极坐标系下主动配电网三相线性潮流计算方法
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摘要
线性潮流计算方法可以提高主动配电网集中优化控制的鲁棒性和快速性。随着分布式电源在主动配电网中的广泛接入,配电网中的电压控制节点逐步增多,以保持正常的电压水平。现有直角坐标系下三相线性潮流无法处理本地压控节点,现有极坐标下的线性潮流模型未能详尽考虑分布式电源控制特性、网损分摊特性与配电网三相特点。因此提出三相极坐标系下的线性潮流计算方法来解决这个问题。所提方法考虑了Y或Delta型连接ZIP负荷、单相或三相分布式电源(Distributed Generators, DGs)等类型。同时考虑了DGs的详细控制模型和分布式松弛母线模型。最后通过三相不平衡的IEEE 13,34,37和123节点系统验证所提方法的精度和对各种节点类型的适应性。
The linear power flow calculation method can improve the robustness and rapidity of the centralized optimization control of active distribution network. With the wide access of distributed generation in active distribution network, voltage control nodes in distribution network gradually increase to maintain normal voltage level. Existing three-phase linear power flow under a rectangular coordinate system cannot cope with local voltage control nodes, the existing linear power flow model under the polar coordinate system failed to consider detailed control characteristics of DGs, network loss allocation and three-phase characteristics of distribution network. Therefore, this paper proposes a linear power flow calculation method in the three-phase polar coordinate system to solve the problem. The proposed method considers the types of Y-connection ZIP load, Delta-connection ZIP load and single-phase or three-phase Distributed Generators(DGs), etc. DGs detailed control model and distributed slack bus model are also considered. Finally, the proposed method's accuracy and adaptability of various node types are verified by the three-phase unbalanced IEEE 13, 34, 37 and 123 nodes system.
The linear power flow calculation method can improve the robustness and rapidity of the centralized optimization control of active distribution network. With the wide access of distributed generation in active distribution network, voltage control nodes in distribution network gradually increase to maintain normal voltage level. Existing three-phase linear power flow under a rectangular coordinate system cannot cope with local voltage control nodes, the existing linear power flow model under the polar coordinate system failed to consider detailed control characteristics of DGs, network loss allocation and three-phase characteristics of distribution network. Therefore, this paper proposes a linear power flow calculation method in the three-phase polar coordinate system to solve the problem. The proposed method considers the types of Y-connection ZIP load, Delta-connection ZIP load and single-phase or three-phase Distributed Generators(DGs), etc. DGs detailed control model and distributed slack bus model are also considered. Finally, the proposed method's accuracy and adaptability of various node types are verified by the three-phase unbalanced IEEE 13, 34, 37 and 123 nodes system.
引文
[1]STOTT B,JARDIM J,ALSAC O.DC power flow revisited[J].IEEE Transactions on Power Systems,2009,24(3):1290-1300.
[2]DING T,BO R,LI F,et al.Interval power flow analysis using linear relaxation and optimality-based bounds tightening(OBBT)methods[J].IEEE Transactions on Power Systems,2014,30(1):177-188.
[3]韩笑,周明,李庚银.基于无迹变换随机潮流建模的主动配电网优化调度[J].电力系统保护与控制,2018,46(3):9-17.HAN Xiao,ZHOU Ming,LI Gengyin.Stochastic optimal dispatching of active distribution networks based on stochastic power flow modeling using unscented transformation[J].Power System Protection and Control,2018,46(3):9-17.
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[10]WU W C,ZHANG B M.A three-phase power flow algorithm for distribution system power flow based on loop-analysis method[J].International Journal of Electrical Power&Energy Systems,2008,30(1):8-15.
[11]CHEN T H,YANG N C.Loop frame of reference based three-phase power flow for unbalanced radial distribution systems[J].Electric Power Systems Research,2010,80(7):799-806.
[12]GARCIA P A N,PEREIRA J L R,CARNEIRO S,et al.Three-phase power flow calculations using the current injection method[J].IEEE Transactions on Power Systems,2000,15(2):508-514.
[13]MARTíJ R,AHMADI H,BASHUALDO L.Linear power-flow formulation based on a voltage-dependent load model[J].IEEE Transactions on Power Delivery,2013,28(3):1682-1690.
[14]GAN L,LOW S H.Convex relaxations and linear approximation for optimal power flow in multiphase radial networks[C]//Power Systems Computation Conference,August 18-22,2014,Wroclaw,Poland:1-9.
[15]DHOPLE S V,GUGGILAM S S,CHEN Y C.Linear approximations to AC power flow in rectangular coordinates[C]//2015 53rd Annual Allerton Conference on Communication,Control,and Computing(Allerton),September 29-October 2,2015,Monticello,IL,USA:211-217.
[16]BOLOGNANI S,D?RFLER F.Fast power system analysis via implicit linearization of the power flow manifold[C]//2015 53rd Annual Allerton Conference on Communication,Control,and Computing(Allerton),September 29-October 2,2015,Monticello,IL,USA:402-409.
[17]GARCES A.A linear three-phase load flow for power distribution systems[J].IEEE Transactions on Power Systems,2015,31(1):827-828.
[18]BOLOGNANI S,ZAMPIERI S.On the existence and linear approximation of the power flow solution in power distribution networks[J].IEEE Transactions on Power Systems,2014,31(1):163-172.
[19]BERNSTEIN A,WANG C,DALL'ANESE E,et al.Load-flow in multiphase distribution networks:existence,uniqueness,and linear models[EB/OL].[2017].https://arxiv.org/abs/1702.03310.
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[21]LI Z,YU J,WU Q H.Approximate linear power flow using logarithmic transform of voltage magnitudes with reactive power and power loss consideration[J].IEEETransactions on Power Systems,2017,33(4):4593-4603.
[22]AHMADI H,MARTI′J R,MEIER A V.A linear power flow formulation for three-phase distribution systems[J].IEEE Transactions on Power Systems,2016,31(6):5012-5021.
[23]WANG Y,ZHANG N,LI H,et al.Linear three-phase power flow for unbalanced active distribution networks with PV nodes[J].CSEE Journal of Power&Energy Systems,2017,3(3):321-324.
[24]TONG S,MIU K N.A network-based distributed slack bus model for DGs in unbalanced power flow studies[J].IEEE Transactions on Power Systems,2005,20(2):835-842.
[25]YANG J,ZHANG N,KANG C,et al.A state-independent linear power flow model with accurate estimation of voltage magnitude[J].IEEE Transactions on Power Systems,2017,32(5):3607-3617.
[26]王家融,艾欣,王坤宇,等.基于增广雅可比矩阵的交直流解耦潮流新算法[J].电工技术学报,2018,33(6):1382-1389.WANG Jiarong,AI Xin,WANG Kunyu,et al.A new AC/DC decoupled power flow algorithm based on augmented Jacobian Matrix[J].Transactions of China Electrotechnical Society,2018,33(6):1382-1389.
[27]廖小兵,刘开培,张亚超,等.基于区间泰勒展开的不确定性潮流分析[J].电工技术学报,2018,33(4):750-758.LIAO Xiaobing,LIU Kaipei,ZHANG Yachao,et al.Uncertain power flow analysis based on interval Taylor expansion[J].Transactions of China Electrotechnical Society,2018,33(4):750-758.
[28]ZIMMERMAN R D,MURILLO-SANCHEZ C E,THOMAS R J.MATPOWER:steady-state operations,planning,and analysis tools for power systems research and education[J].IEEE Transactions on Power Systems,2011,26(1):12-19.
[29]Distribution Test Feeders-Distribution Test Feeder Working Group-IEEE PES distribution system analysis subcommittee[EB/OL].[2018-01-28].http://www.ewh.ieee.org/soc/pes/dsacom/testfeeders/index.html.
[30]田松峰,陈曦,铁成梁,等.基于等效电耗法的分布式系统能量利用研究[J].热力发电,2017,46(3):19-24.TIAN Songfeng,CHEN Xi,TIE Chengliang,et al.Research on energy utilization of distributed system based on equivalent power consumption method[J].Thermal Power Generation,2017,46(3):19-24.
[31]梁捷,李刚,王建楠.基于字典优化法和ε-约束法的双目标热电调度[J].热力发电,2017,46(10):81-87.LIANG Jie,LI Gang,WANG Jiannan.Bi-objective thermoelectric dispatching based on dictionary optimization method andε-constraint method[J].Thermal Power Generation,2017,46(10):81-87.
[32]林城,袁峥,李桂源,等.基于系统静态调节特性的故障后潮流计算[J].智慧电力,2017,45(12):50-54.LIN Cheng,YUAN Zheng,LI Guiyuan,et al.Post-fault power flow calculation based on system static regulation characteristics[J].Smart Power,2017,45(12):50-54.
[33]罗超,林芳,李子,等.考虑连锁故障运行风险的机会约束最优潮流模型[J].智慧电力,2018,46(1):57-62.LUO Chao,LIN Fang,LI Zi,et al.Opportunity constrained optimal power flow model considering cascading failure operational risk[J].Smart Power,2018,46(1):57-62.
[2]DING T,BO R,LI F,et al.Interval power flow analysis using linear relaxation and optimality-based bounds tightening(OBBT)methods[J].IEEE Transactions on Power Systems,2014,30(1):177-188.
[3]韩笑,周明,李庚银.基于无迹变换随机潮流建模的主动配电网优化调度[J].电力系统保护与控制,2018,46(3):9-17.HAN Xiao,ZHOU Ming,LI Gengyin.Stochastic optimal dispatching of active distribution networks based on stochastic power flow modeling using unscented transformation[J].Power System Protection and Control,2018,46(3):9-17.
[4]BENIDRIS M,MITRA J.Reliability and sensitivity analysis of composite power systems under emission constraints[J].IEEE Transactions on Power Systems,2013,29(1):404-412.
[5]FERREIRA R S,BORGES C L T,PEREIRA M V F.Distribution network reconfiguration under modeling of AC optimal power flow equations:a mixed-integer programming approach[C]//Innovative Smart Grid Technologies Latin America,April 15-17,2013,Sao Paulo,Brazil:1-8.
[6]曹煜,郭创新,章禹,等.计及无功潮流影响的传输介数概念及其电网关键线路辨识研究[J].电力系统保护与控制,2017,45(23):9-16.CAO Yu,GUO Chuangxin,ZHANG Yu,et al.Study of the concept of transmission betweenness considering the effect of reactive power flow and its application in identification of critical lines in power grid[J].Power System Protection and Control,2017,45(23):9-16.
[7]KOCAR I,LACROIX J S.Implementation of a modified augmented nodal analysis based transformer model into the backward forward sweep solver[C]//2012 IEEEPower and Energy Society General Meeting,July 22-26,2012,San Diego,CA,USA:1-11.
[8]扈诗扬,杨萌,汪芳宗.基于坐标旋转变换的配电系统快速解耦潮流计算方法[J].电力系统保护与控制,2017,45(4):40-44.HU Shiyang,YANG Meng,WANG Fangzong.A fast decoupled load flow method for distribution system via coordinate rotation transformation[J].Power System Protection and Control,2017,45(4):40-44.
[9]D?AFI?I,JABR R A,HALILOVIC E,et al.Asensitivity approach to model local voltage controllers in distribution networks[J].IEEE Transactions on Power Systems,2014,29(3):1419-1428.
[10]WU W C,ZHANG B M.A three-phase power flow algorithm for distribution system power flow based on loop-analysis method[J].International Journal of Electrical Power&Energy Systems,2008,30(1):8-15.
[11]CHEN T H,YANG N C.Loop frame of reference based three-phase power flow for unbalanced radial distribution systems[J].Electric Power Systems Research,2010,80(7):799-806.
[12]GARCIA P A N,PEREIRA J L R,CARNEIRO S,et al.Three-phase power flow calculations using the current injection method[J].IEEE Transactions on Power Systems,2000,15(2):508-514.
[13]MARTíJ R,AHMADI H,BASHUALDO L.Linear power-flow formulation based on a voltage-dependent load model[J].IEEE Transactions on Power Delivery,2013,28(3):1682-1690.
[14]GAN L,LOW S H.Convex relaxations and linear approximation for optimal power flow in multiphase radial networks[C]//Power Systems Computation Conference,August 18-22,2014,Wroclaw,Poland:1-9.
[15]DHOPLE S V,GUGGILAM S S,CHEN Y C.Linear approximations to AC power flow in rectangular coordinates[C]//2015 53rd Annual Allerton Conference on Communication,Control,and Computing(Allerton),September 29-October 2,2015,Monticello,IL,USA:211-217.
[16]BOLOGNANI S,D?RFLER F.Fast power system analysis via implicit linearization of the power flow manifold[C]//2015 53rd Annual Allerton Conference on Communication,Control,and Computing(Allerton),September 29-October 2,2015,Monticello,IL,USA:402-409.
[17]GARCES A.A linear three-phase load flow for power distribution systems[J].IEEE Transactions on Power Systems,2015,31(1):827-828.
[18]BOLOGNANI S,ZAMPIERI S.On the existence and linear approximation of the power flow solution in power distribution networks[J].IEEE Transactions on Power Systems,2014,31(1):163-172.
[19]BERNSTEIN A,WANG C,DALL'ANESE E,et al.Load-flow in multiphase distribution networks:existence,uniqueness,and linear models[EB/OL].[2017].https://arxiv.org/abs/1702.03310.
[20]BERNSTEIN A,DALL’ANESE E.Linear power-flow models in multiphase distribution networks[C]//2017IEEE PES Innovative Smart Grid Technologies Conference Europe(ISGT-Europe),September 26-29,2017,Torino,Italy:1-6.
[21]LI Z,YU J,WU Q H.Approximate linear power flow using logarithmic transform of voltage magnitudes with reactive power and power loss consideration[J].IEEETransactions on Power Systems,2017,33(4):4593-4603.
[22]AHMADI H,MARTI′J R,MEIER A V.A linear power flow formulation for three-phase distribution systems[J].IEEE Transactions on Power Systems,2016,31(6):5012-5021.
[23]WANG Y,ZHANG N,LI H,et al.Linear three-phase power flow for unbalanced active distribution networks with PV nodes[J].CSEE Journal of Power&Energy Systems,2017,3(3):321-324.
[24]TONG S,MIU K N.A network-based distributed slack bus model for DGs in unbalanced power flow studies[J].IEEE Transactions on Power Systems,2005,20(2):835-842.
[25]YANG J,ZHANG N,KANG C,et al.A state-independent linear power flow model with accurate estimation of voltage magnitude[J].IEEE Transactions on Power Systems,2017,32(5):3607-3617.
[26]王家融,艾欣,王坤宇,等.基于增广雅可比矩阵的交直流解耦潮流新算法[J].电工技术学报,2018,33(6):1382-1389.WANG Jiarong,AI Xin,WANG Kunyu,et al.A new AC/DC decoupled power flow algorithm based on augmented Jacobian Matrix[J].Transactions of China Electrotechnical Society,2018,33(6):1382-1389.
[27]廖小兵,刘开培,张亚超,等.基于区间泰勒展开的不确定性潮流分析[J].电工技术学报,2018,33(4):750-758.LIAO Xiaobing,LIU Kaipei,ZHANG Yachao,et al.Uncertain power flow analysis based on interval Taylor expansion[J].Transactions of China Electrotechnical Society,2018,33(4):750-758.
[28]ZIMMERMAN R D,MURILLO-SANCHEZ C E,THOMAS R J.MATPOWER:steady-state operations,planning,and analysis tools for power systems research and education[J].IEEE Transactions on Power Systems,2011,26(1):12-19.
[29]Distribution Test Feeders-Distribution Test Feeder Working Group-IEEE PES distribution system analysis subcommittee[EB/OL].[2018-01-28].http://www.ewh.ieee.org/soc/pes/dsacom/testfeeders/index.html.
[30]田松峰,陈曦,铁成梁,等.基于等效电耗法的分布式系统能量利用研究[J].热力发电,2017,46(3):19-24.TIAN Songfeng,CHEN Xi,TIE Chengliang,et al.Research on energy utilization of distributed system based on equivalent power consumption method[J].Thermal Power Generation,2017,46(3):19-24.
[31]梁捷,李刚,王建楠.基于字典优化法和ε-约束法的双目标热电调度[J].热力发电,2017,46(10):81-87.LIANG Jie,LI Gang,WANG Jiannan.Bi-objective thermoelectric dispatching based on dictionary optimization method andε-constraint method[J].Thermal Power Generation,2017,46(10):81-87.
[32]林城,袁峥,李桂源,等.基于系统静态调节特性的故障后潮流计算[J].智慧电力,2017,45(12):50-54.LIN Cheng,YUAN Zheng,LI Guiyuan,et al.Post-fault power flow calculation based on system static regulation characteristics[J].Smart Power,2017,45(12):50-54.
[33]罗超,林芳,李子,等.考虑连锁故障运行风险的机会约束最优潮流模型[J].智慧电力,2018,46(1):57-62.LUO Chao,LIN Fang,LI Zi,et al.Opportunity constrained optimal power flow model considering cascading failure operational risk[J].Smart Power,2018,46(1):57-62.