含潮流路由器的配电网最优潮流计算
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摘要
为解决配电网控制分散、控制元件可调范围小等问题,将潮流路由器(Power Flow Router, PFR)应用于配电网。提出了一种适用于配电网的含潮流路由器的改进支路潮流模型,并基于此建立了含PFR的配电网最优潮流模型。对模型进行二阶锥松弛,并采用Gurobi等商用算法包对松弛后的模型进行求解。为考虑负荷和分布式电源出力的不确定性,提出了一种拉丁超立方抽样和二阶锥规划相结合的概率最优潮流求解方法。采用修订的IEEE33节点系统验证了所提方法的有效性。
In order to solve the problem of limited control range of control elements and scattered control pattern of distribution networks, Power Flow Router(PFR) is applied in distribution networks. An improved branch flow model with power flow routers in distribution networks is proposed and an optimal power flow model including PFR is constructed. Second-order cone relaxation is used to relax the model and the relaxed model is solved by using the commercial algorithm package such as Gurobi. Furthermore, a method, which considers the uncertainty of load and distributed generation's output, is presented based on the combination of Latin hypercube sampling and second-order cone programming. The revised IEEE 33-bus system verifies the effectiveness of the proposed method.
In order to solve the problem of limited control range of control elements and scattered control pattern of distribution networks, Power Flow Router(PFR) is applied in distribution networks. An improved branch flow model with power flow routers in distribution networks is proposed and an optimal power flow model including PFR is constructed. Second-order cone relaxation is used to relax the model and the relaxed model is solved by using the commercial algorithm package such as Gurobi. Furthermore, a method, which considers the uncertainty of load and distributed generation's output, is presented based on the combination of Latin hypercube sampling and second-order cone programming. The revised IEEE 33-bus system verifies the effectiveness of the proposed method.
引文
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[10]高红均,刘俊勇,沈晓东,等.主动配电网最优潮流研究及其应用实例[J].中国电机工程学报,2017,37(6):1634-1644.GAO Hongjun,LIU Junyong,SHEN Xiaodong,et al.Optimal power flow research in active distribution network and its application examples[J].Proceedings of the CSEE,2017,37(6):1634-1644.
[11]韩禹歆,陈来军,王召健,等.基于自适应步长ADMM的直流配电网分布式最优潮流[J].电工技术学报,2017,32(11):26-37.HAN Yuxin,CHEN Laijun,WANG Zhaojian,et al.Distributed optimal power flow in direct current distribution network based on alternative direction method of multipliers with dynamic step size[J].Transactions of China Electrotechnical Society,2017,32(11):26-37.
[12]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):10-14.DING Ming,LI Shenghu,HUANG Kai.Probabilistic load flow analysis based on Monte-Carlo simulation[J].Power System Technology,2001,25(11):10-14.
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[14]ZOU Bin,XIAO Qing.Solving probabilistic optimal power flow problem using quasi Monte Carlo method and ninth-order polynomial normal transformation[J].IEEETransactions on Power Systems,2014,29(1):300-307.
[15]潘炜,刘文颖,杨以涵.概率最优潮流的点估计算法[J].中国电机工程学报,2008,28(16):28-33.PAN Wei,LIU Wenying,YANG Yihan.Point estimate method for probabilistically optimal power flow computation[J].Proceedings of the CSEE,2008,28(16):28-33.
[16]代景龙,白晓清,鲍海波.考虑源荷不确定性的概率最优潮流[J].现代电力,2016,33(1):34-40.DAI Jinglong,BAI Xiaoqing,BAO Haibo.Probabilistic optimal power flow by considering the uncertainty of source and demand side[J].Modern Electric Power,2016,33(1):34-40.
[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,2009,33(21):32-35.YU Han,ZHONG Zhiyong,HUANG Jiebo,et al.Digital substation communication network simulation based on epochs[J].Automation of Electric Power Systems,2009,33(21):32-35.
[18]CHEN H,IYER A,HARLE Y R,et al.Dynamic grid power routing using controllable network transformers(CNT)with decoupled closed-loop controller[J].IEEETransactions on Industry Applications,2015,51(3):2361-2372.
[19]NGUYEN P,KLING W,RIBEIRO P.Smart power router:a flexible agent-based converter interface in active distribution networks[J].IEEE Transactions on Smart Grid,2011,2(3):487-495.
[20]SáNCHEZ-SQUELLA A,ORTEGA R,GRI?O R,et al.Dynamic energy router[J].IEEE Control System,2010,30(6):72-80.
[21]LIN J,LI V O K,LEUNG K C,et al.Optimal power flow with power flow routers[J].IEEE Transactions on Power Systems,2017,33(1):531-543.
[22]BARAN M E,WU F F.Network reconfiguration in distribution systems for loss reduction and load balancing[J].IEEE Transactions on Power Delivery,1989,4(2):1401-1407.
[23]GAN Lingwen,LI Na,TOPCU U,et al.Exact convex relaxation of optimal power flow in radial networks[J].IEEE Transactions on Automatic Control,2015,60(1):72-87.
[24]ABDELOUADOUD S Y,GIRARD R,NEIRAC F P,et al.Optimal power flow of a distribution system based on increasingly tight cutting planes added to a second order cone relaxation[J].International Journal of Electrical Power&Energy Systems,2015,69:9-17.
[2]张昕,张勇,钱伟杰,等.基于简化零空间内点法VSC-HVDC离散化最优潮流的研究[J].电力系统保护与控制,2017,45(18):15-23.ZHANG Xin,ZHANG Yong,QIAN Weijie,et al.Research on the optimal power flow of VSC-HVDC based on the simplified null space interior point method[J].Power System Protection and Control,2017,45(18):15-23.
[3]马玲,于青,刘刚,等.基于量子差分进化算法的电力系统无功优化[J].电力系统保护与控制,2013,41(17):39-43.MA Ling,YU Qing,LIU Gang,et al.Power system reactive power optimization based on quantum DEalgorithm[J].Power System Protection and Control,2013,41(17):39-43.
[4]蔡博,黄少锋.基于多目标粒子群算法的高维多目标无功优化[J].电力系统保护与控制,2017,45(15):77-84.CAI Bo,HUANG Shaofeng.Multi-objective reactive power optimization based on the multi-objective partial swarm optimization algorithm[J].Power System Protection and Control,2017,45(15):77-84.
[5]汤晓青,刘辉,范宇,等.基于改进多目标遗传算法的实时发电市场优化调度研究[J].电力系统保护与控制,2017,45(17):65-71.TANG Xiaoqing,LIU Hui,FAN Yu,et al.Analysis of the optimal dispatch in real-time generation market using an improved multi-objective genetic algorithm[J].Power System Protection and Control,2017,45(17):65-71.
[6]何天雨,卫志农,孙国强,等.基于网损等值负荷模型的改进直流最优潮流算法[J].电力系统自动化,2016,40(6):58-64.HE Tianyu,WEI Zhinong,SUN Guoqiang,et al.Modified direct current optimal power flow algorithm based on net loss equivalent load model[J].Automation of Electric Power Systems,2016,40(6):58-64.
[7]FARIVAR M,LOW S H.Branch flow model:relaxations and convexification-part I[J].IEEE Transactions on Power Systems,2013,28(3):2554-2564.
[8]LOW S H.Convex relaxation of optimal power flow-part I:formulations and equivalence[J].IEEE Transactions on Control of Network Systems,2014,1(1):15-27.
[9]刘斌,刘锋,梅生伟,等.基于二阶锥优化的含有载调压变压器主动配电网最优潮流[J].电力系统自动化,2015,39(19):40-47.LIU Bin,LIU Feng,MEI Shengwei,et al.Optimal power flow in active distribution networks with on-load tap changer based on second-order cone programming[J].Automation of Electric Power Systems,2015,39(19):40-47.
[10]高红均,刘俊勇,沈晓东,等.主动配电网最优潮流研究及其应用实例[J].中国电机工程学报,2017,37(6):1634-1644.GAO Hongjun,LIU Junyong,SHEN Xiaodong,et al.Optimal power flow research in active distribution network and its application examples[J].Proceedings of the CSEE,2017,37(6):1634-1644.
[11]韩禹歆,陈来军,王召健,等.基于自适应步长ADMM的直流配电网分布式最优潮流[J].电工技术学报,2017,32(11):26-37.HAN Yuxin,CHEN Laijun,WANG Zhaojian,et al.Distributed optimal power flow in direct current distribution network based on alternative direction method of multipliers with dynamic step size[J].Transactions of China Electrotechnical Society,2017,32(11):26-37.
[12]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):10-14.DING Ming,LI Shenghu,HUANG Kai.Probabilistic load flow analysis based on Monte-Carlo simulation[J].Power System Technology,2001,25(11):10-14.
[13]MORALES J M,PEREZ-RUIZ J.Point estimate schemes to solve the probabilistic power flow[J].IEEE Transactions on Power Systems,2007,22(4):1594-1601.
[14]ZOU Bin,XIAO Qing.Solving probabilistic optimal power flow problem using quasi Monte Carlo method and ninth-order polynomial normal transformation[J].IEEETransactions on Power Systems,2014,29(1):300-307.
[15]潘炜,刘文颖,杨以涵.概率最优潮流的点估计算法[J].中国电机工程学报,2008,28(16):28-33.PAN Wei,LIU Wenying,YANG Yihan.Point estimate method for probabilistically optimal power flow computation[J].Proceedings of the CSEE,2008,28(16):28-33.
[16]代景龙,白晓清,鲍海波.考虑源荷不确定性的概率最优潮流[J].现代电力,2016,33(1):34-40.DAI Jinglong,BAI Xiaoqing,BAO Haibo.Probabilistic optimal power flow by considering the uncertainty of source and demand side[J].Modern Electric Power,2016,33(1):34-40.
[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,2009,33(21):32-35.YU Han,ZHONG Zhiyong,HUANG Jiebo,et al.Digital substation communication network simulation based on epochs[J].Automation of Electric Power Systems,2009,33(21):32-35.
[18]CHEN H,IYER A,HARLE Y R,et al.Dynamic grid power routing using controllable network transformers(CNT)with decoupled closed-loop controller[J].IEEETransactions on Industry Applications,2015,51(3):2361-2372.
[19]NGUYEN P,KLING W,RIBEIRO P.Smart power router:a flexible agent-based converter interface in active distribution networks[J].IEEE Transactions on Smart Grid,2011,2(3):487-495.
[20]SáNCHEZ-SQUELLA A,ORTEGA R,GRI?O R,et al.Dynamic energy router[J].IEEE Control System,2010,30(6):72-80.
[21]LIN J,LI V O K,LEUNG K C,et al.Optimal power flow with power flow routers[J].IEEE Transactions on Power Systems,2017,33(1):531-543.
[22]BARAN M E,WU F F.Network reconfiguration in distribution systems for loss reduction and load balancing[J].IEEE Transactions on Power Delivery,1989,4(2):1401-1407.
[23]GAN Lingwen,LI Na,TOPCU U,et al.Exact convex relaxation of optimal power flow in radial networks[J].IEEE Transactions on Automatic Control,2015,60(1):72-87.
[24]ABDELOUADOUD S Y,GIRARD R,NEIRAC F P,et al.Optimal power flow of a distribution system based on increasingly tight cutting planes added to a second order cone relaxation[J].International Journal of Electrical Power&Energy Systems,2015,69:9-17.