优化旋转备用配置的机组组合研究
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摘要
备用配置是系统抵御风险,提高运行可靠性的重要手段,也是系统运行安全与经济协调决策的问题。随着电力工业的发展和市场机制的引入,系统运行过程中的不确定因素不断增多,更加凸显备用配置的重要性,本文在这一背景下选择此课题进行深入研究,有重要的理论意义和现实价值。
在国内外研究成果的基础上,针对系统运行过程中不确定因素的处理,本文将概率优化理论引入到机组组合和旋转备用配置过程中,力求在系统运行安全与经济协调思想的指导下,实现电能与备用的同步优化以及摆脱人为决策的弊端,实现备用的自动配置,达到在机组组合的同时优化旋转备用的目的。
首先,本文介绍了一种实用的机组组合线性混合整数模型及求解方法。该方法通过对原机组组合模型中非线性目标函数和约束条件进行线性化处理,将之转化为线性混合整数模型,并利用成熟的商业优化软件进行求解。该方法可以方便地对机组组合模型进行扩充,使研究人员专注于模型研究而不用担心算法问题。
随后,就机组组合过程中运行风险与旋转备用优化配置间关系的问题进行研究,提出了计及用户停电损失的机组组合方法。将备用不足造成的用户停电损失加入到机组组合目标中,通过成本和风险在目标中的相互牵制,实现系统运行安全与经济的协调,能够自动配置适宜的备用。在评估用户期望停电损失时,将电量不足期望值(Expected Energy not Severed, EENS)解析表达成机组状态、出力及备用的函数,从而将风险与机组组合有机关联,实现备用配置和机组组合求解完整一体的优化决策。
在此基础上,提出了基于多场景的概率机组组合方法。该方法将系统的运行过程分为多个场景,把计及用户停电损失的思想应用于每个场景,以场景发生的概率协调系统在各场景下的调度决策,并以旋转备用作为正常和事故场景之间机组的调整限制,因此通过安全与经济的协调,能够在机组组合的过程中自动配置合适的备用。同时该方法将网络安全约束和事故后机组组合策略的再调整纳入到模型中,保证系统在各场景下的决策方案均不会造成线路过载。
最后,将基于多场景的概率机组组合方法应用于含风电场电力系统。通过对风电预测误差进行概率表达,建立基于多场景的含风电场概率机组组合模型,能够自动为风电出力的波动配置适宜的备用,且模型中考虑了网络安全约束对机组组合和备用决策的影响。在所建模型基础上,从风电并网经济价值分析的角度,提出了一种以风电并网后系统期望成本最小为目标,确定节点最优经济接入风电功率的方法,对风电的调度和规划具有指导意义。
Spinning reserve (SR) is one of the most important resources used by system operators to maintain system security and improve operational reliability, which is also a decision-making problem coordinating system operation security and economy. With the development of electrical industry and introduction of market mechanism, constantly increasing uncertainties during system operation process have highlighted the importance of SR. It's obviously meaningful for this thesis to choose this subject for deep research.
Based on previous achievement at home and abroad, the thesis focuses on uncertainties in system operation process and introduces probability optimization theory to unit commitment and SR optimization. To make unit commitment and SR optimization more intelligent and reasonable, the thesis strives to achieve coordination of system operation security and economy in unit commitment, simultaneous optimization of generation and SR requirement, as well as shedding off the drawback of human decision.
Firstly, this thesis introduces a practical mixed-integer linear model of unit commitment and its sloving strategy. The nonlinear objective fuction and constraints of unit commitment is transformed into linear form, and therefore the linear form can be sloved by large-scale commercial optimization software. This method can conveniently make extension of unit commitment, and make researchers consantrated on unit commitment model but never mind the sloving algorithm.
Then, based on the research on relationship between system operation risk and SR requirement, a unit commitment model considering expected customer interruption cost (ECOST) is proposed. The proposed model which adds ECOST into unit commitment objective function, can automatically determine optimal SR capacity by making compromise between system operation cost and ECOST. System expected energy not supplied (EENS) is expressed and simplified by unit commitment variables when assess ECOST, so as to achieve simultaneous optimization of generation and SR requirement in unit commitment.
Based on above, a probabilistic unit commitment model based on multi-scenario technique is proposed. In the proposed model, system operation process is represented by several scenarios. ECOST under every scenario is considered in unit commitment, system cost and operation risk under every scenario is coordinated by each scenario occurrence probability. Network security constraints and readjustments of unit commitment after contingencies are included in the model, so as to guarantee the decision plain doesn't violate transmission limits of lines in all scenarios.
At last, probabilistic unit commitment model based on multi-scenario technique is applied to power system with wind power generation. By probabilistic expression of wind power forecast error, probabilistic unit commitment model of power system with wind power generation based on multi-scenario technique is established, and SR requirement according to wind power fluctuation is automatically optimized. Network security constraints are included in the model to consider its impact on unit commitment and SR optimization. From the view of wind power economic value analysis, a new method to determine optimal wind power penetration in each bus is presented based on the proposed unit commitment model. The method which aims at minimizing system expected cost can determine optimal economic wind power penetration in each bus and do have significant meaning in scheduling and planning of wind power.
在国内外研究成果的基础上,针对系统运行过程中不确定因素的处理,本文将概率优化理论引入到机组组合和旋转备用配置过程中,力求在系统运行安全与经济协调思想的指导下,实现电能与备用的同步优化以及摆脱人为决策的弊端,实现备用的自动配置,达到在机组组合的同时优化旋转备用的目的。
首先,本文介绍了一种实用的机组组合线性混合整数模型及求解方法。该方法通过对原机组组合模型中非线性目标函数和约束条件进行线性化处理,将之转化为线性混合整数模型,并利用成熟的商业优化软件进行求解。该方法可以方便地对机组组合模型进行扩充,使研究人员专注于模型研究而不用担心算法问题。
随后,就机组组合过程中运行风险与旋转备用优化配置间关系的问题进行研究,提出了计及用户停电损失的机组组合方法。将备用不足造成的用户停电损失加入到机组组合目标中,通过成本和风险在目标中的相互牵制,实现系统运行安全与经济的协调,能够自动配置适宜的备用。在评估用户期望停电损失时,将电量不足期望值(Expected Energy not Severed, EENS)解析表达成机组状态、出力及备用的函数,从而将风险与机组组合有机关联,实现备用配置和机组组合求解完整一体的优化决策。
在此基础上,提出了基于多场景的概率机组组合方法。该方法将系统的运行过程分为多个场景,把计及用户停电损失的思想应用于每个场景,以场景发生的概率协调系统在各场景下的调度决策,并以旋转备用作为正常和事故场景之间机组的调整限制,因此通过安全与经济的协调,能够在机组组合的过程中自动配置合适的备用。同时该方法将网络安全约束和事故后机组组合策略的再调整纳入到模型中,保证系统在各场景下的决策方案均不会造成线路过载。
最后,将基于多场景的概率机组组合方法应用于含风电场电力系统。通过对风电预测误差进行概率表达,建立基于多场景的含风电场概率机组组合模型,能够自动为风电出力的波动配置适宜的备用,且模型中考虑了网络安全约束对机组组合和备用决策的影响。在所建模型基础上,从风电并网经济价值分析的角度,提出了一种以风电并网后系统期望成本最小为目标,确定节点最优经济接入风电功率的方法,对风电的调度和规划具有指导意义。
Spinning reserve (SR) is one of the most important resources used by system operators to maintain system security and improve operational reliability, which is also a decision-making problem coordinating system operation security and economy. With the development of electrical industry and introduction of market mechanism, constantly increasing uncertainties during system operation process have highlighted the importance of SR. It's obviously meaningful for this thesis to choose this subject for deep research.
Based on previous achievement at home and abroad, the thesis focuses on uncertainties in system operation process and introduces probability optimization theory to unit commitment and SR optimization. To make unit commitment and SR optimization more intelligent and reasonable, the thesis strives to achieve coordination of system operation security and economy in unit commitment, simultaneous optimization of generation and SR requirement, as well as shedding off the drawback of human decision.
Firstly, this thesis introduces a practical mixed-integer linear model of unit commitment and its sloving strategy. The nonlinear objective fuction and constraints of unit commitment is transformed into linear form, and therefore the linear form can be sloved by large-scale commercial optimization software. This method can conveniently make extension of unit commitment, and make researchers consantrated on unit commitment model but never mind the sloving algorithm.
Then, based on the research on relationship between system operation risk and SR requirement, a unit commitment model considering expected customer interruption cost (ECOST) is proposed. The proposed model which adds ECOST into unit commitment objective function, can automatically determine optimal SR capacity by making compromise between system operation cost and ECOST. System expected energy not supplied (EENS) is expressed and simplified by unit commitment variables when assess ECOST, so as to achieve simultaneous optimization of generation and SR requirement in unit commitment.
Based on above, a probabilistic unit commitment model based on multi-scenario technique is proposed. In the proposed model, system operation process is represented by several scenarios. ECOST under every scenario is considered in unit commitment, system cost and operation risk under every scenario is coordinated by each scenario occurrence probability. Network security constraints and readjustments of unit commitment after contingencies are included in the model, so as to guarantee the decision plain doesn't violate transmission limits of lines in all scenarios.
At last, probabilistic unit commitment model based on multi-scenario technique is applied to power system with wind power generation. By probabilistic expression of wind power forecast error, probabilistic unit commitment model of power system with wind power generation based on multi-scenario technique is established, and SR requirement according to wind power fluctuation is automatically optimized. Network security constraints are included in the model to consider its impact on unit commitment and SR optimization. From the view of wind power economic value analysis, a new method to determine optimal wind power penetration in each bus is presented based on the proposed unit commitment model. The method which aims at minimizing system expected cost can determine optimal economic wind power penetration in each bus and do have significant meaning in scheduling and planning of wind power.
引文
[1]刘振亚.特高压电网[M].北京：中国经济出版社,2005.
[2]梁才浩,段献忠.分布式发电及其对电力系统的影响[J].电力系统自动化,2001,25(12)：53-56.
[3]王承煦,张源.风力发电[M].北京：中国电力出版社,2003.
[4]Wood Allen J & Wollenberg Bruce F. Power Generation, Operation and Control[M]. John Wiley & Sons Inc., New York,1996.
[5]李文沅.电力系统安全经济运行——模型与方法[M].重庆：重庆大学出版社,1989.
[6](英)丹尼尔,戈兰.电力系统经济学原理[M].北京：中国电力出版社,2007.
[7]韩学山,赵建国.刚性优化与柔性决策结合的电力系统运行调度理论探讨[J].中国电力,2004,37(1)：15-18.
[8]雷亚洲.与风电并网相关的研究课题[J].电力系统自动化,2003,27(8)：84-89.
[9]查浩.电力系统概率优化调度理论研究.山东大学博士论文,2009,4.
[10]杨明.电力系统超前调度理论与算法研究.山东大学博士论文,2009,4.
[11]韩学山,杨明,张利.价值调度推进智能化电网发展的思考[J].电力系统自动化,2010,34(2)：5-9.
[12]刘宝碇,赵瑞清.随机规划与模糊规划[M].北京：清华大学出版社,1998.
[13]Anstine L T, Burke R E, et al. Application of Probability Methods to the Determination of Spinning Reserve requirements for the Pennsylvania-New Jersey-Maryland Interconnection[J].IEEE Transactions on Power Systems,1963, PAS-82(68):726-735.
[14]王锡凡.电力系统优化规划[M].北京：水利电力出版社,1990.
[15]王锡凡,王秀丽.随机生产模拟及其应用[J].电力系统自动化,2003,27(8)：10-15.
[16]Gooi H B, Mendes D P, Bell K R W, et al. Optimal scheduling of spinning reserve[J]. IEEE Transactions on Power Systems,1999,14(4):1485-1490.
[17]Xia L, Gooi H B. A reserve market with reliability incentives[C]. International
Conference on Power System Technology.2004,1740-1745.
[18]Chattopadhyay D, Baldick R . Unit commitment with probabilistic reserve[C].2002 IEEE Power Engineering society Winter Meeting. New York: 2002.280-285.
[19]杨朋朋,韩学山,王静,孟祥星.用拉格朗日松弛法求解概率备用解析表达的机组组合[J].山东大学学报(工学版).2007,37(2),58-62.
[20]Bouffard F, Galiana F D. An electricity market with a probabilistic spinning reserve criterion[J]. IEEE Transactions on Power Systems,2004,19(1):300-307.
[21]王锡凡,王秀丽,陈浩勇.电力市场基础[M].西安：西安交通大学出版社,2003.
[22]王建学,王锡凡,张显.电力市场中弹性运行备用研究[J].中国电机工程学报,2005,25(18)：20-27.
[23]张国全,王秀丽,王锡凡.电力市场中旋转备用的效益和成本分析[J].电力系统自动化.2000,24(21)：14-18.
[24]Ortega-Vazquez M A, Krischen D S. Optimizing the spinning reserve requirements using a cost/benefit analysis[J]. IEEE Transactions on Power System.2007,22(1):24-33.
[25]杨梓俊,丁明,孙昕.电力市场下综合考虑系统可靠性和旋转备用效益的机组组合[J].电网技术.2003,27(6)：13-18.
[26]Motamedi A, Fotuhi-Firuzabad M, Zareipour H. Optimum Simultaneous Clearing of Energy and Spinning Reserve Markets Using Cost/benefit Analysis[J]. IEEE Power and Energy Society General Meeting.2008, July,1-7.
[27]Galiana F D, Bouffard F, et al. Scheduling and Pricing of Coupled Energy and Primary,Secondary,and Tertiary Reserves[J]. Proceedings of the IEEE,2005, 93(11):1970-1983.
[28]Carpentier P, Cohen G, Culioli. Stochastic optimization of unit commitment:A new decomposition framework[J]. IEEE Transactions on Power Systems,1996, 11(2):1067-1073.
[29]Takriti S, Birge J R, Long E. A stochastic model for the unit commitment problem[J]. IEEE Transactions on Power Systems,1996,11(3):1497-1508.
[30]Bouffard F, Galiana F D, Conejo A J. Market-clearing with stochastic security-ⅠFormulation[J]. IEEE Transactions on Power Systems,2005, 20(4):1818-1826.
[31]Bouffard F, Galiana F D, Conejo A J. Market-clearing with stochastic security-PartⅡ:Case studies[J]. IEEE Transactions on Power Systems,2005, 20(4):1827-1835.
[32]Bouffard F, Galiana F D, Arroyo J M. Umbrella Contingencies in Security-Constrained Optimal Power Flow[C].15th Power systems Computation Conference,2005.
[33]刘海涛,孙元章,等.计及多状态元件模型的系统状态快速排序技术[J].电力系统自动化,2008,32(1)：16-21.
[34]WuLei, Shahidehpour M, LiTao. Stochastic Security-Constrained Unit Commitment[J]. IEEE Transactions on Power Systems,2007,22(2):800-811.
[35]WuLei, Shahidehpour M, LiTao. Cost of Reliability Analysis Based on Stochastic Unit Commitment[J]. IEEE Transactions on Power Systems,2007,23(3): 1364-1374.
[36]宋晓通,谭振宇.改进的重要抽样法在电力系统可靠性评估中的应用[J].电网技术,2005,29(13)：56-59.
[37]Dupacova J, Growe-Kuska N, Romisch W. Scenario reduction in stochastic programming:An approach using probability metrics[J]. Math Program.2003, A(3),493-511.
[38]杨秀媛,肖洋,陈树勇.风电场风速和发电功率预测研究[J].中国电机工程学报,2005,25(11)：1-5.
[39]Pierre Pinson, Henrik Madsen. Probabilistic forecasting of wind power at the minute time-scale with Markov-switching autoregressive models[C].10th International Conference on Probabilistic Methods Applied to Power Systems, 2008,1-8.
[40]Soder L. Reserve Margin Planning in a Wind-hydro-thermal Power system[J]. IEEE Transactions on Power Systems,1993,8(2):564-571.
[41]Black M, Strbac G. Value of Bulk Energy Storage for Mananging Wind Power Fluctuations[J]. IEEE Transactions on Energy Conversion,2007,22(1):197-205.
[42]Methaprayoon K, Chitra Y. An Integration of ANN Wind power Estimation into Unit Commitment Considering the Forecasting Uncertainty[J]. IEEE Transactions on Industry Applications,2007,43(6):1441-1447.
[43]Restrepo J F, Galiana F D. Secondary Reserve Dispatch Accounting for Wind Power Randomness and Spillage[J]. IEEE Power Engineering Society General Meeting.2007,1-3.
[44]Gouveia E M, Matos M A. Operational Reserve of a Power System with a Large Amount of Wind Power[C].8th International Conference on Probabilistic Methods Applied to Power Systems,2004,717-722.
[45]Ronan Doherty, Mark O'Malley. A New Approach to Quantify Reserve Demand in Systems With Significant Installed Wind Capacity[J]. IEEE Transactions on Power Systems,2005,20(2):287-595.
[46]Ortega-Vazquez M A, Krischen D S. Estimating the Spinning Reserve Requirements in Systems With Significant Wind Power Generation Penetration [J]. IEEE Transactions on Power System.2009,24(1):114-124.
[47]Bouffard F, Galiana F D. Stochastic Security for Operations Planning With Significant Wind Power Generation[J]. IEEE Transactions on Power Systems, 2008,23(2):306-316.
[48]Morales J M, Conejo A J, Perez-Ruiz J. Economic Valuation of Reserves in Power Systems with High Penetration of Wind Power[J]. IEEE Transactions on Power Systems,2009,24(2):900-910.
[49]韩学山,柳焯.考虑发电机组输出功率速度限制的最优机组组合[J].电网技术,1994,18(6)：11-16.
[50]张利.电力市场中的机组组合理论研究.山东大学博士论文,2006,10.
[51]何小磊,严正,谢毓广.节能减排背景下的机组组合模型和算法研究[J].水电能源科学,2009,27(3)：154-157.
[52]张利,赵建国,韩学山.考虑网络安全约束的机组组合问题新算法[J].电网技术,2006,30(21)：50-55.
[53]杨朋朋.机组组合理论与算法研究.山东大学博士论文,2008,10.
[54]LiTao, Shahidehpour M. Price-based Unit Commitment:a case of Lagrangian Relaxation versus Mixed Integer Programming[J]. IEEE Transactions on Power Systems,2005,20(4):2015-2025.
[55]Carrion M, Arroyo J M. A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem[J]. IEEE Transactions on Power Systems,2006,21(3):1371-1378.
[56]吴宏宇,管晓宏,翟桥柱,高峰.水火电联合短期调度的混合整数规划算法[J].中国电机工程学报,2009,29(28)：82-88.
[57]FuYong, Shahidehpour M, Li Zuyi. Security-Constrained Unit Commitment with AC Constraints[J]. IEEE Transactions on Power Systems,2005,20(3): 1538-1550.
[58]ILOG CPLEX11.2 User's Manual. ILOG Corporation,2008.
[59]曹世光,杨以涵,于尔铿.缺电成本及其估算方法.电网技术[J],1996,20(11)：72-74.
[60]Wang S J, Shahidehpour S M, Krischen D S. Short-term generation scheduling with transmission and environmental constraints using an augmented lagrangian relaxation[J]. IEEE Transactions on Power Systems,1995,10(3):1294-1301.
[61]Reliability Test System Task Force. The IEEE reliability test system-1996. IEEE Transactions on Power Systems,1999,14(3):1010-1020.
[62]吴文传,宁辽逸,张伯明,孙宏斌.电力系统在线运行风险评估与决策[J].电力科学与技术学报,2009,24(2)：28-34.
[63]刘海涛,程林,孙元章,王鹏.基于实时运行条件的元件停运因素分析与停运率建模[J].电力系统自动化,2007,31(7)：6-11.
[64]孙元章,刘海涛,程林,王鹏.运行可靠性在线短期评估方案[J].电力系统自动化,2008,32(3)：4-8.
[65]雷亚洲,王伟胜,印永华,戴慧珠.基于机会约束规划的风电穿透功率极限计算[J].中国电机工程学报,2002,22(5)：32-35.
[66]吴俊,李国杰,孙元章.基于随机规划的并网风电场最大注入功率计算[J].电 网技术,2007,31(14)：15-19.
[67]雷亚洲,王伟胜,戴慧珠,等.风电对电力系统运行的价值分析[J].电网技术,2002,26(5)：10-14.
[2]梁才浩,段献忠.分布式发电及其对电力系统的影响[J].电力系统自动化,2001,25(12)：53-56.
[3]王承煦,张源.风力发电[M].北京：中国电力出版社,2003.
[4]Wood Allen J & Wollenberg Bruce F. Power Generation, Operation and Control[M]. John Wiley & Sons Inc., New York,1996.
[5]李文沅.电力系统安全经济运行——模型与方法[M].重庆：重庆大学出版社,1989.
[6](英)丹尼尔,戈兰.电力系统经济学原理[M].北京：中国电力出版社,2007.
[7]韩学山,赵建国.刚性优化与柔性决策结合的电力系统运行调度理论探讨[J].中国电力,2004,37(1)：15-18.
[8]雷亚洲.与风电并网相关的研究课题[J].电力系统自动化,2003,27(8)：84-89.
[9]查浩.电力系统概率优化调度理论研究.山东大学博士论文,2009,4.
[10]杨明.电力系统超前调度理论与算法研究.山东大学博士论文,2009,4.
[11]韩学山,杨明,张利.价值调度推进智能化电网发展的思考[J].电力系统自动化,2010,34(2)：5-9.
[12]刘宝碇,赵瑞清.随机规划与模糊规划[M].北京：清华大学出版社,1998.
[13]Anstine L T, Burke R E, et al. Application of Probability Methods to the Determination of Spinning Reserve requirements for the Pennsylvania-New Jersey-Maryland Interconnection[J].IEEE Transactions on Power Systems,1963, PAS-82(68):726-735.
[14]王锡凡.电力系统优化规划[M].北京：水利电力出版社,1990.
[15]王锡凡,王秀丽.随机生产模拟及其应用[J].电力系统自动化,2003,27(8)：10-15.
[16]Gooi H B, Mendes D P, Bell K R W, et al. Optimal scheduling of spinning reserve[J]. IEEE Transactions on Power Systems,1999,14(4):1485-1490.
[17]Xia L, Gooi H B. A reserve market with reliability incentives[C]. International
Conference on Power System Technology.2004,1740-1745.
[18]Chattopadhyay D, Baldick R . Unit commitment with probabilistic reserve[C].2002 IEEE Power Engineering society Winter Meeting. New York: 2002.280-285.
[19]杨朋朋,韩学山,王静,孟祥星.用拉格朗日松弛法求解概率备用解析表达的机组组合[J].山东大学学报(工学版).2007,37(2),58-62.
[20]Bouffard F, Galiana F D. An electricity market with a probabilistic spinning reserve criterion[J]. IEEE Transactions on Power Systems,2004,19(1):300-307.
[21]王锡凡,王秀丽,陈浩勇.电力市场基础[M].西安：西安交通大学出版社,2003.
[22]王建学,王锡凡,张显.电力市场中弹性运行备用研究[J].中国电机工程学报,2005,25(18)：20-27.
[23]张国全,王秀丽,王锡凡.电力市场中旋转备用的效益和成本分析[J].电力系统自动化.2000,24(21)：14-18.
[24]Ortega-Vazquez M A, Krischen D S. Optimizing the spinning reserve requirements using a cost/benefit analysis[J]. IEEE Transactions on Power System.2007,22(1):24-33.
[25]杨梓俊,丁明,孙昕.电力市场下综合考虑系统可靠性和旋转备用效益的机组组合[J].电网技术.2003,27(6)：13-18.
[26]Motamedi A, Fotuhi-Firuzabad M, Zareipour H. Optimum Simultaneous Clearing of Energy and Spinning Reserve Markets Using Cost/benefit Analysis[J]. IEEE Power and Energy Society General Meeting.2008, July,1-7.
[27]Galiana F D, Bouffard F, et al. Scheduling and Pricing of Coupled Energy and Primary,Secondary,and Tertiary Reserves[J]. Proceedings of the IEEE,2005, 93(11):1970-1983.
[28]Carpentier P, Cohen G, Culioli. Stochastic optimization of unit commitment:A new decomposition framework[J]. IEEE Transactions on Power Systems,1996, 11(2):1067-1073.
[29]Takriti S, Birge J R, Long E. A stochastic model for the unit commitment problem[J]. IEEE Transactions on Power Systems,1996,11(3):1497-1508.
[30]Bouffard F, Galiana F D, Conejo A J. Market-clearing with stochastic security-ⅠFormulation[J]. IEEE Transactions on Power Systems,2005, 20(4):1818-1826.
[31]Bouffard F, Galiana F D, Conejo A J. Market-clearing with stochastic security-PartⅡ:Case studies[J]. IEEE Transactions on Power Systems,2005, 20(4):1827-1835.
[32]Bouffard F, Galiana F D, Arroyo J M. Umbrella Contingencies in Security-Constrained Optimal Power Flow[C].15th Power systems Computation Conference,2005.
[33]刘海涛,孙元章,等.计及多状态元件模型的系统状态快速排序技术[J].电力系统自动化,2008,32(1)：16-21.
[34]WuLei, Shahidehpour M, LiTao. Stochastic Security-Constrained Unit Commitment[J]. IEEE Transactions on Power Systems,2007,22(2):800-811.
[35]WuLei, Shahidehpour M, LiTao. Cost of Reliability Analysis Based on Stochastic Unit Commitment[J]. IEEE Transactions on Power Systems,2007,23(3): 1364-1374.
[36]宋晓通,谭振宇.改进的重要抽样法在电力系统可靠性评估中的应用[J].电网技术,2005,29(13)：56-59.
[37]Dupacova J, Growe-Kuska N, Romisch W. Scenario reduction in stochastic programming:An approach using probability metrics[J]. Math Program.2003, A(3),493-511.
[38]杨秀媛,肖洋,陈树勇.风电场风速和发电功率预测研究[J].中国电机工程学报,2005,25(11)：1-5.
[39]Pierre Pinson, Henrik Madsen. Probabilistic forecasting of wind power at the minute time-scale with Markov-switching autoregressive models[C].10th International Conference on Probabilistic Methods Applied to Power Systems, 2008,1-8.
[40]Soder L. Reserve Margin Planning in a Wind-hydro-thermal Power system[J]. IEEE Transactions on Power Systems,1993,8(2):564-571.
[41]Black M, Strbac G. Value of Bulk Energy Storage for Mananging Wind Power Fluctuations[J]. IEEE Transactions on Energy Conversion,2007,22(1):197-205.
[42]Methaprayoon K, Chitra Y. An Integration of ANN Wind power Estimation into Unit Commitment Considering the Forecasting Uncertainty[J]. IEEE Transactions on Industry Applications,2007,43(6):1441-1447.
[43]Restrepo J F, Galiana F D. Secondary Reserve Dispatch Accounting for Wind Power Randomness and Spillage[J]. IEEE Power Engineering Society General Meeting.2007,1-3.
[44]Gouveia E M, Matos M A. Operational Reserve of a Power System with a Large Amount of Wind Power[C].8th International Conference on Probabilistic Methods Applied to Power Systems,2004,717-722.
[45]Ronan Doherty, Mark O'Malley. A New Approach to Quantify Reserve Demand in Systems With Significant Installed Wind Capacity[J]. IEEE Transactions on Power Systems,2005,20(2):287-595.
[46]Ortega-Vazquez M A, Krischen D S. Estimating the Spinning Reserve Requirements in Systems With Significant Wind Power Generation Penetration [J]. IEEE Transactions on Power System.2009,24(1):114-124.
[47]Bouffard F, Galiana F D. Stochastic Security for Operations Planning With Significant Wind Power Generation[J]. IEEE Transactions on Power Systems, 2008,23(2):306-316.
[48]Morales J M, Conejo A J, Perez-Ruiz J. Economic Valuation of Reserves in Power Systems with High Penetration of Wind Power[J]. IEEE Transactions on Power Systems,2009,24(2):900-910.
[49]韩学山,柳焯.考虑发电机组输出功率速度限制的最优机组组合[J].电网技术,1994,18(6)：11-16.
[50]张利.电力市场中的机组组合理论研究.山东大学博士论文,2006,10.
[51]何小磊,严正,谢毓广.节能减排背景下的机组组合模型和算法研究[J].水电能源科学,2009,27(3)：154-157.
[52]张利,赵建国,韩学山.考虑网络安全约束的机组组合问题新算法[J].电网技术,2006,30(21)：50-55.
[53]杨朋朋.机组组合理论与算法研究.山东大学博士论文,2008,10.
[54]LiTao, Shahidehpour M. Price-based Unit Commitment:a case of Lagrangian Relaxation versus Mixed Integer Programming[J]. IEEE Transactions on Power Systems,2005,20(4):2015-2025.
[55]Carrion M, Arroyo J M. A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem[J]. IEEE Transactions on Power Systems,2006,21(3):1371-1378.
[56]吴宏宇,管晓宏,翟桥柱,高峰.水火电联合短期调度的混合整数规划算法[J].中国电机工程学报,2009,29(28)：82-88.
[57]FuYong, Shahidehpour M, Li Zuyi. Security-Constrained Unit Commitment with AC Constraints[J]. IEEE Transactions on Power Systems,2005,20(3): 1538-1550.
[58]ILOG CPLEX11.2 User's Manual. ILOG Corporation,2008.
[59]曹世光,杨以涵,于尔铿.缺电成本及其估算方法.电网技术[J],1996,20(11)：72-74.
[60]Wang S J, Shahidehpour S M, Krischen D S. Short-term generation scheduling with transmission and environmental constraints using an augmented lagrangian relaxation[J]. IEEE Transactions on Power Systems,1995,10(3):1294-1301.
[61]Reliability Test System Task Force. The IEEE reliability test system-1996. IEEE Transactions on Power Systems,1999,14(3):1010-1020.
[62]吴文传,宁辽逸,张伯明,孙宏斌.电力系统在线运行风险评估与决策[J].电力科学与技术学报,2009,24(2)：28-34.
[63]刘海涛,程林,孙元章,王鹏.基于实时运行条件的元件停运因素分析与停运率建模[J].电力系统自动化,2007,31(7)：6-11.
[64]孙元章,刘海涛,程林,王鹏.运行可靠性在线短期评估方案[J].电力系统自动化,2008,32(3)：4-8.
[65]雷亚洲,王伟胜,印永华,戴慧珠.基于机会约束规划的风电穿透功率极限计算[J].中国电机工程学报,2002,22(5)：32-35.
[66]吴俊,李国杰,孙元章.基于随机规划的并网风电场最大注入功率计算[J].电 网技术,2007,31(14)：15-19.
[67]雷亚洲,王伟胜,戴慧珠,等.风电对电力系统运行的价值分析[J].电网技术,2002,26(5)：10-14.