基于拉格朗日对偶松弛的多区域柔性直流互联电网无功优化
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摘要
现有方法对互联后的电网进行无功优化时难以满足大规模电网实时计算、快速反应的需要,并且面临全网数据收集的难题。为了解决上述问题,采用分解协调算法的思想,提出一种基于拉格朗日对偶松弛的多区域柔性直流互联电网无功优化方法。首先根据支路潮流模型,利用二阶锥松弛和二次旋转锥松弛方法建立了多区域柔性直流互联电网的集中式无功优化模型。然后利用拉格朗日对偶松弛理论在集中式优化模型的基础上,提出了可以并行计算的多区域柔性直流互联电网无功优化方法。通过算例计算,验证了所提算法的有效性和正确性。此外,还对比分析了所述的分解协调算法和基于交替方向乘子法(ADMM)的分布式优化算法的计算结果,证明所用算法在计算时间上更具优势。
The existing methods are difficult to meet the real-time calculation needs of large-scale power grid and quick response when performing reactive power optimization for the interconnected power grids, and also facing the problem of data collection throughout the whole network. To solve the problem, this paper uses the idea of decomposition-coordination algorithm and proposes a reactive power optimization method for multi-area voltage source converter based high voltage direct current(VSC-HVDC) interconnected power grid based on the Lagrangian dual relaxation theory. Firstly, according to branch power flow model, a centralized reactive power optimization model of multi-area VSC-HVDC interconnected power grids is established by using the second-order cone relaxation and rotated quadratic cone relaxation technology. Then, a reactive power optimization method is proposed based on decomposition-coordination algorithm for multi-area VSC-HVDC interconnected power grid based on the Lagrangian dual relaxation theory used in the centralized optimization model. The validity and correctness of proposed algorithm are verified by case study. Finally, the results from decomposition-coordination algorithm and alternating direction method of multipliers(ADMM) are compared, proving that the former one has an advantage on compution time.
The existing methods are difficult to meet the real-time calculation needs of large-scale power grid and quick response when performing reactive power optimization for the interconnected power grids, and also facing the problem of data collection throughout the whole network. To solve the problem, this paper uses the idea of decomposition-coordination algorithm and proposes a reactive power optimization method for multi-area voltage source converter based high voltage direct current(VSC-HVDC) interconnected power grid based on the Lagrangian dual relaxation theory. Firstly, according to branch power flow model, a centralized reactive power optimization model of multi-area VSC-HVDC interconnected power grids is established by using the second-order cone relaxation and rotated quadratic cone relaxation technology. Then, a reactive power optimization method is proposed based on decomposition-coordination algorithm for multi-area VSC-HVDC interconnected power grid based on the Lagrangian dual relaxation theory used in the centralized optimization model. The validity and correctness of proposed algorithm are verified by case study. Finally, the results from decomposition-coordination algorithm and alternating direction method of multipliers(ADMM) are compared, proving that the former one has an advantage on compution time.
引文
[1] 李智诚.交直流柔性互联电网最优潮流与自愈重构研究[D].北京:北京交通大学,2017.LI Zhicheng.Optimal power flow and self-healing reconfiguration for AC/DC power systems with VSC-based MTDC[D].Beijing:Beijing Jiao Tong University,2017.
[2] 徐殿国,张书鑫,李彬彬.电力系统柔性一次设备及其关键技术:应用与展望[J].电力系统自动化,2018,42(7):2-22.DOI:10.7500/AEPS20180209010.XU Dianguo,ZHANG Shuxin,LI Binbin.Flexible primary equipment in power system and prospects[J].Automation of Electric Power Systems,2018,42(7):2-22.DOI:10.7500/AEPS20180209010.
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[4] 余秀月,宋少群,郭瑞鹏,等.含电压源换流器的交直流混联电网无功优化模型[J].电力系统保护与控制,2017,45(19):148-153.YU Xiuyue,SONG Shaoqun,GUO Ruipeng,et al.Optimal reactive power flow model for AC/DC hybrid power grid with voltage source converters[J].Power System Protection and Control,2017,45(19):148-153.
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[6] 李晨阳.交直流输电系统无功优化研究[J].济南:山东大学,2011.LI Chenyang.The research on reactive power of hybrid AC-DC power system[D].Jinan:Shandong University,2011.
[7] 黄俊辉,汪惟源,王海潜,等.基于模拟退火遗传算法的交直流系统无功优化与电压控制研究[J].电力系统保护与控制,2016,44(10):37-43.HANG Junhui,WANG Weiyuan,WANG Haiqian,et al.Study of hybrid genetic algorithm and annealing algorithm on reactive power optimization and voltage control in AC/DC transmission system[J].Power System Protection and Control,2016,44(10):37-43.
[8] 殷茂颖.基于量子粒子群算法的交直流系统多目标无功优化[D].济南:山东大学,2012.YIN Maoying.Multi-objective reactive power optimization of hybrid AC-DC power system based on quantum-behaved particle swarm algorithm[D].Jinan:Shandong University,2012.
[9] 钟红梅,任震,张勇军,等.免疫算法及其在电力系统无功优化中的应用[J].电网技术,2004,28(3):16-19.ZHONG Hongmei,REN Zhen,ZHANG Yongjun,et al.Immune algorithm and its application in power system reactive power optimization[J].Power System Technology,2004,28(3):16-19.
[10] CONTRERAS J,LOSI A,RUSSO M,et al.Simulation and evaluation of optimization problem solutions in distributed energy management systems[J].IEEE Transactions on Power Systems,2002,17(1):57-62.
[11] 刘科研,盛万兴,李运华.基于分布式最优潮流算法的跨区输电阻塞管理研究[J].中国电机工程学报,2007,27(19):56-61.LIU Keyan,SHENG Wanxing,LI Yunhua.Multi-region transmission congestion management based on distributed optimal power flow algorithm[J].Proceedings of the CSEE,2007,27(19):56-61.
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[13] CONEJO A J,AGUADO J A.Multi-area coordinated decentralized DC optimal power flow[J].IEEE Transactions on Power Systems,1998,13(4):1272-1278.
[14] 张潼,王毅,翟明玉,等.含电压源换流器的交直流混联电网状态估计快速解耦法[J].电力系统自动化,2018,42(21):70-76.DOI:10.7500/AEPS20170911012.ZHANG Tong,WANG Yi,ZHAI Mingyu,et al.Fast decoupling algorithm of state estimation for hybrid AC/DC power systems with voltage source converters[J].Automation of Electric Power Systems,2018,42(21):70-76.DOI:10.7500/AEPS20170911012.
[15] 程新功,厉吉文,曹立霞,等.基于电网分区的多目标分布式并行无功优化研究[J].中国电机工程学报,2003,23(10):109-113.CHENG Xingong,LI Jiwen,CAO Lixia,et al.Multi-objective distributed parallel reactive power optimization based on subarea division of the power systems[J].Proceedings of the CSEE,2003,23(10):109-113.
[16] 刘志文,刘明波.基于Ward等值的多区域无功优化分解协调算法[J].电力系统自动化,2010,34(14):63-69.LIU Zhiwen,LIU Mingbo.A decomposition and coordination algorithm for multi-area reactive power optimization based on Ward equivalent[J].Automation of Electric Power Systems,2010,34(14):63-69.
[17] 冯汉中,刘明波,赵文猛,等.ADMM应用于求解多区域互联电网分布式无功优化问题[J].电力系统及其自动化学报,2017,29(7):20-26.FENG Hanzhong,LIU Mingbo,ZHAO Wenmeng,et al.Application of ADMM to distributed reactive-power optimization of multi-area interconnected power grids[J].Proceedings of the CSU-EPSA,2017,29(7):20-26.
[18] FARIVAR M,LOW S H.Branch flow model:relaxations and convexification—Part Ⅱ[J].IEEE Transactions on Power Systems,2013,28(3):2565-2572.
[19] 张涛,徐雪琴.基于改进多种群量子粒子群算法的STATCOM选址及容量优化[J].中国电机工程学报,2015,35(30):75-81.ZHANG Tao,XU Xueqin.Optimal location and parameter setting of STATCOM based on improved multiple population quantum particle swarm optimization algorithm[J].Proceedings of the CSEE,2015,35(30):75-81.
[20] PIZANO-MARTINEZ A,FUERTE-ESQUIVEL C R,AMBRIZ-PéREZ H,et al.Modeling of VSC-based HVDC systems for a Newton-Raphson OPF algorithm[J].IEEE Transactions on Power Systems,2007,22(4):1794-1803.
[21] LOTFJOU A,SHAHIDEHPOUR M,FU Y.Hourly scheduling of DC transmission lines in SCUC with voltage source converters[J].IEEE Transactions on Power Delivery,2011,26(2):650-660.
[22] 王永平,赵文强,杨建明,等.混合直流输电技术及发展分析[J].电力系统自动化,2017,41(7):156-167.DOI:10.7500/AEPS20161117005.WANG Yongping,ZHAO Wenqiang,YANG Jianming,et al.Hybrid high-voltage direct current transmission technology and its development analysis[J].Automation of Electric Power Systems,2017,41(7):156-167.DOI:10.7500/AEPS20161117005.
[23] RABIH A.Modeling network losses using quadratic cones[J].IEEE Transactions on Power Systems,2005,20(1):505-506.
[24] LOBO M S,VANDENBERGHE L,BOYD S,et al.Applications of second-order cone programming[J].Linear Algebra & Its Applications,1998,284(1/2/3):193-228.
[25] 赖晓文,马晓伟,白杨,等.基于混合整数二阶锥规划的动态无功优化方法[J].电力系统自动化,2017,41(17):37-42.DOI:10.7500/AEPS20161101004.LAI Xiaowen,MA Xiaowei,BAI Yang,et al.Dynamic reactive power optimization method based on mixed integer second-order cone programming[J].Automation of Electric Power Systems,2017,41(17):37-42.DOI:10.7500/AEPS20161101004.
[26] 孙兴鲁,董萍,王雅平,等.高渗透光伏接入下基于近似值函数的主动配电网鲁棒优化[J].电力系统自动化,2018,42(15):62-69.DOI:10.7500/AEPS20170908016.SUN Xinglu,DONG Ping,WANG Yaping,et al.Robust optimization of active distribution network with high-penetration photovoltaic access based on approximated value function[J].Automation of Electric Power Systems,2018,42(15):62-69.DOI:10.7500/AEPS20170908016.
[27] STEPHEN B,LIEVEN V,王书.凸优化[M].北京:清华大学出版社,2013:207-223.STEPHEN B,LIEVEN V,WANG Shu.Convex optimization[M].Beijing:Tsinghua University Press,2013:207-223.
[28] 张伯明,陈寿孙.高等电力网络分析[M].北京:清华大学出版社,1996:297-302.ZHANG Boming,CHEN Shousun.Advanced power network analysis[M].Beijing:Tsinghua University Press,1996:297-302.
[29] LOFBERG J.YALMIP:a toolbox for modeling and optimization in MATLAB[C]// 2004 IEEE International Conference on Robotics and Automation,September 2-4,2004,New Orleans,USA.
[30] Gurobi Company.Gurobi optimizer[EB/OL].[2018-05-31].http://www.gurobi.com.
[2] 徐殿国,张书鑫,李彬彬.电力系统柔性一次设备及其关键技术:应用与展望[J].电力系统自动化,2018,42(7):2-22.DOI:10.7500/AEPS20180209010.XU Dianguo,ZHANG Shuxin,LI Binbin.Flexible primary equipment in power system and prospects[J].Automation of Electric Power Systems,2018,42(7):2-22.DOI:10.7500/AEPS20180209010.
[3] 柯圣舟,郑欢,林毅,等.计及柔性直流输电系统损耗模型的交直流电网无功优化[J].电网技术,2016,12(10):52-58.KE Shengzhou,ZHNG Huan,LIN Yi,et al.Reactive power optimization of AC-DC grid in consideration of VSC-HVDC transmission loss model[J].Power System Technology,2016,12(10):52-58.
[4] 余秀月,宋少群,郭瑞鹏,等.含电压源换流器的交直流混联电网无功优化模型[J].电力系统保护与控制,2017,45(19):148-153.YU Xiuyue,SONG Shaoqun,GUO Ruipeng,et al.Optimal reactive power flow model for AC/DC hybrid power grid with voltage source converters[J].Power System Protection and Control,2017,45(19):148-153.
[5] 李衍孜.交直流混联系统网损计算及无功优化研究[D].北京:华北电力大学,2016.LI Yanzi.Research on transmission loss calculation and reactive power optimization for AC/DC hybrid power system[D].Beijing:North China Electric Power University,2016.
[6] 李晨阳.交直流输电系统无功优化研究[J].济南:山东大学,2011.LI Chenyang.The research on reactive power of hybrid AC-DC power system[D].Jinan:Shandong University,2011.
[7] 黄俊辉,汪惟源,王海潜,等.基于模拟退火遗传算法的交直流系统无功优化与电压控制研究[J].电力系统保护与控制,2016,44(10):37-43.HANG Junhui,WANG Weiyuan,WANG Haiqian,et al.Study of hybrid genetic algorithm and annealing algorithm on reactive power optimization and voltage control in AC/DC transmission system[J].Power System Protection and Control,2016,44(10):37-43.
[8] 殷茂颖.基于量子粒子群算法的交直流系统多目标无功优化[D].济南:山东大学,2012.YIN Maoying.Multi-objective reactive power optimization of hybrid AC-DC power system based on quantum-behaved particle swarm algorithm[D].Jinan:Shandong University,2012.
[9] 钟红梅,任震,张勇军,等.免疫算法及其在电力系统无功优化中的应用[J].电网技术,2004,28(3):16-19.ZHONG Hongmei,REN Zhen,ZHANG Yongjun,et al.Immune algorithm and its application in power system reactive power optimization[J].Power System Technology,2004,28(3):16-19.
[10] CONTRERAS J,LOSI A,RUSSO M,et al.Simulation and evaluation of optimization problem solutions in distributed energy management systems[J].IEEE Transactions on Power Systems,2002,17(1):57-62.
[11] 刘科研,盛万兴,李运华.基于分布式最优潮流算法的跨区输电阻塞管理研究[J].中国电机工程学报,2007,27(19):56-61.LIU Keyan,SHENG Wanxing,LI Yunhua.Multi-region transmission congestion management based on distributed optimal power flow algorithm[J].Proceedings of the CSEE,2007,27(19):56-61.
[12] NOGALES F J,PRIETO F J,CONEJO A J.A decomposition methodology applied to the multi-area optimal power flow problem[J].Annals of Operations Research,2003,120(1/2/3/4):99-116.
[13] CONEJO A J,AGUADO J A.Multi-area coordinated decentralized DC optimal power flow[J].IEEE Transactions on Power Systems,1998,13(4):1272-1278.
[14] 张潼,王毅,翟明玉,等.含电压源换流器的交直流混联电网状态估计快速解耦法[J].电力系统自动化,2018,42(21):70-76.DOI:10.7500/AEPS20170911012.ZHANG Tong,WANG Yi,ZHAI Mingyu,et al.Fast decoupling algorithm of state estimation for hybrid AC/DC power systems with voltage source converters[J].Automation of Electric Power Systems,2018,42(21):70-76.DOI:10.7500/AEPS20170911012.
[15] 程新功,厉吉文,曹立霞,等.基于电网分区的多目标分布式并行无功优化研究[J].中国电机工程学报,2003,23(10):109-113.CHENG Xingong,LI Jiwen,CAO Lixia,et al.Multi-objective distributed parallel reactive power optimization based on subarea division of the power systems[J].Proceedings of the CSEE,2003,23(10):109-113.
[16] 刘志文,刘明波.基于Ward等值的多区域无功优化分解协调算法[J].电力系统自动化,2010,34(14):63-69.LIU Zhiwen,LIU Mingbo.A decomposition and coordination algorithm for multi-area reactive power optimization based on Ward equivalent[J].Automation of Electric Power Systems,2010,34(14):63-69.
[17] 冯汉中,刘明波,赵文猛,等.ADMM应用于求解多区域互联电网分布式无功优化问题[J].电力系统及其自动化学报,2017,29(7):20-26.FENG Hanzhong,LIU Mingbo,ZHAO Wenmeng,et al.Application of ADMM to distributed reactive-power optimization of multi-area interconnected power grids[J].Proceedings of the CSU-EPSA,2017,29(7):20-26.
[18] FARIVAR M,LOW S H.Branch flow model:relaxations and convexification—Part Ⅱ[J].IEEE Transactions on Power Systems,2013,28(3):2565-2572.
[19] 张涛,徐雪琴.基于改进多种群量子粒子群算法的STATCOM选址及容量优化[J].中国电机工程学报,2015,35(30):75-81.ZHANG Tao,XU Xueqin.Optimal location and parameter setting of STATCOM based on improved multiple population quantum particle swarm optimization algorithm[J].Proceedings of the CSEE,2015,35(30):75-81.
[20] PIZANO-MARTINEZ A,FUERTE-ESQUIVEL C R,AMBRIZ-PéREZ H,et al.Modeling of VSC-based HVDC systems for a Newton-Raphson OPF algorithm[J].IEEE Transactions on Power Systems,2007,22(4):1794-1803.
[21] LOTFJOU A,SHAHIDEHPOUR M,FU Y.Hourly scheduling of DC transmission lines in SCUC with voltage source converters[J].IEEE Transactions on Power Delivery,2011,26(2):650-660.
[22] 王永平,赵文强,杨建明,等.混合直流输电技术及发展分析[J].电力系统自动化,2017,41(7):156-167.DOI:10.7500/AEPS20161117005.WANG Yongping,ZHAO Wenqiang,YANG Jianming,et al.Hybrid high-voltage direct current transmission technology and its development analysis[J].Automation of Electric Power Systems,2017,41(7):156-167.DOI:10.7500/AEPS20161117005.
[23] RABIH A.Modeling network losses using quadratic cones[J].IEEE Transactions on Power Systems,2005,20(1):505-506.
[24] LOBO M S,VANDENBERGHE L,BOYD S,et al.Applications of second-order cone programming[J].Linear Algebra & Its Applications,1998,284(1/2/3):193-228.
[25] 赖晓文,马晓伟,白杨,等.基于混合整数二阶锥规划的动态无功优化方法[J].电力系统自动化,2017,41(17):37-42.DOI:10.7500/AEPS20161101004.LAI Xiaowen,MA Xiaowei,BAI Yang,et al.Dynamic reactive power optimization method based on mixed integer second-order cone programming[J].Automation of Electric Power Systems,2017,41(17):37-42.DOI:10.7500/AEPS20161101004.
[26] 孙兴鲁,董萍,王雅平,等.高渗透光伏接入下基于近似值函数的主动配电网鲁棒优化[J].电力系统自动化,2018,42(15):62-69.DOI:10.7500/AEPS20170908016.SUN Xinglu,DONG Ping,WANG Yaping,et al.Robust optimization of active distribution network with high-penetration photovoltaic access based on approximated value function[J].Automation of Electric Power Systems,2018,42(15):62-69.DOI:10.7500/AEPS20170908016.
[27] STEPHEN B,LIEVEN V,王书.凸优化[M].北京:清华大学出版社,2013:207-223.STEPHEN B,LIEVEN V,WANG Shu.Convex optimization[M].Beijing:Tsinghua University Press,2013:207-223.
[28] 张伯明,陈寿孙.高等电力网络分析[M].北京:清华大学出版社,1996:297-302.ZHANG Boming,CHEN Shousun.Advanced power network analysis[M].Beijing:Tsinghua University Press,1996:297-302.
[29] LOFBERG J.YALMIP:a toolbox for modeling and optimization in MATLAB[C]// 2004 IEEE International Conference on Robotics and Automation,September 2-4,2004,New Orleans,USA.
[30] Gurobi Company.Gurobi optimizer[EB/OL].[2018-05-31].http://www.gurobi.com.
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