FORTISBC ENERGY PERFORMANCE BASED RATEMAKING

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1 ERICA HAMILTON COMMISSION SECRETARY web site: VIA November 8, 213 SIXTH FLOOR, 9 HOWE STREET, BOX 25 VANCOUVER, B.C. CANADA V6Z 2N3 TELEPHONE: (64) BC TOLL FREE: FACSIMILE: (64) Log No , 4429 FORTISBC INC PERFORMANCE BASED RATEMAKING REVENUE REQUIREMENTS EXHIBIT A2-21 Mr. Dennis Swanson Director, Regulatory Affairs Regulatory Affairs Department FortisBC Inc. Suite 1, 1975 Springfield Road Kelowna, BC V1Y 7V7 FORTISBC ENERGY PERFORMANCE BASED RATEMAKING REVENUE REQUIREMENTS EXHIBIT A2-21 Ms. Diane Roy Director, Regulatory Affairs FortisBC Energy Inc Fraser Highway Surrey, BC V4N E8 Dear Mr. Swanson and Ms. Roy: Re: FortisBC Inc. and FortisBC Energy Inc. Project No /Order G Project No /Order Applications for Approval of a Multi-Year Performance Based Ratemaking Plan for 214 through 218 Commission staff submits the following document for the record in this proceeding: Utilizing Bulk Electric System Reliability Performance Index Distributions in a Performance Based Regulation Framework, 9th International Conference on Probabilistic Methods Applied to Power Systems, June 11-15, 26. Yours truly, YD/dg Enclosure cc: Registered Interveners Erica Hamilton PF/FBC/PBR /A2-21_Probabilistic Methods Applied to Power Systems

2 A2-21 A2-21 Utilizing Bulk Electric System Reliability Performance Index Distributions in a Performance Based Regulation Framework 1 Roy Billinton, Fellow, IEEE, and Wijarn Wangdee, Student Member, IEEE Abstract--Parameter distribution analysis and its potential utilization are relatively new concepts in bulk electric system (BES) reliability assessment and decision making. Sequential Monte Carlo simulation is used in this paper to assess the annual variability of BES reliability performance indices. The potential utilization of BES reliability performance index probability distributions is demonstrated by application to the performance based regulation (PBR) concept, proposed by policymakers involved in deregulating the electric power industry. Reliability performance measures such as SAIFI and SAIDI can be used as integral elements in a PBR mechanism to provide power utilities with economic incentives to maintain and improve service reliability, and at the same time to discourage them from sacrificing service reliability in the pursuit of economic objectives. The basic concepts of BES reliability performance index probability distributions associated with a PBR protocol are illustrated in this paper by application to the IEEE-RTS and RBTS using simulation results, and by application using actual historical reliability data. Index Terms--Bulk electric system (BES), performance based regulation (PBR), reliability performance indices, sequential Monte Carlo simulation. T I. INTRODUCTION HE electric power industry in North America and indeed throughout the world is undergoing deregulation in regard to its structure, operation and governance [1]. The basic intention of deregulation in the power industry is to increase competition in order to obtain better service quality and lower production costs. The demand for electricity is very sensitive to price, and therefore the lowest cost power supplier will be the most attractive to a customer. This has put great pressure on electric utilities to reduce costs, either by deferring capital projects or by increasing maintenance intervals, which can result in deterioration of the system reliability [2]. The question of achieving a balance between costs and service quality is therefore a key issue in today s power market. A mechanism known as performance based regulation (PBR) has been introduced to encourage power utilities to become more economically efficient, and at the same time to discourage utilities from sacrificing service quality in the pursuit of economic objectives [3]. The concept of PBR in the power industry was initially introduced for electric distribution systems [2]-[6]. The PBR concept is also under consideration1 The authors are with the Power System Research Group, University of Saskatchewan, Saskatoon, SK, S7N 5A9, Canada ( s: roy.billinton@usask.ca, and wijarn.w@usask.ca). in the field of composite generation and transmission systems and bulk electric system performance indices have the potential to be key elements in this regulated approach. There is an interest in applying reliability index probability distributions to manage bulk electricity system risks [7]. A technique to predict future bulk electric system reliability performance indices associated with their probability distributions is presented in [8], [9]. Sequential Monte Carlo simulation is used in [8], [9] to assess the annual variability of bulk electric system reliability performance indices. References [8], [9] show that the reliability performance index probability distributions have unique characteristics that are basically dependent on the system topology, operating philosophy and system conditions. The potential utilization of bulk electric system reliability performance index probability distributions is demonstrated in this paper by application to the regulatory approach designated as performance based regulation (PBR), proposed by policymakers involved in deregulating the electric power industry. Reliability performance measures such as the system average interruption frequency index (SAIFI) and the system average interruption duration index (SAIDI) [1], [11] can be used as integral elements in a PBR mechanism to incorporate the risk uncertainties associated with expected financial payments in a PBR regime. The basic concepts of bulk electric system reliability performance index probability distributions associated with a PBR protocol are illustrated in this paper by application to the IEEE-RTS and RBTS using simulation results, and by application to bulk electric systems using actual historical reliability data [1], [11] from the Canadian Electricity Association (CEA) and other sources. II. BASIC PERFORMANCE BASED REGULATION FRAMEWORK A PBR regime attempts to link rewards to desired results or targets. It works like a contract that rewards a power utility for providing good reliability or service quality and penalizes a utility for providing poor reliability [2], [5]. Generally, a PBR framework is composed of three different sections designated as the reward, penalty and dead zones. In implementing PBR, a neutral zone or dead zone is introduced where neither a penalty nor a bonus is given. If the reliability performance is worse than the neutral zone boundary, a penalty is applied. Penalties are usually increased as the performance deteriorates and are frozen when a maximum penalty value is reached. Rewards for good reliability performance work in a similar

3 KTH, Stockholm, Sweden June 11-15, 26 2 way. Rewards are increased as the performance improves and are frozen when a maximum bonus value is reached [2]. An appropriate PBR framework has to be constructed in order to initiate a PBR mechanism. The attention is initially focused on the location and the width of the dead zone. References [4]-[6] suggest that the historical average reliability index should reside in the dead zone of the proposed PBR framework, and preferably at the dead zone center. It appears that BES reliability index probability distributions are considerably more dispersed than those of electric distribution systems, and the standard deviations of bulk electric system performance indices are usually large or even larger than their mean values. This is due to the fact that bulk electric systems are normally much more reliable than distribution systems as bulk electric systems are usually well meshed and interconnected. The width of the dead zone was therefore arbitrarily set at one standard deviation (± S.D./2) in the PBR framework applied in this research. The basic PBR framework is shown in Fig. 1. Fig. 1 shows the proposed PBR framework for bulk electric system reliability performance utilization. The width of the dead zone is set at one standard deviation with the mean value of the reliability index at the center of the dead zone. The width of the reward transition from the starting reward point to the maximum reward is one half of the standard deviation (S.D./2). The width of the penalty transition is set in a similar way. The reward and penalty payments shown on the vertical axis are represented as a per unit (p.u.) value in order to make the values adjustable to any maximum payment criterion determined by the regulator. On the horizontal axis, the reliability performance indices used in the PBR protocol are normally SAIFI and SAIDI for distribution systems [2]-[6] as both SAIFI and SAIDI are required to provide an overall appreciation of customer service reliability reflecting different customer impacts (interrupted frequency and accumulated duration respectively). These two performance measures are also applied in the PBR applications in bulk electric systems. In this research work, the PBR procedure is applied to SAIFI and SAIDI separately. The two components are added to provide the overall reward/penalty payment. The mathematical model of the reward/penalty payment structure (RPS) based on a power utility perspective is formulated as shown in equation (1) using SAIFI and the parameters shown in Fig. 1. Payment 1.5 Reward zone Mean value Dead zone Penalty zone a b c d S.D. S.D. S.D. S.D Reliability Index Fig. 1. A basic PBR framework for bulk electric systems. The SAIFI can be modeled by its probability distribution. The expected reward/penalty payment (ERP) is calculated using equation (2). The SAIDI model can also be formulated in the same way. 1 SAIFI a (SAIFI b) slope ab a < SAIFI < b RPS = b SAIFI c (1) -(SAIFI c) slope cd c < SAIFI < d -1 SAIFI d ( RP i P ) ERP = i (2) where: i = An individual element or a class interval in the frequency histogram, RP i = The reward/penalty payment (per unit) calculated using equation (1) based on SAIFI i or SAIDI i, P i = The probability of SAIFI i or SAIDI i. The maximum reward/penalty payments can be determined based on regulatory concerns or on negotiations between the regulatory agency and the power utility. For example, if regulators and power utilities adopt customer interruption cost in the planning and operation process, the interrupted energy assessment rate (IEAR) or value of lost load (VoLL) can be used in conjunction with the annual unserved energy to determine the maximum reward/penalty payments. If the regulator and the power utility do not utilize customer outage costs, then other monetary factors such as an annual price cap, annual allowed revenue, etc., identified by the regulatory agency can be applied, and this amount could be scaled up or down as appropriate in a practical application. The actual maximum payments for an individual power utility will depend on the policy adopted by the associated regulator. The maximum reward/penalty payments applied in this research are therefore presented in terms of per unit (p.u.) values and are adaptable to any payment criterion adopted. III. PBR APPLICATION USING ACTUAL HISTORICAL RELIABILITY DATA The service reliability indices in this section are past performance measures obtained by compiling system outage statistics. Power utilities are normally required to monitor the reliability indices and report them to a regulator on an annual basis. Virtually all the major utilities in Canada are actively engaged in reporting past performance indices, using the Canadian Electricity Association (CEA) protocols [1], [11]. There are also several online publications on bulk electric system reliability performance reporting [12], [13]. This section illustrates the potential utilization of available BES reliability data in the PBR framework described in the previous section. Table I presents actual historical bulk electric system reliability performance data from Canada [1], [11], Philippines (two separate areas) [12] and Thailand [13]. Bulk electric system reliability performance statistics in terms of the mean values and standard deviations (S.D.) of the historical data presented in Table I are shown in Table II. The results shown in Table II are calculated using the available data presented in Table I. The calculated mean values and standard deviations (S.D.) shown in Table II are Copyright KTH 26

4 KTH, Stockholm, Sweden June 11-15, 26 3 used to set the dead zone and other components in the PBR framework described in the previous section. Fig. 2 illustrates the superposition of the SAIFI and SAIDI distributions in the PBR framework for each individual system. The expected reward/penalty payments (ERP) shown in Fig. 2 were calculated using equations (1) and (2) and the data presented in Table I. TABLE I ACTUAL HISTORICAL DATA ON BULK ELECTRIC SYSTEM RELIABILITY PERFORMANCE Country Reliability Year Index Canada SAIFI (occ/yr) (Overall) SAIDI (hrs/yr) Philippines SAIFI (occ/yr) (Mindanao) SAIDI (hrs/yr) Philippines SAIFI (occ/yr) (Luzon) SAIDI (hrs/yr) Thailand SAIFI (occ/yr) SAIDI (hrs/yr) TABLE II HISTORICAL DATA STATISTICS ON BULK ELECTRIC SYSTEM RELIABILITY PERFORMANCE System SAIFI (occ/yr) SAIDI (hrs/yr) Mean S.D. Mean S.D. Canada (overall) Philippines (Mindanao) Philippines (Luzon) Thailand Mean = 1.5, S.D. = ERP = +.4 p.u Mean = 2.7, S.D. = Mean = 3.1, S.D. = 1.4 Canada (Overall) ERP = p.u Mean =.63, S.D. = 6 Philippines (Mindanao) ERP = p.u. Philippines (Luzon) ERP = +.3 p.u Thailand Fig. 2. Combination of the SAIFI and SAIDI histograms and the hypothetical PBR framework Mean = 3.11, S.D. = 2.33 ERP = - 5 p.u Mean = 7.7, S.D. = 5.62 ERP = p.u Mean = 8.76, S.D. = 2.82 ERP = +.14 p.u Mean =.65, S.D. =.42 ERP = +.5 p.u Fig. 2 shows that each individual bulk system will face different reward and penalty payments for its reliability performance. A positive ERP value implies that the utility will expect a reward from the regulator while the negative ERP value indicates an expected penalty payment. The hypothetical PBR structure associated with the historic data tends to provide a reasonable reliability performance range and a target for the power utilities to attain, as all the expected reward/penalty payments are relatively small (close to neutral) with the exception of Canada, in which the expected penalty payment based on SAIDI is quite high (-5 p.u.) and the dead zone width for SAIFI is quite small. This is due to the fact that the historic data for Canada are aggregated values from all the major utilities in Canada, not just from a specific utility. The basic methodology in a PBR application to bulk electric systems is introduced and presented in Fig. 2. This process will, however, involve considerable details and negotiations between power utilities and regulators in actual situations and each situation could be quite unique. The general concepts described in the previous section are quite basic in each process. The decision to use ± S.D./2 in this study is arbitrary and the assigned dead zone width should be cautiously considered by the regulator. The imposed reward/penalty policies should be carefully designed in order to encourage power utilities to maintain appropriate reliability levels. Possible PBR structure modifications can encourage utilities to move their reliability performances in the direction intended by the regulator. The possible adjustments in actual situations are system dependent, and require agreement between the regulatory agency and the power utilities concerned. The application of PBR introduces a form of financial risk to a power utility that did not previously exist. In order to manage this risk, a power utility should attempt to estimate the uncertainty associated with this aspect of system performance. The concept of reliability index probability distribution analysis described in the following section can assist power utilities to deal with the financial uncertainty associated with their reliability performance. IV. PBR APPLICATION USING SIMULATION RESULTS A. Sequential Monte Carlo Simulation The actual reliability performance data for successive years presented in the previous section show that the indices vary from year to year and that the annual performance indices can be considered as random variables. A significant advantage when utilizing sequential Monte Carlo simulation in bulk electric system reliability analysis is the ability to provide reliability index probability distributions in addition to the expected values of their indices. Reliability index probability distributions provide a pictorial representation of the annual variability of these parameters around their mean values. The disadvantage of utilizing a sequential simulation in the early days was the expensive computation effort. Sequential simulation, however, can now be realistically used to assess Copyright KTH 26

5 KTH, Stockholm, Sweden June 11-15, 26 4 reliability indices for bulk electric systems due to the development of high speed computation facilities. In sequential simulation, a chronological history of the up and down times of the system components is generated using random number generators and the probability distributions of the component failure and restoration processes. This technique can be used to model all the contingencies and operating characteristics inherent in the system. Chronological load models can also be easily incorporated. The detailed process used in predicting bulk electric system reliability performance indices using the sequential simulation approach is presented in [8], [9]. B. Case Studies on the IEEE-RTS The reliability performance index probability distribution analysis concept is applied to the IEEE-RTS [14] in this section. A single line diagram of the IEEE-RTS is shown in the Appendix. The simulation period used for the IEEE-RTS is 6, years and provides a coefficient of variation of the expected energy not supplied (EENS) less than 2%. Fig. 3 presents the probability distributions of the SAIFI and SAIDI for the IEEE-RTS using the priority order load curtailment policy [9], [15], implanted on a designated PBR framework based on the structure noted earlier. Mean = 1.33, S.D. = 1.23 ERP = p.u. Fig. 3. SAIFI and SAIDI distributions for the IEEE-RTS obtained using the priority order load curtailment policy implemented in a PBR framework. The expected reward/penalty payment (ERP) shown in Fig. 3 is a positive value (+.526 p.u.). This indicates that the IEEE-RTS based on SAIFI in this PBR framework expects to receive a reward payment from the regulator. For example, if the maximum payment is M$ 1, the power utility can expect to receive 5.26 M$/year on average based on the SAIFI performance. The ERP based on the SAIDI distribution for the IEEE-RTS using the priority order policy under the designated PBR structure is also a positive value (+.34 p.u.). The power utility in this case expects to receive reward payments from the regulator based on both SAIFI and SAIDI performances. Adopting an appropriate load shedding policy can improve the reliability performance of a bulk electric system [9], [15]. Two load curtailment philosophies designated as the priority order and pass-1 policies are used in this section. The priority order policy tends to minimize the overall customer interruption costs by heavily curtailing loads at lower priority PBR Mean = 5.1, S.D. = 5.97 PBR ERP = +.34 p.u load points. In the pass-1 load shedding policy, loads are curtailed at the delivery points that are closest to (or one line away from) the elements on outage. The pass-1 policy tends to localize the severity of the event within areas in which the element outages occur. Fig. 4 presents the IEEE-RTS SAIFI and SAIDI distributions obtained using two different load shedding policies implemented in a PBR framework. In this example, it is assumed that the system is initially operated using a priority order policy before the PBR protocol is activated. The PBR structure is therefore based on the past performance utilizing the priority order policy. The system operator could try to maintain or improve the system reliability performance by changing the operating philosophy to the pass-1 policy after the PBR mechanism has been adopted. In this case, the regulator could also consider changing the PBR framework. The distributions illustrated in Fig. 4 are represented using approximate continuous curves for comparison purposes.. Prob.(priority) Prob.(pass-1) Priority: Mean = 1.33, S.D. = 1.23 Pass-1: Mean = 1.4, S.D. =.95 ERP (prioirty) = p.u. ERP (pass-1) = p.u Prob.(priority) Prob.(pass-1) Priority: Mean = 5.1, S.D. = 5.97 Pass-1: Mean = 3.8, S.D. = 4.33 ERP (prioirty) = +.34 p.u. ERP (pass-1) = p.u Fig. 4. SAIFI and SAIDI distributions for the IEEE-RTS obtained using two different load curtailment policies implemented in a PBR framework. Fig. 4 shows that by changing the load curtailment philosophy from the priority order policy to the pass-1 policy, the utility can expect to receive considerably higher reward payments based on both the SAIFI and SAIDI distribution performances. It is worth noting that applying PBR to the reliability performance of a bulk electric system could be quite different than applying PBR to electric distribution systems. Distribution systems are basically monopoly companies, and have the responsibility to provide electric service within a designated area. This is not the case for bulk electric systems particularly in a deregulated electricity environment where conventional vertically integrated utilities are decomposed into separate commercial entities. This therefore creates a potential difficulty to directly assign PBR frameworks for bulk electric systems in restructured electric structures where separate generation and transmission companies own and operate their own facilities, and Independent System Operators (ISO) coordinate the activities of all these entities to ensure the reliability and security of the entire electric system. Copyright KTH 26

6 KTH, Stockholm, Sweden June 11-15, 26 5 The ISO s activities, however, have a significant impact all the power companies as well as the overall system reliability performance due to the key role it plays. As shown in Fig. 4, the overall bulk electric system reliability performance can be improved by adopting appropriate operating policies such as the load curtailment philosophy. It may therefore be possible to link the ISO to the PBR framework set by the regulator. This could be controversial if the basic PBR protocol is applied directly to the ISO as an ISO is a not-for-profit organization and does not own generation nor transmission facilities for business, and therefore the ISO should not be penalized and faced with financial risk. In order to encourage the ISO to work efficiently, the PBR mechanism could be applied by establishing a reward zone while leaving out a penalty zone in the PBR framework or setting a penalty zone at a very low penalty payment level. In such a framework, the ISO might be motivated by the regulator to work efficiently and receive a bonus based on system reliability performance improvement. This could encourage the ISO to coordinate more effectively with the generation and transmission companies in the system planning, operating and design phases in order to improve the current and future system reliability performance. The general PBR framework and concepts described in this paper can be applied in both regulated and deregulated environments. Another potential utilization of a PBR protocol in bulk electric system reliability performance is to apply it directly to transmission companies (Transcos) who own and operate the regional wires. The following section is focused on the reliability performance index probability distributions of a transmission company (Transco) in a PBR framework by application to the RBTS [16]. C. Case Studies on the RBTS Electric power restructuring and the open access paradigm have resulted in an increased utilization of transmission networks which were not originally designed for competition and extremely heavy utilization. In order to illustrate this, the original RBTS [16] shown in the Appendix has been modified in order to create a scenario where there is an increased utilization of the transmission network. The system modification is as follows: Add 3 2MW generating units at Bus 1. Add a transmission line between Buses 5 and 6 to support the single circuit at Bus 6. The system peak load is increased by 2%. This modified system is designated as the modified RBTS and used as the base case. Under this system condition, the utilization of lines # 1 and 6 (L1 and L6) shown in Fig. A.2 is approximately 85% of the line rating under the modified system peak condition. Losing one of these parallel lines will create an overload on the remaining line during high load periods and could result in load curtailments. The system under this condition has an abundance of generation, but the system tends to have a transmission deficiency. The results obtained using the above modified condition are designated as the base case results. It is assumed in this example that all the transmission facilities of the modified RBTS are owned by one transmission company (Transco), and all the generation facilities are owned by other utilities. Since the focus of this example is specifically on the transmission network, all the generating units are assumed to be 1% reliable, which means that the loss of supply due to generation is excluded from the resulting reliability performance measures, and therefore only the impact of transmission contingencies is considered. Fig. 5 shows the SAIFI and SAIDI distributions due to transmission contingencies in the modified RBTS implemented in a PBR framework. The simulation period used for the RBTS is 8, years with a coefficient of variation of EENS less than 2%. Mean = 8, S.D. = 7 ERP = p.u Mean = 1.33, S.D. = 1.49 PBR. Fig. 5. SAIFI and SAIDI distributions due to transmission contingencies in the modified RBTS obtained using the pass-1 policy implemented in a PBR framework (base case). Fig. 5 indicates that the transmission company expects to receive reward payments from the regulator based on both SAIFI and SAIDI performances under the base case condition. Fig. 6 shows the SAIFI and SAIDI distributions implemented in the PBR mechanism when the peak load increases by 5%... ERP = p.u. Fig. 6. SAIFI and SAIDI distributions due to transmission contingencies for the two scenarios in the modified RBTS obtained using the pass-1 policy implemented in a PBR framework. Fig. 6 shows that when the system peak load is increased by 5%, the SAIFI and SAIDI distributions change PBR Prob.(base case) Prob.(5% increased) Prob.(base case) Base case: Mean = 8, S.D. = 7 5% increased: Mean =.71, S.D. =.63 ERP (base case) = p.u. ERP (5% increased) = p.u. Prob.(5% increased) Base case: Mean = 1.33, S.D. = % increased: Mean = 2.6, S.D. = 2.61 ERP (base case) = p.u. ERP (5% increased) = p.u Copyright KTH 26

7 KTH, Stockholm, Sweden June 11-15, 26 6 considerably. The expected SAIFI and SAIDI approximately increase by a factor of two over the base case. The resulting ERP for both SAIFI and SAIDI switch from positive values to negative values. This implies that the transmission company under this circumstance should expect penalty payments for both SAIFI and SAIDI performances. As noted earlier, the modified RBTS is transmission deficient due to the significant utilization of lines # 1 and 6. The loss of either line on this parallel circuit will lead to an overload on the remaining line and load curtailment may be required. The transmission company in this case should pursue transmission reinforcement in order to support the future load growth. Without any transmission improvement, the transmission company should expect significant penalty payments in future operation under this PBR mechanism. G 3 G G1 2 7 Bus Bus 3 Bus Bus 5 9 Bus 6 Fig. 8. Single line diagram of the original RBTS. G2 Bus 2 Generation Center Load Center V. CONCLUSIONS Sequential Monte Carlo simulation is used in this paper to assess the annual variability of bulk electric system reliability performance indices. The results show that the reliability performance index probability distributions have unique characteristics that are basically dependent on the system topology, operating philosophy and system conditions. The paper illustrates that the ability to predict reliability performance index distributions can be used to provide an appreciation of the financial risk associated with an assigned PBR reward/penalty structure. Both historical and simulated BES reliability performance indices implemented in a hypothetical PBR framework are illustrated in the paper. Reliability performance index probability distribution analysis can provide power engineers and risk managers with fundamental knowledge on bulk electric system adequacy, and assist them in managing and controlling future potential risks under a PBR reward/penalty structure. VI. APPENDIX The single line diagrams of the IEEE-RTS [14] and RBTS [16] are shown in Figs. 7 and 8 respectively. Fig. 7. Single line diagram of the IEEE-RTS. VII. REFERENCES [1] R. Billinton, Reliability Considerations in the New Electric Power Utility Industry, Canadian Electricity Association, Electricity 97 Conference and Exposition, April [2] R. E. Brown and J. J. Burke, Managing the Risk of Performance Based Rates, IEEE Transactions on Power Systems, Vol. 15, No. 2, May 2, pp [3] Ontario Energy Board, Electric Distribution Rate Handbook, 2. [4] R. Billinton and Z. Pan, Incorporating Reliability Index Distributions in Performance Based Regulation, Proceedings of IEEE Canadian Conference on Electrical and Computer Engineering (CCECE2), Vol. 1, May 22, pp [5] R. Billinton, L. Cui and Z. Pan, Quantitative Reliability Considerations in Determination of Performance Based Rates and Customer Service Disruption Payments, IEE Proceedings-Generation, Transmission and Distribution, Vol. 149, No. 6, November 22, pp [6] R. Billinton and Z. Pan, Historic Performance-Based Distribution System Risk Assessment, IEEE Transactions on Power Delivery, Vol. 19, No. 4, October 24, pp [7] R. Billinton and W. Wangdee, Delivery Point Reliability Indices of a Bulk Electric System Using Sequential Monte Carlo Simulation, IEEE Transactions on Power Delivery, Vol. 2, No. 4, October 25 (in press). [8] W. Wangdee and R. Billinton, Reliability Performance Index Distribution Analysis of Bulk Electricity Systems, Proceedings of IEEE Canadian Conference on Electrical and Computer Engineering (CCECE5), May 25. [9] R. Billinton and W. Wangdee, Predicting Bulk Electricity System Performance Indices Using Sequential Monte Carlo Simulation, IEEE Transactions on Power Delivery, to be published. [1] Canadian Electricity Association, Bulk Electricity System: Delivery Point Interruptions and Significant Power Interruptions Report, August 23. [11] Canadian Electricity Association, Bulk Electricity System: Delivery Point Interruptions and Significant Power Interruptions Report, December 24. [12] Energy Regulatory Commission, Regulatory Reset for the National Transmission Corporation (TRANSCO) for 26 to 21, September 24. Available: [13] Electricity Generating Authority of Thailand, Annual Reports ( ). Available: [14] IEEE Task Force, IEEE Reliability Test System, IEEE Transactions on Power Apparatus and Systems, Vol. PAS-98, November/December 1979, pp [15] W. Wangdee and R. Billinton, Impact of Load Shedding Philosophies on Bulk Electric System Reliability Analysis Using Sequential Monte Carlo Simulation, Electric Power Components and Systems, Vol. 34, No. 3, March 26 (in press). [16] R. Billinton and et al, A Reliability Test System for Educational Purposes- Basic Data, IEEE Transactions on Power Systems, Vol. PWRS-3, No. 4, August 1989, pp Copyright KTH 26