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220kV变电站电气一次系统设计的文献综述一、变电站的概述随着经济的发展，工业水平的进步，人们生活水平的不断提高，电力系统在整个行业中的比例逐渐趋大。现在电力系统是一个巨大的、严密的整体。各类发电厂、变电站分工完成整个电力系统的发电、变电和配电的任务。电力系统是国民经济的重要能源部门，而变电站的设计是电力工业建设中必不可少的一个项目，由于变电站的设计内容多，范围广，逻辑性强。不同电压等级，不同类型，不同性质负荷的变电站设计时所侧重的方面也不一样。设计过程中具体问题具体分析2。变电站是电力系统中变换电压，接受和分配电能，控制电力的流向和调整电压的电力设施。它通过变压器将各级电压的电网联系起来。结合我国的电力现状，为国民经济各部门和人民生活供给充足，可靠，优质，经济的电能。优化发展变电站，规划以220/110/10kV电压等级设计变电站3，新建变电站应该充分体现出安全性，可靠性，经济性，和先进性。二、具体设计内容变电站设计的内容力求概念清楚，层次分明，结合自己设计的原始资料，参考变电站电气设计工程规范。经过翻阅工作，了解设计基本过程，从而进一步指导设计内容的展开。现将自己查阅文献的工作综述为：通过查阅馆藏书籍，课本网络资源，了解电力工业的相关政策，技术工程等方面的有关知识，理清自己的设计思路，查询有关电气设备的价格和参数。从而为设计提供依据6。本次设计建设一座220KV降压变电所，首先，根据主接线的经济可靠、运行灵活的要求选择各个电压等级的接线方式，在技术方面和经济方面进行比较，选取灵活的最优接线方式。其次进行短路电流计算，根据各短路点计算出各点短路稳态电流和短路冲击电流，从三相短路计算中得到当短路发生在各电压等级的工作母线时，其短路稳态电流和冲击电流的值。然后，根据各电压等级的额定电压和最大持续工作电流进行设备选择和校验。最后进行配电装置设计和总平面布置，防雷保护的设计。具体如下：1、 电气主接线的选择和比较根据原始的数据和变电站类型进行主接线方案拟定，对各方案进行讨论进而确定最终的电气主接线方案,电气主接线的选择是变电站设计的首要部分，也是构成电系统的主要环节。主接线的拟定直接关系着变电站电气设备的选择，配电装置的配置，继电保护和自动装置的确定，是变电站电气-部分投资大小的决定性因素。结合原始资料的分析，及各种接线方式的优缺点，确定最终的接线方案。2、 主变压器的选择按照主变压器的一般确定原则，结合计算确定变压器的台数和容量进而选择合适的变压器型号7 。3、 短路电流计算短路电流计算是为了更好的选择电电气设备，继电保护的计算及整定等，了解了电力系统短路电流计算的知识，学习了计算的方法，选择合适的短路点对各短路点进行计算，完成短路电流计算部分67。4、 导体和电气设备的选择导体和电气设备的选择是设计的主要内容之一，因电力系统中各种电气设备的作用和工作条件不一样，具体的选择方法也不完全相同，但它们的基本要求是一致的，电气设备要可靠的工作，必须按正常条件进行选择，并按短路状态来进行动稳定和热稳定的校验7。5、导线的选择主要是母线的选择，变电站主接线的基本环节是电源和出线，母线是连接电源和出线的中间环节，起着汇集和分配电能的作用。5、 防雷与接地保护设计（1）避雷器的选择（2）保护范围及计算7、屋内外配电装置设计和总平面布置 通过以上的文献查阅资料，为这次的设计提供了有力的依据，这次的毕业设计，是对自己已学知识的整理和进一步的理解、认识，学习和掌握变电所电气部分设计的基本方法培养独立分析和解决问题的工作能力及实际工程 设计的基本技能。电力工业的迅速发展，对变电所的设计提出了更高的要求，更需要 我们提高知识理解应用水平，认真对待。三、总结部分本次设计使我们的毕业设计，在这次设计中我们设计一个电压等级为220/110/10kV的变电站一次系统的全部内容。本次设计变电站的类型为地方变电站，是为了满足市区的生产和生活的要求。根据老师给出的设计资料和要求，结合所学的知识和文献资料所给的。通过这次设计，对以前的知识加强了理解和掌握，掌握了电力工程的设计过程，熟悉了设计方法，为以后的工作打下了基础。参考文献 1 曹绳敏. 电力系统课程设计及毕业设计参考资料M. 水利电力出版社，1995 2 范锡普. 发电厂电气部分第二版M北京电力出版社， 1995. 3 宋继成. 220-500kV变电所二次接线，中国电力出版社，1996 4 西北电力设计院. 发电厂变电所电气接线和布置.北京 ： 水利电力出版社，1992,7 5 西安交通大学. 发电厂变电所电气主接线设计.2000,5 6 王锡凡. 电力工程基础.西安交通大学出版，2001,1 7 供电技术第四版.机械工业出版社 8 于沈阳. 10-220kV变电所设计.辽宁科学技术出版社.1993. 10 9 陈衍. 电力系统稳态分析，中国电力出版10 刘吉来.黄瑞梅. 高电压技术M. 中国水利电力出版社200411 黄益庄.变电站综合自动化M. 中国电力出版,200112 Network communications Fechonlogy Ata ElahiM.科学出版社，200213 Kuffel E.et al.Hing-voltage Eundemnetals M new York,pergamon press,198414 Naildu ms.et al.Hing-voltage tage Engineering M,New Delhi Tata McGraw-Hill,publ.,198215 贺家李. 电力系统继电保护原理第四版，中国电力出版 16 李鑫. 数字化变电站自动化系统，科技资讯，2011,3317 任海燕等. 常用主接线的方式及优缺点，实用技术 18 变电运行M.中国电力出版社，200519 蒙祥萍. 电力系统分析M.高等教育出版社，2004IEEE Transactions on Power Delivery, Vol. 13, No. 4, October 1998 1425 EFFECTS OF TOPOLOGY AND FEEDER CAPACITY ON SUBSTATION DISTRIBUTION TRANSFORMER LOADING D. J. Tylavsky Department of Electrical Engineering N. R. Tatikonda Arizona State University Tempe, AZ 85287 Abstract As loads on substation distribution transformers (SDTs) increase, engineers must decide at what point in time a second transformer bay needs to be added to keep loss of load expectation (LOLE) values at acceptable levels. An alternative to adding an additional transformer bay is to add ties to physically-close SDTs to provide backup power on outage; adding ties improves the SDT LOLE for any given loading level. Presented in this paper is a method for assessing the effects of interconnection topology, SDT forced outage rate (FOR), feeder capacity limitation, and load duration data on customer reliability. Included in this paper are the theory and results associated with an application software program that is being used by utility engineers to calculate LOLE for an interconnected SDT system. Keywords: Substations, Power distribution reliability, power distribution planning I. INTRODUCTION Deregulation of the electric utility industry and the competition it brings has caused utilities around the country to focus on cost cutting measures throughout the range of the utilities operations, design, and maintenance. This paper presents a computer based program to provide information to utility engineers so that they can more effectively amortize the capital costs of substation distribution transformers over load served. Engineers can do this by loading the transformers at the maximum level which guarantees a customer LOLE value which is acceptable. This loading level is one of the pieces of information provided by our application software. PE-255-PWRD-0-1-1998 A paper recommended and approved by the IEEE Transmission and Distribution Committee of the IEEE Power Engineering Society for publication in the IEEE Transactions on Power Delivery. Manuscript submitted July 31, 1997; made available for printing January 16, 1998. Ken Alteneder Kennneth E. Brown Electric System Planning & Performance Salt River Project Tempe, AZ Often the loading of substation distribution transformers is set using deterministic criteria i.e., some percent of transformer peak load. Using a deterministic approach gives no measure of customer service reliability; hence this approach provides little information about whether the transformers are being used to full measure o r whether transformers are being loaded at levels which will yield unacceptable customer service reliability. Using a probabilistic approach allows customer service reliability to be calculated as a function of loading level; such data can then be used to load the transformers intelligently. For example, these data can be used to justify loading a transformer to the maximum load which guarantees a desired customer service reliability, or a loading beyond that point in an extreme situation with quantified measures of the reliability and monetary consequences. The use of a probabilistic approach is widely recommended as it models the power system more realistically considering the uncertainty in the state of the system and it also provides data on severity as well as the probability of unserved energy l. Typically, research into reliability of power systems focus on either the generation and bulk transmission system or on a characteristic portion of the distribution system. Reliability measures and calculation technologies for these two different systems vary considerably. For reliability studies in the generation and bulk transmission systems, LOLE is the measure widely used for system risk assessment l-41. LOLE is calculated using the forced outage rates of generators and bulk transmission system equipment. LOLE can be calculated using two approaches: state enumeration (SE) l-41 and Monte Carlo (MC) simulation l-71. The advantage of the MC approach over SE is that it does not require knowledge of the number of states that a system may have. This is important for complex systems where the number of states that need to be considered is large. When the number of system states of interest is small SE yields an answer which is theoretically correct within one iteration. Depending on the complexity of the model for the bulk transmission and generation system, researchers have found both SE and MC approaches appropriate as shown in Table 1. For reliability studies in the distribution systems, a number of reliability indices are used 4, 81. They include SAIDI, SAUT, CAIDI, and CAIFI etc. These indices are calculated using empirical data but 4, 81 do not suggest methods for analytically predicting these indices. (See Table 1) 0885-8977/98/$10.00 0 1998 IEEE 1426 Table 1. Review of reliability indices and approaches used to calculate indices for generation and dishbution systems. A paper, R. Billinton et al. 9 presents the usage of the MC approach for substation reliability evaluation. Other works lo-141 present approaches which may also be used for tackling the reliability of an interconnected grid of SDTs, but none have applied their techniques to calculating the reliability of this type of regularly connected grid. The substation distribution transformer system we are dealing with is intermediate between the generation system and distribution system. Either LOLE or SAID1 type of indices can be used to assess the outage risk of this type of system. If we consider each transformer in the substation distribution system as an independent power source, then this system is most similar in structure to an interconnected multi- area generation system. Hence we have chosen to assess the system outage risk using LOLE. Because the system we are considering for study requires only about 5 states (and a handful of sub states), we have chosen the SE approach for calculating LOLE. . SYSTEM TOPOLOGY The substation distribution transformer system of Salt River Project is interconnected so that once a transformer at a particular substation is lost, other transformers located at the same substation or nearby substations with spare capacity can supply the load of the transformer on outage. The amount of load which can be picked up by the physically- near transformers depends on several factors, principal among these is the transformer interconnection topology. Fig. 1 shows a typical interconnection topology in which a (main) transformer is tied to four adjacent transformers. (Boxes in this figure represent loads. This figure represents the essential features necessary to describe the segmenting of load and the operation of the back-up transformers; some circuit breakers and feeder connection details unnecessary to our investigation have been omitted.) Each tie connects one of the transformers 4 feeders to one of the 4 feeders of physically close transformers. Each tie consists of a feeder conductor connecting feeders of adjacent transformers and a normally open switch. The operation philosophy used with this topology is simple; once a transformer goes on outage, the (four) normally open switches are closed allowing the backup transformers to wheel power over its feeders to the load. Fig. 1 shows only a small part of the SDT interconnection. In practice each backup transformer is connected to other transformers (referred to as tertiary transformers) which serve to improve the customer reliability of the backup transformer. This interconnection goes on in a regular way (almost ad infinitum). A practical way of showing this interconnection topology is as in Fig. 2. In Fig. 2, each transformer is represented as a square box. The transformers in this figure are grouped into three classes. The transformer located at the center of the system is the Main transformer (represented as M). Transformers topologically adjacent to the main transformer (the backup transformers of Fig. 1) are shown using the B symbol. Transformers topologically adjacent to B transformers (excluding the main transformer) are referred to as tertiary transformers and are shown in Fig. 2 using the T symbol. Each transformer in the system of Fig. 2 has four feeders and each of these four feeders are connected via ties to feeders of physically close transformers. The area enclosed by the box in Fig. 2 represents the portion of the system shown in Fig. 1. Backup Backup Backup Backup Xfmr #4 Xfmr #3 Xfmr #2 Xfmr #I Normally Open Switch - 6 3 - T i e Figure 1. Main and backup transformers in the system. d -transformer M - main transformer T - tertiary transformer B - backup transformer Figure 2. Substation interconnection topology: number of ties equals FOUR. 1427 The “Four Ties Topology” of Fig. 2 is an approximation to one subset of the many different topologies the utility has in their system. Because of the large number of different possible topologies, two additional topologies for study were selected, the “Six Ties” and “Eight Ties” topologies are shown in Figs. 3 and 4 respectively. 111. BOUNDARY CONDITIONS AND ASSUMPTIONS The goal of this work was to develop a user-fiiendly personal-computer-based software program that calculates LOLE for the above discussed system configurations. The challenge in calculating LOLE is that the size of the system of interest (a portion of which is shown in Fig. 2) makes the LOLE calculations (by either MC or SE) unwieldy. To make the calculations feasible, we decided to study a portion of the system (shown within the dotted boxes of figures 2, 3 and 4) and to apply boundary conditions to account for (in an approximate way) the effects of the discarded system. We considered two different boundary conditions: deterministic and stochastic. The simplest is the deterministic boundary condition. Under this assumption we treat all tertiary transformers as 100% reliable and power supplied to all transformers as 100% reliable. The more complex is the stochastic boundary condition. Under this condition we treat the tertiary transformer as having the same FOR as the main and backup transformers and the power supplied to the SDTs as having some value of FOR. Because transformers outside of the main, backup or tertiary cannot contribute power to the area under study (e.g., within the dotted box of Fig. 2), assumptions about their reliability do not affect the LOLE of the system under study. Because of the limitations of time and resources, we chose the deterministic boundary condition for this work. Figure 3. Substation interconnection topology: number of ties equals SIX. Figure 4 . Substation interconnection topology: number of ties equals EIGHT. Within the system of interest, we calculated two values of LOLE. We calculated the LOLE for customers served by the main transformer and we calculate the LOLE for the customers served by all of the transformers within the area of interest (i.e., the dotted boxes of figures 2, 3 and 4); we refer to this second LOLE as the system LOLE. The main transformer LOLE is a true stochastic result because all transformers that can supply power to the load served by the main transformer are modeled stochastically. (The outage of the tertiary transformer can have no effect on the customers served by the main transformer.) Hence the main transformer LOLE is conservative provided the assumptions about transformer FOR are conservative. The outage of a tertiary transformer will impact the load normally served by the backup transformers. Because the tertiary transformers are modeled deterministically, the LOLE values of the system under study (system LOLE) will not necessarily be conservative; however these results can still be used to compare the effects on LOLE of varying number of ties, tie capacity etc. Including the boundary condition assumption discussed above, the complete list of assumptions used in this work is shown below: i. (Boundary Conditions) The tertiary transformers (which are outside the system represented by dotted box) are modeled with the deterministic assumption; they are 100% reliable in service. The power supplied to the high voltage side of all transformers in the study is 100% reliable. ii. (Capacity Uniformity) All the transformers in the system are considered identical and have equal capacity ratings. All feeders and ties have the same capacity. 1428 iii. (Stochastic Uniformity) All the transformers have All other equal forced outage rate (FOR) values. equipment is 100% reliable. iv. (Loading Uniformity) The load on a transformer never exceeds its capacity and all the transformer loads have identical time histories. LOLE is the probability that the system is in a given state multiplied by time that load is not served in that state. If the probability of being in state k is pk and tk is the time that load is not served (given an assumed loading level), then the LOLE for the kth state is: In a system with more than one state, the LOLE is simply the sum of the LOLE due to all possible states (i.e., all possible combinations of transformer outages). That is, There are three steps which must precede this calculation; first we must identify the system states, second we must calculate the probability that the system will operate in each of these state. Then, from load duration data, we must calculate the amount of time load will not be served for each of these states. (Note that the time load is not served will be a function of the load duration curve shape as well as the peak load from the load duration curve.) State Probabilities The probabilities of the five system states are calculated using Binomial Probability Equation 1. If n is the number of transformers (in the dotted boxes of figures 2, 3, and 4), FOR is the (constant) probability of outage, then the probability of exactly r transformers in service and n-r transformers on outage is given by the expression - P, = .C, * (1-FOR) * FOR (2) = n! * (1-FOR) * FOR n-r r ! (n-r) ! For example, consider four transformers in a system (e.g., the four backup transformers of Fig. 2) and assume the probability of losing a transformer OR) as 0.005. Then from equations (1) and (2), the probability of losing two transformers (State 4) in the system is given as P 4 = 4! * 0.995 * (0.005) This probability does not account for the requirement in State 4 that the main transformer is in service; hence we must multiply the above result by (1-FOR) to get the probability of being in State 4. P 4 = = 4! * 0.995 * (0.005)*0.995 - 4! *2! 4! *2! Table 2 shows the general equations for the probabilities of system states. Here, NT represents the value of the number of ties in the topology (4 or 6 o r 8). Table 2. Generalized probability equations for the five There is a large number of different possible combinations of transformer outages for the systems of figures 2, 3 and 4. This number can be reduced to 5 states (with a few sub-states) as follows: for typical SDT FOR values, the probability of states where three or more transformers are on outage is so small that their LOLE contribution can be neglected; hence only the states where two or fewer transformers are on outage are considered here. Further, because of the Loading Uniformity assumptions (listed above), having one backup transformer on outage is indistinguishable from having any other single backup transformer on outage. Using this approach we can reduce the number of states to 5 with the following transformers on outage: i. ii. iii. iv. v. State 0 no transformer on outage, State 1: the main transformer on outage, State 2 one backup on outage, State 3: main and one backup on outage, and State 4: two backups on outage. system states. I State I Transformer I Probability (P) I NT = Number of ties in the touolom. I w, FOR = Forced Outage Rate of the transfomer. Time Load is Not Served So far we have identified the states in which the system may operate and the probabilities that the system may exist in these state. The next step is to find the time that load will not be served for each of these states. To find the amount of time the load is not served for any system state, we first calculate the amount of load not served in each system state. Consider State 1 for the 4-tie case. Assume, for example purposes, that each transformer has a capacity of 25 PAW, and serves a peak load of 20 MW. Assume that the tie capacity is limited to 7 MW. Each backup transformer has 5 MW of spare capacity (enough to supply the load normally 1429 20 served by Main) but since each feeder already must carry 5 MW to serve its load, only 2 MW of spare capacity is available; hence the load not served is 20-(4*2)=12 MW and the actual load served is 8 MW. (Note that this calculation assumes the load to be distributed, rather than concentrated, and that segmenting switches along the length of each feeder can be opened or closed to allow the load served by the backup transformer to be the maximum possible.) Using the sample load duration data shown in Fig. 5, the time that load is not served is 15.7%. The main-transformer LOLE contribution by State 1 then is: LOLEI = 15.7% * (0.005) * (&* (0.995)4 * (0.005)0) Load Duration Curve - LOLE Plots 1 7 0.1 - ? & 0.01 - 9 go.001 - 0.0001 - If we sum the LOLE contributions from every state, we get the LOLE for the assumed peak load. This gives one point on the LOLE versus peak load plot. If we repeatedly perform this LOLE calculation while varying the assumed peak loads (and while keeping fixed the load duration curve shape of Fig. 5), we can get a plot of LOLE versus main transformer peak load as shown in Fig. 6. Note that the abscissa in this plot is main transformer peak load scaled as a % of main transformer capacity. The system LOLE value is calculated similarly; here however we calculate the time load is not served for each transformer within the system and use the maximum value (of time load is not served) in the LOLE calculation. Note that this calculation depends on the number of ties, transformer capacity, feeder (tie) capacity, and transformer load. V. SOITWARE BENEFITS We have developed a user fi-iendly software package, P, that automatically generates the LOLE versus peak load plots for the 4-, 6, and 8-ties topologies. This software requires the following- input data. 1. Number of Ties 2. Transformer Capacity 3. Tie Capacity 4. SDTFOR 5. BayName 6. Season (Summer, Fall, Winter, Spring, Annual) The Bay Name and Season inputs are used by the software to uniquely identify the data file that contains sampled load duration data for the transformer bay and season of interest. The software is Excel based to provide an intuitive user interface (within the Windows environment) and uses Visual Basic modules to perform the complex repetitive LOLE calculations. 0- 1 0 10 20 30 40 50 60 70 80 90 IOC % Time at or above MW load Figure 5. Summer load duration (LD) curve. f 10.00001 ! I 60 70 80 90 100 I 50 Main Xfmr Load (%of Xfmr Capacity) Figure 6. The main transformer LOLE versus % capacity for 25 MW capacity, 7MW Tie Capacity, 4 Ties and FOR=0.005 Benefits The P3 software provides many benefits to utility engineers. It gives the exact value of system and the main transformer LOLE and provides the plots OF LOLE for varying transformer-loading levels. Engineers can quickly look at the effects on LOLE of varying number of ties, transformer capacity, feeder capacity and FOR for different types of load duration profiles (e.g., summer versus annual, residential versus commercial etc.) Utility engineers are using the LOLE plots produced by P3 to determine the optimum loading of the SDT for a given tolerable value of LOLE or to load beyond the optimum point in extreme situations with quantified measures of the reliability and monetary consequences. Also, by observing the break points in the LOLE plots, engineers can avoid increasing the load on SDTs to levels that cause a sudden increase in the LOLE value. Loading the SIDTs to the maximum load which guarantees the desired customer service reliability allows utility engineers to more effectively amortize the capital cost of the SDTs. The P3 software can be used to study the effects on LOLE of varying study parameters. For example, as loads on SDTs increase, engineers must decide at what point in time a second transformer bay needs to be added to keep LOLE 1430 values at acceptable levels. Sometimes, it may be cost effective to lower the LQLE in the short term up upgrading feeder capacities and/or installing ties to back up transformers. The economic impact of either installing additional brans former capacity or adding additional ties can be studied (with full knowledge of the effects of each on LOLE) and the appropriate decision made. which calculate loss of load expectation (LOLE) for the interconnected substation distribution transformer system. This software is capable of adjusting its output to take into account changes in connection topologies, transformer capacities, transformer forced outage rates, feederbe capacities, and load duration profiles. This application software was developed for the Salt River Project, Tempe, Az. I 95 T Effect of No. Ties on Loading for Fixed LOLE I The LQLE versus transformer loading level plots generated by this software are being used by utility engineers to aid in determining the optimum loading of the substation distribution transformers. By optimum, we mean the maximum load which guarantees a desired customer service reliability (i.e. LQLE.) This information allows utility engineers to more effectively amortize the capital cost of substation distribution transformers. 4 5 6 7 Number of 12KV Ties VII. ACKOWLEGEMET Figure 7. % Loading versus Number of Ties for an LOLE value of 0.0001%. Financial support for this research was provided by Salt River Project through the ACEPS center at Arizona State University. Fig. 7 shows plots of acceptable percent loadmg for six different combinations of transformer capacity and tie capacity values using the commercial load duration curve of Fig. 5. This figure was constructed by plotting the maximum transformer load that will yield an LOLE value of 0.0001% for the feederhie and transformer capacities shown in Table 3. These curves show that as the transformer capacity increases, the percent loading at a constant LOLE decreases. This occurs because the fixed feeder/tie capacity limits the backup power that can be supplied upon an outage. In the case of curves 4 and 5, the tie capacity limit is not encountered; hence this curves are identical. Curves like these can be used to get a qualitative as well as quantitative measure of the effects of varying the number of ties and/or tie capacities on the maximum load a transformer can supply for a given LOLE value. VI. CONCLUSIONS Utilities around the country have been focusing on cost cutting measures throughout the range of the utilities operations, design and maintenance. This paper presents a user friendly, personal computer based application software REFERENCES I. P. M. Anderson, S. K. Agarwal and G. M. Chintaluri, “Seminar Notes from the Introduction to Power System Reliability”, presented at Salt River Project, Tempe, AZ, April 18-20, 1994. 2. Harry G. Stoll, “Least-Cost electric utility planning”, A Wiley-Interscience publication, 1989. 3. J. Endrenyi, “Reliability Modeling in Electric Power Systems”, Wiley, New York, 1978. 4. Roy Billinton and Ronald Allan, “Reliability Evaluation of Power Systems”, Plenum Press, NY, 1984. I. A. D. Patton and S. K. Sung, “A Transmission Network Model for Multi-Area Reliability Studies”, A paper recommended and approved by the IEEE Power Engineering Society for presentation at the IEEPES 1992 Winter Meeting, NY, January 26-30, 1992. 6. Glenn E. Haringa, Gary A. Jordan, and Dr. Leonard L. Garver, “Application of Monte Carlo Simulation to Multi- Area Reliability Evaluations.”, IEEE Computer Applications in Power, January 1991. 7. R. Billinton and W. Li, “A Monte Carlo method for multi-area generation system reliability assessment”, A paper recommended and approved by the IEEE Power Engineering Society for presentation at the IEE/PES 1992 Winter Meeting, NY, January 26-30, 1992. 1431 8. R. Billinton and J. E. Billinton, “Distribution System Reliability Indices”, IEEE Transactions on Power Delivery, Vol. 4, NO. 1, January 1989, pp. 561-568. 9. R. Billinton and G. Lian, “Station reliability evaluation using a Monte Carlo approach”, A paper recommended and approved by the IEEE Power Eng
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