基于凸差规划的有源配电网电压无功协调控制方法
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摘要
分布式电源的高渗透率接入加剧了有源配电网的电压波动,以静止无功发生器和分布式电源逆变器为代表的新型电力电子装置作为连续无功源可以对配网电压进行快速的实时调节,给配电网的运行方式带来了巨大变革。本文提出了一种基于凸差规划的有源配电网多时间尺度电压无功协调控制方法。首先,建立了有源配电网电压无功协调控制时序模型;通过线性化和凸松弛处理,将原非凸非线性优化模型转化为可有效求解的二阶锥规划模型,并采用凸差规划方法进行求解,保证凸松弛的准确性满足计算精度要求;最后,基于改进的IEEE33节点系统验证了本文方法的正确性和有效性,通过各种电压无功调节手段的协调配合,在改善配电网电压水平的同时,提高配电网运行的经济性。
The increasing penetration rate of distributed generations(DGs)exacerbates the voltage fluctuations in active distribution networks(ADNs).Some novel power electronic devices,such as static var generator(SVG)and gridconnected inverters of DGs,can be used as continuous reactive power sources to realize the real-time regulation of voltage of distribution network,which brings enormous changes to the operation mode of distribution network.In this paper,a coordinated control method for voltage and reactive power on multiple time scales is proposed based on difference-of-convex programming(DCP)for ADNs.First,a time-series model of coordinated control of voltage and reactive power of ADNs is built.Then,the original non-convex nonlinear optimization model is converted into an effectively solved second-order cone programming(SOCP)model using linearization and convex relaxation.In addition,to make the accuracy of convex relaxation satisfy the requirement of calculation precision,a DCP-based approach is adopted to solve the proposed model.Finally,case studies are performed on a modified IEEE 33-node system to verify the correctness and efficiency of the proposed method;through the coordination of various regulation means for voltage and reactive power,the economic efficiency of the operation of distribution network can be raised while improving its voltage level.
The increasing penetration rate of distributed generations(DGs)exacerbates the voltage fluctuations in active distribution networks(ADNs).Some novel power electronic devices,such as static var generator(SVG)and gridconnected inverters of DGs,can be used as continuous reactive power sources to realize the real-time regulation of voltage of distribution network,which brings enormous changes to the operation mode of distribution network.In this paper,a coordinated control method for voltage and reactive power on multiple time scales is proposed based on difference-of-convex programming(DCP)for ADNs.First,a time-series model of coordinated control of voltage and reactive power of ADNs is built.Then,the original non-convex nonlinear optimization model is converted into an effectively solved second-order cone programming(SOCP)model using linearization and convex relaxation.In addition,to make the accuracy of convex relaxation satisfy the requirement of calculation precision,a DCP-based approach is adopted to solve the proposed model.Finally,case studies are performed on a modified IEEE 33-node system to verify the correctness and efficiency of the proposed method;through the coordination of various regulation means for voltage and reactive power,the economic efficiency of the operation of distribution network can be raised while improving its voltage level.
引文
[1]王成山,李鹏(Wang Chengshan,Li Peng).分布式发电、微网与智能配电网的发展与挑战(Development and challenges of distributed generation,the micro-grid and smart distribution system)[J].电力系统自动化(Automation of Electric Power Systems),2010,34(2):10-14,23.
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[9]刘一兵,吴文传,张伯明,等(Liu Yibing,Wu Wenchuan,Zhang Boming,et al).基于混合整数二阶锥规划的三相有源配电网无功优化(Reactive power optimization for three-phase distribution networks with distributed generators based on mixed integer second-order cone programming)[J].电力系统自动化(Automation of Electric Power Systems),2014,38(15):58-64.
[10]赵金利,于莹莹,李鹏,等(Zhao Jinli,Yu Yingying,Li Peng,et al).基于锥优化的储能系统参与配电网运行调节快速计算方法(A fast calculation method of energy storage system for distribution network regulation based on conic programming)[J].电力系统自动化(Automation of Electric Power Systems),2016,40(2):30-35,48.
[11]Ji Haoran,Wang Chengshan,Li Peng,et al.An enhanced SOCP-based method for feeder load balancing using the multi-terminal soft open point in active distribution networks[J].Applied Energy,2017,208:986-995.
[12]Wei W,Wang J,Li N,et al.Optimal power flow of radial networks and its variations:a sequential convex optimization approach[J].IEEE Trans on Smart Grid,2017,8(6):2974-2987.
[13]赵金利,李雨薇,李鹏,等(Zhao Jinli,Li Yuwei,Li Peng,et al).基于二阶锥规划的有源配电网SNOP电压无功时序控制方法(Sequential voltage regulation of soft normally open point in active distribution network based on second-order cone programming)[J].高电压技术(High Voltage Engineering),2016,42(7):2134-2141.
[14]Baran M E,Wu F F.Network reconfiguration in distribution systems for loss reduction and load balancing[J].IEEE Trans on Power Delivery,1989,4(2):1401-1407.
[15]Jabr R A.Radial distribution load flow using conic programming[J].IEEE Trans on Power Systems,2006,21(3):1458-1459.
[16]Lipp T,Boyd S.Variations and extension of the convexconcave procedure[J].Optimization&Engineering,2016,17(2):263-287.
[17]Baran M E,Wu F F.Optimal capacitor placement on radial distribution systems[J].IEEE Trans on Power Delivery,2002,4(1):725-734.
[18]Bonami P,Biegler L T,Conn A R,et al.An algorithmic framework for convex mixed integer nonlinear programs[J].Discrete Optimization,2008,5(2):186-204.
[2]李鹏,窦鹏冲,李雨薇,等(Li Peng,Dou Pengchong,Li Yuwei,et al).微电网技术在主动配电网中的应用(Application of microgrid technology in active distribution network)[J].电力自动化设备(Electric Power Automation Equipment),2015,35(4):8-16.
[3]李旷,刘进军,魏标,等(Li Kuang,Liu Jinjun,Wei Biao,et al).静止无功发生器补偿电网电压不平衡的控制及其优化方法(Control and optimization of static var generator for grid voltage unbalance mitigation)[J].中国电机工程学报(Proceedings of the CSEE),2006,26(5):58-63.
[4]Li P,Ji H,Wang C,et al.Coordinated control method of voltage and reactive power for active distribution networks based on soft open point[J].IEEE Trans on Sustainable Energy,2017,8(4):1430-1442.
[5]卓煜,陈维荣,戴朝华(Zhuo Yu,Chen Weirong,Dai Chaohua).基于灵敏度分析的主动配电网无功电压控制(Reactive power/voltage control strategy for active distribution network based on sensitivity analysis)[J].电力系统及其自动化学报(Proceedings of the CSU-EPSA),2017,29(5):21-27.
[6]王成山,宋关羽,李鹏,等(Wang Chengshan,Song Guanyu,Li Peng,et al).一种联络开关和智能软开关并存的配电网运行时序优化方法(A hybrid optimization method for distribution network operation with SNOP and Tie switch)[J].中国电机工程学报(Proceedings of the CSEE),2016,36(9):2315-2321.
[7]Daratha N,Das B,Sharma J.Coordination between OLTCand SVC for voltage regulation in unbalanced distribution system distributed generation[J].IEEE Trans on Power Systems,2014,29(1):289-299.
[8]Rajan A,Malakar T.Optimal reactive power dispatch using hybrid Nelder-Mead simplex based firefly algorithm[J].International Journal of Electrical Power&Energy Systems,2015,66:9-24.
[9]刘一兵,吴文传,张伯明,等(Liu Yibing,Wu Wenchuan,Zhang Boming,et al).基于混合整数二阶锥规划的三相有源配电网无功优化(Reactive power optimization for three-phase distribution networks with distributed generators based on mixed integer second-order cone programming)[J].电力系统自动化(Automation of Electric Power Systems),2014,38(15):58-64.
[10]赵金利,于莹莹,李鹏,等(Zhao Jinli,Yu Yingying,Li Peng,et al).基于锥优化的储能系统参与配电网运行调节快速计算方法(A fast calculation method of energy storage system for distribution network regulation based on conic programming)[J].电力系统自动化(Automation of Electric Power Systems),2016,40(2):30-35,48.
[11]Ji Haoran,Wang Chengshan,Li Peng,et al.An enhanced SOCP-based method for feeder load balancing using the multi-terminal soft open point in active distribution networks[J].Applied Energy,2017,208:986-995.
[12]Wei W,Wang J,Li N,et al.Optimal power flow of radial networks and its variations:a sequential convex optimization approach[J].IEEE Trans on Smart Grid,2017,8(6):2974-2987.
[13]赵金利,李雨薇,李鹏,等(Zhao Jinli,Li Yuwei,Li Peng,et al).基于二阶锥规划的有源配电网SNOP电压无功时序控制方法(Sequential voltage regulation of soft normally open point in active distribution network based on second-order cone programming)[J].高电压技术(High Voltage Engineering),2016,42(7):2134-2141.
[14]Baran M E,Wu F F.Network reconfiguration in distribution systems for loss reduction and load balancing[J].IEEE Trans on Power Delivery,1989,4(2):1401-1407.
[15]Jabr R A.Radial distribution load flow using conic programming[J].IEEE Trans on Power Systems,2006,21(3):1458-1459.
[16]Lipp T,Boyd S.Variations and extension of the convexconcave procedure[J].Optimization&Engineering,2016,17(2):263-287.
[17]Baran M E,Wu F F.Optimal capacitor placement on radial distribution systems[J].IEEE Trans on Power Delivery,2002,4(1):725-734.
[18]Bonami P,Biegler L T,Conn A R,et al.An algorithmic framework for convex mixed integer nonlinear programs[J].Discrete Optimization,2008,5(2):186-204.