电网可靠性评估方法及可靠性基础理论研究
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摘要
客观定量地评估电力系统可靠性能探明系统的薄弱环节,指导电力系统规划、生产与维护,以实现电力系统安全、稳定、可靠等运行目标,达到可靠性与经济性的有机统一。近年来,一方面,为实现更大范围的资源优化配置,促进我国能源集约化开发和高效率利用,促进经济与社会的可持续发展,多项高压/特高压直流输电工程陆续投运,受端电网形成了多直流馈入系统;输电网规模日益庞大且复杂。另一方面,为应对全球能源危机和气候变暖,清洁可再生能源的开发利用和智能电网的研究建设,已成为能源战略的重要组成部分。分布式电源出力的强随机性和间歇性,大大增加了电网规划与运行的不确定性;以高级资产管理体系为基石的智能电网尤为强调基于可靠性条件的状态检修技术。因此,电力系统可靠性研究与应用领域正面临着许多重大科学技术问题亟待攻关。为此,本论文针对高压直流输电系统概率风险评估、输电系统充裕度与安全性评估以及可靠性基础理论与应用研究中存在的若干问题进行科学性的探索,主要研究工作和成果如下:
1.针对特高压/高压直流系统运行特性和结构特点,在对各子系统划分与建模的基础上,提出直流系统可靠性评估模型及其评估方法,计及直流控制保护系统和无功补偿对系统可靠性的影响。以换相电压时间面积为换相失败判据,在构建换相失败风险评价指标体系的基础上,提出了交流系统故障诱发多直流馈入系统换相失败风险评估方法,计及了多个不确定因素的综合作用。以南方电网实际直流系统为算例实现了对所提风险评估方法的验证。
2.针对交直流混联系统运行条件复杂、运行约束多的特点和直流系统的运行特性,建立了以直流极功率方向系数为控制变量的最优负荷削减模型,有效计及了互联电网间直流系统功率支援与功率调制功能,以及由运行条件约束导致的直流极投退等工程实际问题。同时,为了克服平启动时原始对偶内点法收敛困难的局限性,引入了一种将初值寻优过程等效为求取动态系统稳定平衡点的思想,基于伪暂态连续法实现初值寻优。经IEEE RTS96交直流混联输电可靠性测试系统测试,验证了所提模型更加符合工程实际,求解方法收敛性能好、鲁棒性强,为大规模交直流混联输电系统充裕度评估提供了强有力工具。
3.为避免确定性暂态稳定分析结果过于保守与不全面等问题,以安全域概率稳定模型为基础,基于动力系统理论确定电力系统暂态稳定主导不稳定平衡点附近的动态安全域线性边界,并采用以半不变量为基础的埃奇沃斯级数展开获得随机变量加权的联合概率分布,从而构建电力系统暂态稳定概率模型。该模型能有效计及发电机的出力和内电势、负荷的有功功率和无功功率、故障类型、故障位置和故障切除时间等多个不确定性因素。较传统方法,本文模型和方法不需要繁琐的公式推导,物理意义清晰,实现简单,计算效率高。通过IEEE 10机39节点系统对上述模型和方法进行了全面的验证。
4.为克服电力系统可靠性应用研究中假设预防性检修间隔时间和修复持续时间为指数分布造成的模型失真,本文从可靠性数学基础理论出发,以电力系统继电保护为例,计及其预防性检修,研究建立了基于半马尔可夫过程的具有多停运模式的系统可靠性模型及其解析求解方法;提出了以保护年均经济损失最小为目标确定单一保护和双重化保护的最优预防性检修策略;研发了继电保护最优预防性检修分析决策系统。以某电网典型保护系统进行了验证,结果表明所提模型和方法具备计算速度快、精度高的优势。
5.为彻底解决电力系统可靠性研究以状态转移函数服从指数分布为假设前提造成的问题,提高电力系统可靠性研究的精细化水平,以电力设备可靠性研究为例,建立了基于位相型分布的可靠性解析模型及其矩阵解析求解方法;以可靠性应用研究的电力设备检修优化为例,分别建立了以可靠性最优和经济性最优为目标的检修优化模型;通过电力变压器检修优化算例,实现了上述模型和方法的全面验证。为解决经典分布无法反映分布式电源有功出力间歇性问题,建立风力发电机与光伏发电系统出力的位相型分布随机模型,在此基础上构建了随机潮流的位相型分布模型,并采用以半不变量法为基础的埃奇沃斯级数实现其高效求解,另外还分析了分布式电源、无功补偿对支路负载安全性和电压质量的影响。
本文研究工作得到了国家自然科学基金项目(50337010,50977032),国家重点基础研究发展计划项目(973项目)(2009CB219704),“十一五”国家科技支撑计划重大项目(2006BAA02A30),粤港关键领域重点突破项目(2009A091300011),广东省高新技术产业化重点项目(2010A010200005)的资助。
Objective and quantitative reliability evaluation of power system can explore the weakness and point out a way for power system planning, operation and maintenance, in order to achieve the goal of keeping security, stability and reliability of power system operation, realizing the integration of reliability and economy. Recently, aiming at economical and social sustainable development, achieving greater scope of resource allocation optimization and promoting the development of China's energy intensive and efficient utilization, the receiving-end grid forms a large scale multi-infeed high voltage direct current system thanks to several high voltage / ultra high voltage direct current transmission projects commissioning successively. Meanwhile, to cope with energy crisis and global warming, the development and utilization of renewable energy and the research of smart grid have been the important component of energy strategy. However, distribution generation is stochastic and intermittent so that it throws more uncertainty into power system planning and operation. Based on advanced asset management, smart grid attaches special importance to reliability condition-based maintenance. Therefore, power system reliability research and application are facing huge amounts of main technical problems to overcome. For this reason, the dissertation discussed probabilistic risk evaluation of HVDC transmission system, adequacy and security evaluation of transmission system, and the basic theory of reliability. The main work is as follows:
1. According to the operation characteristics and structure features of UHVDC/HVDC system, the reliability model and evaluation of DC systems was presented based on modeling of subsystems, considering the effects of protection and reactive compensation on system reliability. This paper built the commutation failure risk index system and further proposed the risk evaluation approach of multi-infeed HVDC system under AC system fault conditions considering multiple uncertain factors, which took the commutation voltage-time area as criterion. The DC systems of China south grid is used to validate the risk evaluation.
2. An optimal load shedding model, which took polar power-direction coefficient as controlling variable, was proposed, for the complicated conditions and multi-constraints of AC/DC hybrid transmission system and HVDC operation characteristic. The model not only takes into account the outage of DC polar due to operation restricting, but also considers the case of HVDC power reverse. Meanwhile, to overcome the shortcomings of convergence difficulties of current primal-dual interior point methods with flat starting, the paper applied the pseudo transient continuation method to seek the optimal initial point, introducing the idea of converting the problem of finding an initial point into that of finding a stable equilibrium point of active-set based dynamic system. The numerical results demonstrate that the proposed approach provides a novel powerful tool for the adequacy evaluation of AC/DC hybrid transmission systems.
3. The linear boundary of dynamic security region of the controlling unstable equilibrium point was determined on the basis of dynamical system theory. Then, Edgeworth series expansion based on semi-invariant was employed to calculate the weighted joint probability distribution. Consequently, power system transient stability probabilistic model, which avoided conservative and incomplete results using determinate analysis of transient stability, was established. The proposed transient stability probabilistic model can effectively take many uncertain factors into account, such as generator output and internal potential, load active power and reactive power, fault location, fault type, fault-clearing time, et al. Finally, the numerical results of IEEE 10-machine 39-bus system indicated that the proposed model and its solution are effective and feasible, and have broad prospects for engineering application.
4. To overcome the distortion caused by the assumption that preventive maintenance intervals and repair time are exponential, this paper studied the system reliability model with multi-outage states and its analytical solution based on semi-Markov process derived from the fundamental theory on reliability mathematics, took protection system and its preventive maintenance for the instance. The paper also proposed optimum routine maintenance intervals for protection by minimizing the annual average economic losses, and then developed optimum routine maintenance decision system for protection. The numerical results of typical protection systems showed that the advantages of the proposed method are also reflected in high precision and fast speed.
5. To break the limitation of assuming state transfer functions follow exponential distribution and to improve the fineness level of reliability study, reliability studies of electrical devices as an instance, a reliability model based on phase-type distributions was proposed, deriving from the stochastic process fundamental theory, which was solved by matrix-analytic method. On the basis, the optimum maintenance models aiming at reliability and economic were designed, respectively. To solve intermittent problem of distributed generation that classical distribution can not reflect, the paper also built stochastic models of wind turbine and solar photovoltaic system based on phase-type distribution, employed Edgeworth series to solve probabilistic power flow model on the basis of semi-invariant. At the end, the effects of distributed generator and reactive compensation on branch load security and voltage quality were analyzed.
This dissertation is supported by the nation natural science foundation of China (No. 50337010, 50977032), the national basic research program of China (973 Program) (No. 2009CB219704), the ministry of science and technology of the people’s republic of China (No. 2006BAA02A30), the crucial field and key breakthrough project in“Guangdong- Hongkong”(No. 2009A091300011), and high-tech industrialization key project in Guangdong (No. 2010A010200005).
1.针对特高压/高压直流系统运行特性和结构特点,在对各子系统划分与建模的基础上,提出直流系统可靠性评估模型及其评估方法,计及直流控制保护系统和无功补偿对系统可靠性的影响。以换相电压时间面积为换相失败判据,在构建换相失败风险评价指标体系的基础上,提出了交流系统故障诱发多直流馈入系统换相失败风险评估方法,计及了多个不确定因素的综合作用。以南方电网实际直流系统为算例实现了对所提风险评估方法的验证。
2.针对交直流混联系统运行条件复杂、运行约束多的特点和直流系统的运行特性,建立了以直流极功率方向系数为控制变量的最优负荷削减模型,有效计及了互联电网间直流系统功率支援与功率调制功能,以及由运行条件约束导致的直流极投退等工程实际问题。同时,为了克服平启动时原始对偶内点法收敛困难的局限性,引入了一种将初值寻优过程等效为求取动态系统稳定平衡点的思想,基于伪暂态连续法实现初值寻优。经IEEE RTS96交直流混联输电可靠性测试系统测试,验证了所提模型更加符合工程实际,求解方法收敛性能好、鲁棒性强,为大规模交直流混联输电系统充裕度评估提供了强有力工具。
3.为避免确定性暂态稳定分析结果过于保守与不全面等问题,以安全域概率稳定模型为基础,基于动力系统理论确定电力系统暂态稳定主导不稳定平衡点附近的动态安全域线性边界,并采用以半不变量为基础的埃奇沃斯级数展开获得随机变量加权的联合概率分布,从而构建电力系统暂态稳定概率模型。该模型能有效计及发电机的出力和内电势、负荷的有功功率和无功功率、故障类型、故障位置和故障切除时间等多个不确定性因素。较传统方法,本文模型和方法不需要繁琐的公式推导,物理意义清晰,实现简单,计算效率高。通过IEEE 10机39节点系统对上述模型和方法进行了全面的验证。
4.为克服电力系统可靠性应用研究中假设预防性检修间隔时间和修复持续时间为指数分布造成的模型失真,本文从可靠性数学基础理论出发,以电力系统继电保护为例,计及其预防性检修,研究建立了基于半马尔可夫过程的具有多停运模式的系统可靠性模型及其解析求解方法;提出了以保护年均经济损失最小为目标确定单一保护和双重化保护的最优预防性检修策略;研发了继电保护最优预防性检修分析决策系统。以某电网典型保护系统进行了验证,结果表明所提模型和方法具备计算速度快、精度高的优势。
5.为彻底解决电力系统可靠性研究以状态转移函数服从指数分布为假设前提造成的问题,提高电力系统可靠性研究的精细化水平,以电力设备可靠性研究为例,建立了基于位相型分布的可靠性解析模型及其矩阵解析求解方法;以可靠性应用研究的电力设备检修优化为例,分别建立了以可靠性最优和经济性最优为目标的检修优化模型;通过电力变压器检修优化算例,实现了上述模型和方法的全面验证。为解决经典分布无法反映分布式电源有功出力间歇性问题,建立风力发电机与光伏发电系统出力的位相型分布随机模型,在此基础上构建了随机潮流的位相型分布模型,并采用以半不变量法为基础的埃奇沃斯级数实现其高效求解,另外还分析了分布式电源、无功补偿对支路负载安全性和电压质量的影响。
本文研究工作得到了国家自然科学基金项目(50337010,50977032),国家重点基础研究发展计划项目(973项目)(2009CB219704),“十一五”国家科技支撑计划重大项目(2006BAA02A30),粤港关键领域重点突破项目(2009A091300011),广东省高新技术产业化重点项目(2010A010200005)的资助。
Objective and quantitative reliability evaluation of power system can explore the weakness and point out a way for power system planning, operation and maintenance, in order to achieve the goal of keeping security, stability and reliability of power system operation, realizing the integration of reliability and economy. Recently, aiming at economical and social sustainable development, achieving greater scope of resource allocation optimization and promoting the development of China's energy intensive and efficient utilization, the receiving-end grid forms a large scale multi-infeed high voltage direct current system thanks to several high voltage / ultra high voltage direct current transmission projects commissioning successively. Meanwhile, to cope with energy crisis and global warming, the development and utilization of renewable energy and the research of smart grid have been the important component of energy strategy. However, distribution generation is stochastic and intermittent so that it throws more uncertainty into power system planning and operation. Based on advanced asset management, smart grid attaches special importance to reliability condition-based maintenance. Therefore, power system reliability research and application are facing huge amounts of main technical problems to overcome. For this reason, the dissertation discussed probabilistic risk evaluation of HVDC transmission system, adequacy and security evaluation of transmission system, and the basic theory of reliability. The main work is as follows:
1. According to the operation characteristics and structure features of UHVDC/HVDC system, the reliability model and evaluation of DC systems was presented based on modeling of subsystems, considering the effects of protection and reactive compensation on system reliability. This paper built the commutation failure risk index system and further proposed the risk evaluation approach of multi-infeed HVDC system under AC system fault conditions considering multiple uncertain factors, which took the commutation voltage-time area as criterion. The DC systems of China south grid is used to validate the risk evaluation.
2. An optimal load shedding model, which took polar power-direction coefficient as controlling variable, was proposed, for the complicated conditions and multi-constraints of AC/DC hybrid transmission system and HVDC operation characteristic. The model not only takes into account the outage of DC polar due to operation restricting, but also considers the case of HVDC power reverse. Meanwhile, to overcome the shortcomings of convergence difficulties of current primal-dual interior point methods with flat starting, the paper applied the pseudo transient continuation method to seek the optimal initial point, introducing the idea of converting the problem of finding an initial point into that of finding a stable equilibrium point of active-set based dynamic system. The numerical results demonstrate that the proposed approach provides a novel powerful tool for the adequacy evaluation of AC/DC hybrid transmission systems.
3. The linear boundary of dynamic security region of the controlling unstable equilibrium point was determined on the basis of dynamical system theory. Then, Edgeworth series expansion based on semi-invariant was employed to calculate the weighted joint probability distribution. Consequently, power system transient stability probabilistic model, which avoided conservative and incomplete results using determinate analysis of transient stability, was established. The proposed transient stability probabilistic model can effectively take many uncertain factors into account, such as generator output and internal potential, load active power and reactive power, fault location, fault type, fault-clearing time, et al. Finally, the numerical results of IEEE 10-machine 39-bus system indicated that the proposed model and its solution are effective and feasible, and have broad prospects for engineering application.
4. To overcome the distortion caused by the assumption that preventive maintenance intervals and repair time are exponential, this paper studied the system reliability model with multi-outage states and its analytical solution based on semi-Markov process derived from the fundamental theory on reliability mathematics, took protection system and its preventive maintenance for the instance. The paper also proposed optimum routine maintenance intervals for protection by minimizing the annual average economic losses, and then developed optimum routine maintenance decision system for protection. The numerical results of typical protection systems showed that the advantages of the proposed method are also reflected in high precision and fast speed.
5. To break the limitation of assuming state transfer functions follow exponential distribution and to improve the fineness level of reliability study, reliability studies of electrical devices as an instance, a reliability model based on phase-type distributions was proposed, deriving from the stochastic process fundamental theory, which was solved by matrix-analytic method. On the basis, the optimum maintenance models aiming at reliability and economic were designed, respectively. To solve intermittent problem of distributed generation that classical distribution can not reflect, the paper also built stochastic models of wind turbine and solar photovoltaic system based on phase-type distribution, employed Edgeworth series to solve probabilistic power flow model on the basis of semi-invariant. At the end, the effects of distributed generator and reactive compensation on branch load security and voltage quality were analyzed.
This dissertation is supported by the nation natural science foundation of China (No. 50337010, 50977032), the national basic research program of China (973 Program) (No. 2009CB219704), the ministry of science and technology of the people’s republic of China (No. 2006BAA02A30), the crucial field and key breakthrough project in“Guangdong- Hongkong”(No. 2009A091300011), and high-tech industrialization key project in Guangdong (No. 2010A010200005).
引文
[1]印永华,郭剑波,赵建军,等.美加“8.14”大停电事故初步分析以及应吸取的教训[J].电网技术. 2003(10).
[2]唐斯庆,张弥,李建设,等.海南电网“9·26"大面积停电事故的分析与总结[J].电力系统自动化. 2006(01).
[3]李再华,白晓民,丁剑,等.西欧大停电事故分析[J].电力系统自动化. 2007(01).
[4] Allan R N, Billinton R, Breipohl A M, et al. Bibliography on the application of probability methods in power system reliability evaluation: 1987-1991[J]. IEEE Transactions on Power Systems. 1994, 9(1): 41-49.
[5] Allan R N, Billinton R, Breipohl A M, et al. Bibliography on the application of probability methods in power system reliability evaluation 1992-1996[J]. IEEE Transactions on Power Systems. 1999, 14(1): 51-57.
[6] Billinton R, Fotuhi-Firuzabad M, Bertling L. Bibliography on the application of probability methods in power system reliability evaluation 1996-1999[J]. IEEE Transactions on Power Systems. 2001, 16(4): 595-602.
[7]郭波,武小悦.系统可靠性分析[M].长沙:国防科技大学出版社, 2002.
[8]李海泉,李刚.系统可靠性分析与设计[M].北京:科学出版社, 2003.
[9]金星,洪延姬.系统可靠性与可用性分析方法[M].北京:国防工业出版社, 2007.
[10] Brown H. The use of digital computer in a generator reserve requirement study[J]. AIEE Transactions on PAS. 1958, 77: 82-85.
[11] Ralperin H, Adler H. A determination of reserve-generating capability[J]. AIEE Transactions on PAS. 1958, 77: 530-544.
[12] Richard E. Mathematical theory of reliability: A historical perspective[J]. IEEE Transactions on Reliability. 1984, 33(1): 16-20.
[13] Noferi P, Paris L, Salvaderi L. Monte Carlo methods for Power System Reliability Evaluation in Transmission and Generation Planning[C]. Washington D.C.: 1975.
[14] Patton A D, Blackstone J H, Balu N J. A Monte Carlo simulation approach to the reliability modeling of generating systems recognizing operating considerations[J]. IEEE Transactions on Power Systems. 1988, 3(3): 1174-1180.
[15] Gubbala N, Singh C. Models and considerations for parallel implementation of MonteCarlo simulation method for power system reliability evaluation[J]. IEEE Transactions on Power Systems. 1995, 10(2): 779-787.
[16]别朝红,王锡凡.蒙特卡洛法在评估电力系统可靠性的应用[J].电力系统及其自动化. 1997, 21(6): 68-75.
[17]丁明,张瑞华.发输电组合系统可靠性评估的蒙特卡罗模拟[J].电网技术. 2003, 24(3): 9-12.
[18]肖炎,郭永基,席勇健,等.一种评估大规模电力系统可靠性的新算法[J].清华大学学报(自然科学版). 1999, 39(1): 12-15.
[19] Desieno C F, Stine L L. A probability method for determining the reliability of electric power systems[J]. IEEE Transactions on Power Apparatus and Systems. 1964, PAS-83(2): 174-179.
[20] Billinton R, Bollinger K E. Transmission system reliability evaluation using Markov processes[J]. IEEE Transactions on Power Apparatus and Systems. 1968, PAS-87(2): 538-547.
[21]黄雯莹,任震.高压直流输电系统可靠性评估的FD法[J].重庆大学学报. 1985, 8(1): 9-19.
[22]何建军,任震,王官洁.变电站主接线可靠性评估的逐次FD法[J].电力系统及其自动化学报. 1998, 10(1): 1-6.
[23] Schiling M T, Filho G M B D, Silva D A M L. An Integrated approach to power system reliability assessment[J]. Eletrical power and energy system. 1995, 17(6): 381-390.
[24]任震,湛军.大型电力系统可靠性评估的模型和算法[J].电力系统自动化. 1999, 23(5): 25-27.
[25]任震,何建军,湛军,等.交直流网络系统可靠性评估的混合法[J].电网技术. 2000, 24(5): 13-19.
[26]万国成,任震,吴日昇,等.混合法在复杂配电网可靠性评估中的应用[J].中国电机工程学报. 2004, 24(9): 92-98.
[27] Billinton R, Li W. Hybrid approach for reliability evaluation of composite generation and transmission systems using Monte-Carlo simulation and enumeration technique[J]. Generation, Transmission and Distribution, IEE Proceedings. 1991, 138(3): 233-241.
[28] Billinton R, Sachdev M. Direct current transmission system reliability evaluation[J]. Trans. CEA. 1968, 7(3): 68-170.
[29] Billinton R, Prasad V. Quantitative Reliability Analysis of HVDC Transmission Systems:Part I and II[J]. IEEE Transactions on Power Apparatus and Systems. 1971, PAS-90(3): 1034-1054.
[30] Billinton R, Ahluwalia D S. Incorporation of A DC Link in A Composite System Adequacy Assessment - DC System Modeling[J]. IEE Proceedings-C. 1992, 139(3): 211-220.
[31]任震,武娟,陈丽芳.高压直流输电可靠性评估的等效模型[J].电力系统自动化. 1999, 23(9): 38-41.
[32]陈永进,任震.模型组合及其在直流输电系统可靠性评估中的应用[J].电网技术. 2004, 28(13): 18-22.
[33] Dialynas E N, Koskolos N C. Reliability modeling and evaluation of HVDC power transmission systems[J]. IEEE Transactions on Power Delivery. 1994, 9(2): 872-878.
[34]张静伟,任震,黄雯莹.直流系统可靠性故障树评估模型及应用[J].电力自动化设备. 2005, 25(6): 62-65.
[35]张雪松,王超,常勇,等. GO法在特高压直流输电可靠性研究中的应用[J].高电压技术. 2009, 35(2): 236-241.
[36]洪潮,饶宏.多馈入直流系统的量化分析指标及其应用[J].南方电网技术. 2008, 2(4): 37-41.
[37] Kundur P. Power system stability and control[M]. New York: McGraw-Hill Inc, 1994.
[38]浙江大学发电教研组直流输电科研组.直流输电[M].北京:电力工业出版社, 1982.
[39]李海锋,张璞,王钢,等.直流馈入下的工频变化量方向纵联保护动作特性分析(二)故障线路的方向保护[J].电力系统自动化. 2009, 33(10): 47-52.
[40]李海锋,张璞,王钢,等.直流馈入下的工频变化量方向纵联保护动作特性分析(三)非故障线路的方向保护[J].电力系统自动化. 2009, 33(11): 43-47.
[41]刘之尧,唐卓尧,张文峰,等.直流换相失败引起继电保护误动分析[J].电力系统自动化. 2006, 30(19): 104-107.
[42]项玲,郑建勇,胡敏强.多端和多馈入直流输电系统中换相失败的研究[J].电力系统自动化. 2005, 29(11): 29-33.
[43]杨秀,陈鸿煜.高压直流输电系统换相失败的仿真研究[J].高电压技术. 2008, 34(2): 247-252.
[44] Thio C V, Davies J B, Kent K L. Commutation failures in HVDC transmission systems[J]. IEEE Transactions on Power Delivery. 1996, 2(11): 946-957.
[45]任震,陈永进,梁振升.高压直流输电系统换相失败的概率分析[J].电力系统自动化. 2004, 24(28): 19-22.
[46] Billinton R, Li W. Reliability assessment of electrical power systems using Monte Carlo methods[M]. New York and London: Plenum Press, 1994.
[47]郭永基.电力系统可靠性分析[M].北京:清华大学出版社, 2003.
[48] Li W. Risk assessment of power systems:models,methods and applications[M]. IEEE Computer Society Press, 2005.
[49] Billinton R. Composite system reliability evaluation[J]. IEEE Transactions on Power Apparatus and Systems. 1969, PAS-88(4): 276-281.
[50] Billinton R, Allan R N. Reliability Evaluation of Power Systems (second edition)[M]. New York and London: Plenum Press, 1996.
[51] Li W, Billinton R. Common Cause Outage Models in Power System Reliability Evaluation[J]. IEEE Transactions on Power Systems. 2003, 18(2): 966-968.
[52] Billinton R, Medicherla T K P. Station originated multiple outages in the reliability analysis of a composite generation and transmission system[J]. IEEE Transactions on Power Apparatus and Systems. 1981, PAS-100(8): 3870-3878.
[53] Cunha S H F, Gomes F B M, Oliveira G C, et al. Reliability evaluation in hydrothermal generating systems[J]. IEEE Transactions on Power Apparatus and Systems. 1982, PAS-101(12): 4665-4673.
[54] Allan R N, Roman J. Reliability assessment of generation systems containing multiple hydro plant using simulation techniques[J]. IEEE Transactions on Power Systems. 1988, 4(3): 1074-1080.
[55] Allan R N, Roman J. Reliability assessment of hydrothermal generation systems containing pumped storage plant[J]. IEE Proeeedings-C. 1991, 138(6): 471-478.
[56] Ubeda J R, Allan R N. Reliability assessment of composite hydrothemal generation and transmission systems using sequential simulation[J]. IEE Proceedings-C. 1994, 141(4): 257-262.
[57] Leite Da Silva A M, Da Fonseca Manso L A, De Oliveira Mello J C, et al. Pseudo-chronological simulation for composite reliability analysis with time varying loads[J]. IEEE Transactions on Power Systems. 2000, 15(1): 73-80.
[58] Sankarakrishnan A, Billinton R. Sequential Monte Carlo simulation for composite power system reliability analysis with time varying loads[J]. IEEE Transactions on Power Systems. 1995, 10(3): 1540-1545.
[59] Li W, Billinton R. Effects of bus load uncertainty and correlation in composite system adequacy evaluation[J]. IEEE Transactions on Power Systems. 1991, 6(4): 1522-1529.
[60]刘海涛,程林,孙元章,等.交直流系统可靠性评估[J].电网技术. 2004, 28(23): 27-30.
[61] Billinton R, Ahluwalia D S. Incorporation of a DC-link in a composite system adequacy assessment-composite system analysis[J]. Generation, Transmission and Distribution, IEE Proceedings. 1992, 139(3): 221-225.
[62] Li W. Incorporating aging failures in power system reliability evaluation[J]. IEEE Transactions on Power Systems. 2002, 17(3): 918-923.
[63] Rios M A, Kirschen D S, Jayaweera D, et al. Value of security: modeling time-dependent phenomena and weather conditions[J]. IEEE Transactions on Power Systems. 2002, 17(3): 543-548.
[64]丁明,戴仁昶,刘亚成,等.概率稳定性的蒙特卡罗仿真[J].清华大学学报. 1997, 39(3): 79-83.
[65]王韶,周家启.双回平行输电线路可靠性模型[J].中国电机工程学报. 2003, 23(9): 53-56.
[66]赵渊,周家启.静止无功补偿器和移相器的最优配置及其对发输电系统可靠性的影响[J].电工技术学报. 2004, 19(1): 55-60.
[67] Billinton R, Li W. A Hybrid Approach for Reliability Evaluation of Composite Generation and Transmission Systems Using Monte Carlo Simulation and Enumeration Technique[J]. IEE Proceedings-C. 1991, 138(3): 233-241.
[68]丁明,李生虎,吴红斌.基于充分性和安全性的电力系统运行状态分析和量化评价[J].中国电机工程学报. 2004, 24(4): 43-49.
[69]赵渊,周家启,刘洋.发输电组合系统可靠性评估的最优负荷削减模型研究[J].电网技术. 2004, 28(10): 34-37.
[70]赵渊.大电力系统可靠性评估的灵敏度分析及其校正措施模型研究[D].重庆:重庆大学, 2004.
[71] Zhang W, Billinton R. Application of an adequacy equivalent method in bulk power system reliability evaluation[J]. IEEE Transactions on Power Systems. 1998, 13(2): 661-666.
[72]吴开贵,吴中福.基于敏感度分析的电网可靠性算法[J].中国电机工程学报. 2003, 23(4): 53-56.
[73]吴开贵,王韶,张安邦,等.基于RBF神经网络的电网可靠性评估模型研究[J].中国电机工程学报. 2000, 21(6): 9-12.
[74]谢开贵,周家启.基于ANN削减负荷的发输电组合系统可靠性评估[J].电力系统自动化. 2002, 26(22): 31-33.
[75]刘洋,周家启,谢开贵,等.基于Beowulf集群的大电力系统可靠性评估蒙特卡罗并行仿真[J].中国电机工程学报. 2006, 26(10): 9-14.
[76]刘洋,周家启,谢开贵,等.基于集群技术构建电力系统高性能计算平台[J].计算机仿真. 2005, 22(5): 239-243.
[77]陈华,周家启.大型网络可靠性评估的增流减流交叉网流法[J].重庆大学学报. 1990, 13(4): 2-6.
[78] Li W, Mansour Y, Korczynski J K, et al. Application of transmission reliability assessment in probabilistic planning of BC Hydro Vancouver South Metro system[J]. IEEE Transactions on Power Systems. 1995, 10(2): 964-970.
[79]王超,徐政,高慧敏.基于TPLAN的中国南方电网可靠性与经济性评估[J].继电器. 2006, 34(16): 61-67.
[80] Burchett R C, Heydt G T. Probabilistic method for power system dynamic stability studies[J]. IEEE Transactions on Power Apparatus and Systems. 1978, PAS-97(3): 695-702.
[81] Billinton R, Kuruganty P R S. An approximate method for probabilistic assessment of transient stability[J]. IEEE Transactions on Reliability. 1979, 28(3): 255-258.
[82] Billinton R, Kuruganty P R S. A probabilistic index for transient stability[J]. IEEE Transactions on Power Apparatus and Systems. 1980, PAS-99(1): 195-206.
[83] Billinton R, Kuruganty P R S. Probabilistic assessment of transient stability in a practical multi-machine system[J]. IEEE Transactions on Power Apparatus and Systems. 1981, PAS-100(7): 3634-3641.
[84] Hsu Y Y, Chang C L. Probabilistic transient stability studies using the conditional probability approach[J]. IEEE Transactions on Power Systems. 1988, 3(4): 1565-1572.
[85]甘德强,王锡凡,杜正春.电力系统暂态稳定性的分析[J].中国电力. 1994, 27(4): 32-35.
[86]鞠平,吴耕扬,李扬.电力系统概率稳定的基本定理及算法[J].中国电机工程学报. 1991, 11(6): 17-25.
[87] Xue Y, Li J. Probabilistic transient stability assessment with EEAC[Z]. Singapore: 1997.
[88]王成山,余旭阳.基于能量函数法的暂态稳定概率评估方法[J].电力系统自动化. 2003, 27(6): 5-9.
[89]崔凯,房大中,钟德成.电力系统暂态稳定性概率评估方法研究[J].电网技术. 2005, 29(1): 44-49.
[90] Anderson P M, Bose A. A probabilistic approach to power system stability analysis[J]. IEEE Transactions on Power Apparatus and Systems. 1983, PAS-102(8): 2430-2439.
[91] Timko K J, Bose A, Anderson P M. Monte Carlo Simulation of Power System Stability[J]. IEEE Transactions on Power Apparatus and Systems. 1983, PAS-102(10): 3453-3459.
[92]任震,冉立,李正然.交直流并联系统可靠性与概率动态安全分析(I)(II)[J].华南理工大学学报(自然科学版). 1997, 25(6): 1-11.
[93]丁明,黄凯,李生虎.概率暂态稳定研究中紧急控制措施的模拟及效果分析[J].电工技术学报. 2002, 17(5): 72-77.
[94]丁明,黄凯,李生虎.交直流混合系统的概率稳定性分析[J].中国电机工程学报. 2002, 22(8): 11-16.
[95]李文沅,卢继平.暂态稳定概率评估的蒙特卡罗方法[J].中国电机工程学报. 2005, 25(10): 18-23.
[96] Wu F F, Tsai Y K, Yu Y X. Probabilistic steady-state and dynamic security assessment[J]. IEEE Transactions on Power Systems. 1988, 3(1): 1-9.
[97]余贻鑫,陈礼义.电力系统的安全性与稳定性[M].北京:科学出版社, 1988.
[98]付川,余贻鑫,王东涛.电力系统暂态稳定概率[J].电力系统自动化. 2006, 30(1): 24-28.
[99]余贻鑫,王东涛,王成山,等.基于安全域的输电系统概率安全评估系统框架[J].天津大学学报. 2007, 40(6): 699-703.
[100]王东涛,余贻鑫,付川.基于实用动态安全域的输电系统概率动态安全评估[J].中国电机工程学报. 2007, 27(7): 29-33.
[101]王超.电力系统可靠性评估中的几个重要问题研究[D].浙江大学, 2007.
[102]贺家李,郭征,杨晓军,等.继电保护的可靠性与动态性能仿真[J].电网技术. 2004, 28(9): 18-22.
[103]曾克娥.电力系统继电保护装置运行可靠性指标探讨[J].电网技术. 2004, 28(14): 83-85.
[104]尹相根,陈德树.主设备保护运行情况评价方法的讨论[J].电力自动化设备. 1996, 60(4): 17-19.
[105]王钢,丁茂生,李晓华,等.数字继电保护装置可靠性研究[J].中国电机工程学报. 2004, 24(7): 47-52.
[106]沈智健,周家启,卢继平,等.距离保护运行风险评估模型[J].电力系统自动化. 2008, 32(12): 7-11.
[107]沈智健,卢继平,赵渊,等.变压器比率差动保护判据的可靠性评估模型[J].电网技术. 2008, 32(7): 14-18.
[108]沈智健,卢继平,赵渊,等.阶段式电流保护运行风险评估模型[J].中国电机工程学报. 2008, 28(13): 70-77.
[109]赵自刚.关于新形势下继电保护检修策略的几点思考[J].继电器. 2000, 28(11): 68-72.
[110]李英姿,牛进苍.继电保护装置的现场检修试验[J].华北电力技术. 1999(2): 38-39.
[111]吴杰余,张哲,尹项根,等.电气二次设备状态检修研究[J].继电器. 2002, 30(2): 22-24.
[112] Kumm J J, Weber M S, Hou D, et al. Predicting the optimum routine test interval for protective relays[J]. IEEE Transactions on Power Delivery. 1995, 10(2): 659-665.
[113]李永丽,李致中,杨维.继电保护装置可靠性及其最佳检修周期的研究[J].中国电机工程学报. 2001, 21(6): 63-65.
[114] Billinton R, Fotuhi-Firuzabad M, Sidhu T S. Determination of the optimum routine test and self-checking intervals in protective relaying using a reliability model[J]. IEEE Transactions on Power Systems. 2002, 17(3): 663-669.
[115]丁茂生.电力系统数字式保护控制及自动化系统可靠性研究[D].广州:华南理工大学, 2005.
[116] Howard R A. System analysis of semi-Markov processes[J]. IEEE Transactions on Military Electronics. 1964, 8(2): 114-224.
[117] Feller W. An Introduction to Probability Theory and Its Applications, Vol. 2[M]. New York: Wiley, 1972.
[118]曹晋华,程侃.可靠性数学引论[M].北京:高等教育出版社, 2006.
[119]邓永录.随机模型及其应用[M].北京:高等教育出版社, 1994.
[120]王梓坤.生灭过程与马尔科夫链[M].北京:科学出版社, 1980.
[121]田乃硕.休假随机服务系统[M].北京:北京大学出版社, 2001.
[122] Kaminskiy M P, Krivtsov V V. A simple procedure for Bayesian estimation of the Weibull distribution[J]. IEEE Transactions on Reliability. 2005, 54(4): 612-616.
[123] Ng H K T. Parameter estimation for a modified Weibull distribution, for progressively type-II censored samples[J]. IEEE Transactions on Reliability. 2005, 54(3): 374-380.
[124] Van Casteren J F L, Bollen M H J, Schmieg M E. Reliability assessment in electrical power systems: the Weibull-Markov stochastic model[J]. IEEE Transactions on Industry Applications. 2000, 36(3): 911-915.
[125] Cao Y, Sun H, Trivedi K S, et al. System availability with non-exponentially distributed outages[J]. IEEE Transactions on Reliability. 2002, 51(2): 193-198.
[126]刘振亚.特高压交流输电技术研究成果专辑(2005年)[M].北京:中国电力出版社, 2006.
[127]张文亮,于永清,李光范,等.特高压直流技术研究[J].中国电机工程学报. 2007, 27(22): 1-7.
[128]王钢,李志铿,黄敏,等. HVDC输电系统换相失败的故障合闸角影响机理[J].电力系统自动化. 2010, 34(4): 49-54.
[129] Desrochers G, Lefebvre S, Rioux B. Reliability assessment of HVDC transmission[R]. Canadian Electrical Association,Report CEA 222 T 506,Prepared by IREQ, 1987.
[130]南方电网技术研究中心,华南理工大学电力学院.贵广二回直流系统可用率与可靠性[R].中国南方电网公司, 2006.
[131]周静,马为民,石岩,等.±800 kV直流输电系统的可靠性及其提高措施[J].电网技术. 2007, 31(3): 7-12.
[132]马为民,李亚男,周静.特高压直流输电系统可靠性和可用率指标研究[J].电力设备. 2007, 8(3): 85-88.
[133]欧开健,任震,荆勇.直流输电系统换相失败的研究: (一)换相失败的影响因素分析[J].电力自动化设备. 2003, 23(5): 5-8.
[134] Mckay M D, Beckman R J, Conover W J. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code[J]. Technometrics. 1979, 2: 239-245.
[135] Olsson A, Sandberg G, Dahlblom O. On Latin hypercube sampling for structural reliability analysis[J]. Structural Safety. 2003, 25: 47-68.
[136] Li W, Zhou J, Hu X. Comparison of Transmission Equipment Outage Performance inCanada, USA and China[C]. Vancouver, BC: 2008.
[137] Vaahedi E, Li W, Chia T, et al. Large-scale probabilistic transient stability assessment using[J]. IEEE Transactions on Power Systems. 2000, 15(2): 661-667.
[138] Fotuhi-Firuzabad M, Billinton R, Faried S O. Transmission system reliability evaluation incorporating HVDC links and facts devices[C]. Vancouver, Canada: 2001.
[139] Liu M B, Tso S K, Cheng Y. An extended nonlinear primal-dual interior-point algorithm for reactive-power optimization of large-scale power systems with discrete control variables[J]. IEEE Transactions on Power Systems. 2002, 17(4): 982-991.
[140] Lee J, Chiang H D. A dynamical trajectory-based methodology for systematically computing multiple optimal solutions of nonlinear programming problems[J]. IEEE Transactions on Automation Control. 2004, 49(6): 888-899.
[141] Jiang Q, Han Z. Solvability identification and feasibility restoring of divergent optimal power flow problems [J]. Science in China Series E:Technological Sciences. 2009, 52(4): 944-954.
[142]王锡凡,方万良,杜正春.现代电力系统分析[M].北京:科学出版社, 2003.
[143]颜伟,张海兵,田甜,等.交直流系统的动态无功优化[J].电力系统自动化. 2009, 33(10): 43-46.
[144] Wei H, Sasaki H, Kubokawa J, et al. An interior point nonlinear programming for optimal power flow problems with a novel data structure[J]. IEEE Transactions on Power Systems. 1998, 13(3): 870-877.
[145] Kelley C T, Keyes D E. Convergence analysis of pseudo-transient continuation[J]. SIAM Journal of Numerical Analysis. 1998, 35(2): 508-523.
[146] Task F R T S. The IEEE reliability test system-1996[J]. IEEE Transactions on Power Systems. 1999, 14(3): 1010-1020.
[147] Pinheiro J M S, Dornellas C R R, Schilling M T, et al. Probing the new IEEE Reliability Test System (RTS-96): HL-IIassessment[J]. IEEE Transactions on Power Systems. 1998, 13(1): 171-176.
[148]丁明,李生虎,吴红斌.电力系统概率充分性和概率稳定性的综合评估[J].中国电机工程学报. 2003, 23(3): 20-25.
[149] Vittal V, Mccalley J D, Vanacker V, et al. Transient instability risk assessment[C]. Edmonton,Alberta,Canada: 1999.
[150]曾沅,余贻鑫.电力系统动态安全域的实用解法[J].中国电机工程学报. 2003, 23(5): 24-28.
[151] Xue A, Wu F F, Lu Q, et al. Power system dynamic security region and its approximations[J]. IEEE Transactions on Circuits and Systems I:Regular Papers. 2006, 53(12): 2849-2859.
[152]薛安成,胡伟,梅生伟,等.电力系统动态安全域线性近似方法比较[J].电力系统自动化. 2006, 30(5): 9-13.
[153]余贻鑫.电力系统安全域方法研究述评[J].天津大学学报. 2008, 41(6): 635-646.
[154]王锡凡.电力系统优化规划[M].北京:水利电力出版社, 1990.
[155]王克文,钟志勇,谢志棠,等.混合使用中心矩与累加量的电力系统概率特征根分析方法[J].中国电机工程学报. 2000, 20(5): 37-41.
[156] Kendall M, Stuart A. The Advanced Theory of Statistics,4th ed[M]. London: Charles Griffin, 1997.
[157] Tian W D, Sutanto D, Lee Y B, et al. Cumulant based probabilitstic power system simulation using laguerre polynomials[J]. IEEE Transactions on Energy Conversion. 1989, 4(4): 567-574.
[158] Chiang H D, Wu F F, Varaiya P P. A BCU method for direct analysis of power system transient stability[J]. IEEE Transactions on Power Systems. 1994, 9(3): 1208-1294.
[159] Chen D Z, Ma J. Calculation of stability region[C]. Maui,Hawaii,USA: 2003.
[160] Pai M A, Padiyar K R, Radhakrishnan C. Transient stability of multi-machine AC/DC power systems via energy function method[J]. IEEE Transactions on Power Apparatus and Systems. 1981, PAS-100(12): 5027-5035.
[161]倪以信,陈寿孙,张宝霖.动态电力系统的理论和分析[M].北京:清华大学出版社, 2002.
[162] Laufenberg M J, Pai M A. A new approach to dynamic security assessment using trajectory sensitivities[J]. IEEE Transactions on Power Systems. 1998, 9(3): 953-958.
[163] Pai M A. Energy function analysis for power system stability[M]. Boston: Kluwer Academic Publishers, 1989.
[164]薛安成,梅生伟,卢强,等.基于网络约化模型的电力系统动态安全域近似[J].电力系统自动化. 2005, 29(10): 18-23.
[165] Phadke A G, Thorp J S. Expose hidden failures to prevent cascading outages[J]. IEEE Computer Application in Power. 1996, 9(3): 20-23.
[166] Singh C, Patton A D. Protection system reliability modeling: unreadiness probability and mean duration of undetected faults[J]. IEEE Transactions on Reliability. 1980,R-29(4): 339-340.
[167] Anderson P M, Chintaluri G M, Magbuhat S M, et al. An improved reliability model for redundant protections– Markov models[J]. IEEE Transactions on Power Systems. 1997, 12(2): 573-578.
[168]孙福寿,汪熊海.一种分析继电保护系统可靠性的算法[J].电力系统自动化. 2006, 30(16): 32-35, 76.
[169]陈少华,马碧燕,雷宇,等.综合定量计算继电保护系统可靠性[J].电力系统自动化. 2007, 31(15): 111-115.
[170]熊小伏,陈飞,周家启,等.计及不同保护配置方案的继电保护系统可靠性[J].电力系统自动化. 2008, 32(14): 21-24.
[171] Perman M, Senegacnik A, Tuma M. Semi-Markov models with an application to power-plant reliability analysis[J]. IEEE Transactions on Reliability. 1997, 46(4): 526-532.
[172] Liang Y, Fricks R M, Trivedi K S. Application of Semi-Markov Process and CTMC to Evaluation of UPS System Availability[C]. Seattle,Washington,USA: 2002.
[173]熊俊,肖先勇.一种基于半马尔柯夫过程的配电系统可靠性经济评估方法[J].继电器. 2006, 34(12): 57-62.
[174] Jia X, Christer A H. A periodic testing model for a preparedness system with a defective state[J]. IMA Journal of Management Mathematics. 2002, 13(1): 39-49.
[175] Erlang A K. Solution of some problems in the theory of probabilities of sighicance in automatic telephone exchanges[J]. The Post Office Eletrical Engineer's Journal. 1917, 10: 189-197.
[176] Gupta S K, Goyal J K. Queues with poisson input and Hyper-Exponential output with finite waiting space[J]. Operations Research. 1964, 12(1): 75-81.
[177] Gupta S K. Queues fed by Poisson input and hyper-mixed Erlangian service time distribution with finite waiting space[J]. Mathematical Methods of Operations Research. 1965, 9(2): 80-90.
[178] Cox D R. A use of complex probabilities in the theory of stochastic processes[J]. Proc. Cambridge Philosophical Society (Math. and Phys. Sciences). 1955, 51: 313-319.
[179] Cox D R. The analysis of non-Markovian stchastic process by the inclusion of supplementary variables[J]. Proc. Cambridge Philosophical Society (Math. and Phys. Sciences). 1955, 51: 433-441.
[180]田乃硕,李泉林. PH分布及其在随机模型中的应用[J].应用数学与计算数学学报. 1995, 9(2): 1-15.
[181] Jensen A. A distribution model applicable to economics[M]. Copenhangen: Munksgaard, 1954.
[182] Neuts M F. Matrix-Geometric Solutions in Stochastic Models—An Algorithmic Approach[M]. Baltimore: The Johns Hopkins University Press, 1981.
[183] Asmussen S, Nerman O, Olsson M. Fitting phase-type distributions via the EM algorithm[J]. Scandinavian Journal of Statistics. 1996, 23(4): 419-441.
[184] Thummler A, Buchholz P, Telek M. A Novel Approach for Phase-Type Fitting with the EM Algorithm[J]. IEEE Transactions on dependable and secure computing. 2006, 3(3): 245-258.
[185] Montoro-Cazorla D, Pérez-Ocón R, Segovia M D C. Shock and wear models under policy N using phase-type distributions[J]. Applied Mathematical Modelling. 2009, 33(1): 543-554.
[186] Pérez-Ocón R, Segovia M D C. Shock models under a Markovian arrival process[J]. Mathematical and Computer Modelling. 2009, 50(5): 879-884.
[187] Madan K C, Al-Rub A Z A. On a single server queue with optional phase type server vacations based on exhaustive deterministic service and a single vacation policy[J]. Applied Mathematics and Computation. 2004, 149(3): 723-734.
[188] Gómez-Corral A, Martos M E. Performance of two-stage tandem queues with blocking: The impact of several flows of signals[J]. Performance Evaluation. 2006, 63(9-10): 910-938.
[189] Manuela P, Sivakumarb B, Arivarignan G. A perishable inventory system with service facilities and retrial customers[J]. Computers & Industrial Engineering. 2007, 54(3): 484-501.
[190] Dharmaraja S, Jindal V, Alfa A S. Phase-type models for cellular networks supporting voice, video and data traffic[J]. Mathematical and Computer Modelling. 2008, 47(11-12): 1167-1180.
[191] Johnson M A, Taaffe M R. Matching Moments to Phase Distributions: Mixtures of Erlang Distributions of Common Order[J]. Stochastic Models. 1989, 5(4): 711-743.
[192] Bellman R. Introduction to matrix analysis[M]. New York: McGraw-Hill, 1960.
[193] Sim S H, Endrenyi J. Optimal preventive maintenance with repair[J]. IEEE Transactions on Reliability. 1988, 37(1): 92-96.
[194] Sim S H, Endrenyi J. A failure-repair model with minimal & major maintenance[J]. IEEE Transactions on Reliability. 1993, 42(1): 134-140.
[195] Arshad M, Islam S M, Khaliq A. Power Transformer Asset Management[C]. Singapore,: 2004.
[196] Neuts M F, Pagano M E. Generating random variates from a distribution of phase type[C]. Piscataway,NJ,USA: 1981.
[197]王成山,郑海峰,谢莹华,等.计及分布式发电的配电系统随机潮流计算[J].电力系统自动化. 2005, 29(24): 39-44.
[198]朱能臣,汪建文.风工况双参数威布尔分布k值影响研究[J].太阳能. 2007(6): 34-36.
[199] Prasada G D, Janaa A K, Tripathy S C. Modifications to Newton-Raphson load flow for ill-conditioned power systems[J]. International Journal of Electrical Power & Energy Systems. 1990, 12(3): 192-196.
[200] Zhang P, Lee S T. Probabilistic load flow computation using the method of combined cumulants and Gram-Charlier expansion[J]. IEEE Transactions on Power Systems. 2004, 19(1): 676-682.
[2]唐斯庆,张弥,李建设,等.海南电网“9·26"大面积停电事故的分析与总结[J].电力系统自动化. 2006(01).
[3]李再华,白晓民,丁剑,等.西欧大停电事故分析[J].电力系统自动化. 2007(01).
[4] Allan R N, Billinton R, Breipohl A M, et al. Bibliography on the application of probability methods in power system reliability evaluation: 1987-1991[J]. IEEE Transactions on Power Systems. 1994, 9(1): 41-49.
[5] Allan R N, Billinton R, Breipohl A M, et al. Bibliography on the application of probability methods in power system reliability evaluation 1992-1996[J]. IEEE Transactions on Power Systems. 1999, 14(1): 51-57.
[6] Billinton R, Fotuhi-Firuzabad M, Bertling L. Bibliography on the application of probability methods in power system reliability evaluation 1996-1999[J]. IEEE Transactions on Power Systems. 2001, 16(4): 595-602.
[7]郭波,武小悦.系统可靠性分析[M].长沙:国防科技大学出版社, 2002.
[8]李海泉,李刚.系统可靠性分析与设计[M].北京:科学出版社, 2003.
[9]金星,洪延姬.系统可靠性与可用性分析方法[M].北京:国防工业出版社, 2007.
[10] Brown H. The use of digital computer in a generator reserve requirement study[J]. AIEE Transactions on PAS. 1958, 77: 82-85.
[11] Ralperin H, Adler H. A determination of reserve-generating capability[J]. AIEE Transactions on PAS. 1958, 77: 530-544.
[12] Richard E. Mathematical theory of reliability: A historical perspective[J]. IEEE Transactions on Reliability. 1984, 33(1): 16-20.
[13] Noferi P, Paris L, Salvaderi L. Monte Carlo methods for Power System Reliability Evaluation in Transmission and Generation Planning[C]. Washington D.C.: 1975.
[14] Patton A D, Blackstone J H, Balu N J. A Monte Carlo simulation approach to the reliability modeling of generating systems recognizing operating considerations[J]. IEEE Transactions on Power Systems. 1988, 3(3): 1174-1180.
[15] Gubbala N, Singh C. Models and considerations for parallel implementation of MonteCarlo simulation method for power system reliability evaluation[J]. IEEE Transactions on Power Systems. 1995, 10(2): 779-787.
[16]别朝红,王锡凡.蒙特卡洛法在评估电力系统可靠性的应用[J].电力系统及其自动化. 1997, 21(6): 68-75.
[17]丁明,张瑞华.发输电组合系统可靠性评估的蒙特卡罗模拟[J].电网技术. 2003, 24(3): 9-12.
[18]肖炎,郭永基,席勇健,等.一种评估大规模电力系统可靠性的新算法[J].清华大学学报(自然科学版). 1999, 39(1): 12-15.
[19] Desieno C F, Stine L L. A probability method for determining the reliability of electric power systems[J]. IEEE Transactions on Power Apparatus and Systems. 1964, PAS-83(2): 174-179.
[20] Billinton R, Bollinger K E. Transmission system reliability evaluation using Markov processes[J]. IEEE Transactions on Power Apparatus and Systems. 1968, PAS-87(2): 538-547.
[21]黄雯莹,任震.高压直流输电系统可靠性评估的FD法[J].重庆大学学报. 1985, 8(1): 9-19.
[22]何建军,任震,王官洁.变电站主接线可靠性评估的逐次FD法[J].电力系统及其自动化学报. 1998, 10(1): 1-6.
[23] Schiling M T, Filho G M B D, Silva D A M L. An Integrated approach to power system reliability assessment[J]. Eletrical power and energy system. 1995, 17(6): 381-390.
[24]任震,湛军.大型电力系统可靠性评估的模型和算法[J].电力系统自动化. 1999, 23(5): 25-27.
[25]任震,何建军,湛军,等.交直流网络系统可靠性评估的混合法[J].电网技术. 2000, 24(5): 13-19.
[26]万国成,任震,吴日昇,等.混合法在复杂配电网可靠性评估中的应用[J].中国电机工程学报. 2004, 24(9): 92-98.
[27] Billinton R, Li W. Hybrid approach for reliability evaluation of composite generation and transmission systems using Monte-Carlo simulation and enumeration technique[J]. Generation, Transmission and Distribution, IEE Proceedings. 1991, 138(3): 233-241.
[28] Billinton R, Sachdev M. Direct current transmission system reliability evaluation[J]. Trans. CEA. 1968, 7(3): 68-170.
[29] Billinton R, Prasad V. Quantitative Reliability Analysis of HVDC Transmission Systems:Part I and II[J]. IEEE Transactions on Power Apparatus and Systems. 1971, PAS-90(3): 1034-1054.
[30] Billinton R, Ahluwalia D S. Incorporation of A DC Link in A Composite System Adequacy Assessment - DC System Modeling[J]. IEE Proceedings-C. 1992, 139(3): 211-220.
[31]任震,武娟,陈丽芳.高压直流输电可靠性评估的等效模型[J].电力系统自动化. 1999, 23(9): 38-41.
[32]陈永进,任震.模型组合及其在直流输电系统可靠性评估中的应用[J].电网技术. 2004, 28(13): 18-22.
[33] Dialynas E N, Koskolos N C. Reliability modeling and evaluation of HVDC power transmission systems[J]. IEEE Transactions on Power Delivery. 1994, 9(2): 872-878.
[34]张静伟,任震,黄雯莹.直流系统可靠性故障树评估模型及应用[J].电力自动化设备. 2005, 25(6): 62-65.
[35]张雪松,王超,常勇,等. GO法在特高压直流输电可靠性研究中的应用[J].高电压技术. 2009, 35(2): 236-241.
[36]洪潮,饶宏.多馈入直流系统的量化分析指标及其应用[J].南方电网技术. 2008, 2(4): 37-41.
[37] Kundur P. Power system stability and control[M]. New York: McGraw-Hill Inc, 1994.
[38]浙江大学发电教研组直流输电科研组.直流输电[M].北京:电力工业出版社, 1982.
[39]李海锋,张璞,王钢,等.直流馈入下的工频变化量方向纵联保护动作特性分析(二)故障线路的方向保护[J].电力系统自动化. 2009, 33(10): 47-52.
[40]李海锋,张璞,王钢,等.直流馈入下的工频变化量方向纵联保护动作特性分析(三)非故障线路的方向保护[J].电力系统自动化. 2009, 33(11): 43-47.
[41]刘之尧,唐卓尧,张文峰,等.直流换相失败引起继电保护误动分析[J].电力系统自动化. 2006, 30(19): 104-107.
[42]项玲,郑建勇,胡敏强.多端和多馈入直流输电系统中换相失败的研究[J].电力系统自动化. 2005, 29(11): 29-33.
[43]杨秀,陈鸿煜.高压直流输电系统换相失败的仿真研究[J].高电压技术. 2008, 34(2): 247-252.
[44] Thio C V, Davies J B, Kent K L. Commutation failures in HVDC transmission systems[J]. IEEE Transactions on Power Delivery. 1996, 2(11): 946-957.
[45]任震,陈永进,梁振升.高压直流输电系统换相失败的概率分析[J].电力系统自动化. 2004, 24(28): 19-22.
[46] Billinton R, Li W. Reliability assessment of electrical power systems using Monte Carlo methods[M]. New York and London: Plenum Press, 1994.
[47]郭永基.电力系统可靠性分析[M].北京:清华大学出版社, 2003.
[48] Li W. Risk assessment of power systems:models,methods and applications[M]. IEEE Computer Society Press, 2005.
[49] Billinton R. Composite system reliability evaluation[J]. IEEE Transactions on Power Apparatus and Systems. 1969, PAS-88(4): 276-281.
[50] Billinton R, Allan R N. Reliability Evaluation of Power Systems (second edition)[M]. New York and London: Plenum Press, 1996.
[51] Li W, Billinton R. Common Cause Outage Models in Power System Reliability Evaluation[J]. IEEE Transactions on Power Systems. 2003, 18(2): 966-968.
[52] Billinton R, Medicherla T K P. Station originated multiple outages in the reliability analysis of a composite generation and transmission system[J]. IEEE Transactions on Power Apparatus and Systems. 1981, PAS-100(8): 3870-3878.
[53] Cunha S H F, Gomes F B M, Oliveira G C, et al. Reliability evaluation in hydrothermal generating systems[J]. IEEE Transactions on Power Apparatus and Systems. 1982, PAS-101(12): 4665-4673.
[54] Allan R N, Roman J. Reliability assessment of generation systems containing multiple hydro plant using simulation techniques[J]. IEEE Transactions on Power Systems. 1988, 4(3): 1074-1080.
[55] Allan R N, Roman J. Reliability assessment of hydrothermal generation systems containing pumped storage plant[J]. IEE Proeeedings-C. 1991, 138(6): 471-478.
[56] Ubeda J R, Allan R N. Reliability assessment of composite hydrothemal generation and transmission systems using sequential simulation[J]. IEE Proceedings-C. 1994, 141(4): 257-262.
[57] Leite Da Silva A M, Da Fonseca Manso L A, De Oliveira Mello J C, et al. Pseudo-chronological simulation for composite reliability analysis with time varying loads[J]. IEEE Transactions on Power Systems. 2000, 15(1): 73-80.
[58] Sankarakrishnan A, Billinton R. Sequential Monte Carlo simulation for composite power system reliability analysis with time varying loads[J]. IEEE Transactions on Power Systems. 1995, 10(3): 1540-1545.
[59] Li W, Billinton R. Effects of bus load uncertainty and correlation in composite system adequacy evaluation[J]. IEEE Transactions on Power Systems. 1991, 6(4): 1522-1529.
[60]刘海涛,程林,孙元章,等.交直流系统可靠性评估[J].电网技术. 2004, 28(23): 27-30.
[61] Billinton R, Ahluwalia D S. Incorporation of a DC-link in a composite system adequacy assessment-composite system analysis[J]. Generation, Transmission and Distribution, IEE Proceedings. 1992, 139(3): 221-225.
[62] Li W. Incorporating aging failures in power system reliability evaluation[J]. IEEE Transactions on Power Systems. 2002, 17(3): 918-923.
[63] Rios M A, Kirschen D S, Jayaweera D, et al. Value of security: modeling time-dependent phenomena and weather conditions[J]. IEEE Transactions on Power Systems. 2002, 17(3): 543-548.
[64]丁明,戴仁昶,刘亚成,等.概率稳定性的蒙特卡罗仿真[J].清华大学学报. 1997, 39(3): 79-83.
[65]王韶,周家启.双回平行输电线路可靠性模型[J].中国电机工程学报. 2003, 23(9): 53-56.
[66]赵渊,周家启.静止无功补偿器和移相器的最优配置及其对发输电系统可靠性的影响[J].电工技术学报. 2004, 19(1): 55-60.
[67] Billinton R, Li W. A Hybrid Approach for Reliability Evaluation of Composite Generation and Transmission Systems Using Monte Carlo Simulation and Enumeration Technique[J]. IEE Proceedings-C. 1991, 138(3): 233-241.
[68]丁明,李生虎,吴红斌.基于充分性和安全性的电力系统运行状态分析和量化评价[J].中国电机工程学报. 2004, 24(4): 43-49.
[69]赵渊,周家启,刘洋.发输电组合系统可靠性评估的最优负荷削减模型研究[J].电网技术. 2004, 28(10): 34-37.
[70]赵渊.大电力系统可靠性评估的灵敏度分析及其校正措施模型研究[D].重庆:重庆大学, 2004.
[71] Zhang W, Billinton R. Application of an adequacy equivalent method in bulk power system reliability evaluation[J]. IEEE Transactions on Power Systems. 1998, 13(2): 661-666.
[72]吴开贵,吴中福.基于敏感度分析的电网可靠性算法[J].中国电机工程学报. 2003, 23(4): 53-56.
[73]吴开贵,王韶,张安邦,等.基于RBF神经网络的电网可靠性评估模型研究[J].中国电机工程学报. 2000, 21(6): 9-12.
[74]谢开贵,周家启.基于ANN削减负荷的发输电组合系统可靠性评估[J].电力系统自动化. 2002, 26(22): 31-33.
[75]刘洋,周家启,谢开贵,等.基于Beowulf集群的大电力系统可靠性评估蒙特卡罗并行仿真[J].中国电机工程学报. 2006, 26(10): 9-14.
[76]刘洋,周家启,谢开贵,等.基于集群技术构建电力系统高性能计算平台[J].计算机仿真. 2005, 22(5): 239-243.
[77]陈华,周家启.大型网络可靠性评估的增流减流交叉网流法[J].重庆大学学报. 1990, 13(4): 2-6.
[78] Li W, Mansour Y, Korczynski J K, et al. Application of transmission reliability assessment in probabilistic planning of BC Hydro Vancouver South Metro system[J]. IEEE Transactions on Power Systems. 1995, 10(2): 964-970.
[79]王超,徐政,高慧敏.基于TPLAN的中国南方电网可靠性与经济性评估[J].继电器. 2006, 34(16): 61-67.
[80] Burchett R C, Heydt G T. Probabilistic method for power system dynamic stability studies[J]. IEEE Transactions on Power Apparatus and Systems. 1978, PAS-97(3): 695-702.
[81] Billinton R, Kuruganty P R S. An approximate method for probabilistic assessment of transient stability[J]. IEEE Transactions on Reliability. 1979, 28(3): 255-258.
[82] Billinton R, Kuruganty P R S. A probabilistic index for transient stability[J]. IEEE Transactions on Power Apparatus and Systems. 1980, PAS-99(1): 195-206.
[83] Billinton R, Kuruganty P R S. Probabilistic assessment of transient stability in a practical multi-machine system[J]. IEEE Transactions on Power Apparatus and Systems. 1981, PAS-100(7): 3634-3641.
[84] Hsu Y Y, Chang C L. Probabilistic transient stability studies using the conditional probability approach[J]. IEEE Transactions on Power Systems. 1988, 3(4): 1565-1572.
[85]甘德强,王锡凡,杜正春.电力系统暂态稳定性的分析[J].中国电力. 1994, 27(4): 32-35.
[86]鞠平,吴耕扬,李扬.电力系统概率稳定的基本定理及算法[J].中国电机工程学报. 1991, 11(6): 17-25.
[87] Xue Y, Li J. Probabilistic transient stability assessment with EEAC[Z]. Singapore: 1997.
[88]王成山,余旭阳.基于能量函数法的暂态稳定概率评估方法[J].电力系统自动化. 2003, 27(6): 5-9.
[89]崔凯,房大中,钟德成.电力系统暂态稳定性概率评估方法研究[J].电网技术. 2005, 29(1): 44-49.
[90] Anderson P M, Bose A. A probabilistic approach to power system stability analysis[J]. IEEE Transactions on Power Apparatus and Systems. 1983, PAS-102(8): 2430-2439.
[91] Timko K J, Bose A, Anderson P M. Monte Carlo Simulation of Power System Stability[J]. IEEE Transactions on Power Apparatus and Systems. 1983, PAS-102(10): 3453-3459.
[92]任震,冉立,李正然.交直流并联系统可靠性与概率动态安全分析(I)(II)[J].华南理工大学学报(自然科学版). 1997, 25(6): 1-11.
[93]丁明,黄凯,李生虎.概率暂态稳定研究中紧急控制措施的模拟及效果分析[J].电工技术学报. 2002, 17(5): 72-77.
[94]丁明,黄凯,李生虎.交直流混合系统的概率稳定性分析[J].中国电机工程学报. 2002, 22(8): 11-16.
[95]李文沅,卢继平.暂态稳定概率评估的蒙特卡罗方法[J].中国电机工程学报. 2005, 25(10): 18-23.
[96] Wu F F, Tsai Y K, Yu Y X. Probabilistic steady-state and dynamic security assessment[J]. IEEE Transactions on Power Systems. 1988, 3(1): 1-9.
[97]余贻鑫,陈礼义.电力系统的安全性与稳定性[M].北京:科学出版社, 1988.
[98]付川,余贻鑫,王东涛.电力系统暂态稳定概率[J].电力系统自动化. 2006, 30(1): 24-28.
[99]余贻鑫,王东涛,王成山,等.基于安全域的输电系统概率安全评估系统框架[J].天津大学学报. 2007, 40(6): 699-703.
[100]王东涛,余贻鑫,付川.基于实用动态安全域的输电系统概率动态安全评估[J].中国电机工程学报. 2007, 27(7): 29-33.
[101]王超.电力系统可靠性评估中的几个重要问题研究[D].浙江大学, 2007.
[102]贺家李,郭征,杨晓军,等.继电保护的可靠性与动态性能仿真[J].电网技术. 2004, 28(9): 18-22.
[103]曾克娥.电力系统继电保护装置运行可靠性指标探讨[J].电网技术. 2004, 28(14): 83-85.
[104]尹相根,陈德树.主设备保护运行情况评价方法的讨论[J].电力自动化设备. 1996, 60(4): 17-19.
[105]王钢,丁茂生,李晓华,等.数字继电保护装置可靠性研究[J].中国电机工程学报. 2004, 24(7): 47-52.
[106]沈智健,周家启,卢继平,等.距离保护运行风险评估模型[J].电力系统自动化. 2008, 32(12): 7-11.
[107]沈智健,卢继平,赵渊,等.变压器比率差动保护判据的可靠性评估模型[J].电网技术. 2008, 32(7): 14-18.
[108]沈智健,卢继平,赵渊,等.阶段式电流保护运行风险评估模型[J].中国电机工程学报. 2008, 28(13): 70-77.
[109]赵自刚.关于新形势下继电保护检修策略的几点思考[J].继电器. 2000, 28(11): 68-72.
[110]李英姿,牛进苍.继电保护装置的现场检修试验[J].华北电力技术. 1999(2): 38-39.
[111]吴杰余,张哲,尹项根,等.电气二次设备状态检修研究[J].继电器. 2002, 30(2): 22-24.
[112] Kumm J J, Weber M S, Hou D, et al. Predicting the optimum routine test interval for protective relays[J]. IEEE Transactions on Power Delivery. 1995, 10(2): 659-665.
[113]李永丽,李致中,杨维.继电保护装置可靠性及其最佳检修周期的研究[J].中国电机工程学报. 2001, 21(6): 63-65.
[114] Billinton R, Fotuhi-Firuzabad M, Sidhu T S. Determination of the optimum routine test and self-checking intervals in protective relaying using a reliability model[J]. IEEE Transactions on Power Systems. 2002, 17(3): 663-669.
[115]丁茂生.电力系统数字式保护控制及自动化系统可靠性研究[D].广州:华南理工大学, 2005.
[116] Howard R A. System analysis of semi-Markov processes[J]. IEEE Transactions on Military Electronics. 1964, 8(2): 114-224.
[117] Feller W. An Introduction to Probability Theory and Its Applications, Vol. 2[M]. New York: Wiley, 1972.
[118]曹晋华,程侃.可靠性数学引论[M].北京:高等教育出版社, 2006.
[119]邓永录.随机模型及其应用[M].北京:高等教育出版社, 1994.
[120]王梓坤.生灭过程与马尔科夫链[M].北京:科学出版社, 1980.
[121]田乃硕.休假随机服务系统[M].北京:北京大学出版社, 2001.
[122] Kaminskiy M P, Krivtsov V V. A simple procedure for Bayesian estimation of the Weibull distribution[J]. IEEE Transactions on Reliability. 2005, 54(4): 612-616.
[123] Ng H K T. Parameter estimation for a modified Weibull distribution, for progressively type-II censored samples[J]. IEEE Transactions on Reliability. 2005, 54(3): 374-380.
[124] Van Casteren J F L, Bollen M H J, Schmieg M E. Reliability assessment in electrical power systems: the Weibull-Markov stochastic model[J]. IEEE Transactions on Industry Applications. 2000, 36(3): 911-915.
[125] Cao Y, Sun H, Trivedi K S, et al. System availability with non-exponentially distributed outages[J]. IEEE Transactions on Reliability. 2002, 51(2): 193-198.
[126]刘振亚.特高压交流输电技术研究成果专辑(2005年)[M].北京:中国电力出版社, 2006.
[127]张文亮,于永清,李光范,等.特高压直流技术研究[J].中国电机工程学报. 2007, 27(22): 1-7.
[128]王钢,李志铿,黄敏,等. HVDC输电系统换相失败的故障合闸角影响机理[J].电力系统自动化. 2010, 34(4): 49-54.
[129] Desrochers G, Lefebvre S, Rioux B. Reliability assessment of HVDC transmission[R]. Canadian Electrical Association,Report CEA 222 T 506,Prepared by IREQ, 1987.
[130]南方电网技术研究中心,华南理工大学电力学院.贵广二回直流系统可用率与可靠性[R].中国南方电网公司, 2006.
[131]周静,马为民,石岩,等.±800 kV直流输电系统的可靠性及其提高措施[J].电网技术. 2007, 31(3): 7-12.
[132]马为民,李亚男,周静.特高压直流输电系统可靠性和可用率指标研究[J].电力设备. 2007, 8(3): 85-88.
[133]欧开健,任震,荆勇.直流输电系统换相失败的研究: (一)换相失败的影响因素分析[J].电力自动化设备. 2003, 23(5): 5-8.
[134] Mckay M D, Beckman R J, Conover W J. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code[J]. Technometrics. 1979, 2: 239-245.
[135] Olsson A, Sandberg G, Dahlblom O. On Latin hypercube sampling for structural reliability analysis[J]. Structural Safety. 2003, 25: 47-68.
[136] Li W, Zhou J, Hu X. Comparison of Transmission Equipment Outage Performance inCanada, USA and China[C]. Vancouver, BC: 2008.
[137] Vaahedi E, Li W, Chia T, et al. Large-scale probabilistic transient stability assessment using[J]. IEEE Transactions on Power Systems. 2000, 15(2): 661-667.
[138] Fotuhi-Firuzabad M, Billinton R, Faried S O. Transmission system reliability evaluation incorporating HVDC links and facts devices[C]. Vancouver, Canada: 2001.
[139] Liu M B, Tso S K, Cheng Y. An extended nonlinear primal-dual interior-point algorithm for reactive-power optimization of large-scale power systems with discrete control variables[J]. IEEE Transactions on Power Systems. 2002, 17(4): 982-991.
[140] Lee J, Chiang H D. A dynamical trajectory-based methodology for systematically computing multiple optimal solutions of nonlinear programming problems[J]. IEEE Transactions on Automation Control. 2004, 49(6): 888-899.
[141] Jiang Q, Han Z. Solvability identification and feasibility restoring of divergent optimal power flow problems [J]. Science in China Series E:Technological Sciences. 2009, 52(4): 944-954.
[142]王锡凡,方万良,杜正春.现代电力系统分析[M].北京:科学出版社, 2003.
[143]颜伟,张海兵,田甜,等.交直流系统的动态无功优化[J].电力系统自动化. 2009, 33(10): 43-46.
[144] Wei H, Sasaki H, Kubokawa J, et al. An interior point nonlinear programming for optimal power flow problems with a novel data structure[J]. IEEE Transactions on Power Systems. 1998, 13(3): 870-877.
[145] Kelley C T, Keyes D E. Convergence analysis of pseudo-transient continuation[J]. SIAM Journal of Numerical Analysis. 1998, 35(2): 508-523.
[146] Task F R T S. The IEEE reliability test system-1996[J]. IEEE Transactions on Power Systems. 1999, 14(3): 1010-1020.
[147] Pinheiro J M S, Dornellas C R R, Schilling M T, et al. Probing the new IEEE Reliability Test System (RTS-96): HL-IIassessment[J]. IEEE Transactions on Power Systems. 1998, 13(1): 171-176.
[148]丁明,李生虎,吴红斌.电力系统概率充分性和概率稳定性的综合评估[J].中国电机工程学报. 2003, 23(3): 20-25.
[149] Vittal V, Mccalley J D, Vanacker V, et al. Transient instability risk assessment[C]. Edmonton,Alberta,Canada: 1999.
[150]曾沅,余贻鑫.电力系统动态安全域的实用解法[J].中国电机工程学报. 2003, 23(5): 24-28.
[151] Xue A, Wu F F, Lu Q, et al. Power system dynamic security region and its approximations[J]. IEEE Transactions on Circuits and Systems I:Regular Papers. 2006, 53(12): 2849-2859.
[152]薛安成,胡伟,梅生伟,等.电力系统动态安全域线性近似方法比较[J].电力系统自动化. 2006, 30(5): 9-13.
[153]余贻鑫.电力系统安全域方法研究述评[J].天津大学学报. 2008, 41(6): 635-646.
[154]王锡凡.电力系统优化规划[M].北京:水利电力出版社, 1990.
[155]王克文,钟志勇,谢志棠,等.混合使用中心矩与累加量的电力系统概率特征根分析方法[J].中国电机工程学报. 2000, 20(5): 37-41.
[156] Kendall M, Stuart A. The Advanced Theory of Statistics,4th ed[M]. London: Charles Griffin, 1997.
[157] Tian W D, Sutanto D, Lee Y B, et al. Cumulant based probabilitstic power system simulation using laguerre polynomials[J]. IEEE Transactions on Energy Conversion. 1989, 4(4): 567-574.
[158] Chiang H D, Wu F F, Varaiya P P. A BCU method for direct analysis of power system transient stability[J]. IEEE Transactions on Power Systems. 1994, 9(3): 1208-1294.
[159] Chen D Z, Ma J. Calculation of stability region[C]. Maui,Hawaii,USA: 2003.
[160] Pai M A, Padiyar K R, Radhakrishnan C. Transient stability of multi-machine AC/DC power systems via energy function method[J]. IEEE Transactions on Power Apparatus and Systems. 1981, PAS-100(12): 5027-5035.
[161]倪以信,陈寿孙,张宝霖.动态电力系统的理论和分析[M].北京:清华大学出版社, 2002.
[162] Laufenberg M J, Pai M A. A new approach to dynamic security assessment using trajectory sensitivities[J]. IEEE Transactions on Power Systems. 1998, 9(3): 953-958.
[163] Pai M A. Energy function analysis for power system stability[M]. Boston: Kluwer Academic Publishers, 1989.
[164]薛安成,梅生伟,卢强,等.基于网络约化模型的电力系统动态安全域近似[J].电力系统自动化. 2005, 29(10): 18-23.
[165] Phadke A G, Thorp J S. Expose hidden failures to prevent cascading outages[J]. IEEE Computer Application in Power. 1996, 9(3): 20-23.
[166] Singh C, Patton A D. Protection system reliability modeling: unreadiness probability and mean duration of undetected faults[J]. IEEE Transactions on Reliability. 1980,R-29(4): 339-340.
[167] Anderson P M, Chintaluri G M, Magbuhat S M, et al. An improved reliability model for redundant protections– Markov models[J]. IEEE Transactions on Power Systems. 1997, 12(2): 573-578.
[168]孙福寿,汪熊海.一种分析继电保护系统可靠性的算法[J].电力系统自动化. 2006, 30(16): 32-35, 76.
[169]陈少华,马碧燕,雷宇,等.综合定量计算继电保护系统可靠性[J].电力系统自动化. 2007, 31(15): 111-115.
[170]熊小伏,陈飞,周家启,等.计及不同保护配置方案的继电保护系统可靠性[J].电力系统自动化. 2008, 32(14): 21-24.
[171] Perman M, Senegacnik A, Tuma M. Semi-Markov models with an application to power-plant reliability analysis[J]. IEEE Transactions on Reliability. 1997, 46(4): 526-532.
[172] Liang Y, Fricks R M, Trivedi K S. Application of Semi-Markov Process and CTMC to Evaluation of UPS System Availability[C]. Seattle,Washington,USA: 2002.
[173]熊俊,肖先勇.一种基于半马尔柯夫过程的配电系统可靠性经济评估方法[J].继电器. 2006, 34(12): 57-62.
[174] Jia X, Christer A H. A periodic testing model for a preparedness system with a defective state[J]. IMA Journal of Management Mathematics. 2002, 13(1): 39-49.
[175] Erlang A K. Solution of some problems in the theory of probabilities of sighicance in automatic telephone exchanges[J]. The Post Office Eletrical Engineer's Journal. 1917, 10: 189-197.
[176] Gupta S K, Goyal J K. Queues with poisson input and Hyper-Exponential output with finite waiting space[J]. Operations Research. 1964, 12(1): 75-81.
[177] Gupta S K. Queues fed by Poisson input and hyper-mixed Erlangian service time distribution with finite waiting space[J]. Mathematical Methods of Operations Research. 1965, 9(2): 80-90.
[178] Cox D R. A use of complex probabilities in the theory of stochastic processes[J]. Proc. Cambridge Philosophical Society (Math. and Phys. Sciences). 1955, 51: 313-319.
[179] Cox D R. The analysis of non-Markovian stchastic process by the inclusion of supplementary variables[J]. Proc. Cambridge Philosophical Society (Math. and Phys. Sciences). 1955, 51: 433-441.
[180]田乃硕,李泉林. PH分布及其在随机模型中的应用[J].应用数学与计算数学学报. 1995, 9(2): 1-15.
[181] Jensen A. A distribution model applicable to economics[M]. Copenhangen: Munksgaard, 1954.
[182] Neuts M F. Matrix-Geometric Solutions in Stochastic Models—An Algorithmic Approach[M]. Baltimore: The Johns Hopkins University Press, 1981.
[183] Asmussen S, Nerman O, Olsson M. Fitting phase-type distributions via the EM algorithm[J]. Scandinavian Journal of Statistics. 1996, 23(4): 419-441.
[184] Thummler A, Buchholz P, Telek M. A Novel Approach for Phase-Type Fitting with the EM Algorithm[J]. IEEE Transactions on dependable and secure computing. 2006, 3(3): 245-258.
[185] Montoro-Cazorla D, Pérez-Ocón R, Segovia M D C. Shock and wear models under policy N using phase-type distributions[J]. Applied Mathematical Modelling. 2009, 33(1): 543-554.
[186] Pérez-Ocón R, Segovia M D C. Shock models under a Markovian arrival process[J]. Mathematical and Computer Modelling. 2009, 50(5): 879-884.
[187] Madan K C, Al-Rub A Z A. On a single server queue with optional phase type server vacations based on exhaustive deterministic service and a single vacation policy[J]. Applied Mathematics and Computation. 2004, 149(3): 723-734.
[188] Gómez-Corral A, Martos M E. Performance of two-stage tandem queues with blocking: The impact of several flows of signals[J]. Performance Evaluation. 2006, 63(9-10): 910-938.
[189] Manuela P, Sivakumarb B, Arivarignan G. A perishable inventory system with service facilities and retrial customers[J]. Computers & Industrial Engineering. 2007, 54(3): 484-501.
[190] Dharmaraja S, Jindal V, Alfa A S. Phase-type models for cellular networks supporting voice, video and data traffic[J]. Mathematical and Computer Modelling. 2008, 47(11-12): 1167-1180.
[191] Johnson M A, Taaffe M R. Matching Moments to Phase Distributions: Mixtures of Erlang Distributions of Common Order[J]. Stochastic Models. 1989, 5(4): 711-743.
[192] Bellman R. Introduction to matrix analysis[M]. New York: McGraw-Hill, 1960.
[193] Sim S H, Endrenyi J. Optimal preventive maintenance with repair[J]. IEEE Transactions on Reliability. 1988, 37(1): 92-96.
[194] Sim S H, Endrenyi J. A failure-repair model with minimal & major maintenance[J]. IEEE Transactions on Reliability. 1993, 42(1): 134-140.
[195] Arshad M, Islam S M, Khaliq A. Power Transformer Asset Management[C]. Singapore,: 2004.
[196] Neuts M F, Pagano M E. Generating random variates from a distribution of phase type[C]. Piscataway,NJ,USA: 1981.
[197]王成山,郑海峰,谢莹华,等.计及分布式发电的配电系统随机潮流计算[J].电力系统自动化. 2005, 29(24): 39-44.
[198]朱能臣,汪建文.风工况双参数威布尔分布k值影响研究[J].太阳能. 2007(6): 34-36.
[199] Prasada G D, Janaa A K, Tripathy S C. Modifications to Newton-Raphson load flow for ill-conditioned power systems[J]. International Journal of Electrical Power & Energy Systems. 1990, 12(3): 192-196.
[200] Zhang P, Lee S T. Probabilistic load flow computation using the method of combined cumulants and Gram-Charlier expansion[J]. IEEE Transactions on Power Systems. 2004, 19(1): 676-682.