直流配电系统潮流解的存在性分析
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摘要
直流配电系统的输电能力受网络拓扑、线路阻抗以及电压等级的限制,当负载需求超过配电网的最大输电功率时,系统将失去平衡点,从而导致电压坍塌。因此,研究潮流解的存在性对保证直流配电系统稳定可靠运行至关重要。该文建立了直流配电系统潮流数学模型,通过闭区间套定理求得了系统存在潮流可行解的充分条件,基于极限的唯一性证明了潮流可行解的唯一性,并提出了一种大范围收敛的潮流解迭代算法,为直流配电系统稳定性研究提供了新的有效途径。另外,该文得到了解析的和基于数值型的平衡点存在性条件。根据解析条件可快速地评估负载接入和电压突变后系统的潮流可行解存在性,大幅度减少了计算量;根据数值型条件可更为准确计算潮流可行解存在的负载上限,降低了存在性条件的保守性。通过算例验证了所得结论的正确性以及所提潮流解迭代算法的有效性。
The transmission capacity of a DC distribution system is limited by the network topology, line impedance, and voltage level. When the load demand exceeds the maximum transmission power of the distribution network, the system will lose its balance point, resulting in voltage collapse. Therefore,studying the existence of the power flow solution is essential to ensure the stable and reliable operation of the DC power distribution system. Firstly, the mathematical model of the power flow of the DC power distribution system was established. The sufficient conditions for the feasible solution of the power flow were obtained by the closed interval theorem.The uniqueness of the feasible solution of the power flow was proved by the uniqueness of the limit. And a large-scale convergence power flow iterative algorithm was proposed,which provided a new and effective way for the stability study of DC power distribution system. In addition, this paper obtained analytical and numerical-based equilibrium point existence conditions. According to the analysis conditions, the existence of the power flow feasible solution of the system after load access and voltage abrupt change can be quickly evaluated, and the calculation amount is greatly reduced.According to the numerical conditions, the upper limit of the load of the feasible solution of the power flow can be calculated more accurately, and the conservativeness of the existence condition was reduced. Finally, an example was given to verify the correctness of the obtained conclusions and the effectiveness of the proposed iterative algorithm.
The transmission capacity of a DC distribution system is limited by the network topology, line impedance, and voltage level. When the load demand exceeds the maximum transmission power of the distribution network, the system will lose its balance point, resulting in voltage collapse. Therefore,studying the existence of the power flow solution is essential to ensure the stable and reliable operation of the DC power distribution system. Firstly, the mathematical model of the power flow of the DC power distribution system was established. The sufficient conditions for the feasible solution of the power flow were obtained by the closed interval theorem.The uniqueness of the feasible solution of the power flow was proved by the uniqueness of the limit. And a large-scale convergence power flow iterative algorithm was proposed,which provided a new and effective way for the stability study of DC power distribution system. In addition, this paper obtained analytical and numerical-based equilibrium point existence conditions. According to the analysis conditions, the existence of the power flow feasible solution of the system after load access and voltage abrupt change can be quickly evaluated, and the calculation amount is greatly reduced.According to the numerical conditions, the upper limit of the load of the feasible solution of the power flow can be calculated more accurately, and the conservativeness of the existence condition was reduced. Finally, an example was given to verify the correctness of the obtained conclusions and the effectiveness of the proposed iterative algorithm.
引文
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[16]Barabanov N,Ortega R,Gri?óR,et al.On existence and stability of equilibria of linear time-invariant systems with constant power loads[J].IEEE Transactions on Circuits and Systems I:Regular Papers,2016,63(1):114-121.
[17]Garces A.Uniqueness of the power flow solutions in low voltage direct current grids[J].Electric Power Systems Research,2017,151:149-153.
[18]张聪,彭克,徐丙垠,等.直流配电系统潮流可行解与电压稳定性分析方法[J].电力系统自动化,2018,42(14):48-53.Zhang Cong,Peng Ke,Xu Bingyin,et al.Feasible power flow solution and voltage stability analysis method for DCdistribution system[J].Automation of Electric Power Systems,2018,42(14):48-53(in Chinese).
[19]Liu Zhangjie,Su Mei,Sun Yao,et al.Existence and stability of equilibrium of DC microgrid with constant power loads[J].IEEE Transactions on Power Systems,2018 33(6):6999-7010.
[20]Polyak B,Gryazina E.Convexity/nonconvexity certificates for power flow analysis[C]//Proceedings of the first International Symposium on Energy System Optimization.Cham:Birkh?user,2015.
[2]薛士敏,陈超超,金毅,等.直流配电系统保护技术研究综述[J].中国电机工程学报,2014,34(19):3114-3122.Xue Shimin,Chen Chaochao,Jin Yi,et al.A research review of protection technology for DC distribution system[J].Proceedings of the CSEE,2014,34(19):3114-3122(in Chinese).
[3]王一振,赵彪,袁志昌,等.柔性直流技术在能源互联网中的应用探讨[J].中国电机工程学报,2015,35(14):3551-3560.Wang Yizhen,Zhao Biao,Yuan Zhichang,et al.Study of the application of VSC-based DC technology in energy internet[J].Proceedings of the CSEE,2015,35(14):3551-3560(in Chinese).
[4]吴鸣,刘海涛,陈文波,等.中低压直流配电系统的主动保护研究[J].中国电机工程学报,2016,36(4):891-899.Wu Ming,Liu Haitao,Chen Wenbo,et al.Research on active protection for MV/LV DC distribution system[J].Proceedings of the CSEE,2016,36(4):891-899(in Chinese).
[5]李斌,何佳伟.柔性直流配电系统故障分析及限流方法[J].中国电机工程学报,2015,35(12):3026-3036.Li Bin,He Jiawei.DC fault analysis and current limiting technique for VSC-based DC distribution system[J].Proceedings of the CSEE,2015,35(12):3026-3036(in Chinese).
[6]雷婧婷,安婷,杜正春,等.含直流配电网的交直流潮流计算[J].中国电机工程学报,2016,36(4):911-918.Lei Jingting,An Ting,Du Zhengchun,et al.A unified AC/DC power flow algorithm with DC distribution[J].Proceedings of the CSEE,2016,36(4):911-918(in Chinese).
[7]盛万兴,李蕊,李跃,等.直流配电电压等级序列与典型网络架构初探[J].中国电机工程学报,2016,36(13):3391-3403.Sheng Wanxing,Li Rui,Li Yue,et al.A preliminary study on voltage level sequence and typical network architecture of direct current distribution network[J].Proceedings of the CSEE,2016,36(13):3391-3403(in Chinese).
[8]李霞林,郭力,王成山,等.直流微电网关键技术研究综述[J].中国电机工程学报,2016,36(1):2-17.Li Xialin,Guo Li,Wang Chengshan,et al.Key technologies of DC microgrids:an overview[J].Proceedings of the CSEE,2016,36(1):2-17(in Chinese).
[9]支娜,张辉,肖曦,等.分布式控制的直流微电网系统级稳定性分析[J].中国电机工程学报,2016,36(2):368-378.Zhi Na,Zhang Hui,Xiao Xi,et al.System-level stability analysis of DC microgrid with distributed control strategy[J].Proceedings of the CSEE,2016,36(2):368-378(in Chinese).
[10]van der Blij N H,Ramirez-Elizondo L M,Spaan M T J,et al.Stability of DC distribution systems:an algebraic derivation[J].Energies,2017,10(9):1412.
[11]Su Mei,Liu Zhangjie,Sun Yao,et al.Stability analysis and stabilization methods of DC microgrid with multiple parallel-connected DC-DC converters loaded by CPLs[J].IEEE Transactions on Smart Grid,2018,9(1):132-142.
[12]Liu Zhangjie,Su Mei,Sun Yao,et al.Stability analysis of DC microgrids with constant power load under distributed control methods[J].Automatica,2018,90:62-72.
[13]Liutanakul P,Awan A B,Pierfederici S,et al.Linear stabilization of a DC bus supplying a constant power load:a general design approach[J].IEEE Transactions on Power Electronics,2010,25(2):475-488.
[14]Simpson-Porco J W,D?rfler F,Bullo F.Voltage collapse in complex power grids[J].Nature Communications,2016,7:10790.
[15]Sanchez S,Ortega R,Gri?o R,et al.Conditions for existence of equilibria of systems with constant power loads[J].IEEE Transactions on Circuits and Systems I:Regular Papers,2014,61(7):2204-2211.
[16]Barabanov N,Ortega R,Gri?óR,et al.On existence and stability of equilibria of linear time-invariant systems with constant power loads[J].IEEE Transactions on Circuits and Systems I:Regular Papers,2016,63(1):114-121.
[17]Garces A.Uniqueness of the power flow solutions in low voltage direct current grids[J].Electric Power Systems Research,2017,151:149-153.
[18]张聪,彭克,徐丙垠,等.直流配电系统潮流可行解与电压稳定性分析方法[J].电力系统自动化,2018,42(14):48-53.Zhang Cong,Peng Ke,Xu Bingyin,et al.Feasible power flow solution and voltage stability analysis method for DCdistribution system[J].Automation of Electric Power Systems,2018,42(14):48-53(in Chinese).
[19]Liu Zhangjie,Su Mei,Sun Yao,et al.Existence and stability of equilibrium of DC microgrid with constant power loads[J].IEEE Transactions on Power Systems,2018 33(6):6999-7010.
[20]Polyak B,Gryazina E.Convexity/nonconvexity certificates for power flow analysis[C]//Proceedings of the first International Symposium on Energy System Optimization.Cham:Birkh?user,2015.