基于频率动态特性的电力系统频率稳定概率安全风险评估
|
摘要
本文受国家自然科学基金项目(柔性发输电系统概率风险评估和优化配置模型研究,项目号50977094;大电网概率风险评估的解析计算模型和算法研究,项目号50607021)资助。
现代电力系统表现出大机组、大容量远距离输电的主要特征,系统在遭受随机严重功率缺额时保持频率稳定的能力正面临严峻挑战,将风险评估的观点引入频率稳定研究中以全面客观地反映频率稳定风险水平成为了迫切需要。因此,研究合适的频率稳定概率风险评估理论、模型和算法,为规划和运行人员提供系统频率稳定风险水平,已成为急需解决的重要研究课题。
本文从频率动态特性角度对频率稳定问题进行了研究,并且为克服频率稳定评价中对旋转备用考虑的不足和减少低频减载各轮动作时间近似计算带来的误差,论文详细推导了考虑旋转备用影响的频率动态特性,并建立了低频减载作用下频率稳定的分析模型;为实现频率稳定的概率风险评估,对发电方式和负荷水平分别建立了随机模型;并构建了反映频率失稳严重程度的期望值指标和反映风险水平分布规律的概率分布指标。
在频率稳定计算模型和指标的基础上,本文提出了一种计及发电系统运行状态不确定性和自动低频减载作用的频率稳定概率风险评估算法。该算法首先建立系统各元件的停运模型,然后利用非序贯蒙特卡洛模拟形成系统可能的各种故障状态,在计及低频减载作用的基础上,针对无备用和有备用两种情况,基于各故障状态下频率动态特性,对系统进行了频率稳定性分析,最后形成各风险指标;本文对反映频率稳定风险分布规律的系统最低频率、稳态频率和频率偏移安全裕度的概率分布进行了计算分析,并对有无备用两种情况下的频率失稳时间大小进行了比较;探讨了旋转备用容量变化和发电机部分失效模式对频率稳定性的影响;计算了多层负荷模型在不计及不确定性和计及不确定性两种情况下的频率稳定年度指标,并分析比较了各负荷层对年度指标的贡献程度。应用IEEE-RTS 24可靠性测试系统验证了算法的有效性,各计算结果反映了频率稳定概率风险水平。
This dissertation is supported by National Natural Science Foundation of China (No.50977094, No.50607021).
The modern power systems have showed the main features of large units and large capacity remote transmission, the ability to maintain frequency stability is facing serious challenge while the system are subjected to random serious power shortage, in order to objectively reflect the risk level of frequency stability, introducing the risk assessment to the study of frequency stability has become an urgent task. Therefore, study on appropriate theories, models and algorithms of probabilistic risk evaluation for frequency stability to provide the risk level of frequency stability for the planning and operation personnel have become an important research topic which needs to solve urgently.
This dissertation studies the frequency stability problem based on frequency dynamic characteristics. To overcome the frequency stability assessment in consideration of the lack of spinning reserve and reduce the approximate calculation error of the action time in the under frequency load shedding, this dissertation derives the dynamic frequency characteristics which accounting the impact of spinning reserve, and the analysis model of frequency stability is built for under frequency load shedding. To achieve probabilistic risk assessment for frequency stability, the stochastic models of generating dispatch and load demand are established, and the expected indices which reflect the severity of the frequency instability and the probability distribution indices which reflect the risk level are constructed.
Based on the probabilistic risk assessment model and the indices, this dissertation proposes an algorithm of probabilistic risk evaluation of frequency stability which considers the uncertainty of generating system’s operational state and the effect of under frequency load shedding, in this algorithm the outage models of components are built, then the outage probabilities are calculated in order to consider the randomness of the system, non-sequential Monte Carlo simulation is utilized to sample system states. Taking into account the role of automatic under frequency load shedding, according to non existence and existence of spinning reserve, frequency stability analysis is made based on the frequency dynamic characteristic for every contingency, finally formatting the cumulative risk index. The probability distribution of system lowest frequency, steady state frequency and frequency deviation safety margin which reflect the distribution of frequency stability risk are analyzed, and the time of frequency instability are compared, moreover the influence of spinning reserve capacity diversification and generator partial failure mode on frequency stability are discussed as well. Finally the annual indices of the multi-level load model including uncertainty and excluding uncertainty in load are calculated, and the analysis and comparison of the various load levels on the contribution of the annual indices are made. The calculation and analysis of IEEE-RTS 24 are showed to verify the validity of the proposed algorithm, the results reflect the probabilistic risk level of frequency stability.
现代电力系统表现出大机组、大容量远距离输电的主要特征,系统在遭受随机严重功率缺额时保持频率稳定的能力正面临严峻挑战,将风险评估的观点引入频率稳定研究中以全面客观地反映频率稳定风险水平成为了迫切需要。因此,研究合适的频率稳定概率风险评估理论、模型和算法,为规划和运行人员提供系统频率稳定风险水平,已成为急需解决的重要研究课题。
本文从频率动态特性角度对频率稳定问题进行了研究,并且为克服频率稳定评价中对旋转备用考虑的不足和减少低频减载各轮动作时间近似计算带来的误差,论文详细推导了考虑旋转备用影响的频率动态特性,并建立了低频减载作用下频率稳定的分析模型;为实现频率稳定的概率风险评估,对发电方式和负荷水平分别建立了随机模型;并构建了反映频率失稳严重程度的期望值指标和反映风险水平分布规律的概率分布指标。
在频率稳定计算模型和指标的基础上,本文提出了一种计及发电系统运行状态不确定性和自动低频减载作用的频率稳定概率风险评估算法。该算法首先建立系统各元件的停运模型,然后利用非序贯蒙特卡洛模拟形成系统可能的各种故障状态,在计及低频减载作用的基础上,针对无备用和有备用两种情况,基于各故障状态下频率动态特性,对系统进行了频率稳定性分析,最后形成各风险指标;本文对反映频率稳定风险分布规律的系统最低频率、稳态频率和频率偏移安全裕度的概率分布进行了计算分析,并对有无备用两种情况下的频率失稳时间大小进行了比较;探讨了旋转备用容量变化和发电机部分失效模式对频率稳定性的影响;计算了多层负荷模型在不计及不确定性和计及不确定性两种情况下的频率稳定年度指标,并分析比较了各负荷层对年度指标的贡献程度。应用IEEE-RTS 24可靠性测试系统验证了算法的有效性,各计算结果反映了频率稳定概率风险水平。
This dissertation is supported by National Natural Science Foundation of China (No.50977094, No.50607021).
The modern power systems have showed the main features of large units and large capacity remote transmission, the ability to maintain frequency stability is facing serious challenge while the system are subjected to random serious power shortage, in order to objectively reflect the risk level of frequency stability, introducing the risk assessment to the study of frequency stability has become an urgent task. Therefore, study on appropriate theories, models and algorithms of probabilistic risk evaluation for frequency stability to provide the risk level of frequency stability for the planning and operation personnel have become an important research topic which needs to solve urgently.
This dissertation studies the frequency stability problem based on frequency dynamic characteristics. To overcome the frequency stability assessment in consideration of the lack of spinning reserve and reduce the approximate calculation error of the action time in the under frequency load shedding, this dissertation derives the dynamic frequency characteristics which accounting the impact of spinning reserve, and the analysis model of frequency stability is built for under frequency load shedding. To achieve probabilistic risk assessment for frequency stability, the stochastic models of generating dispatch and load demand are established, and the expected indices which reflect the severity of the frequency instability and the probability distribution indices which reflect the risk level are constructed.
Based on the probabilistic risk assessment model and the indices, this dissertation proposes an algorithm of probabilistic risk evaluation of frequency stability which considers the uncertainty of generating system’s operational state and the effect of under frequency load shedding, in this algorithm the outage models of components are built, then the outage probabilities are calculated in order to consider the randomness of the system, non-sequential Monte Carlo simulation is utilized to sample system states. Taking into account the role of automatic under frequency load shedding, according to non existence and existence of spinning reserve, frequency stability analysis is made based on the frequency dynamic characteristic for every contingency, finally formatting the cumulative risk index. The probability distribution of system lowest frequency, steady state frequency and frequency deviation safety margin which reflect the distribution of frequency stability risk are analyzed, and the time of frequency instability are compared, moreover the influence of spinning reserve capacity diversification and generator partial failure mode on frequency stability are discussed as well. Finally the annual indices of the multi-level load model including uncertainty and excluding uncertainty in load are calculated, and the analysis and comparison of the various load levels on the contribution of the annual indices are made. The calculation and analysis of IEEE-RTS 24 are showed to verify the validity of the proposed algorithm, the results reflect the probabilistic risk level of frequency stability.
引文
[1] IEEE/CIGRE joint task force on stability terms and definitions. Definition and classification of power system stability[J]. IEEE Transaction on Power System, 2004, 19(2): 1387-1401.
[2]薛禹胜,任先成, Wu Q H,等.关于低频低压切负荷决策优化协调的评述[J].电力系统自动化, 2009, 33(9): 100-107.
[3]孙华东,汤涌,马世英.电力系统稳定的定义与分类述评[J].电网技术, 2006, 30(17): 31-35.
[4]蔡邠.电力系统频率[M].北京:中国电力出版社, 1998.
[5] DL 428-91.电力系统自动低频减负荷技术规定[S]. 1991.
[6] Imai S, Yasuda T. UFLS program to ensure stable island operation[C]. Power Systems Conference and Exposition, New York, USA, 2004: 1-6.
[7]周孝信,李兴源,刘俊勇,等译.电力系统稳定与控制[M].北京:中国电力出版社, 2002.
[8] Inoue T, Taniguchi H, Ikeguchi Y, et al. Estimation of power system inertia constant and capacity of spinning reserve support generators using measured frequency transients[J]. IEEE Transactions on Power Systems, 1997, 12(1): 136-143..
[9] Anderson P M, Mirheydar M. A low-order system frequency response model[J]. IEEE Transactions on Power Systems, 1990, 5(3): 720-729.
[10]王梅义,吴竞昌,蒙定中.大电网系统技术[M].北京:中国电力出版社, 1995.
[11]李艳,李如琦,孙志媛.快速评估电力系统频率稳定性的方法[J].电网技术, 2009, 33(18): 73-77.
[12]蔡泽祥,倪腊琴,徐泰山.电力系统频率稳定分析的直接法[J].电力系统及其自动化学报, 1999, 11(Z1):13-17.
[13] Chan M L, Dunlop R D, Schweppe F. Dynamic equivalents for average system frequency behavior following major disturbances[C]. IEEE PES Winter Meeting, New York, USA, 1972(4): 1637-1642.
[14]李常刚,刘玉田,张恒旭,等.基于直流潮流的电力系统频率响应分析方法[J].中国电机工程学报, 2009, 29(34): 36-41.
[15] Denis Lee Hau Aik. A general-order system frequency response model incorporating load shedding analytic modeling and applications[J]. IEEE Transaction on Power System, 2006, 21(2): 709-717.
[16]周海锋,徐志勇,申洪.电力系统功率频率动态特性研究[J].电网技术, 2009, 33(16): 58-62.
[17]李爱民,蔡泽祥.基于轨迹分析的互联电网频率动态特性及低频减载的优化[J].电工技术学报, 2009, 24(9): 171-177.
[18]刘洪波,穆钢,徐兴伟,等.使功频过程仿真轨迹逼近实测轨迹的模型参数调整[J].电网技术, 2006, 30(18): 20-24.
[19] Mahat P, Chen Z, Bak Jensen B. Underfrequency Load Shedding for an Islanded distribution system with distributed generators[J]. IEEE Transaction on Power Delivery, 2006, 25(2): 911-918.
[20]杨冠城.电力系统自动装置原理[M].北京:水利电力出版社, 1995.
[21]王葵,潘贞存.一种新型低频减载方案的研究[J].电网技术, 2001, 25(12): 31-33.
[22]熊小伏,周永忠,周家启.计及负荷频率特性的低频减载方案研究[J].中国电机工程学报, 2005, 25(19): 48-51.
[23] Pasand M S, Seyedi H. New centralized adaptive under frequency load shedding algorithms[C]. Large Engineering System Conference on Power Engineering, Dec 10-12, 2007, Montreal, Que, 2007: 44-48.
[24]刘朝章,姜云等.基于调度自动化系统实现低频减负荷方案的探讨[J].电网技术, 2007, 31(Z2): 139-142.
[25]李秀卿,蔡泽祥.电力系统低频减载控制优化算法[J].电力系统自动化, 1998, 22(10): 23-25.
[26] Chin V, Dong Z Y, Saha T K, et al. Adaptive and optimal under frequency load shedding[C]. Australasian Universities Power Engineering Conference, Dec 14-17, 2008, Sydnew, NSW, Australia, 2008: 1-6.
[27] Halevi Y, Kottick D. Optimization of load shedding system[J]. IEEE Transaction on Energy Convers, 1993, 8(2): 207-213.
[28] Juhua Liu, Krogh B H, Ilic M D. Saturation-induced frequency instability in electric power systems[C]. Conversion and Delivery of Electrical Energy in the 21st Century Power and Energy Society General Meeting, Jul, 20-24, 2008, Pittsburgh, PA, USA, 2008: 1:7.
[29] Ying Lu, Wen-Shiow Kao, Yung-Tien Chen. Study of applying load shedding scheme with dynamic D-factor values of various dynamic load models to Taiwan power system[J]. IEEE Transaction on Power System, 2005, 20(4): 1976-1984.
[30] Dadashzaden M R, Sanaye-Pasand M. Simulation and investigation of load shedding algotithms for a real network using dynamic modeling[C]. 39th International UPEC, Sept, 6-8, 2004, 2004(2): 1111-1115.
[31]吴起,林莉. SVC对电力系统频率稳定性影响的仿真分析[J].电力自动化设备, 2007, 27(5): 58-60.
[32] Erlich I, Rensch K, Shewarega F. Impact of large wind power generation on frequency stability[C]. IEEE Power Engineering Society General Meeting, Jun 18-22, 2006, Montreal, Canada, 2006: 1-8.
[33] Helmy W, Hegazy Y G, Mostafa M A, et al. Implementing distributed generation to mitigate under-frequency load shedding[C]. 12th International Middle-East Power System Conference, Mar 12-15, 2008, Aswan, Egypt, 2008: 136-140.
[34] Mahatp, Chen Z, Bak-Jensen B. Underfrequency Load Shedding for an Islanded distribution system with distributed generators[J]. IEEE Transaction on Power Delivery, 2010, 25(2): 911-918.
[35] Horne J, Flynn D, Littler T. Frequency stability issues for islanded power systems[C]. Proceedings of 2004 IEEE PES Power Systems Conference and Expositon, Oct 10-13, 2004, New York, USA, 2004(1): 299-306.
[36] Shrestha G B, Lee K C. Load Shedding Schedules Considering Probabilistic Outages[C]. The 7th International Power Engeineering Conference, Nov 29-Dec 2, 2005, Nanyang Technol Univ, Singapore, 2005(2): 950-955.
[37]韩英铎,闵勇,洪绍斌.复杂扩展式电力系统功率频率动态过程分析[J].电力系统自动化, 1992, 16(1): 28-33.
[38]陆佳政,蒋正龙,雷红才,等.湖南电网2008年冰灾事故分析[J].电力系统自动化, 2008, 32(11): 16-19.
[39]潘力强,张文磊,汤吉鸿,等. 2008年湖南电网特大冰灾事故综述[J].电网技术, 2008, 32(Z2): 20-25.
[40]刘有飞,蔡斌,吴素农.电网冰灾事故应急处理及反思[J].电力系统自动化, 2008, 32(8): 10-13.
[41] Wenyuan L. Risk assessment of power systems-models, methods, and applications[M]. IEEE Press and Wiley&Sons, USA and Canada, 2005.
[42]周家启,任震译.工程系统可靠性评估[M].重庆:科学技术文献出版社重庆分社, 1988.
[43]盛骤,谢式千,潘承毅.概率论与数理统计[M].北京:高等教育出版社, 2003.
[44] Wenyuan L. Incorporating Aging Failures in Power System Reliability Evaluation[J]. IEEE Trans. on Power Systems, August 2002, 22(7): 918-923.
[45] Billinton R, Medicherla T K P, Sachdev M S. Common cause outages in multiple circuit transmission lines[J]. IEEE Trans. on Reliability, June 1978, 27(2): 128-131.
[46] Billinton R, Wenyuan L. Reliability assessment of electric power system using monte carlo methods[M]. New York and London: Plenum Press, 1994.
[47] Wenyuan L, Billinton R. Common cause outage models in power system reliability evaluation[J]. IEEE Trans. on Power Systems, May 2003, 18(2): 966-968.
[48] Rubinstein R Y. Simulation and monte carlo method[M]. New York: Wiley, 1981.
[49]李光琦.电力系统暂态分析[M].北京:中国电力出版社, 2007.
[50]周守昌.电路原理[M].北京:高等教育出版社, 2002.
[51] IEEE Task Force.IEEE reliability test system[J]. IEEE Transaction on Power Apparatus and Systems, 1979, 98(6): 2047-2054.
[52]韩祯祥.电力系统稳定[M].北京:中国电力出版社, 1993.
[53]陈珩.电力系统稳态分析(第二版)[M].北京:中国电力出版社, 1995.
[2]薛禹胜,任先成, Wu Q H,等.关于低频低压切负荷决策优化协调的评述[J].电力系统自动化, 2009, 33(9): 100-107.
[3]孙华东,汤涌,马世英.电力系统稳定的定义与分类述评[J].电网技术, 2006, 30(17): 31-35.
[4]蔡邠.电力系统频率[M].北京:中国电力出版社, 1998.
[5] DL 428-91.电力系统自动低频减负荷技术规定[S]. 1991.
[6] Imai S, Yasuda T. UFLS program to ensure stable island operation[C]. Power Systems Conference and Exposition, New York, USA, 2004: 1-6.
[7]周孝信,李兴源,刘俊勇,等译.电力系统稳定与控制[M].北京:中国电力出版社, 2002.
[8] Inoue T, Taniguchi H, Ikeguchi Y, et al. Estimation of power system inertia constant and capacity of spinning reserve support generators using measured frequency transients[J]. IEEE Transactions on Power Systems, 1997, 12(1): 136-143..
[9] Anderson P M, Mirheydar M. A low-order system frequency response model[J]. IEEE Transactions on Power Systems, 1990, 5(3): 720-729.
[10]王梅义,吴竞昌,蒙定中.大电网系统技术[M].北京:中国电力出版社, 1995.
[11]李艳,李如琦,孙志媛.快速评估电力系统频率稳定性的方法[J].电网技术, 2009, 33(18): 73-77.
[12]蔡泽祥,倪腊琴,徐泰山.电力系统频率稳定分析的直接法[J].电力系统及其自动化学报, 1999, 11(Z1):13-17.
[13] Chan M L, Dunlop R D, Schweppe F. Dynamic equivalents for average system frequency behavior following major disturbances[C]. IEEE PES Winter Meeting, New York, USA, 1972(4): 1637-1642.
[14]李常刚,刘玉田,张恒旭,等.基于直流潮流的电力系统频率响应分析方法[J].中国电机工程学报, 2009, 29(34): 36-41.
[15] Denis Lee Hau Aik. A general-order system frequency response model incorporating load shedding analytic modeling and applications[J]. IEEE Transaction on Power System, 2006, 21(2): 709-717.
[16]周海锋,徐志勇,申洪.电力系统功率频率动态特性研究[J].电网技术, 2009, 33(16): 58-62.
[17]李爱民,蔡泽祥.基于轨迹分析的互联电网频率动态特性及低频减载的优化[J].电工技术学报, 2009, 24(9): 171-177.
[18]刘洪波,穆钢,徐兴伟,等.使功频过程仿真轨迹逼近实测轨迹的模型参数调整[J].电网技术, 2006, 30(18): 20-24.
[19] Mahat P, Chen Z, Bak Jensen B. Underfrequency Load Shedding for an Islanded distribution system with distributed generators[J]. IEEE Transaction on Power Delivery, 2006, 25(2): 911-918.
[20]杨冠城.电力系统自动装置原理[M].北京:水利电力出版社, 1995.
[21]王葵,潘贞存.一种新型低频减载方案的研究[J].电网技术, 2001, 25(12): 31-33.
[22]熊小伏,周永忠,周家启.计及负荷频率特性的低频减载方案研究[J].中国电机工程学报, 2005, 25(19): 48-51.
[23] Pasand M S, Seyedi H. New centralized adaptive under frequency load shedding algorithms[C]. Large Engineering System Conference on Power Engineering, Dec 10-12, 2007, Montreal, Que, 2007: 44-48.
[24]刘朝章,姜云等.基于调度自动化系统实现低频减负荷方案的探讨[J].电网技术, 2007, 31(Z2): 139-142.
[25]李秀卿,蔡泽祥.电力系统低频减载控制优化算法[J].电力系统自动化, 1998, 22(10): 23-25.
[26] Chin V, Dong Z Y, Saha T K, et al. Adaptive and optimal under frequency load shedding[C]. Australasian Universities Power Engineering Conference, Dec 14-17, 2008, Sydnew, NSW, Australia, 2008: 1-6.
[27] Halevi Y, Kottick D. Optimization of load shedding system[J]. IEEE Transaction on Energy Convers, 1993, 8(2): 207-213.
[28] Juhua Liu, Krogh B H, Ilic M D. Saturation-induced frequency instability in electric power systems[C]. Conversion and Delivery of Electrical Energy in the 21st Century Power and Energy Society General Meeting, Jul, 20-24, 2008, Pittsburgh, PA, USA, 2008: 1:7.
[29] Ying Lu, Wen-Shiow Kao, Yung-Tien Chen. Study of applying load shedding scheme with dynamic D-factor values of various dynamic load models to Taiwan power system[J]. IEEE Transaction on Power System, 2005, 20(4): 1976-1984.
[30] Dadashzaden M R, Sanaye-Pasand M. Simulation and investigation of load shedding algotithms for a real network using dynamic modeling[C]. 39th International UPEC, Sept, 6-8, 2004, 2004(2): 1111-1115.
[31]吴起,林莉. SVC对电力系统频率稳定性影响的仿真分析[J].电力自动化设备, 2007, 27(5): 58-60.
[32] Erlich I, Rensch K, Shewarega F. Impact of large wind power generation on frequency stability[C]. IEEE Power Engineering Society General Meeting, Jun 18-22, 2006, Montreal, Canada, 2006: 1-8.
[33] Helmy W, Hegazy Y G, Mostafa M A, et al. Implementing distributed generation to mitigate under-frequency load shedding[C]. 12th International Middle-East Power System Conference, Mar 12-15, 2008, Aswan, Egypt, 2008: 136-140.
[34] Mahatp, Chen Z, Bak-Jensen B. Underfrequency Load Shedding for an Islanded distribution system with distributed generators[J]. IEEE Transaction on Power Delivery, 2010, 25(2): 911-918.
[35] Horne J, Flynn D, Littler T. Frequency stability issues for islanded power systems[C]. Proceedings of 2004 IEEE PES Power Systems Conference and Expositon, Oct 10-13, 2004, New York, USA, 2004(1): 299-306.
[36] Shrestha G B, Lee K C. Load Shedding Schedules Considering Probabilistic Outages[C]. The 7th International Power Engeineering Conference, Nov 29-Dec 2, 2005, Nanyang Technol Univ, Singapore, 2005(2): 950-955.
[37]韩英铎,闵勇,洪绍斌.复杂扩展式电力系统功率频率动态过程分析[J].电力系统自动化, 1992, 16(1): 28-33.
[38]陆佳政,蒋正龙,雷红才,等.湖南电网2008年冰灾事故分析[J].电力系统自动化, 2008, 32(11): 16-19.
[39]潘力强,张文磊,汤吉鸿,等. 2008年湖南电网特大冰灾事故综述[J].电网技术, 2008, 32(Z2): 20-25.
[40]刘有飞,蔡斌,吴素农.电网冰灾事故应急处理及反思[J].电力系统自动化, 2008, 32(8): 10-13.
[41] Wenyuan L. Risk assessment of power systems-models, methods, and applications[M]. IEEE Press and Wiley&Sons, USA and Canada, 2005.
[42]周家启,任震译.工程系统可靠性评估[M].重庆:科学技术文献出版社重庆分社, 1988.
[43]盛骤,谢式千,潘承毅.概率论与数理统计[M].北京:高等教育出版社, 2003.
[44] Wenyuan L. Incorporating Aging Failures in Power System Reliability Evaluation[J]. IEEE Trans. on Power Systems, August 2002, 22(7): 918-923.
[45] Billinton R, Medicherla T K P, Sachdev M S. Common cause outages in multiple circuit transmission lines[J]. IEEE Trans. on Reliability, June 1978, 27(2): 128-131.
[46] Billinton R, Wenyuan L. Reliability assessment of electric power system using monte carlo methods[M]. New York and London: Plenum Press, 1994.
[47] Wenyuan L, Billinton R. Common cause outage models in power system reliability evaluation[J]. IEEE Trans. on Power Systems, May 2003, 18(2): 966-968.
[48] Rubinstein R Y. Simulation and monte carlo method[M]. New York: Wiley, 1981.
[49]李光琦.电力系统暂态分析[M].北京:中国电力出版社, 2007.
[50]周守昌.电路原理[M].北京:高等教育出版社, 2002.
[51] IEEE Task Force.IEEE reliability test system[J]. IEEE Transaction on Power Apparatus and Systems, 1979, 98(6): 2047-2054.
[52]韩祯祥.电力系统稳定[M].北京:中国电力出版社, 1993.
[53]陈珩.电力系统稳态分析(第二版)[M].北京:中国电力出版社, 1995.