不确定条件下提高静态电压稳定性的优化方法
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摘要
以最小化静态电压失稳概率为优化目标,基于概率空间中静态电压稳定域边界及其关于控制变量的灵敏度,提出了不确定条件下提高电力系统静态电压稳定性的优化方法。为求得静态电压稳定域边界的显式逼近表达式及其灵敏度,利用参数化非线性规划模型刻画稳定域边界,而后基于广义多项式混沌思想,将随机Galerkin方法与原-对偶内点法相结合予以求解。IEEE-39节点系统算例分析验证了所提优化方法的有效性和精确性。
By minimizing the probability of instability,an optimization approach to enhancing static voltage stability of power system under uncertain conditions was proposed on the basis of the static voltage stability region boundary(SVSRB)and its sensitivity to control variables.To obtain the explicit approximations to the SVSRB and the sensitivities,on the basis of the idea of generalized polynomial chaos(gPC),an approach combining stochastic Galerkin method and primal-dual interior point method was introduced.Case study in IEEE 39-bus system verified the validity and accuracy of the proposed optimization approach.
By minimizing the probability of instability,an optimization approach to enhancing static voltage stability of power system under uncertain conditions was proposed on the basis of the static voltage stability region boundary(SVSRB)and its sensitivity to control variables.To obtain the explicit approximations to the SVSRB and the sensitivities,on the basis of the idea of generalized polynomial chaos(gPC),an approach combining stochastic Galerkin method and primal-dual interior point method was introduced.Case study in IEEE 39-bus system verified the validity and accuracy of the proposed optimization approach.
引文
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[2]GAUTAM D,VITTAL V,HARBOUR T.Impact of increased penetration of DFIG-based wind turbine generators on transient and small signal stability of power systems[J].IEEE Transactions on Power Systems,2009,24(3):1426-1434.
[3]张谦,唐飞,刘涤尘,等.计及电动汽车充电和负荷波动极限的电力系统静态电压稳定性评估方案[J].电网技术,2017,41(6):1888-1895.ZHANG Q,TANG F,LIU D C,et al.A static voltage stability assessment scheme of electric power systems considering charging state of plug-in electric vehicles and load fluctuation limits[J].Power System Technology,2017,41(6):1888-1895.
[4]李生虎,丁明,汪兴强.电力系统静态电压安全问题的概率评价[J].电力系统自动化,2003,27(20):26-30.LI S H,DING M,WANG X Q.Probabilistic evaluation to static voltage security of power systems[J].Autormation of Electric Power Systems,2003,27(20):26-30.
[5]HAESEN E,BASTIAENSEN C,DRIESEN J,et al.A probabilistic formulation of load margins in power systems with stochastic generation[J].IEEE Transactions on Power Systems,2009,24(2):951-958.
[6]赵建伟,李禹鹏,杨增辉,等.基于拟蒙特卡罗模拟和核密度估计的概率静态电压稳定计算方法[J].电网技术,2016,40(12):3833-3839.ZHAO J W,LI Y P,YANG Z H,et al.Probabilistic static voltage stability calculation based on quasi-Monte Carlo and kernel density estimation[J].Power System Technology,,2016,40(12):3833-3839.
[7]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.YU Y X.Review of study on methodology of security regions of power system[J].Journal of Tianjin University,2008,41(6):635-646.
[8]刘文颖,徐鹏,赵子兰,等.基于区间估计的风电出力多场景下静态电压安全域研究[J].电工技术学报,2015,30(3):172-178.LIU W Y,XU P,ZHANG Z L,et al.A research of static voltage stability region in wind power scenario based on interval estimation[J].Transactions of China Electrotechnical Society,2015,30(3):172-178.
[9]QIU Y,WU H,ZHOU Y,et al.Global parametric polynomial approximation of static voltage stability region boundaries[J].IEEE Transactions on Power Systems,2017,32(3):2362-2371.
[10]QIU Y,WU H,SONG Y,et al.Global approximation of static voltage stability region boundaries considering generator reactive power limits[J].IEEE Transactions on Power Systems,2018,33(5):5682-5691.
[11]吴浩,邱一苇,何哲楠,等.基于Mathematica的电力系统分析和仿真工具包[EB/OL].[2017-12-07].http://www.sgool.cn/mastes/home.html.
[12]CUTSEM T V,VOURNAS C.Voltage stability of electric power systems[M].Berlin,Heidelberg:Springer Science&Business Media,1998.
[13]孙明,吴浩,邱一苇,等.基于广义多项式混沌法的含风电电力系统随机潮流[J].电力系统自动化,2017,41(7):54-60.SUN M,WU H,QIU Y W,et al.Probabilistic load flow for wind power integrated system based on generalized polynomial chaos methods[J].Automation of Electric Power Systems,2017,41(7):54-60.
[14]孙鑫,陈金富,段献忠,等.计及高维随机变量的随机响应面法概率潮流计算[J].中国电机工程学报,2018,38(9):2551-2560.SUN X,CHEN J F,DUAN X Z,et al.Probabilistic load flow calculation based on stochastic response surface method considering high-dimension stochastic variables[J].Proceeding of the CSEE,2018,38(9):2551-2560.
[15]IRISARRI G D,WANG X,TONG J,et al.Maximum loadability of power systems using interior point nonlinear optimization method[J].IEEE Transactions on Power Systems,1997,12(1):162-172.
[16]WU H,ZHOU Y,DONG S,et al.Probabilistic load flow based on generalized polynomial chaos[J].IEEE Transactions on Power Systems,2017,32(1):820-821.
[17]XIU D.Numerical methods for stochastic computations:a spectral method approach[M].New Jersey:Princeton University Press,2010.