A new approach to dynamic contingency selection

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A NEW APPROACH TO DYNAMIC CONTINGENCY SELECTION

Chung-Liang Chang Y ~ a n - Y i h 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 computational effort by ranking the various outage events according to 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 t o 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). T o 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. T o 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 to 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 t o 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 o n top of the ranking lists.

In addition t o 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 t o insufficient damping for the electromechanical

mode [ I 1 - 12

I .

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 t o the significant advances in steady-state contingency selection, developments in dynamic contingency selection have been rather limited. Venikov e t al. [I31 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 eigenvalues from the first iteration of an iterative eigenvalue computation method are used to 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 a t 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 [ 11. The method has been shown to be capable of alleviating the computational 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 to extend this concept t o estimate eigenvalues.

In this paper, an iterative algorithm based on modified AESOPS (Analysis of Essentially Spontaneous Oscillations in Power Systems) program [ 1 7 ] is employed to 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 to 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

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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 t o 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.

~~~~~~

bus name type

First Nuclear plant # 1 nuclear First Nuclear plant # 2 nuclear Second Nuclear plant # I nuclear Second Nuclear plant # 2 nuclear thermal Shenao # 1 Shenao # 2 thermal Taipei (synchronous S.C. condensers) Chinshan hydro Churkung hydro Takuan hydro T a l i # 1 thermal Hsinta # 1 thermal Hsinta # 2 thermal Nanpu # 1 & 2 thermal Nanpu # 3 thermal Kaohsung S.C. POWER FLOW AND EIGENVALUE

ANALYSlS OF BASE CASE (PREFAULT CONDITION) ~ ~~ area N 582.0 N 587.0 N 950.0 N 853.0 N 38.0 N 85.0 N 0.0 C 74.1 C 22.0 C 33.0 S 112.0 S 220.0 S 220.0 S 40.0 S 57.0

s

0.0 CONTINGENCY ,oltage nagnitude 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 OPERATING CONDITION USING

FIRST 1TERATlON METHOD

voltage angle 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 ESTIMATE THE WORST-

DAMPED EIGENVALUE USING FIRST ITERATION METHOD

Center (SI

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South POWER FLOW AND EIGENVALUE

ANALYSIS OF BASE CASE

COMPUTE LEFT AND RIGHT EIGENVECTORS 129.1 3.3% 940 24.8% 649 16.7% 1450 38.2% SELECT DEFINED Total COMPUTE SENSITIVITY

I

OF SYSTEM STATE MATRIX

I

3873.1 100% 3790 100% COMPUTE SENSITIVITIES EIGENVALUES USING SYSTEM DAMPING

I

CONTINGENCY LIST USING SYSTEM DAMPING

1

CONTINGENCIES

(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 I6 generating units including 2 synchronous condensers as shown in Fig. 2. These generating units are geographically located a t 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

fifteen electromechanical oscillation modes of the system are listed in Table 3, where the blocked entries correspond t o 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 (1.181

Hz)

is very poor. This is due t o 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 27 100 112 116 118 219 237 238 257 258 300

-

Table 1. Summary of generator bus data

-

reactive 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

-

~

Table 2 . Real power generations and load demands in the three areas load demand

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Table 3. Electromechanical oscillation modes for the base case

-

mode Mmbel __ 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 f I e q u e n c y (Hz) 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 q -0.063837.4191 -3.76 16*j8.4815 -3.292338.7223 -1.485 249.4 176 -0.344 1tj9.6400 -0.3493410.5105 -0.2542+10.7894 -0.1562j11.2513 -0.4937?j11.4603 -0.1829fjl1.6828 -2.1951*j11.726C -1.584ej12.1176 -0.1656*j12.1784 -0.272Ctkj12.8381 -0.342Wj18.780; driven generator #9 #loo #300 #112 #lo #4 #27 #219 #3 #237 #116 #118 #257 #2S8 #25

bus normalized speed eigenvectors

3 4 9 10 25 27 100 112 116 118 219 237 238 257 258 300 1.00 -0.02 0.00 -0.01 -0.03 -0.05 -0.05 -0.01 -0.01 -0.01

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-0.14 -0.05 -0.02 0.00 0.01 0.01 -0.02 -0.02 0.00 0.02 0.00 -0.02 0.23 0.01 0.07 0.00 0.00 0.00 0.07 OiOO 0.00 0.01 0.01 0.01 0.00 -0.01 0.00 0.00 0.00 -0.01 -0.01 0.02 -0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01 -0.11 -0.11 0.00 -0.02 0.00 -0.01 -0.02 -0.04 -0.04 -0.01 -0.01 0.00 0.00 0.00 0.00 _0.00 _0.00 _0.00 0.00 -0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 4. RESULTS

Using the normal operating condition (base case solution) as the initial guess, the first iteration of fast decoupled load flow is performed t o estimate the operating condition after a line outage event. Then the first iteration of AESOPS is used t o 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 worst-damped electromechanical oscillation mode, is of major concern. T o 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 ( a o ) and the oscillation frequencies ( p o / 2 n ) 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

ranking 1 2 3 4 5 6 7 8 9 10 11 12 13 14 426-5 1 1 1.086 346-416 1.113 416-426 1.150 1-346 1.167 326-346 511-521 -0.0582 1.177 5 11-235 -0.0585 1.170 -0.0615 1.179 311-326 -0.0616 1.178 32-306 -0.0622 1.179 306-326 -0.0625 1.179 7-3 11 -0.0632 1.180 -0.0632 1.180 -0.0637 1.181 241

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Table 7. Double-line-fault contingency evaluation using

' 9 32-306

1

11 i 306-326

1

12

i

7-311

I

10

I

32-7

Table 5 . Single-line-fault contingency evaluation using the first-iteration method

i

-0.0577 ~ 1.172 -0.0593 1.175 -0.0607 ~ 1.177 -0.058 1 ~ 1.173 1 2 3 4 5 6 7 1 8 9 10 1 11 ' 12 426-5 11 346-416 416-426 1 --346 326-346 511-521 5 11-235 1-7 3 11-326 32-306 306-326 7-311 32-7 1-311 --- .____ -0.1 115 (mode 5) 1.258 -0.0327 1.120 -0.0495 -0.0556 -0.0596 -0.06 16 -0.0619 -0.0584 -0.0600 -0.0628 -0.063 1 1.151 1.168 1.172 1.178 1.172 1.179 1.178 1.179 1.179 -0 0632 1 1180 -0 0633

'

1180 -0 0637 1181 _ _ p- ~

By comparing the results in Tables 4 and 5 , i t is concluded that the first-iteration method can yield the same ranking list as that acheved by the exact method. But the first-iteration method requires much less computational effort. It is worth noting that the eigenvalues for mode 1 under the severest outage case (an outage on branch 426-5 1 1 ) 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

the first-iteration method

Outage;-

I

real part of mode 1 ( a o ) branch 511-235 ~ islanding 346-416

'

-0 1528 (mode 5) 416-426 ~ -0 1643 (mode 5) 426-5 11 -0 1659 (mode 5) 326-346 -0 0460 511 -521 -00511 311-326 -0 0566 32-306

1

-00586 32-7 -0 0587 306-326 -0 0603 7-311

1

-00632 p - ~- _ _ +- - 1-346 1 -00381 1.318 1.328 1.141

1

1.177 1.170 1.173 1.173 1.175 1.180 I 1.328

I

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 first- iteration method with much less computational effort. I t 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 operating 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.

7 mode 1

''

- base case

+

- single-line-fault

( 1 -346) contingency

A - double-line-fault (1-346) contingency 5 - . I O -.75 -.50 - . 2 5

Fig. 3 Effect of line outage on electromechanical mode eigenvalues

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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 computational 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 considerations 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 contingency selection algorithm,” IEEE Trans. PAS, vol. 100, G. D. lrisarri 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 contingency 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 selection for voltage security analysis,” IEEE Trans. PAS. vol. 104, G . C . Ejebe, H.P. Van Meetercn. B.F. Wollenberg. “Fast contingency screening and evaluation for voltage security analysis.” Paper 88 W M 161-2. prcsented at the IEEEjPES 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, 1919. Y.Y. Hsu, S.W. Shyii, and C.C. Su, “Low frequency oscillations 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.1. 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 sensitivities 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 engineering, 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 resedrch interests include power system dynamics, control and stability analysis, power system reliability analysis short-term load forecasting. economic operation, dnd the application of coinpiiter methods to power system problem\

He I S a member of I E E E

Chung-Liang Chang was born i n 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 T i w a n Power Company and the support of National Science Council of R 0 C.. he has been working toward his Ph D degree in the Electricdl Engneering Department of National Taiwan University, Taipei, Taiwan

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