面向高精度状态感知的配电系统微型同步相量测量单元优化配置
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摘要
可再生能源、电动汽车等大量无序接入使得配电系统运行在越来越复杂和不确定的工况中,迫切需要高精度实时状态感知以实现弹性提升,然而现有的配电量测系统远不能满足新一代配电系统对网络状态进行实时感知的要求。为此,提出了一种面向高精度状态感知的配电系统微型同步相量测量单元(micro-phasor measurement units,μPMU)优化配置方法。首先,在高级量测体系(advancedmeasurement infrastructure,AMI)满足网络可观测的基础上,以状态估计均方误差最小为目标,以任意一致的系统运行状态作为参数代入状态估计误差协方差矩阵,建立了μPMU优化配置模型;其次,通过对增益矩阵进行Cholesky分解,将目标函数采用决策变量显式表达出来,从而可采用成熟的商业求解器快速获得高质量的可行解;最后,采用IEEE33节点和69节点配电系统进行测试,验证了所提方法的有效性。
Integration of large amount of distributed energy and electric vehicles makes modern distribution systems operate under more and more complicated conditions, resulting in urgent need of highly accurate real-time perception for resilience enhancement. However, measurement infrastructure nowadays is still far from meeting real-time state perception requirement. This paper proposes a novel method for placement of micro-phasor measurement units(μPMUs) in distribution systems for highly accurate state perception. Firstly, the μPMU placement problem is formulated by minimizing the mean squared error of distribution system state estimation while randomly selecting one operating point to extract parameters of covariance matrix of state estimation errors. Then objective function is expressed explicitly with decision variables by executing Cholesky decomposition on gain matrix. Therefore, commercial solvers can be adopted to obtain high quality feasible solutions in an efficient manner. Finally, IEEE 33 and 69 bus distribution systems are used to validate effectiveness of the proposed method.
Integration of large amount of distributed energy and electric vehicles makes modern distribution systems operate under more and more complicated conditions, resulting in urgent need of highly accurate real-time perception for resilience enhancement. However, measurement infrastructure nowadays is still far from meeting real-time state perception requirement. This paper proposes a novel method for placement of micro-phasor measurement units(μPMUs) in distribution systems for highly accurate state perception. Firstly, the μPMU placement problem is formulated by minimizing the mean squared error of distribution system state estimation while randomly selecting one operating point to extract parameters of covariance matrix of state estimation errors. Then objective function is expressed explicitly with decision variables by executing Cholesky decomposition on gain matrix. Therefore, commercial solvers can be adopted to obtain high quality feasible solutions in an efficient manner. Finally, IEEE 33 and 69 bus distribution systems are used to validate effectiveness of the proposed method.
引文
[1]别朝红,林雁翎,邱爱慈.弹性电网及其恢复力的基本概念与研究展望[J].电力系统自动化,2015,39(22):1-9.Bie Zhaohong,Lin Yanling,Qiu Aici.Concept and research prospects of power system resilience[J].Automation of Electric Power Systems,2015,39(22):1-9(in Chinese).
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[3]吴在军,徐俊俊,余星火,等.主动配电网状态估计技术评述[J].电力系统自动化,2017,41(13):182-191.Wu Zaijun,Xu Junjun,Yu Xinghuo,et al.Review on state estimation technique of active distribution network[J].Automation of Electric Power Systems,2017,41(13):182-191(in Chinese).
[4]林佳颖,栾文鹏,余贻鑫,等.AMI量测用于配电网在线状态估计的可信度建模及分析[J].电网技术,2018,42(4):1191-1199.Lin Jiaying,Luan Wenpeng,Yu Yixin,et al.Credibility modelling and analysis of AMI measurements for on-line distribution state estimation[J].Power System Technology,2018,42(4):1191-1199(in Chinese).
[5]徐臣,余贻鑫.提高配电网状态估计精度的量测配置优化方法[J].电力自动化设备,2009,29(7):17-21.Xu Chen,Yu Yixin.Evaluation and optimization of meter placement to enhance distribution state estimation[J].Electric Power Automation Equipment,2009,29(7):17-21(in Chinese).
[6]Xiang Y,Ribeiro P F,Cobben J F G.Optimization of state-estimator-based operation framework including measurement placement for medium voltage distribution grid[J].IEEE Transactions on Smart Grid,2014,5(6):2929-2937.
[7]Pegoraro P A,Sulis S.Robustness-oriented meter placement for distribution system state estimation in presence of network parameter uncertainty[J].IEEE Transactions on Instrumentation and Measurement,2013,62(5):954-962.
[8]王红,张文,冯宗英.计及故障重构的配电网量测系统鲁棒性配置[J].电力系统自动化,2016,40(16):98-104.Wang Hong,Zhang Wen,Feng Zongying.Robust measurement placement method for distribution systems considering fault reconfiguration[J].Automation of Electric Power Systems,2016,40(16),98-104(in Chinese).
[9]王红,张文,刘玉田.考虑分布式电源出力不确定性的主动配电网量测配置[J].电力系统自动化,2016,40(12):9-14.Wang Hong,Zhang Wen,Liu Yutian.Measurement placement in active distribution networks considering output uncertainty of distributed generators[J].Automation of Electric Power Systems,2016,40(12):9-14(in Chinese).
[10]徐俊俊,戴桂木,吴在军,等.计及电动汽车和光伏不确定性的主动配电网量测优化配置[J].电力系统自动化,2017,41(1):57-64.Xu Junjun,Dai Guimu,Wu Zaijun,et al.Optimal meter placement for active distribution network considering uncertainties of plug-in electric vehicles and photovoltaic systems[J].Automation of Electric Power Systems,2017,41(1):57-64(in Chinese).
[11]徐航,鞠力,董树锋,等.提高配电网状态估计精度的智能配电单元优化布点方法[J].电网技术,2018,42(4):1210-1216.Xu Hang,Ju Li,Dong Shufeng,et al.Optimization of intelligent distribution unit placement to improve accuracy of distribution network state estimation[J].Power System Technology,2018,42(4):1210-1216(in Chinese).
[12]Singh R,Pal B C,Vinter R B.Measurement placement in distribution system state estimation[J].IEEE Transactions on Power Systems,2009,24(2):668-675.
[13]Singh R,Pal B C,Jabr R A,et al.Meter placement for distribution system state estimation:an ordinal optimization approach[J].IEEETransactions on Power Systems,2011,26(4):2328-2335.
[14]Liu J,Ponci F,Monti A,et al.Optimal meter placement for robust measurement systems in active distribution grids[J].IEEETransactions on Instrumentation and Measurement,2014,63(5):1096-1105.
[15]Damavandi M G,Krishnamurthy V,MartíJ R.Robust meter placement for state estimation in active distribution systems[J].IEEETransactions on Smart Grid,2015,6(4):1972-1982.
[16]Chen X,Lin J,Wan C,et al.Optimal meter placement for distribution network state estimation:A circuit representation based MILPapproach[J].IEEE Transactions on Power Systems,2016,31(6):4357-4370.
[17]Xygkis T C,Korres G N,Manousakis N M.Fisher information-based meter placement in distribution grids via the D-optimal experimental design[J].IEEE Transactions on Smart Grid,2018,9(2):1452-1461.
[18]Kekatos V,Giannakis G B,Wollenberg B.Optimal placement of phasor measurement units via convex relaxation[J].IEEE Transactions on power systems,2012,27(3):1521-1530.
[19]Li Q,Cui T,Weng Y,et al.An information-theoretic approach to PMU placement in electric power systems[J].IEEE Transactions on Smart Grid,2012,4(1):446-456.
[20]张恒旭,靳宗帅,刘玉田.轻型广域测量系统及其在中国的应用[J].电力系统自动化,2014,38(22):85-90.Zhang Hengxu,Jin Zongshuai,Liu Yutian.Wide-area measurement system light and its application in China[J].Automation of Electric Power Systems,2014,38(22):85-90(in Chinese).
[21]王宾,孙华东,张道农.配电网信息共享与同步相量测量应用技术评述[J].中国电机工程学报,2015,35(S1):1-7.Wang Bin,Sun Huadong,Zhang Daonong.Review on data sharing and synchronized phasor measurement technique with application in distribution systems[J].Proceedings of the CSEE,2015,35(S1):1-7(in Chinese).
[22]严正,孔祥瑞,徐潇源,等.微型同步相量测量单元在智能配电网运行状态估计中的应用[J].上海交通大学学报(自然版),2018,52(10):1195-1205.Yan Zheng,Kong Xiangrui,Xu Xiaoyuan,et al.Applications of micro synchronous phasor measurement units in state estimation of smart distribution network[J].Journal of Shanghai Jiaotong University(Science),2018,52(10),1195-1205(in Chinese).
[23]Liu J,Tang J,Ferdinanda P,et al.Trade-offs in PMU deployment for state estimation in active distribution grids[J].IEEE Transactions on Smart Grid,2012,3(2):915-924.
[24]王澍,严正,孔祥瑞,等.主动配电网多目标PMU最优配置[J].电网技术,2019,43(3):833-840.Wang Shu,Yan Zheng,Kong Xiangrui,et al.Multi-objective optimal placement of PMU in active distribution network[J].Power System Technology,2019,43(3):833-840(in Chinese).
[25]于尔铿.电力系统状态估计[M].北京:水利电力出版社,1985.
[26]Joshi S,Boyd S.Sensor selection via convex optimization[J].IEEETransactions on Signal Processing,2009,57(2):451-462.
[27]Zhu J,Abur A.Effect of phasor measurements on the choice of reference bus for state estimation[C]//2007 IEEE Power Engineering Society General Meeting(PESGM).Tampa,FL,USA:IEEE,2007:1-5.
[28]Press W H,et al.Numerical recipes in C++(2nd Edition)[M].Cambridge,UK:Cambridge University Press,1992.
[29]Benoist T,Estellon B,Gardi F,et al.Localsolver 1.x:a black-box local-search solver for 0-1 programming[J].4OR:A Quarterly Journal of Operations Research,2011,9(3):299-316.
[30]Wang S,Liang D,Ge L,et al.Analytical FRTU deployment approach for reliability improvement of integrated cyber-physical distribution systems[J].IET Generation,Transmission&Distribution,2016,10(11):2631-2639.
[31]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.
[32]Das D.Optimal placement of capacitors in radial distribution system using a Fuzzy-GA method[J].International Journal of Electrical Power&Energy Systems,2008,30(6-7):361-367.
[2]王守相,梁栋,葛磊蛟.智能配电网态势感知和态势利导关键技术[J].电力系统自动化,2016,40(12):2-8.Wang Shouxiang,Liang Dong,Ge Leijiao.Key technologies of situation awareness and orientation for smart distribution systems[J].Automation of Electric Power Systems,2016,40(12):2-8(in Chinese).
[3]吴在军,徐俊俊,余星火,等.主动配电网状态估计技术评述[J].电力系统自动化,2017,41(13):182-191.Wu Zaijun,Xu Junjun,Yu Xinghuo,et al.Review on state estimation technique of active distribution network[J].Automation of Electric Power Systems,2017,41(13):182-191(in Chinese).
[4]林佳颖,栾文鹏,余贻鑫,等.AMI量测用于配电网在线状态估计的可信度建模及分析[J].电网技术,2018,42(4):1191-1199.Lin Jiaying,Luan Wenpeng,Yu Yixin,et al.Credibility modelling and analysis of AMI measurements for on-line distribution state estimation[J].Power System Technology,2018,42(4):1191-1199(in Chinese).
[5]徐臣,余贻鑫.提高配电网状态估计精度的量测配置优化方法[J].电力自动化设备,2009,29(7):17-21.Xu Chen,Yu Yixin.Evaluation and optimization of meter placement to enhance distribution state estimation[J].Electric Power Automation Equipment,2009,29(7):17-21(in Chinese).
[6]Xiang Y,Ribeiro P F,Cobben J F G.Optimization of state-estimator-based operation framework including measurement placement for medium voltage distribution grid[J].IEEE Transactions on Smart Grid,2014,5(6):2929-2937.
[7]Pegoraro P A,Sulis S.Robustness-oriented meter placement for distribution system state estimation in presence of network parameter uncertainty[J].IEEE Transactions on Instrumentation and Measurement,2013,62(5):954-962.
[8]王红,张文,冯宗英.计及故障重构的配电网量测系统鲁棒性配置[J].电力系统自动化,2016,40(16):98-104.Wang Hong,Zhang Wen,Feng Zongying.Robust measurement placement method for distribution systems considering fault reconfiguration[J].Automation of Electric Power Systems,2016,40(16),98-104(in Chinese).
[9]王红,张文,刘玉田.考虑分布式电源出力不确定性的主动配电网量测配置[J].电力系统自动化,2016,40(12):9-14.Wang Hong,Zhang Wen,Liu Yutian.Measurement placement in active distribution networks considering output uncertainty of distributed generators[J].Automation of Electric Power Systems,2016,40(12):9-14(in Chinese).
[10]徐俊俊,戴桂木,吴在军,等.计及电动汽车和光伏不确定性的主动配电网量测优化配置[J].电力系统自动化,2017,41(1):57-64.Xu Junjun,Dai Guimu,Wu Zaijun,et al.Optimal meter placement for active distribution network considering uncertainties of plug-in electric vehicles and photovoltaic systems[J].Automation of Electric Power Systems,2017,41(1):57-64(in Chinese).
[11]徐航,鞠力,董树锋,等.提高配电网状态估计精度的智能配电单元优化布点方法[J].电网技术,2018,42(4):1210-1216.Xu Hang,Ju Li,Dong Shufeng,et al.Optimization of intelligent distribution unit placement to improve accuracy of distribution network state estimation[J].Power System Technology,2018,42(4):1210-1216(in Chinese).
[12]Singh R,Pal B C,Vinter R B.Measurement placement in distribution system state estimation[J].IEEE Transactions on Power Systems,2009,24(2):668-675.
[13]Singh R,Pal B C,Jabr R A,et al.Meter placement for distribution system state estimation:an ordinal optimization approach[J].IEEETransactions on Power Systems,2011,26(4):2328-2335.
[14]Liu J,Ponci F,Monti A,et al.Optimal meter placement for robust measurement systems in active distribution grids[J].IEEETransactions on Instrumentation and Measurement,2014,63(5):1096-1105.
[15]Damavandi M G,Krishnamurthy V,MartíJ R.Robust meter placement for state estimation in active distribution systems[J].IEEETransactions on Smart Grid,2015,6(4):1972-1982.
[16]Chen X,Lin J,Wan C,et al.Optimal meter placement for distribution network state estimation:A circuit representation based MILPapproach[J].IEEE Transactions on Power Systems,2016,31(6):4357-4370.
[17]Xygkis T C,Korres G N,Manousakis N M.Fisher information-based meter placement in distribution grids via the D-optimal experimental design[J].IEEE Transactions on Smart Grid,2018,9(2):1452-1461.
[18]Kekatos V,Giannakis G B,Wollenberg B.Optimal placement of phasor measurement units via convex relaxation[J].IEEE Transactions on power systems,2012,27(3):1521-1530.
[19]Li Q,Cui T,Weng Y,et al.An information-theoretic approach to PMU placement in electric power systems[J].IEEE Transactions on Smart Grid,2012,4(1):446-456.
[20]张恒旭,靳宗帅,刘玉田.轻型广域测量系统及其在中国的应用[J].电力系统自动化,2014,38(22):85-90.Zhang Hengxu,Jin Zongshuai,Liu Yutian.Wide-area measurement system light and its application in China[J].Automation of Electric Power Systems,2014,38(22):85-90(in Chinese).
[21]王宾,孙华东,张道农.配电网信息共享与同步相量测量应用技术评述[J].中国电机工程学报,2015,35(S1):1-7.Wang Bin,Sun Huadong,Zhang Daonong.Review on data sharing and synchronized phasor measurement technique with application in distribution systems[J].Proceedings of the CSEE,2015,35(S1):1-7(in Chinese).
[22]严正,孔祥瑞,徐潇源,等.微型同步相量测量单元在智能配电网运行状态估计中的应用[J].上海交通大学学报(自然版),2018,52(10):1195-1205.Yan Zheng,Kong Xiangrui,Xu Xiaoyuan,et al.Applications of micro synchronous phasor measurement units in state estimation of smart distribution network[J].Journal of Shanghai Jiaotong University(Science),2018,52(10),1195-1205(in Chinese).
[23]Liu J,Tang J,Ferdinanda P,et al.Trade-offs in PMU deployment for state estimation in active distribution grids[J].IEEE Transactions on Smart Grid,2012,3(2):915-924.
[24]王澍,严正,孔祥瑞,等.主动配电网多目标PMU最优配置[J].电网技术,2019,43(3):833-840.Wang Shu,Yan Zheng,Kong Xiangrui,et al.Multi-objective optimal placement of PMU in active distribution network[J].Power System Technology,2019,43(3):833-840(in Chinese).
[25]于尔铿.电力系统状态估计[M].北京:水利电力出版社,1985.
[26]Joshi S,Boyd S.Sensor selection via convex optimization[J].IEEETransactions on Signal Processing,2009,57(2):451-462.
[27]Zhu J,Abur A.Effect of phasor measurements on the choice of reference bus for state estimation[C]//2007 IEEE Power Engineering Society General Meeting(PESGM).Tampa,FL,USA:IEEE,2007:1-5.
[28]Press W H,et al.Numerical recipes in C++(2nd Edition)[M].Cambridge,UK:Cambridge University Press,1992.
[29]Benoist T,Estellon B,Gardi F,et al.Localsolver 1.x:a black-box local-search solver for 0-1 programming[J].4OR:A Quarterly Journal of Operations Research,2011,9(3):299-316.
[30]Wang S,Liang D,Ge L,et al.Analytical FRTU deployment approach for reliability improvement of integrated cyber-physical distribution systems[J].IET Generation,Transmission&Distribution,2016,10(11):2631-2639.
[31]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.
[32]Das D.Optimal placement of capacitors in radial distribution system using a Fuzzy-GA method[J].International Journal of Electrical Power&Energy Systems,2008,30(6-7):361-367.