含风能电力系统的概率分析与优化运行方法
|
摘要
电力系统中的风电并网容量正在快速增长，这给电力系统分析与优化运行的理论研究和工程实际都带来了巨大的挑战。风电除了一般意义上的随机性外，还具有有界性、相关性、难以预测性和剧烈波动性等多种与传统电源不同的特点，现有的电力系统分析与优化运行方法在应对风电的这些特点时呈现出不同的缺陷。本文对此进行深入研究，提出含风能电力系统概率潮流、概率最优潮流与概率调度的新方法。本文的主要研究工作如下：
提出一种考虑风速有界性的概率潮流计算方法。风速具有有界性，采用传统点估计方法进行概率潮流计算时可能产生超出边界的风速位置样本值，导致概率潮流无法准确计算甚至根本无法计算。本文在点估计方法的基础上提出一种考虑风速有界性的改进概率潮流方法，在点估计方法中引入一般变换与幂变换相互配合，保证所使用的点估计风速样本计算值满足物理边界的要求，进而确保概率潮流计算的可行性和准确性。通过使用多个地点的风速数据对IEEE14节点系统进行仿真分析，对所提方法进行验证。这个方法也可以推广到概率潮流计算中处理其它概率参数（如负荷）的边界。
提出一种考虑不同分布风速相关性的概率最优潮流点估计方法。传统的概率最优潮流方法，难以直接处理具有相关性的风速。本文提出一种考虑不同分布风速相关性的概率最优潮流点估计方法。服从任意分布并且具有相关性的风速，经过累积概率分布函数变换以及相关矩阵变换，可以变为独立的随机变量，进而可以根据点估计方法对每个独立随机变量选取特征点并确定权重，再经过逆变换回到原始风速空间后，进行确定性最优潮流计算以及概率统计量的计算。通过对IEEE14和118节点系统以及重庆系统进行仿真分析，说明方法的有效性。
结合点估计与遗传算法提出一种考虑风电功率预测误差的概率调度计划制定方法。采用点估计方法进行概率调度模型中期望值目标的计算与概率约束条件的判断，从而进行遗传算法的适应度函数计算。在适应度计算中，需要进行多次潮流计算，因而提出一种基于拓扑分区的潮流计算方法，在潮流计算时将电网划分为3种不同类型的子网交替进行潮流迭代，加快计算速度。通过多个系统的仿真计算说明方法的有效性。
提出一种降低火电机组寿命损耗的调度计划制定方法。风电功率发生频繁而剧烈的波动时，为了保证功率平衡，传统的火电机组需要大量频繁地进行功率调节，这将造成火电机组的寿命损耗。本文提出一种在风电功率剧烈波动环境下降低传统火电机组寿命损耗的调度计划制定方法。通过对火电机组调节过程中寿命损耗造成的经济损失进行估算，在目标函数中引入调节费用，并加入调节次数限制约束，构建降低机组调节频繁程度的调度计划机会约束模型，同时提出结合点估计与负荷曲线分段的遗传算法对模型进行求解。通过IEEE30、118节点系统和重庆系统的仿真分析，证明所提模型和方法的有效性。
综上所述，本文针对风电的有界性、相关性、难以预测性和剧烈波动性等特点，提出多种电力系统概率分析与优化运行的有效方法，为风电并网电力系统的安全、优质、经济运行提供保障。
The integration capacity of wind power has been growing rapidly in power system,which brings inevitable challenges to both academic study and engineering practice inpower system analysis and optimal operation. In addition to randomness, thecharachteristics of wind sources in boundedness, correlation, difficulties in forecastingand fluctuation arevery diffirent from traditional sources and cannot be handled byexisting analysis and optimal operation methods. This thesis developed new methods ofprobabilistic power flow, probabilistic optimal power flow and probabilistic generationdispatching to address these problems caused by wind sources.
A point estimation method (PEM) based probabilistic power flow (PPF) techniqueconsidering bounded wind speeds is proposed. The domain of wind speed is alwaysbounded. Unfortunately, the locations computed from PEM may fall outside the domain.In this case, the PPF cannot be calculated accurately or even cannot be calculated at all.A universal transformation and a power transformation are combined with thetraditional PEM to address this issue. The IEEE14-bus system and several wind speedcurve data are used to demonstrate the effectiveness of the presented technqiue. Thepresented transformation method can be extended to deal with the boundedness of otherrandom variables such as loads.
A probabilistic optimal power flow (POPF) technique considering the correlationsbetween wind speeds following arbitrary probability distributions using PEM isproposed. Correlated wind speeds following different distributions are transformed intorandom variables following correlated normal distributions and then into thosefollowing independent normal distributions so that the traditional2m+1PEM can beapplied to solve the probabilistic optimal power flow with wind speed correlations. TheIEEE14-bus system, IEEE118-bus system and an actual utility system in the southwestof China with additional wind farms are used to demonstrate the effectiveness of thepresented method.
A chance constrained programming generation dispatching model consideringforecasting errors of wind power is developed and a genetic algorithm combined withthe PEM is proposed to solve the presented model. The expeted objective function andprobabilistic constrains are obtained using the point estimation method in evaluating thefitness function. To reduce computaional burdens in power flow analyses required in implementation, a new power flow algorithm for composite meshed and radial systemsis also presented using the topological division of system structure as a part of theimproved genetic algorithm. The effectiveness of the presented model and algorithm isdemonstrated using several systems.
A probabilistic model of daily generation scheduling for reducing losses of thermalunits’ lives under the environment of fluctuated wind sources is developmed. Animproved multi-population genetic algorithm (IMPGA) is presented to solve the modelbased on load curve segmentation. The cost for regulation of thermal units is estimatedfirst. A chance constrained programming model for reducing units’ regulationfrequencies is then proposed by introducing the regulation cost in the objective functionand regulation frequency limits in the constraints. Load points on a load curve areaggregated to form an equivalent multiple-level load curve representation. The globaloptimization is reached with coordination between the multiple-level load model andmulti-population strategy of GA. The effectiveness of the presented model andalgorithm is demonstrated using the IEEE30-bus and IEEE118-bus systems.
In this thesis, the efficient probabilistic analysis and optimal operation methods areproposed to address the boundedness, correlation, difficulties in forecasting andfluctuation of wind sources. These methods provide a useful package in helping ensuresecurity, high quality and economic operation of power systems.
提出一种考虑风速有界性的概率潮流计算方法。风速具有有界性，采用传统点估计方法进行概率潮流计算时可能产生超出边界的风速位置样本值，导致概率潮流无法准确计算甚至根本无法计算。本文在点估计方法的基础上提出一种考虑风速有界性的改进概率潮流方法，在点估计方法中引入一般变换与幂变换相互配合，保证所使用的点估计风速样本计算值满足物理边界的要求，进而确保概率潮流计算的可行性和准确性。通过使用多个地点的风速数据对IEEE14节点系统进行仿真分析，对所提方法进行验证。这个方法也可以推广到概率潮流计算中处理其它概率参数（如负荷）的边界。
提出一种考虑不同分布风速相关性的概率最优潮流点估计方法。传统的概率最优潮流方法，难以直接处理具有相关性的风速。本文提出一种考虑不同分布风速相关性的概率最优潮流点估计方法。服从任意分布并且具有相关性的风速，经过累积概率分布函数变换以及相关矩阵变换，可以变为独立的随机变量，进而可以根据点估计方法对每个独立随机变量选取特征点并确定权重，再经过逆变换回到原始风速空间后，进行确定性最优潮流计算以及概率统计量的计算。通过对IEEE14和118节点系统以及重庆系统进行仿真分析，说明方法的有效性。
结合点估计与遗传算法提出一种考虑风电功率预测误差的概率调度计划制定方法。采用点估计方法进行概率调度模型中期望值目标的计算与概率约束条件的判断，从而进行遗传算法的适应度函数计算。在适应度计算中，需要进行多次潮流计算，因而提出一种基于拓扑分区的潮流计算方法，在潮流计算时将电网划分为3种不同类型的子网交替进行潮流迭代，加快计算速度。通过多个系统的仿真计算说明方法的有效性。
提出一种降低火电机组寿命损耗的调度计划制定方法。风电功率发生频繁而剧烈的波动时，为了保证功率平衡，传统的火电机组需要大量频繁地进行功率调节，这将造成火电机组的寿命损耗。本文提出一种在风电功率剧烈波动环境下降低传统火电机组寿命损耗的调度计划制定方法。通过对火电机组调节过程中寿命损耗造成的经济损失进行估算，在目标函数中引入调节费用，并加入调节次数限制约束，构建降低机组调节频繁程度的调度计划机会约束模型，同时提出结合点估计与负荷曲线分段的遗传算法对模型进行求解。通过IEEE30、118节点系统和重庆系统的仿真分析，证明所提模型和方法的有效性。
综上所述，本文针对风电的有界性、相关性、难以预测性和剧烈波动性等特点，提出多种电力系统概率分析与优化运行的有效方法，为风电并网电力系统的安全、优质、经济运行提供保障。
The integration capacity of wind power has been growing rapidly in power system,which brings inevitable challenges to both academic study and engineering practice inpower system analysis and optimal operation. In addition to randomness, thecharachteristics of wind sources in boundedness, correlation, difficulties in forecastingand fluctuation arevery diffirent from traditional sources and cannot be handled byexisting analysis and optimal operation methods. This thesis developed new methods ofprobabilistic power flow, probabilistic optimal power flow and probabilistic generationdispatching to address these problems caused by wind sources.
A point estimation method (PEM) based probabilistic power flow (PPF) techniqueconsidering bounded wind speeds is proposed. The domain of wind speed is alwaysbounded. Unfortunately, the locations computed from PEM may fall outside the domain.In this case, the PPF cannot be calculated accurately or even cannot be calculated at all.A universal transformation and a power transformation are combined with thetraditional PEM to address this issue. The IEEE14-bus system and several wind speedcurve data are used to demonstrate the effectiveness of the presented technqiue. Thepresented transformation method can be extended to deal with the boundedness of otherrandom variables such as loads.
A probabilistic optimal power flow (POPF) technique considering the correlationsbetween wind speeds following arbitrary probability distributions using PEM isproposed. Correlated wind speeds following different distributions are transformed intorandom variables following correlated normal distributions and then into thosefollowing independent normal distributions so that the traditional2m+1PEM can beapplied to solve the probabilistic optimal power flow with wind speed correlations. TheIEEE14-bus system, IEEE118-bus system and an actual utility system in the southwestof China with additional wind farms are used to demonstrate the effectiveness of thepresented method.
A chance constrained programming generation dispatching model consideringforecasting errors of wind power is developed and a genetic algorithm combined withthe PEM is proposed to solve the presented model. The expeted objective function andprobabilistic constrains are obtained using the point estimation method in evaluating thefitness function. To reduce computaional burdens in power flow analyses required in implementation, a new power flow algorithm for composite meshed and radial systemsis also presented using the topological division of system structure as a part of theimproved genetic algorithm. The effectiveness of the presented model and algorithm isdemonstrated using several systems.
A probabilistic model of daily generation scheduling for reducing losses of thermalunits’ lives under the environment of fluctuated wind sources is developmed. Animproved multi-population genetic algorithm (IMPGA) is presented to solve the modelbased on load curve segmentation. The cost for regulation of thermal units is estimatedfirst. A chance constrained programming model for reducing units’ regulationfrequencies is then proposed by introducing the regulation cost in the objective functionand regulation frequency limits in the constraints. Load points on a load curve areaggregated to form an equivalent multiple-level load curve representation. The globaloptimization is reached with coordination between the multiple-level load model andmulti-population strategy of GA. The effectiveness of the presented model andalgorithm is demonstrated using the IEEE30-bus and IEEE118-bus systems.
In this thesis, the efficient probabilistic analysis and optimal operation methods areproposed to address the boundedness, correlation, difficulties in forecasting andfluctuation of wind sources. These methods provide a useful package in helping ensuresecurity, high quality and economic operation of power systems.
引文
[1]朱四海.电力节能减排政策解析[M].北京:中国电力出版社,2010.
[2]刘传庚,谭玲玲,丛威,赵龙翔.中国能源低碳之路[M].北京:中国经济出版社,2011.
[3]张建英.新能源和可再生能源[M].北京:线装书局,2011.
[4]周双喜,鲁宗相.风力发电与电力系统[M].北京:中国电力出版社,2011.
[5] Holttinen H. Handing of wind power forecst errors in the Nordic power market[C].95hInternational Conference on Probabilistic Methods Applied to Power Systems KTH,Stockholm, Sweden-Jun11-15,2006.
[6] Lemer J, Grundmeyer M, Garvert M. The importance of wind forecasting[J]. RenewableEnergy Focus,2009,10(2):64-66.
[7] Qin Z, Li W, Xiong X. Incorporating multiple correlations among wind speeds, photovoltaicpowers and bus loads in composite system reliability evaluation[J]. Applied Energy,2013,110:285-294.
[8] Villanueva D, Feijoo A, Pazos J L. Probabilistic load flow considering correlation betweengeneration, loads and wind Power[J]. Smart Grid and Renewable Energy,2011,2(1):12-20.
[9]丁明,李生虎,黄凯.基于蒙特卡罗模拟的概率潮流计算[J].电网技术,2001,25(11):10-22.
[10] Soleimanpour N, Mohammadi M. Probabilistic load flow by using nonparametric densityestimators[J]. IEEE Transactions on Power Systems,2013,28(4):3747-3755.
[11]邓威,李欣然,徐振华,等.考虑风速相关性的概率潮流计算及影响分析[J].电网技术,2012,36(4):45-50.
[12]蔡德福,石东源,陈金富.基于Copula理论的计及输入随机变量相关性的概率潮流计算[J].电力系统保护与控制,2013,41(20:13-19.
[13] Cai D, Shi D, Chen J. Probabilistic load flow computation with polynomial normaltransformation and Latin hypercube sampling[J]. IET Generation, Transmission&Distribution,2013,7(5):474-482.
[14]蔡德福,石东源,陈金富.基于多项式正态变换和拉丁超立方采样的概率潮流计算方法[J].中国电机工程学报,2013,33(13):92-100.
[15] Chen Y, Wen, J, Cheng S. Probabilistic load flow method based on Nataf transformation andLatin hypercube sampling[J]. IEEE Transactions on Sustainable Energy,2013,4(2):294-301.
[16] Hajian M, Rosehart W D, Zareipour H. Probabilistic power flow by Monte Carlo simulationwith Latin supercube sampling[J]. IEEE Transactions on Power Systems,2013,28(2):1550-1559.
[17]于晗,钟志勇,黄杰波,等.采用拉丁超立方采样的电力系统概率潮流计算方法[J].电力系统自动化,2009,32(21):32-35,81.
[18]李俊芳,张步涵.基于进化算法改进拉丁超立方抽样的概率潮流计算[J].中国电机工程学报,2011,31(25):90-96.
[19]丁明,王京景,李生虎.基于扩展拉丁超立方采样的电力系统概率潮流计算[J].中国电机工程学报.2013,33(4):163-170.
[20] Borkowska B. Probabilistic load flow[J]. IEEE Transactions on Apparatus and Systems,1974,93(3):752-759.
[21]李雪,李渝曾,李海英.几种概率潮流算法的比较与分析[J].电力系统及其自动化学报,2009,21(3):12-17.
[22]王锡凡,王秀丽.电力系统的随机潮流分析[J].西安交通大学学报,1988,22(3):87-97.
[23] Zhang P, Lee S T. Probabilistic load flow computation using the method of combinedcumulants and Gram-Charlier Expansion[J]. IEEE Transactions on Power Systems,2004,19(1):676-682.
[24]董雷,程卫东,杨以涵.含风电场的电力系统概率潮流计算[J].电网技术,2009,33(16):87-91.
[25]胡泽春,王锡凡.基于半不变量法的随机潮流误差分析[J].电网技术,2009,33(18):32-37.
[26]周建华,袁越.含风电场电力系统的Cornish-Fisher级数概率潮流计算[J].电力自动化设备,2011,31(12):68-71.
[27]朱星阳,刘文霞,张建华.考虑大规模风电并网的电力系统随机潮流[J].中国电机工程学报,2013,33(7):77-85.
[28] Fan M, Vittal V, Heydt G T, Ayyanar R. Probabilistic power flow analysis with generationdispatch including photovoltaic resources[J]. IEEE Transactions on Power Systems,2013,28(2):1797-1805.
[29] Su C-L. Probabilistic load-flow computation using point estimate method[J]. IEEETransactions on Power Systems,2005,20(4):1843-1851.
[30] Morales J M, Pérez-Ruiz J, Point estimate schemes to solve the probabilistic power flow[J].IEEE Trans. Power Systems,2007,22(4):1594-1601.
[31] Ai X, Wen J, Wu T, et al. A discrete point estimate method for probabilistic load flow basedon the measured data of wind power[J]. IEEE Transactions on Industry Applications,2013,49(5):2244-2252.
[32] Mohammadi M, Shayegani A, Adaminejad H. A new approach of point estimate method forprobabilistic load flow[J]. Electrical Power and Energy Systems,2013,51:54-60.
[33] Morales J M, Baringo L, Conejo A J. Probabilistic power flow with correlated wind sources[J].IET Generation, Transmission&Distribution,2010,4(5):641-651.
[34]陈雁,文劲宇,程时杰.考虑输入变量相关性的概率潮流计算方法[J].中国电机工程学报,2011,31(22):80-87.
[35]艾小猛,文劲宇,吴桐,等.基于点估计和Gram-Charlier展开的含风电电力系统概率潮流实用算法[J].中国电机工程学报,2013,33(16):16-22.
[36]石东源,蔡德福,陈金富,等.计及输入变量相关性的半不变量法概率潮流计算[J].中国电机工程学报,2012,32(28):104-113.
[37]杨欢,邹斌.含相关性随机变量的概率潮流三点估计法[J].电力系统自动化,2012,36(15):51-56.
[38]范荣奇,陈金富,段献忠,等.风速相关性对概率潮流计算的影响分析[J].电力系统自动化,2011,35(4):18-22,76.
[39] Zhang H, Li P. Probabilistic analysis for optimal power flow under uncertainty[J]. IETGeneration, Transmission&Distribution,2010,4(5):553-561.
[40] Rodrigues A B, Da S M G. Probabilistic assessment of available transfer capability based onMonte Carlo method with sequential simulation[J]. IEEE Transactions on Power Systems2007,22(1):484-492.
[41] Shi L, Wang C, Yao L. Optimal power flow solution incorporating wind power[J]. IEEESystems Journal,2012,2:233-241.
[42] Mardrigal M, Ponnambalam K, Quintana V H. Probabilistic optimal power flow[C]. Proc.IEEE Can. Conf. Electrical and Computer Engineering, Waterloo, Canada1998:385-388.
[43] Li X, Li Y, Zhang S. Analysis of Probabilistic Optimal Power Flow Taking Account of theVariation of Load Power[J]. IEEE Transactions on Power Systems,2008,23(3):992-999.
[44] Schellenberg A, Rosehart W, Aguado J. Cumulant-based probabilistic optimal power flowwith Gaussian and gamma distributions[J]. IEEE Transactions on Power Systems,2005,20(2):773-781.
[45] Saunders C S. Point estimate method addressing correlated wind power for probabilisticoptimal power flow[J]. IEEE Transactions on Power Systems, accepted.
[46]潘炜,刘文颖,杨以涵.概率最优潮流的点估计计算法[J].中国电机工程学报,2008,28(16):28-33.
[47] Su C, Lu C. Two-point estimate method for quantifying transfer capability uncertainty[J].IEEE Transactions on Power Systems,2005,20(2):573-579.
[48] Aien M, Fotuhi-Firuzabad M, Rashidinejad M. Probabilistic Optimal Power Flow inCorrelated Hybrid Wind-Photovoltaic Power Systems[J]. IEEE Transactions on Smart Grid,2014,5(1):130-138.
[49] Li W. Probabilistic transmission system planning[M]. New Jersey: John Wiley&Sons, Inc,2011.
[50] Li W. Risk Assessment Of Power Systems: Models, Methods, and Applications[M]. USA andCanada: IEEE Press and Wiley&Sons,2005.
[51]梁忠民,戴昌军.水文分析计算中两种正态变换方法的比较研究[J].水电能源科学,2005,23(2):1-3.
[52]李文沅.电力系统安全经济运行[M].重庆:重庆大学出版社,1989.
[53] Mitra C S. Composite system reliability evaluation using state space pruning[J], IEEETransactions on power systems,1997,12(1):471-479.
[54] Cunha S H F, Pereira M V F,. Pinto L M V G, Oliveira C. Composite Generation andTransmission Reliability Evaluation in Large Hydroelectric Systems[J]. IEEE Transactions onPower Apparatus and Systems,1985, PAS(104):2657-2663.
[55]宋晓通谭震宇.基于最优抽样与选择性解析的电力系统可靠性评估[J].电力系统自动化,2009,33(5):29-33,60.
[56] Breipohl A, Lee F N, HuangQ J. Sample size reduction in stochastic production simulation[J].IEEE Transactions on Power Systems,1990,5(3):984-992.
[57] Li W, Billinton R. Effect of bus load uncertainty and correlation in composite systemadequacy evaluation[J]. IEEE Trans on Power Systems,1991,6(4):1522-1529.
[58]赵宏伟,任震.计及线路安全约束的机组最优投入[J].电力系统自动化,1997,21(5):41-45.
[59] Ma H, Shahidehpour S. M. Unitcommitment with transmission security and voltageconstraints[J]. IEEE Transactions on Power Systems,1999,14(2):757-764.
[60] Sheble G, Fahd G. Unit commitment literature synopsis[J]. IEEE Transactions on PowerSystems on Power Systems,1994,9(1):128-135.
[61] Jiang R Wang J Zhang M Guan Y. Two-stage minimax regret robust unit commitment[J].IEEE Transactions on Power Systems,2013,28(3):2271-2282.
[62] Bertsimas D, Litvinov E, Sun X A, Zhao J, Zheng T. Adaptive robust optimization for thesecurity constrained unit commitment problem[J]. IEEE Transactions on Power Systems,2013,28(1):52-63.
[63] Papala V S, Erlich I, Rohrig K, Dobschinski J. A stochastic model for the optimal operation ofa wind-thermal power system[J]. IEEE Transactions on Power Systems,2009,24(2):940-950.
[64] Wang Q, Watson J-P, Guan Y. Two-stage robust optimization for N-k contingency-constrainedunit commitment[J]. IEEE Transactions on Power Systems,2013,28(3):2366-2375.
[65] Ozturk U A, Mazumdar M, Norman B A. A solution to the stochastic unit commitmentproblem using chance constrained programming[J].2004,19(3):1589-1598.
[66]赵书强,刘晨亮,王明雨,等.基于机会约束规划的储能日前优化调度[J].电网技术,2013,37(11):3055-3059.
[67]孙元章,吴俊,李国杰,何剑.基于风速预测和随机规划的含风电场电力系统动态经济调度[J].中国电机工程学报,2012,29(4):41-47.
[68]杨洪明,王爽,易德鑫,易俊,刘党峰.考虑多风电场出力相关性的电力系统随机优化调度[J].电力自动化设备,2012,33(1):114-113,120.
[69]于佳,任建文,周明.基于机会约束规划的风-蓄联合动态经济调度[J].电网技术,2013,37(8):2116-2122.
[70] Pozo D, Contreras J. A chance-constrained unit commitment with an n-K security criterionand significant wind generation[J]. IEEE Transactions on Power Systems,2013,28(3):2842-2851.
[71]张宁宁,高山,赵欣.一种考虑风电随机性的机组组合模型及其算法[J].电工技术学报,2013,28(5):22-29.
[72]娄素华,王志磊,吴耀武,侯婷婷.基于机会约束规划的含大规模风电电力系统协调经济调度[J].电工技术学报,2013,28(10):337-345.
[73] Constantinescu M., Victor M, Zavala, Rocklin M. A computational framework for uncertaintyquantification and stochastic optimization in unit commitment with wind power generation[J].IEEE Transactions on Power systems,2011,26(1):431-441.
[74]白杨,汪洋,夏清,孙欣,杨明辉,张建.水-火-风协调优化的全景安全约束经济调度[J].中国电机工程学报,2013,33(13):2-9.
[75] Wu L, Shahidehpour M, Li Z. Comparison of scenario-based and interval optimizationapproaches to stochastic SCUC[J]. IEEE Transactions on Power Systems,2012,27(2):913-921.
[76] Samer T, Birge J R, Long E, A Stochastic Model for the Unit Commitment Problem[J]. IEEETransactions on Power Systems,1996,11(3):1497-1508.
[77] Bouffard F, Galiana F D. Stochastic security for operations planning with significant windpower generation[J]. IEEE Transactions on Power Systems,2008,23(2):306-316.
[78] Liu B. Theory and practice of uncertain programming[M]. Verlag Berlin Heidelberg: Springer,2009.
[79] Birge J R, Louveaux F. Introduction to stochastic programming[M]. Verlag Berlin Heidelberg:Springer,2011.
[80] Parvania M, Fothi-Firuzabad M. Demand response scheduling by stochastic SCUC[J]. IEEETransactions on Smart Grid,2010,1(1):89-98.
[81] Wang Q, Guan Y, Wang J. A chance-constrained two stage stochastic program for unitcommitment with uncertain wind power output[J]. IEEE Transactions on Power Systems,2012,27(1):206-215.
[82]刘德伟,郭剑波,黄越辉,王伟胜.基于风电功率概率预测和运行风险约束的含风电场电力系统动态经济调度[J].中国电机工程学报,2013,33(16):9-15
[83] Box G E P, Cox D R. An analysis of transformations[J]. Journal of the Royal Statistical Society.Series B (Methodological),1964,26(2):211-252.
[84] MATPOWER.[EB/OL].[2012-10-1]. http://www.pserc.cornell.edu/matpower/.ASOS/AWOS data download.[EB/OL].
[2013-12-10]. http://mesonet.agron.iastate.edu/request/download.phtml
[85] Yu J, Yan W, Li W, Chung C Y, Wong K P. An unfixed piecewise optimal reactive power-flowmodel and its algorithm for AC-DC systems[J]. IEEE Transactions on Power Systems,2008,23(2):170-176.
[86] Qin Z, Li W, Xiong X. Generation system reliability evaluation incorporating correlations ofwind speeds with different distributions[J]. IEEE Trans. Power Systems,2013,28(2):551-558.
[87] Qin Z, LI W, Xiong X. Estimating wind speed probabilisty distribution using kernel dnsitymethod[J]. Electric Power Systems Research,81(12):2139-2146.
[88]贾晓峰,颜伟,周家启,余娟,黄正波, David C. Yu.复杂电网的分层解耦潮流算法[J].中国电机工程学报,2010,30(7):56-61.
[89]颜伟,宋林滔,余娟,卢建刚,李钦,张海兵.基于权函数的电网参数分区辨识与估计方法[J].电力系统自动化,2011,35(5):25-30.
[90]阚伟民,张俊杰,顾红柏.国产200MW汽轮机组调峰运行转子热应力场和寿命损耗分析[J].广东电力,1999,12(2):24-27.
[91]张克纯,顾金芳,吕永鑫. AGC负荷变化率对汽轮机寿命的影响[J].华东电力,2003,(7):27-30.
[92]张保衡.大容量火电机组寿命管理与调峰运行[M].北京:水利电力出版社.
[93]张保衡.调峰机组热应力及疲劳寿命[J].中国电机工程学报,1986,6(2):1-13.
[94]余加喜，白雪峰，郭志忠，等．考虑负荷变化率的日发电计划[J]．电力系统自动化，2008，32(18)：39-43.
[95]颜伟，刘方，王官洁，等．辐射型网络潮流的分层前推回代算法[J]．中国电机工程学报，2003，23(8)：76-80．
[96]孙立勇,张焰,蒋传文.基于矩阵实数编码遗传算法求解大规模机组组合问题[J].中国电机工程学报,2006,26(2):82-87.
[97] Park Y M, Won J R, Park J B, et al. Generation expansion planning based on an adevancedevolutionary programming[J]. IEEE Transactions on Power Systems,1999,14(1):299-305.
[2]刘传庚,谭玲玲,丛威,赵龙翔.中国能源低碳之路[M].北京:中国经济出版社,2011.
[3]张建英.新能源和可再生能源[M].北京:线装书局,2011.
[4]周双喜,鲁宗相.风力发电与电力系统[M].北京:中国电力出版社,2011.
[5] Holttinen H. Handing of wind power forecst errors in the Nordic power market[C].95hInternational Conference on Probabilistic Methods Applied to Power Systems KTH,Stockholm, Sweden-Jun11-15,2006.
[6] Lemer J, Grundmeyer M, Garvert M. The importance of wind forecasting[J]. RenewableEnergy Focus,2009,10(2):64-66.
[7] Qin Z, Li W, Xiong X. Incorporating multiple correlations among wind speeds, photovoltaicpowers and bus loads in composite system reliability evaluation[J]. Applied Energy,2013,110:285-294.
[8] Villanueva D, Feijoo A, Pazos J L. Probabilistic load flow considering correlation betweengeneration, loads and wind Power[J]. Smart Grid and Renewable Energy,2011,2(1):12-20.
[9]丁明,李生虎,黄凯.基于蒙特卡罗模拟的概率潮流计算[J].电网技术,2001,25(11):10-22.
[10] Soleimanpour N, Mohammadi M. Probabilistic load flow by using nonparametric densityestimators[J]. IEEE Transactions on Power Systems,2013,28(4):3747-3755.
[11]邓威,李欣然,徐振华,等.考虑风速相关性的概率潮流计算及影响分析[J].电网技术,2012,36(4):45-50.
[12]蔡德福,石东源,陈金富.基于Copula理论的计及输入随机变量相关性的概率潮流计算[J].电力系统保护与控制,2013,41(20:13-19.
[13] Cai D, Shi D, Chen J. Probabilistic load flow computation with polynomial normaltransformation and Latin hypercube sampling[J]. IET Generation, Transmission&Distribution,2013,7(5):474-482.
[14]蔡德福,石东源,陈金富.基于多项式正态变换和拉丁超立方采样的概率潮流计算方法[J].中国电机工程学报,2013,33(13):92-100.
[15] Chen Y, Wen, J, Cheng S. Probabilistic load flow method based on Nataf transformation andLatin hypercube sampling[J]. IEEE Transactions on Sustainable Energy,2013,4(2):294-301.
[16] Hajian M, Rosehart W D, Zareipour H. Probabilistic power flow by Monte Carlo simulationwith Latin supercube sampling[J]. IEEE Transactions on Power Systems,2013,28(2):1550-1559.
[17]于晗,钟志勇,黄杰波,等.采用拉丁超立方采样的电力系统概率潮流计算方法[J].电力系统自动化,2009,32(21):32-35,81.
[18]李俊芳,张步涵.基于进化算法改进拉丁超立方抽样的概率潮流计算[J].中国电机工程学报,2011,31(25):90-96.
[19]丁明,王京景,李生虎.基于扩展拉丁超立方采样的电力系统概率潮流计算[J].中国电机工程学报.2013,33(4):163-170.
[20] Borkowska B. Probabilistic load flow[J]. IEEE Transactions on Apparatus and Systems,1974,93(3):752-759.
[21]李雪,李渝曾,李海英.几种概率潮流算法的比较与分析[J].电力系统及其自动化学报,2009,21(3):12-17.
[22]王锡凡,王秀丽.电力系统的随机潮流分析[J].西安交通大学学报,1988,22(3):87-97.
[23] Zhang P, Lee S T. Probabilistic load flow computation using the method of combinedcumulants and Gram-Charlier Expansion[J]. IEEE Transactions on Power Systems,2004,19(1):676-682.
[24]董雷,程卫东,杨以涵.含风电场的电力系统概率潮流计算[J].电网技术,2009,33(16):87-91.
[25]胡泽春,王锡凡.基于半不变量法的随机潮流误差分析[J].电网技术,2009,33(18):32-37.
[26]周建华,袁越.含风电场电力系统的Cornish-Fisher级数概率潮流计算[J].电力自动化设备,2011,31(12):68-71.
[27]朱星阳,刘文霞,张建华.考虑大规模风电并网的电力系统随机潮流[J].中国电机工程学报,2013,33(7):77-85.
[28] Fan M, Vittal V, Heydt G T, Ayyanar R. Probabilistic power flow analysis with generationdispatch including photovoltaic resources[J]. IEEE Transactions on Power Systems,2013,28(2):1797-1805.
[29] Su C-L. Probabilistic load-flow computation using point estimate method[J]. IEEETransactions on Power Systems,2005,20(4):1843-1851.
[30] Morales J M, Pérez-Ruiz J, Point estimate schemes to solve the probabilistic power flow[J].IEEE Trans. Power Systems,2007,22(4):1594-1601.
[31] Ai X, Wen J, Wu T, et al. A discrete point estimate method for probabilistic load flow basedon the measured data of wind power[J]. IEEE Transactions on Industry Applications,2013,49(5):2244-2252.
[32] Mohammadi M, Shayegani A, Adaminejad H. A new approach of point estimate method forprobabilistic load flow[J]. Electrical Power and Energy Systems,2013,51:54-60.
[33] Morales J M, Baringo L, Conejo A J. Probabilistic power flow with correlated wind sources[J].IET Generation, Transmission&Distribution,2010,4(5):641-651.
[34]陈雁,文劲宇,程时杰.考虑输入变量相关性的概率潮流计算方法[J].中国电机工程学报,2011,31(22):80-87.
[35]艾小猛,文劲宇,吴桐,等.基于点估计和Gram-Charlier展开的含风电电力系统概率潮流实用算法[J].中国电机工程学报,2013,33(16):16-22.
[36]石东源,蔡德福,陈金富,等.计及输入变量相关性的半不变量法概率潮流计算[J].中国电机工程学报,2012,32(28):104-113.
[37]杨欢,邹斌.含相关性随机变量的概率潮流三点估计法[J].电力系统自动化,2012,36(15):51-56.
[38]范荣奇,陈金富,段献忠,等.风速相关性对概率潮流计算的影响分析[J].电力系统自动化,2011,35(4):18-22,76.
[39] Zhang H, Li P. Probabilistic analysis for optimal power flow under uncertainty[J]. IETGeneration, Transmission&Distribution,2010,4(5):553-561.
[40] Rodrigues A B, Da S M G. Probabilistic assessment of available transfer capability based onMonte Carlo method with sequential simulation[J]. IEEE Transactions on Power Systems2007,22(1):484-492.
[41] Shi L, Wang C, Yao L. Optimal power flow solution incorporating wind power[J]. IEEESystems Journal,2012,2:233-241.
[42] Mardrigal M, Ponnambalam K, Quintana V H. Probabilistic optimal power flow[C]. Proc.IEEE Can. Conf. Electrical and Computer Engineering, Waterloo, Canada1998:385-388.
[43] Li X, Li Y, Zhang S. Analysis of Probabilistic Optimal Power Flow Taking Account of theVariation of Load Power[J]. IEEE Transactions on Power Systems,2008,23(3):992-999.
[44] Schellenberg A, Rosehart W, Aguado J. Cumulant-based probabilistic optimal power flowwith Gaussian and gamma distributions[J]. IEEE Transactions on Power Systems,2005,20(2):773-781.
[45] Saunders C S. Point estimate method addressing correlated wind power for probabilisticoptimal power flow[J]. IEEE Transactions on Power Systems, accepted.
[46]潘炜,刘文颖,杨以涵.概率最优潮流的点估计计算法[J].中国电机工程学报,2008,28(16):28-33.
[47] Su C, Lu C. Two-point estimate method for quantifying transfer capability uncertainty[J].IEEE Transactions on Power Systems,2005,20(2):573-579.
[48] Aien M, Fotuhi-Firuzabad M, Rashidinejad M. Probabilistic Optimal Power Flow inCorrelated Hybrid Wind-Photovoltaic Power Systems[J]. IEEE Transactions on Smart Grid,2014,5(1):130-138.
[49] Li W. Probabilistic transmission system planning[M]. New Jersey: John Wiley&Sons, Inc,2011.
[50] Li W. Risk Assessment Of Power Systems: Models, Methods, and Applications[M]. USA andCanada: IEEE Press and Wiley&Sons,2005.
[51]梁忠民,戴昌军.水文分析计算中两种正态变换方法的比较研究[J].水电能源科学,2005,23(2):1-3.
[52]李文沅.电力系统安全经济运行[M].重庆:重庆大学出版社,1989.
[53] Mitra C S. Composite system reliability evaluation using state space pruning[J], IEEETransactions on power systems,1997,12(1):471-479.
[54] Cunha S H F, Pereira M V F,. Pinto L M V G, Oliveira C. Composite Generation andTransmission Reliability Evaluation in Large Hydroelectric Systems[J]. IEEE Transactions onPower Apparatus and Systems,1985, PAS(104):2657-2663.
[55]宋晓通谭震宇.基于最优抽样与选择性解析的电力系统可靠性评估[J].电力系统自动化,2009,33(5):29-33,60.
[56] Breipohl A, Lee F N, HuangQ J. Sample size reduction in stochastic production simulation[J].IEEE Transactions on Power Systems,1990,5(3):984-992.
[57] Li W, Billinton R. Effect of bus load uncertainty and correlation in composite systemadequacy evaluation[J]. IEEE Trans on Power Systems,1991,6(4):1522-1529.
[58]赵宏伟,任震.计及线路安全约束的机组最优投入[J].电力系统自动化,1997,21(5):41-45.
[59] Ma H, Shahidehpour S. M. Unitcommitment with transmission security and voltageconstraints[J]. IEEE Transactions on Power Systems,1999,14(2):757-764.
[60] Sheble G, Fahd G. Unit commitment literature synopsis[J]. IEEE Transactions on PowerSystems on Power Systems,1994,9(1):128-135.
[61] Jiang R Wang J Zhang M Guan Y. Two-stage minimax regret robust unit commitment[J].IEEE Transactions on Power Systems,2013,28(3):2271-2282.
[62] Bertsimas D, Litvinov E, Sun X A, Zhao J, Zheng T. Adaptive robust optimization for thesecurity constrained unit commitment problem[J]. IEEE Transactions on Power Systems,2013,28(1):52-63.
[63] Papala V S, Erlich I, Rohrig K, Dobschinski J. A stochastic model for the optimal operation ofa wind-thermal power system[J]. IEEE Transactions on Power Systems,2009,24(2):940-950.
[64] Wang Q, Watson J-P, Guan Y. Two-stage robust optimization for N-k contingency-constrainedunit commitment[J]. IEEE Transactions on Power Systems,2013,28(3):2366-2375.
[65] Ozturk U A, Mazumdar M, Norman B A. A solution to the stochastic unit commitmentproblem using chance constrained programming[J].2004,19(3):1589-1598.
[66]赵书强,刘晨亮,王明雨,等.基于机会约束规划的储能日前优化调度[J].电网技术,2013,37(11):3055-3059.
[67]孙元章,吴俊,李国杰,何剑.基于风速预测和随机规划的含风电场电力系统动态经济调度[J].中国电机工程学报,2012,29(4):41-47.
[68]杨洪明,王爽,易德鑫,易俊,刘党峰.考虑多风电场出力相关性的电力系统随机优化调度[J].电力自动化设备,2012,33(1):114-113,120.
[69]于佳,任建文,周明.基于机会约束规划的风-蓄联合动态经济调度[J].电网技术,2013,37(8):2116-2122.
[70] Pozo D, Contreras J. A chance-constrained unit commitment with an n-K security criterionand significant wind generation[J]. IEEE Transactions on Power Systems,2013,28(3):2842-2851.
[71]张宁宁,高山,赵欣.一种考虑风电随机性的机组组合模型及其算法[J].电工技术学报,2013,28(5):22-29.
[72]娄素华,王志磊,吴耀武,侯婷婷.基于机会约束规划的含大规模风电电力系统协调经济调度[J].电工技术学报,2013,28(10):337-345.
[73] Constantinescu M., Victor M, Zavala, Rocklin M. A computational framework for uncertaintyquantification and stochastic optimization in unit commitment with wind power generation[J].IEEE Transactions on Power systems,2011,26(1):431-441.
[74]白杨,汪洋,夏清,孙欣,杨明辉,张建.水-火-风协调优化的全景安全约束经济调度[J].中国电机工程学报,2013,33(13):2-9.
[75] Wu L, Shahidehpour M, Li Z. Comparison of scenario-based and interval optimizationapproaches to stochastic SCUC[J]. IEEE Transactions on Power Systems,2012,27(2):913-921.
[76] Samer T, Birge J R, Long E, A Stochastic Model for the Unit Commitment Problem[J]. IEEETransactions on Power Systems,1996,11(3):1497-1508.
[77] Bouffard F, Galiana F D. Stochastic security for operations planning with significant windpower generation[J]. IEEE Transactions on Power Systems,2008,23(2):306-316.
[78] Liu B. Theory and practice of uncertain programming[M]. Verlag Berlin Heidelberg: Springer,2009.
[79] Birge J R, Louveaux F. Introduction to stochastic programming[M]. Verlag Berlin Heidelberg:Springer,2011.
[80] Parvania M, Fothi-Firuzabad M. Demand response scheduling by stochastic SCUC[J]. IEEETransactions on Smart Grid,2010,1(1):89-98.
[81] Wang Q, Guan Y, Wang J. A chance-constrained two stage stochastic program for unitcommitment with uncertain wind power output[J]. IEEE Transactions on Power Systems,2012,27(1):206-215.
[82]刘德伟,郭剑波,黄越辉,王伟胜.基于风电功率概率预测和运行风险约束的含风电场电力系统动态经济调度[J].中国电机工程学报,2013,33(16):9-15
[83] Box G E P, Cox D R. An analysis of transformations[J]. Journal of the Royal Statistical Society.Series B (Methodological),1964,26(2):211-252.
[84] MATPOWER.[EB/OL].[2012-10-1]. http://www.pserc.cornell.edu/matpower/.ASOS/AWOS data download.[EB/OL].
[2013-12-10]. http://mesonet.agron.iastate.edu/request/download.phtml
[85] Yu J, Yan W, Li W, Chung C Y, Wong K P. An unfixed piecewise optimal reactive power-flowmodel and its algorithm for AC-DC systems[J]. IEEE Transactions on Power Systems,2008,23(2):170-176.
[86] Qin Z, Li W, Xiong X. Generation system reliability evaluation incorporating correlations ofwind speeds with different distributions[J]. IEEE Trans. Power Systems,2013,28(2):551-558.
[87] Qin Z, LI W, Xiong X. Estimating wind speed probabilisty distribution using kernel dnsitymethod[J]. Electric Power Systems Research,81(12):2139-2146.
[88]贾晓峰,颜伟,周家启,余娟,黄正波, David C. Yu.复杂电网的分层解耦潮流算法[J].中国电机工程学报,2010,30(7):56-61.
[89]颜伟,宋林滔,余娟,卢建刚,李钦,张海兵.基于权函数的电网参数分区辨识与估计方法[J].电力系统自动化,2011,35(5):25-30.
[90]阚伟民,张俊杰,顾红柏.国产200MW汽轮机组调峰运行转子热应力场和寿命损耗分析[J].广东电力,1999,12(2):24-27.
[91]张克纯,顾金芳,吕永鑫. AGC负荷变化率对汽轮机寿命的影响[J].华东电力,2003,(7):27-30.
[92]张保衡.大容量火电机组寿命管理与调峰运行[M].北京:水利电力出版社.
[93]张保衡.调峰机组热应力及疲劳寿命[J].中国电机工程学报,1986,6(2):1-13.
[94]余加喜，白雪峰，郭志忠，等．考虑负荷变化率的日发电计划[J]．电力系统自动化，2008，32(18)：39-43.
[95]颜伟，刘方，王官洁，等．辐射型网络潮流的分层前推回代算法[J]．中国电机工程学报，2003，23(8)：76-80．
[96]孙立勇,张焰,蒋传文.基于矩阵实数编码遗传算法求解大规模机组组合问题[J].中国电机工程学报,2006,26(2):82-87.
[97] Park Y M, Won J R, Park J B, et al. Generation expansion planning based on an adevancedevolutionary programming[J]. IEEE Transactions on Power Systems,1999,14(1):299-305.