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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 15, NO. 2, MAY 2000

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Large Scale Probabilistic Transient Stability Assessment Using B.C. Hydro’s On-Line Tool Ebrahim Vaahedi, Senior Member, IEEE, Wenyuan Li, Senior Member, IEEE, Timothy Chia, Member, IEEE, and Hermann Dommel, Fellow, IEEE

Abstract—This paper presents the results of a probabilistic transient stability assessment conducted on the large scale system of B.C. Hydro, including a generation rejection study on the Peace system and a transfer limit study on the Columbia system. In these studies, B.C. Hydro’s historical statistics on the probabilistic states of load level factor, fault type, fault location, fault clearing, and automatic reclosing were used in a Monte Carlo formulation to generate sample states for the studies. For each study, 1000 cases were generated for which the transient stability limits were calculated using a modified shell of B.C. Hydro’s on-line transient stability program. The shell which was developed for this project uses PTI’s PSSE simulation program and the Second Kick method. The results obtained showed that BC Hydro’s existing deterministic criteria are very conservative with a probability of instability of smaller than 0.2%. The studies also revealed that the deterministic criteria do not always correspond to the “worst case” as it is normally assumed. Index Terms—Probabilistic, Transient Stability.

I. INTRODUCTION

T

RADITIONALLY, power systems have been planned and operated using deterministic transient stability criteria. To comply with such criteria, the system would have to stand a “worst case” scenario. The “worst case” scenario then gets translated to a number of extreme operating conditions together with a number of most critical contingencies for which the system should be designed to withstand the test. While this “worst case” approach has served the industry well, in a competitive environment, the utilities will need to know the level of risk associated with their observed criteria so that they adjust their service quality based on consumer’s expectation i.e. the acceptable level of risk and corresponding price. The use of probabilistic techniques in transient stability studies was presented in a series of papers by Billinton & Kuruganty [1]–[3], laying the foundation for the work of the others. They also used the conditional probability approach to develop a single stability index for any fault. Anderson & Bose [4] discussed the broader subject of probabilistic power system stability. Their approach to transient stability analysis involved a complex analytical transformation. Hsu & Chang [5] carried out a transient stability analysis on the Taiwan power system deriving the joint probability distribution function for the Critical Clearing Time (CCT) and each of the five Manuscript received June 1, 1998; revised May 10, 1999. E. Vaahedi and W. Li are with B.C. Hydro, Burnaby, Canada. T. Chia is with Epoch Networks, Irvine, California. H. Dommel is with The University of British Columbia, Vancouver, Canada. Publisher Item Identifier S 0885-8950(00)03802-5.

variables considered. Recent publications [6]–[8] have made advancements in stochastic modeling, as well as in employing the bisection method to speed up the calculation of the critical clearing time. The work reported in this paper applies the fundamentals developed by others to a realistic utility power system. It considers the probabilistic factors and uses them on a full model of the BC Hydro interconnected system (4000 buses 500 machines). Stability limits and remedial actions are derived considering the impact of the probabilistic factors. The contributions of the work reported in this paper are: • Using a realistic system and historical data from that system. • Providing a direct comparison between existing deterministic limits and probabilistic limits, taking into consideration the remedial actions that are required to maintain system stability during and after disturbances. • Demonstrating how probabilistic methods can be applied in real power systems to establish “stability criteria” or other types of planning studies. II. PROCEDURE Traditional transient stability studies have been deterministic in nature. That is, they follow a step-by-step process in which the factors such as the fault type, fault location, load level, etc., are selected beforehand, usually in accordance to the “worst-case” philosophy described earlier. The disturbance type and location are also selected such that the most severe disturbance, covered by the criteria, is selected. The block diagram in Fig. 1 outlines the usual procedure. Probabilistic studies, however, take into account the stochastic nature of the power system. Some consideration is given to the credibility and probability of a certain event occurring. Fig. 1 also shows the procedure for including probabilistic factors in transient stability studies. Unlike the deterministic approach, this process must be repeated many times to include a spectrum of different states with their probabilities of occurrence. For example, while for deterministic transient stability, one network topology is used, in the probabilistic studies, for each sample a determination has to be made for the forced transmission outages. Also as will be explained later, in the probabilistic studies, the disturbance sequence becomes dynamic since it is driven by the operation status of the circuit breakers. For example while in the deterministic studies it is assumed that a circuit breaker opens after 4 cycles following a 500 kV fault, in the probabilistic studies, first of all it can fail

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TABLE I PROBABILITY OF DIFFERENT LOAD LEVELS

III. MODELS, DATA AND TOOLS This section covers the development of stochastic models and parameters for different components as well as the mechanics and tools used for the transient stability limit calculations. A. Historical Data/Model Development

Fig. 1. Procedures for deterministic and probabilistic transient stability studies.

to operate and even if it is successful, the operation time can vary. The sample selection in the probabilistic studies were derived using Monte-Carlo method. Also in Fig. 1, barely stable means a case where by increasing the stability parameter by the threshold will result in an unstable case. For example if the stability studies would have to have a one MW threshold accuracy, then a case is barely stable if first of all it is a stable case but by increasing the stability parameter by 1 MW it will become unstable.

Historical data from the BC Hydro system was used to develop stochastic models for the load level, fault type, fault location, fault duration, and successful/ unsuccessful reclosing. Load Level: The system load varies during the day and throughout the year. As shown in previous work [1]–[3],[5]–[7], a multi-step load model derived from the hourly annual load duration curves for the system can be used to provide a reduced, yet fairly accurate, load model. Taking the actual hourly load data from the BC Hydro 1995/96 fiscal year, a load duration curve was developed. Based on the probabilities from this load duration curve, the load forecast for the 1997 summer season was divided into 6 semi-equal load steps (not including exports) as shown in Table I. These load steps formed the basis for developing the different base case load flows used in the studies. Fault Model: Fault type, fault location, and probability of successful automatic reclosing were derived from actual BC Hydro 500 kV fault incidence data from 1977 to 1996, retrieved from BC Hydro’s corporate mainframe computers. During this time, a total of 2,419 faults were recorded on the 500 kV transmission system, for an average of 121 events per year. Prior to 1989, data regarding the location of faults were not recorded, so only the data from the events recorded after 1989 were used to gather statistics on fault location. Unlike previous work by others [3],[6], models to calculate the probability of successful automatic high-speed reclosing were not employed. In reviewing the cause of the historical fault events, it was noted that there was a very high correlation between the cause of the fault and the probability of successful automatic reclosing. In over 90% of the faults caused by lightning, automatic reclosing was successful, but that was the case in less than 50% of faults due to all other causes. According to B.C. Hydro’s historical records, 82.51% of faults are due to lightning and 17.49% are due to other causes. The probability of successful automatic reclosing was thus estimated at:

(1)

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TABLE II PROBABILITY OF SUCCESSFUL/UNSUCCESSFUL RECLOSING

TABLE III FAULT LOCATION PROBABILITIES

Fig. 2. Probability density function used for fault clearing times.

TABLE IV PROBABILITY OF FAULT TYPE

where and are probabilities of faults caused by lightand ning and other causes respectively and are probabilities of successful reclosing given that the fault are caused by lightning and other causes respectively. Table II shows the probability of successful and unsuccessful automatic reclosing used in the studies. To determine the probability of fault location, with respect to the master end of the line, each 500 kV transmission line was divided into three parts: • close-in (first 20% of the line) • mid-line (middle 60% of the line) • far-end (last 20% of the line) Recorded data from the faults between 1989–1996 were used to calculate the fault location probabilities as shown in Table III. Studies concerning the frequency of the different fault types have been carried out in the past [9]. The BC Hydro data, although not always complete, seems to agree with previously published data. Of the 2,419 fault events recorded, 43 did not have the fault type noted. Although these cases could have been ignored or allocated based upon the derived probabilities, it was faults, (pridecided to consider these unknown events as marily in accordance with the traditional “worst-case” utility approach). Table IV shows the probability of fault type and compares it to numbers published by an IEEE Power Systems Relaying Committee Working Group [9]. Fault Protection Model: The process of clearing faults is composed of three distinct components: the fault detection, the relay operation (including communications time), and the high voltage breaker operation. Traditional BC Hydro studies have used a deterministic mean value of 4 cycles for 500 kv clearing (and have assumed zone I clearing). However, upon discussions

with protection and equipment specialists at BC Hydro, it was found that the breaker operating time was strictly fixed at 1.5 or 2.0 cycles, depending on which side of the breaker opened first. Since no other data on breaker operation was available, it was assumed that the probability of breaker operation was evenly split between the two times. However, it was decided that the relay operating time could be modeled using a normal distribution with a mean of 2 cycles and a 10% standard deviation. Fault detection was assumed to occur instantaneously. In essence, a linear combination of two normal distributions, with means of 3.5 and 4.0 cycles respectively, was developed. The actual probability density function used is represented by Equation (2) and shown in Fig. 2. In this function the first term is a normal distribution with a mean value of 3.5 cycles and the second term is a normal distribution with a mean value of 4.0 cycles.

where

cycles

(2)

B. Simulation Tools Utilities use time domain simulation packages to derive transient stability limits, because of their accuracy and unlimited modeling capability. Recently, an on-line transient stability assessment (TSA) method has been developed for B.C. Hydro’s Energy Management System (EMS) [10] which efficiently derives the limits by using a combination of a time domain simulation package (PTI’s PSSE) with an algorithm called the Second Kick. This algorithm speeds up the limit calculation process by early termination of simulations as well as associating a margin of stability with each case for fast limit search. This combination is robust, provides efficient formulation, and allows full modeling on existing transient stability programs. To perform the limit calculations in this work, a simulation shell was developed which dynamically feeds the probabilistic factors into the On-line TSA module for limit calculation. The main purpose of the shell was to dynamically construct the PTI’s PSS/E command files based on whatever probabilistic states were randomly selected. These PSS/E command files specify the complete disturbance sequence for a dynamic simulation and allow it to be carried out in an automated fashion. To facilitate the process of the disturbance sequence development, a

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UNIX script was developed to “piece together” the PSS/E command file depending on which pieces were required. This allowed the disturbance sequence for each particular simulation to be dynamically constructed. The inputs to the script were the relay operating time, the load level, the fault type. fault location, and, the reclosure operation (successful/unsuccessful). In these studies, the random parameters were simulated using a using a Monte-Carlo method. A variance reduction technique employing the enumeration technique was used to enhance the efficiency in the Monte-Carlo simulation.

TABLE V DISTRIBUTION OF TRANSFER LIMIT REDUCTION

IV. RESULTS B.C. Hydro’s bulk system is composed of two main generation subsystems, the Peace River and the Columbia River Systems. The Peace River system has a generating capacity of 3400 MW located about 1000 km away from the main load center compared to the Columbia system with a generating capacity of 4730 MW with a distance of between 200 to 500 km. The large transfers over long distances characterizes the B.C Hydro system as one limited by transient stability, with generation shedding used as an effective control for maintaining stability. To demonstrate the impact on the calculated stability limit results, probabilistic transient stability studies were conducted for a transfer limit study on the Columbia system and a generation rejection study on the Peace system. The results have been compared to the limits obtained using traditional deterministic methods. A. Transfer Limit Calculation in the Columbia System The first test was a fault on a 500 kV line close to the Columbia generation system. In this study the transfer flow was adjusted to make the system stable. The sequence of events for this contingency is given below. Time (cycles) Event Fault ((SL, DLG, PP, or 3 ) Series capacitor control. Clear fault Trip generator to maintain stability Reclose on fault at the master end if unsuccessful reclosure Clear fault.(3 phase) For the above study, one thousand sample cases were generated, for all of which stability limits were calculated. The results obtained are summarized in Table V below. Comparative studies using existing BC Hydro deterministic criteria (for the identical contingency studied) revealed that a reduction of 640 MW in transfer capability was required to maintain system transient stability. By contrast, the numerical results from the probabilistic studies are given in Table V and Fig. 3. These results, which provide the distribution of the transfer limit reduction required to maintain stability for all 1000 cases, indicate that in 847 of the 1000 cases, no reduction in transfer capacity was required to maintain system stability. The maximum amount of reduction required was 780 MW. It is interesting to note that this amount was required at a load factor of 95% (not 100% as

Fig. 3. Distribution of transfer reduction to required.

might be assumed) and was higher than the 640 MW required when the normal deterministic criteria (i.e., 100% load, 4 cycle clearing, unsuccessful reclose) was applied. This result is due to the fact that at the 95% load factor, the amount of power being transmitted over the faulted line is higher than when the load factor is 100%. Fig. 41 shows the probability of instability associated with each transfer limit reduction. This figure indicates that a transfer limit reduction of 800 MW corresponds to 0% risk of instability. These results also indicate that the existing deterministic criteria are conservative and include accepting a 0.1% probability of instability. For the specific contingency studied, current practice would be to reduce the generation output in the Columbia region by a combined 640 MW, in turn reducing the power transfer by a similar amount. An equivalent amount of generation would need 1In this article, the term “risk of instability” is meant to reflect on the “probability of instability”.

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TABLE VI DISTRIBUTION OF GEN. SHEDDING TO MAINTAIN STABILITY

Fig. 4. Transfer limit reduction vs. probability of instability.

to be obtained by increasing output at other generators in the system, increasing imports, or reducing exports. Since this contingency also includes firm exports of 2000 MW to the United States, this reduction in transfer capability would require exports to be reduced by about 600 MW at the higher load factors. At the lower load factors, there would be enough surplus generation capacity in the system to shift the generation pattern without impacting exports. If the company were willing to accept just a 0.1% chance of instability, then the transfer limit could be increased by 100 MW (when compared to the deterministic reduction of 640 MW). Accepting a 1% chance of instability would increase the limit by a further 100 MW. B. Generation Rejection Requirement in Peace System The second test was a fault on a 500 kV line close to the peace generation system. The switching sequence for the contingency is given below: Time (cycles) Event (SLG, DLG, PP, or 3 ) fault at a 500 kV bus Bypass series capacitor if rating is exceeded Clear fault and trip the line ( is the random clearing time) Switch 200-400 MW of braking resistor on. Trip generation to maintain stability. Reclose if fault (if reclosing unsuccessful) at the master end Clear fault. Switch braking resistor off. For the above study, one thousand sample cases were generated, for all of which stability limits were calculated. The results obtained are summarized in Table VI below. Comparative studies using existing BC Hydro deterministic criteria (for the identical contingency studied) revealed that a total of 1490 MW of generation shedding was required to maintain system transient stability. By contrast, the numerical results from the probabilistic studies are given in Table VI and Fig. 5. These results which provide the distribution of the

Fig. 5. Distribution of the required generation shedding.

required generation shedding to maintain stability for all 1000 cases, showed that in 821 of the 1000 cases, no generation shedding was required to maintain system stability. The maximum amount of shedding required was 1240 MW. However, it should be noted that the usual deterministic case of 100% load, 3 permanent (unsuccessful reclosing) fault, did not appear in the 1000 cases selected using Monte Carlo techniques. If that particular case had been selected, the maximum amount of shedding required would also have been 1490 MW. Fig. 6 shows the probability of instability for each level of generation shedding. These results indicate that the existing deterministic criteria are very conservative. For the specific contingency studied, current practice would be to arm the generation shedding equipment to shed 1490 MW of generation for the study contingency. Since this contingency also includes firm exports, this rejected generation would amount to lost export sales. Although Table VI and Fig. 5 show a 0% risk of instability if

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Fig. 6. Generation shedding vs. probability of instability.

1490 MW of generation shedding is armed, the actual probability is very small (between 0% and 0.2%), but a rounding error in the experiments resulted in the 0%. This is due to the fact that no case requiring 1490 MW of shedding (corresponding to the normal deterministic case) appeared in the 1000 samples selected in the experiment. The remainder of the results indicate that if the company were willing to accept just a 0.2% chance of instability, then the generation shedding equipment could be armed to shed only 1000 MW in the event that this particular contingency occurs. Accepting a risk of 1.4% would reduce this figure by another 500 MW. V. CONCLUSION The work reported in this paper has shown that considering the probabilistic nature of the power system in transient stability studies provides a deeper insight into the physical limits manifested by the system. The current deterministic criteria employed by BC Hydro has been shown to be conservative, with a probability of instability between 0% and 0.2% in the Peace case and 0.1% in the Columbia case. Although the probability of instability was calculated as 0% for the Peace case, this is due to an approximation introduced because of the relatively small number of samples used (1,000). The risk calculation would be more accurate if the number of samples were increased to 10 000 or even 100 000. Another interesting result was that no remedial action was required in 821 of the 1000 samples for the Peace cases and no reduction in pre-disturbance transfer limit was required in 847 of the 1000 samples for the Columbia cases. The existing deterministic criteria are applied partly because of the belief that the system should survive the “worst case” credible contingency, and partly because it is very time consuming to analyze all credible contingencies. However, the studies on the Columbia system have shown that the deterministic criteria does not always correspond to the “worst case”. Line flows are dependent on generation patterns, load levels, and reactive support. Sometimes the highest line flows do not correspond to the 100% load factor case that is normally studied. As seen in the Columbia studies, the worst case for the contingency studied was actually at a load factor of 95%. By employing only the normal deterministic criteria, the

“worst case” may actually be missed and a small probability of instability may be unwittingly accepted. While the work presented here shows that significant gains can be made from considering probabilistic factors in dynamic security assessment studies, the following improvements and extensions are needed if the results are to form the basis of major decisions such as changing the existing criteria: • improving the accuracy of the results by significantly increasing the number of samples (to 10 000 or 100 000) so that a better assessment of the risk associated with the deterministic criteria can be made. Alternatively a convergence criteria should be selected which stops the limit derivations once the criteria is met. This criteria can use indecies related to the limit distribution curves such as those given in Figs. 4 and 6. • a cost/benefit analysis to establish new criteria based on the risk worth assessment to the utility (i.e., quantifying the value of the risk) and a comparison to the deterministic criteria, to gauge whether the existing criteria are warranted; • making modeling improvements, including probabilistic modeling of reclosers and braking resistors, better transfer limit modeling, and inclusion of zone 2 and zone 3 relaying; • repeating the studies for more contingencies. APPENDIX BC HYDRO’S SECOND KICK This method [10] which has been developed to enhance the efficiency of stability limit calculations performs two tasks of a) interrupting stability simulations as early as possible and b) attaching a margin of stability to each case. The stability attaching a margin helps to zoom to the limiting case faster than doing the conventional bi-section method. Both the interruption capability and the margin calculation capability are obtained using system energy properties and added to the original simulations. For more information please refer to Ref. [10]. ACKNOWLEDGMENT The authors would like to thank Messrs Allen Chang and Bryan Corns of B.C. Hydro who were instrumental in the adaptation of the On-line TSA shell for use by this project. REFERENCES [1] R. Billinton and P.R.S. Kuruganty, “A Probabilistic Index for Transient Stability,” IEEE Trans. PAS, vol. PAS-99, no. 1, pp. 195–206, 1980. [2] R. Billinton and P.R.S. Kuruganty, “Probabilistic Assessment of Transient Stability in a Practical Multimachine System,” IEEE Trans. PAS, vol. PAS-100, no. 7, pp. 3634–3641, 1981. [3] P.R.S. Kuruganty and R. Billinton, “Protection System Modeling in a Probabilistic Assessment of Transient Stability,” IEEE Trans. PAS, vol. PAS-100, no. 5, pp. 2163–2170, 1981. [4] P.M. Anderson and A. Bose, “A Probabilistic Approach to Power System Stability Analysis,” IEEE Trans. PAS, vol. PAS-102, no. 8, pp. 2430–2439, 1983. [5] Y.Y. Hsu and C.L. Chang, “Probabilistic Transeint Stability Studies Using the Conditional Probability Approach,” IEEE Trans. on Power Systems, vol. 3, no. 4, pp. 1565–1572, 1988.

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[6] R. Billinton and S. Aboreshaid, “Stochastic Modeling of High-Speed Reclosing in Probabilistic Transient Stability Studies,” IEE Proc. Part C, vol. 142, no. 4, pp. 350–354, 1995. [7] S. Aboreshaid, R. Billinton, and M. Fotuhi-Firuzhbad, “Probabilistic Transient Stability Studies Using the Method of Bisection,” IEEE Trans. on Power Systems, vol. 11, no. 4, pp. 1990–1995, Nov. 1996. [8] J.D. McCalley, A.A. Fouad, B.L. Agrawal, and R.G. Farmer, “A Riskbased Security Index for Determining Operating Limits in Stability Limited Electric Power Systems,” IEEE Trans. on Power Systems, vol. 12, no. 4, pp. 1210–1219, August 1997. [9] IEEE Committee Report, “Single Phase Tripping and Auto Reclosing of Transmission Lines,” IEEE Trans. on Power Delivery, vol. 7, no. 1, pp. 182–192, 1992. [10] Y. Mansour, E. Vaahedi, and A.Y. Chang et al., “B.C.Hydro’s On-line Transient Stability Assessment (TSA) Model Development, Analysis, and Post-processing,” IEEE Trans. on Power Systems, vol. 10, February 1995.

Wenyuan Li is a Senior Engineer in the Control Centre Technologies Department of B.C. Hydro. Dr. Wenyuan Li is a co-author of a book entitled “Reliability Assessment of Electric Power Systems Using Monte Carlo Methods”, Plenum Press, New York and London, 1994.

Ebrahim Vaahedi presently is the Manager of the Control Centre Technologies Department of B.C. Hydro and serves as an Adjunct Professor in the Department of Electrical & Computer Engineering at the University of British Columbia.

Hermann Dommel is a professor in the Department of Electrical and Computer Engineering at the University of British Columbia, Vancouver, Canada, and the holder of the B.C. Hydro /NSERC Industrial Chair.

Timothy Chia is a registered Professional Engineer in the Province of British Columbia and hold a B.A.Sc. and M.A.Sc. in Electrical Engineering from the University of British Columbia. He has over 8 years experience in the power utility and telecommuications industry. He is currently employed as a Sr. Network Planner with Epoch Networks, Inc., a national, Tier 1, Internet Service Provider.