 8 9 10 11 12 13 14 outaged branch 426-5 11 346-416 416-426 1-346 326-346 511-521 511-235 1-7 311-326 32-306 306-326 7-3 11 32-7 1-311

real part of mode 1 (ao)

-0.11 15 (mode 5) -0.0327 -0.0495 -0.0556 -0.0584 -0.0596 -0.0600 -0.0616 -0.0619 -0.0628 -0.0631 -0.0632 -0.0633 -0.0637 frequency Q0/27r) 1.258 1.120 1.151 1.168 1.172 1.178 1.172 1.179 1.178 1.179 1.179 1.180 1.180 1.181

By comparing the results in Tables 4 and 5 , it is concluded that the first-iteration method can yield the same ranking list as that achieved by the exact method. But the first-iteration method requires much less computational effort. It is worth noting that the eigen- values for mode 1 under the severest outage case (an outage on branch 426-5 11) can not be found by the first-iteration method. Instead, the eigenvalues for another mode (mode 5 ) are obtained. Previous experience revealed that, under such circumstances, the outage would be severer than other cases in which the eigenvalues for mode 1 can be figured out by the first-iteration method.

4.2 Double-line-fault contingency ranking compared in Table 6 and Table 7.

The results of contingency ranking for double-line-faults are

Table 6. Double-line-fault contingency evaluation using the exact method

1 2 3 4 5 6 7 8 9 10 11 12 511-235 346-416 416-426 426-5 11 1-346 511-521 326-346 311-326 32-306 32-7 306-326 7-3 11

real part of mode 1 (ao)

islanding divergent divergent divergent -0.0332 -0.0359 -0.0402 -0.0556 -0.0577 -0.0581 -0.0593 -0.0607 1.138 1.163 1.144 1.170 1.172 1.173 1.175 1.177

Table 7. Double-line-fault contingency evaluation using the first-iteration method

326-346 311-326 32-306 51 1-521 10 32-7 12 7-311 - islanding -0.1528 (mode 5) -0.1643 (mode 5) -0.1659 (mode 5) -0.0381 -0.0460 -0.051 1 -0.0566 -0.0586 -0.0587 -0.0603 -0.0632 1.318 1.328 1.328 1.141 1.149 1.177 1.170 1.173 1.173 1.175 1.180

Again, it is observed that there is only slight difference between the ranking lists in Table 6 and Table 7. This confirms the assertion that accurate contingency ranking can be achieved by the fmt- iteration method with much less computational effort. It is also noted that, in the first iteration method, the eigenvalues for mode 1 can not be found for those outage cases which cause islanding

or

divergent power flows. Of course, these cases are ranked as the severest among the outage events studied.

One may wonder how the eigenvalues associated with other modes than mode 1 would drift from their base case values when an outage takes place. To this end,

Fig.

3 illustrates the most dominant eigenvalues for electromechanical modes for both the normal operat- ing condition and the outaged conditions. It is observed that only mode 1 is critical for dynamic stability considerations. Thus, the eigenvalues for other modes need not be computed.

B

f

l4 ** 13

*+d

1

l3

9 '

+A

7 I l l

:.

5 - base case

+

- single-line-fault (1-346) contingency

A

- double-line-fault (1-346) contingency -.lo -.75 -.SO -.25 Fig. 3 Effect of line outage on electromechanical

(5)

1528

5. CONCLUSIONS

A novel approach using the first iteration of FDLF and the first iteration of AESOPS has been proposed for dynamic contingency selection. It is found that accurate ranking list can be achieved very efficiently by using the developed first-iteration method. The com- putational burden incurred in dynamic security assessment can thus be alleviated since only those cases on top of the ranking list require detailed dynamic stability analyses. It is expected that further developments in this respect can lead t o the possible implementation of on-line dynamic contingency ranking and security assessment packages on an energy management system in the near future.

6 . REFERENCES

F. Albuyeh, A. Bose, and B. Heath, “Reactive power con- siderations in automatic contingency selection,” IEEE Trans. G.C. Ejebe and B.F. Wollenberg, “Automatic contingency selection,” IEEE Trans. PAS, vol. 98, pp. 97-109, 1979. T.A. Mikolinnas and B.F. Wollenberg, “An advanced con- tingency selection algorithm,” IEEE Trans. PAS, vol. 100, G.D. Irisarri and A.M. Sasson, “An automatic contingency selection method for on-line security analysis,” IEEE Trans. G.D. Irisarri, D. Levner, and A.M. Sasson, “Automatic con- tingency selection for on-line security analysis-real time results,” IEEE Trans. PAS, vol. 98, pp. 1552-1559, 1979.

I. Dabbaghchi and G. Irisarri, “AEP automatic contingency selector: branch outage impacts on load bus voltage profile,” IEEE Trans. PWRS, vol. 1, No. 2, pp. 37-45, 1986.

T. K. P. Medicherla and S. C. Rastogi, “A voltage-criterion based contingency selection technique,” IEEE Trans. PAS, vol. 10, M.G. Lauby, T.A. Mikolinnas, and N.D. Reppen, “Contingency selection of branch outages causing voltage problems,” IEEE Trans. PAS, vol. 102, pp. 3899-3904, December 1983. K. Nara, K. Tanaka, H. Kodama, R.R. Shoults, M.S. Chen, P. Van Olinda and D. Bertagnolli, “On-line contingency selec- tion for voltage security analysis,” IEEE Trans. PAS, vol. 104, G.C. Ejebe, H.P. Van Meeteren, B.F. Wollenberg, “Fast con- tingency screening and evaluation for voltage security analysis,” Paper 88 WM 161-2, presented at the IEEE/PES 1988 Winter Meeting.

C. Barlier, E. Ferrari, and K.E. Johansson, “Questionnaire on electromechanical oscillation damping in power systems: Report on answers,” ELECTRA, Vol. 64, pp. 59-90, 1979. Y.Y. Hsu, S.W. Shyu, and C.C. Su, “Low frequency oscilla- tions in longitudinal power systems: experience with dynamic stability of Taiwan power system,” IEEE Trans. PWRS, vol. 2, V. A. Venikov, V. A. Stroev, V.I. Idelchick, and V.I. Tarasov, “Estimation of electrical power system steady-state stability in load flow calculations,” IEEE Trans. PAS, vol. 94, pp. 1034- 1041, 1975.

M. El-Din and T.H. Alden, “Second order eigenvalue sen- sitivities applied t o power system dynamies,” IEEE Trans. R.C. Burchett and G.T. Heydt, “Probabilistic methods for power system dynamic stability studies,” IEEE Trans. PAS, EPRI Report, A Probabilistic Approach to Stability Analysis, R.T. Ryerly, D.E. Sherman, and R.J. Bennon, Frequency Domain Analysis of Low Frequency Oscillations in Large Electric Power Systems, EPRI Research Project 744-1, vol. 1-5, 1982.

PAS, vol. 101, NO. 1, pp. 107-1 12, 1982.

pp. 608-619, 1981. PAS, vol. 100, pp. 1838-1844, 1981. pp. 3523-3531, 1982. pp. 847-856, 1985. NO. 1, pp. 92-100, 1987. PAS, vol. 96, pp. 1928-1936, 1977. vol. 97, pp. 695-702, 1978. EL-2797, 1983.

Yuan-Yih Hsu was born in Taiwan on June 19, 1955. He received his B.Sc., M.Sc., and Ph.D. degrees, all in electrical engineer- ing, from National Taiwan University, Taipei, Taiwan.

From 1982 till 1983, he worked at the university of Calgary, Alberta, Canada, as a postdoctoral research fellow and instructor. Since 1984, he has been an associate professor at the Department of Electrical Engineering, National Taiwan University. At present, his research interests include power system dynamics, control and stability analysis, power system reliability analysis, short-term load forecasting, economic operation, and the application of computer methods to power system problems.

He is a member of IEEE.

Chung-Liang Chang was born in Taiwan on Feburary 16, 1958. He received his B.S. and M.S. degrees in electrical engineering from National Tsing Hua University, Hsinchu, Taiwan, in 1980 and 1982, respectively.

Since joining Taiwan Power Company in 1982, Mr. Chang has been working with the System Planning Department. From June, 1983 t o March, 1987 he also taught at the Taiwan Power Company’s Training Center. Since 1987, with the recommenda- tion of Taiwan Power Company and the support of National Science Council of R.O.C., he has been working toward his Ph.D. degree in the Electrical Engineering Department of National Taiwan University, Taipei, Taiwan.

數據

Fig.  1  A comparison of the proposed  first-iteration method and  the sensitivity method
Table 3.  Electromechanical  oscillation  modes  for  the  base  case  node  mmbe  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  -  Ir  uency 82) 1.181 1.350 1.388 1.499 1.534 1.673 1.717 1.791 1.824 1.859 1.866 1.929 1.938 2.043 2.989  ~  eigenvalue
Table  6.  Double-line-fault contingency evaluation using  the exact method

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