A New Tool for Dynamic Security Assessment of Power Systems

Copyright «:> IFAC Control of Power Systems and Power Plants, Beijing, China, 1997

A NEW TOOL FOR DYNAMIC SECURITY ASSESSMENT OF POWER SYSTEMS Y. Xue Y. Yu J. Li Z. Gao C. Ding F. Xue

L. Wang G.K. Morison P. Kundur

Nanjing Automation Research Institute 24 Caijiaxiang, Nanjing 210003 P.R. China

Powertech Labs Inc. 12388 - 8Et' Ave. Surrey, B.C. V3W 7R7 Ctl1'UlIkl

Abstract: This paper describes a new tool for dynamic security assessment of power systems, in which two technologies are combined: the EEAC method and time-domain simulations. Details of the structure and functionalities of the tool are discussed. The applications of the tool are illustrated with a realistic power system model as an example. The results show that both fast computation speed and reliable perfonnance are achieved. Copyright © 1998 IFAC Keywords: power systems, stability, security analysis, simulation

automated solution methods for DSA, and some degree of success has been achieved (Xue et al., 1993; Mansour et al., 1995; Ejebe et al., 1996).

1. INTRODUCTION

The dynamic security assessment (DSA) of a power system usually refers to the problem of how well a particular system condition can withstand all credible contingencies, taking into consideration the detailed dynamic characteristics of the system (Fouad, 1988). As the power utilities around the world are being required to operate power systems closer and closer to stability limits, it has become increasingly important for system planners and operators to use DSA to ensure secure operation. Traditionally, DSA has been perfonned by relying solely on off-line studies involving step-by-step (SBS) time-domain simulations. This approach, while it can model large systems in detail, is very slow even with the most advanced computers available. It also cannot give stability margin and sensitivity infonnation which is necessary in determining power transfer limits and in designing preventive controls. As a result, considerable human interaction is usually required to perform studies and interpret results. These limitations have made DSA a computationally formidable task and have thus prevented it from being applied in the on-line environment. To date, a significant amount of research has been focused on developing faster, reliable

Although DSA encompasses all forms of stability, including transient stability and voltage stability, in this paper only the assessment of transient stability is addressed. A new software tool, FASTEST (Fast Analysis of STability using EEAC and Simulation Technologies), has been developed for dynamic security assessment of power systems. FASlEST combines two technologies to achieve fast and reliable DSA:

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•

A direct stability assessment method based on the Extended Equal-Area Criterion (EEAC) (Xue and Pavella, 1989; Pavella and Murthy, 1993; Xue, 1996). This method is used in two key areas in FASlEST: fast contingency screening and ranking (S&R), and post-processing of the SBS simulations.

•

The conventional SBS simulation technique. This is used for accurate analysis of the critical contingencies identified by the contingency S&R

module. The Extended TransientlMidtenn Stability Program (ETMSP) (Kundur et al., 1994) developed by the Electric Power Research Institute of USA is used as the SBS simulation engine.

• There is support for different modelling levels in different classes of the assessment: simplified models in the contingency S&R module for fast computational speed; and detailed models in the SBS simulations for greater accuracy.

While FASTEST has been developed up to now as an off-line DSA tool, it is expected to be well suited for on-line applications because of its functionalities and performance. In fact, the EEAC technology has already been used in on-line systems (Xue, et aI., 1993) and the ETMSP program is also being developed to serve as the SBS simulation engine in a major on-line DSA implementation (Ejebe et al., 1996). The integration of these two technologies will provide an excellent foundation for the development of the next generation on-line DSA.

• The contingency S&R module (EEAC) ranks the contingencies using one of two quantities: (1) critical clearing time (CCn of faults; and (2) stability margin. The non-critical contingencies can be filtered out from further studies, based on a userspecified criterion on either CCT or stability margin. •

Various modules of FASTEST have been tested on a large, realistic power system model. The results show that FASTEST perfonns well in DSA applications.

• The post-processing of the SBS simulations using EEAC produces very useful infonnation about the stability property of the system. This includes an overall system stability margin which indicates the degree of the stability of the system, and the critical cluster of generators (CCG) which indicates how the system splits when becoming unstable.

2. OVERVIEW OF FASTEST The structure of FASTEST is shown in Figure 1. It has four major functional modules: • • • •

Data input and system initialization Contingency screening and ranking (S&R) Detailed SBS simulation Post-processing of the SBS simulation results

3. CONTINGENCY SCREENING AND RANKING Previous research on speeding up DSA has suggested that one of the most efficient ways is to screen and rank, using a very fast computational tool, all credible contingencies in terms of the severity of their impact on system security. Those contingencies which are unlikely to threaten the system security can simply be dropped from the detailed studies. Many techniques have been proposed over the years to serve as the contingency S&R tool. Examples are the methods based on EEAC (Gamier et al., 1993), transient energy function (TEF) (EPRI, 1994a), the neural network theory (Mansour et al., 1996), and artificial intelligence systems (EPRI, 1994b). FASTEST uses an EEAC implementation developed by the Nanjing Automation Research Institute (NARI) as the contingency S&R tool.

These functional modules are interfaced to provide the following features: •

The SBS simulation module (ETMSP) alone can be used to perfonn the normal time-domain transient and midtenn stability analysis, with all standard features plus many extended features needed for such studies.

All credible contingencies to be analyzed can be processed with one system initialization. These contingencies can be either specified by a predefined contingency table or generated by the program using user-defined rules.

Continglncy specification - Contingency tlble • SYltem t Cln

EEAC separates the observation planes from the multimachine integration space by using the Complementary Group Centre Of Inertia (CGCOI) transformation. This mapping exactly preserves the stability status of the multimachine dynamics. On the one hand, the multimachine integration space allows full mathematical models and any scenarios. On the other hand, the image on each observation plane is a time-varying one-machine infinite-bus (OMID)

Figure I - Structure of FASTEST

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proxImIty to instability). In DSA, however, it is important to provide quantitative measures of the system stability in order to perform such tasks as power transfer limit search and preventive control design. Several attempts have been made to derive an index from the post-fault system that will provide stability margin information for the specific system operating condition and contingency. These include the index based on the transient energy margin (TEM) (Mansour et al., 1995; EPRI, 1994a), and the index based on the signal energy from the pest-processing of SBS simulations (Marceau et al., 1994).

system; and its stability can be quantitatively assessed based on a rigorously defined margin. Both stability margin and limits of the critical image can be taken as those of the original multimachine system. Therefore, EEAC has the s~me accuracy and modelling flexibility as the utilized numerical integration. Moreover, many technologies can be introduced to exclude the detailed integration to the full extent due to the quantitative feature of EEAC.

In FASTEST, a stability margin index based on the EEAC theory is used to measure the degree of stability with respect to a particular contingency. It is defined as

4. SBS SIMULA nONS In FASTEST, ETMSP is used as the SBS simulation engine for the detailed analysis of the system under various contingencies. These contingencies can be specified by the user (the common practice in conventional transient stability analysis), or they can be the set of critical contingencies identified by the contingency S&R module.

Ad-A.

T)

•

Aa

(1)

where A. and Ad represent the acceleration and deceleration areas, respectively, on the P-o plane of the aggregated OMm system. Thus, T)>O corresponds to a stable case and vice versa. From the definition of T), the value of the stability margin is directly related to the degree of the stability, hence making T) a suitable stability index. Numerical results have shown that this index gives consistent accuracy in quantifying the system stability.

ETMSP is a product of a number of research and development projects mainly sponsored by EPRI. It incorporates many leading-edge technologies in the modelling and solution techniques for the time-domain analysis of large power systems. It has been widely used in utility applications, consulting studies, and research. Among its unique features are: •

=--

When multiple contingencies are considered in a DSA problem, the stability margin from the worst contingency defines the overall system stability index. This usually corresponds to the smallest value of stability margins.

Extensive modelling capability. ETMSP supports a very wide array of models, including a complete library of standard models for generators and loads, plus advanced model.s for FACTS, multi~terminal HVDC systems, and other special devices for midterm stability studies. In addition, all control devices in the system can be represented by userdefined models, which makes it easy to study any specialized models. This level of modelling support guarantees the accuracy of the SBS simulations to meet the most rigorous requirements.

Another important result from the post-processing of the SBS simulations using EEAC is the identification of the critical cluster of generators (CCG). These are the set of generators that will separate themselves from the rest of the system when the stability is lost due to a critical contingency. This information can be very useful in DSA when designing preventive controls, such as generation rejection, in order to maintain secure operation of the system.

Computational speed. ETMSP incorporates several numerical integration techniques. The implicit trapezoidal rule with the Very Dishonest Newton (VDHN) implementation (Kundur, 1994b) has consistently shown superior computational speed for many studies performed to date.

All potentially fatal loading patterns can be automatically recognized, and the stability-oriented maximum loadability can be estimated for both originally unstable cases and originally stable cases.

6. RESULTS

5. POST-PROCESSING OF TIlE SBS SIMULA nONS

FAS1EST has been tested on a realistic power system model representing part of the Western System Coordinating Council (WSCC) interconnection in North America. The test system has 1430 buses and 186 generators. Detailed dynamic models are included

Traditionally, the SBS simulation results are interpreted using human expertise. This approach gives only qualitative measures of system stability (stable vs. unstable), without quantitative information (i.e., the

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for generators and their control devices, resulting in a system with 2627 dynamic states.

No. of contingencies 300 256

250 228

6.1 Contingency S&R

200

To test the accuracy of the contingency S&R module in FAS1EST, two powerflow cases were used:

150 100

• •

Base case, with all circuits in service. Change case, with one key 500 kV line out of service.

50 9 1 .l..l..J., ~ I":''':' 1 ~ ~ Q ·30 ·25 ·20 ·15 ·10 ·5 0 5 10 15 20 25 30 35 40 Error Range

o

w.)

A total of 621 contingencies were considered for the two cases. These contingencies consisted of a three phase fault at one end of each 500 kV line followed by tripping of the faulted line. The contingency ranking was based on the critical clearing time (CCT) of the fault. Two tests were performed to verify the accuracy of the contingency ranking results: (1) a method accuracy test in which the CCTs by EEAC and by the SBS simulations are computed and compared under the same modelling assumption (classical generator model was used); (2) a model impact test in which the contingency ranking produced by EEAC using the classical model is verified with the SBS simulations using the detailed dynamic models. These two tests are designed to exercise different properties of the S&R algorithm: the method accuracy test helps to clarify the actual accuracy of the algorithm and the model impact test will prove its suitability for practical applications.

Figure 2 - Error distribution of CCTs from contingency S&Rmodule contingencies would easily be filtered out, resulting in a significant speed gain.

6.2 Stability margin

The stability margin computed by EEAC gives a quantitative measure of the proximity of the system to instability. Table 1 shows the stability margins of the 10 most critical contingencies in the base case with a fault clearing time of 100 rns (the results were obtained from the post-processing of the SBS simulations using the detailed dynamic models). As comparisons, the maximum relative rotor angle swings for these contingencies are listed. It can be clearly seen that the stability margin not only correctly distinguishes the unstable contingencies from stable ones, its value is also consistent with the degree of the stability.

Figure 2 shows the results of the method accuracy test. The error distributions of the CCTs are displayed. For example, there are 256 contingencies for which the errors of the CCTs computed by EEAC and by the SBS simulations are between 0% and 5%. Figure 2 demonstrates a typical normal distribution, with 588 (94.7%) contingencies having CCT errors within ±1O%. A further examination revealed that most of the larger errors (> 10%) were caused by the ISD (Xue, 1996). This interesting phenomenon certainly calls for more research and investigation. Overall, the results in Figure 2 show that the S&R algorithm has very good accuracy and can be trusted for the results under the modelling assumption.

Table I - Stability margin of the 10 most critical contingencies in the base case

For the model impact test, a 100 IllS (6-cycles) fault clearing time was considered as critical. Using the SBS simulations with the detailed dynamic models, 16 contingencies were found to be critical. On the other hand, from the contingency ranking results, 25 contingencies were identified to have CCTs less than lOOms. These 25 contingencies include 15 critical ones from the detailed SBS simulations, with only one actual critical contingency missed. Such a capture rate is considered to be fairly good. If a margin is included when selecting critical contingencies from the ranking list for detailed studies, a large number of non-critical

Rank

Stability margin

Max relative angle swing

Stability status

1

-100.0

10616

Unstable

2

-100.0

10006

Unstable

3

-100.0

5979

Unstable

4

-90.3

15745

Unstable

5

-20.9

4657

Unstable

6 7

14.1

166

Stable

34.1

148

Stable

8

43.8

161

Stable

9

48.0

145

Stable

10

63.7

142

Stable

In addition to serving as a stability index, stability margin can also be used for other applications. The following example shows the use of the stability margin in the search for power transfer limits.

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Figure 3 shows a power transfer limit search test using stability margin information. A major power transfer corridor in the base case was considered, over which power is transmitted from a large hydraulic power plant to the load centre through three 500 kV lines. The following contingency was applied: a three phase fault at a sending end 500 kV bus, cleared 100 rns later by tripping one 500 kV circuit of the corridor. The power transfer limit for this corridor was obtained by progressively increasing the power output of the plant. As the power transfer increases, the stability margin decreases as shown in the figure. Two schemes were tried when computing the stability margins:

The second implication above is certainly the more interesting one. The only problem remaining is to efficiently find out the CCG at the critical instability point. Further research work is required in this area. Nevertheless, using the stability margin for power transfer limit search not only helps to accurately find the value of the limit, but also reduces the number of iterations required in the search cycles.

6.3 Computation speed

•

Using the actual CCGs identified at each powerflow condition (Scheme 1)

FAS1EST has achieved very good computation speed. Table 2 shows the CPU time required for some typical computations (timing was taken on a Sun UltraSparc Model 140).

•

Using the CCG identified when the system loses stability (Scheme 2)

Table 2 - CPU time requirements for typical computations by FASTEST

It can be seen that in Scheme 1, the relationship between stability margin (1l) and the power transfer (P) exhibits a nonlinear pattern; however, when using a fixed CCG as in Scheme 2, the 1l-P relationship becomes fairly linear. In fact, the 1l-P relationship in Scheme 1 also approaches linear when the power transfer is close to the limit (in this case the CCG is gradually converging to the set used in Scheme 2). This kind of TJ-P relationship has two implications:

Computation

CPU time (sec) per case

3-second SBS simulation using detailed models (ETMSP)

16.40

Contingency S&R (EEAC) based on stability margin

0.81

Post-processing of SBS simulation - calculation of stability margin (EEAC)

0.70

• If the power transfer is close enough to the limit, simple linear extrapolation based on the stability margins should give good prediction of the power transfer limit.

The above CPU time can also be expressed in terms of how long the normal SBS simulations can go within the same CPU time periods. Thus,

•

•

If the CCG at the critical instability point is known, simple linear extrapolation over a much wider power transfer range should also give good prediction on power transfer limit. For instance, in Figure 3, using the first two power transfer points at 2704 MW and 2974 MW, the actual power transfer limit of 3448 MW can almost be predicted just by one extrapolation.

• The time spent on post-processing of one SBS simulation is equivalent to the time required for 0.13 seconds of the normal SBS simulations These times are almost negligible in comparison with the detailed SBS simulations (note that the amount of computation required for these two tasks is almost independent of the length for the base SBS simulations). This little overhead, however, can help to drastically speed up the DSA by filtering out a large number of non-critical contingencies and can provide stability margin information useful for determining the degree of the system stability and the power transfer limits.

Stability margin (t'll

600

500 400 300

200

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byEEAC(_,) WI1h _ syoIIm _1IaIlIiIIy(_2)

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........ ~

r-.... ~

100

-

-....:::

o . · 100 2.600

-

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The time spent on one contingency S&R is equivalent to the time required for 0.15 seconds of the normal SBS simulations

~

.

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2,800 3.000 3,200 3,400 Power transfer (P) across the corridor

7. CONCLUSIONS

l 3,600

This paper described a new software tool, FASTEST, for dynamic security assessment of power systems, with in-depth discussion on its major components and

Figure 3 - Power transfer limit search

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Gamier, B., J.N. Marquet, M. Trotignon, P. Rousseaux, Y. Xue, Z. Gao, L. Wehenkel, and M. Pavella (1993). Methode Rapide d'evaluation de la Stabilite Transitoire - Application de ces Methodes en Planfication et Exploitation. CIGRE Study Committe 38 Colloquium on Power System Dynamic Performance, Brazil. Kundur, P., G.K. Morison, N.J. Balu (1994a). A Comprehensive Approach To Power System Analysis. CIGRE Paper 38-106. Kundur, P. (1994b). Power System Stability and Control, McGraw-Hill. Mansour, Y., E. Vaahedi, A.Y. Chang, B.R. Corns, B.W. Garrett. K. Demaree, T. Athay, K. Cheung (1995). B.C. Hydro's On-line Transient Stability Assessment (TSA) Model Development, Analysis, and Post-processing. IEEE Trans. Vol. PWRS-10, No. I, 241-253. Mansour, Y., E. Vaahedi, A.Y. Chang, B.R. Corns, J. Tamby, M.A. El-Sharkawi (1996). Large Scale Dynamic Security Screening and Ranking Using Neural Networks. Paper 96 SM 579-3 PWRS presented at 1996 IEEE/PES Summer Meeting. Marceau, R.J, F.D. Galiana, R. Mailhot, F. Denomme, and D. McGillis (1994). Fourier Methods for Estimating Power System Stability Limits. IEEE Trans. Vol. PWRS-9, No. 2, 764-771. PavelIa, M. and P.G. Murthy (1993). Transient Stability of Power Systems - Theory and Practice. John WHey & Sons. Xue, Y. and M. Pavella (1989). Extended Equal-Area Criterion: An Analytical Ultra-fast Method for Transient Stability Assessment and Preventive Control of Power Systems. Int. Journal Electrical Power & Energy Systems, Vol. 11, No. 2, 131-149. Xue, Y., Y. Luo, F. Xue, W. Zhu, K. Yang, and J. Jiang (1993). On-line Transient Stability Assessment in Operation - DEEAC in Northeast China Power System. IEEE Region 10 Conference on Computer, Communication, Control and Power Engineering, Beijing. Xue, Y. (1996). Integrated Extended Equal Area Criterion - Theory and Application. V Symposium of Specialists in Electric Operational and Expansion Planning, Brazil.

their functionalities. The theoretical basis of FAS1EST is the integration of the Extended Equal-Area Criterion (EEAC) and the SBS simulation technique for which the ETMSP program is used. Numerical results on a large, realistic power system model show that FASTEST has favourable accuracy and performance. Work is currently under way to extend the functions of FASTEST, one of which is. the capability of searching the power transfer limit using the stability margin and sensitivity information produced from FAS1EST. This work will be directly beneficial to on-line applications where the knowledge of the real-time power transfer limits is critical.

8. ACKNOWLEDGEMENTS This work is funded by the Canadian International Development Agency (CIDA) in cooperation with the Ministry of Foreign Trade and Economic Cooperation, and its designate Ministry of Electric Power, People's Republic of China. Thanks are also due to the CIDA project managers, Mr. Bill Seyers and Ms. Lolo Young of B.C. Hydro International Limited.

9. REFERENCES Ejebe, G.C., C. Jing, J.G. Waight, G. Pieper, and F. Jamshidian (1996). Security Monitor for On-line Dynamic • Security Assessment. Fourth International Conferences on Power System Control and Management, London, England, 58-64. EPRI Report lR-I04352 (1994a). Analytical Methods for Contingency Selection and Ranking for Dynamic Security Analysis. Prepared by Siemens Energy & Automation Inc.. EPRI Report lR-I03607 (1994b). Power System Dynamic Security Analysis Using Artificial Intelligence Systems: Phase 1 - Feasibility Evaluation. Prepared by ABB Systems Control Company Inc .. Fouad, A.A. (1988). Dynamic Security Assessment Practices in North America. IEEE Trans. Vol. PWRS-3, No. 3, 1310-1321.

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