大规模输配一体化系统牛顿法潮流计算性能分析及改进方法
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摘要
为满足输配电网一体化潮流计算精度和计算速度需求,提出了一种改进的牛顿法潮流计算方法。针对输配电网一体化牛顿法雅可比矩阵病态严重、收敛性能较差等问题,采用自适应Levenberg-Marquardt算法初始精度提升速度快的特征选取初值、不完全三角分解法预处理雅可比矩阵,有效地保证了数值稳定性,提高了牛顿法的收敛性能。针对输配电网一体化后规模庞大、计算效率低等问题,利用图形处理器并行加速技术对算法中的一些计算量密集的步骤,包括雅可比矩阵的生成、矩阵—向量运算等进行加速处理。算例测试表明,该算法能够显著提高大规模输配电网一体化潮流计算的速度和精度,对于多配电网区域、环网、分布式电源、病态系统等多种情形具有较强的普适性。
In order to meet the demand of integrated power flow calculation speed,an improved Newton method is proposed.In view of the seriously ill-conditioned Jacobian matrix and poor convergence and so on,an adaptive Levenberg-Marquardt method is used to choose the initial values,and incomplete LU decomposition method is used to preprocess Jacobian matrices,which effectively guarantees the numerical stability and improves the convergence of Newton method.To solve the problem of largescale and low computing efficiency after integration of transmission and distribution networks,the GPU parallel acceleration technology is used to accelerate some steps with intensive computation including the formation of Jacobian matrix,matrixvector operation and so on.The numerical experiments show that,the proposed algorithm can significantly improve the speed and accuracy of the large-scale integrated transmission and distribution networks,and it has a strong universality for different situations such as multiple distribution network areas,distribution network with loops or distributed generators,ill-conditioned systems.
In order to meet the demand of integrated power flow calculation speed,an improved Newton method is proposed.In view of the seriously ill-conditioned Jacobian matrix and poor convergence and so on,an adaptive Levenberg-Marquardt method is used to choose the initial values,and incomplete LU decomposition method is used to preprocess Jacobian matrices,which effectively guarantees the numerical stability and improves the convergence of Newton method.To solve the problem of largescale and low computing efficiency after integration of transmission and distribution networks,the GPU parallel acceleration technology is used to accelerate some steps with intensive computation including the formation of Jacobian matrix,matrixvector operation and so on.The numerical experiments show that,the proposed algorithm can significantly improve the speed and accuracy of the large-scale integrated transmission and distribution networks,and it has a strong universality for different situations such as multiple distribution network areas,distribution network with loops or distributed generators,ill-conditioned systems.
引文
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[10]SUN Hongbin,GUO Qinglai,ZHANG Boming,et al.Masterslave-splitting based distributed global power flow method for integrated transmission and distribution analysis[J].IEEETransactions on Smart Grid,2015,6(3):1484-1492.
[11]孙宏斌,郭烨,张伯明.含环状配电网的输配全局潮流分布式计算[J].电力系统自动化,2008,32(13):11-15.SUN Hongbin,GUO Ye,ZHANG Boming.Distributed global power flow calculation for whole transmission and looped distribution networks[J].Automation of Electric Power Systems,2008,32(13):11-15.
[12]CHEN Ying,SHEN Chen.A Jacobian-free Newton-GMRES(m)method with adaptive preconditioner and its application for power flow calculations[J].IEEE Transactions on Power Systems,2006,21(3):1096-1103.
[13]HUANG W T,YAO K C.New network sensitivity-based approach for real-time complex power flow calculation[J].IETGeneration Transmission and Distribution,2012,6(2):109-120.
[14]YANG H,WEN F,WANG L.Newton-Raphson on power flow algorithm and Broyden method in the distribution system[C]//IEEE Power and Energy Conference,December 1-3,2008,Johor Bahru,Malaysia:1613-1618.
[15]LAGACE P J,VUONG M H,KAMWA I.Improving power flow convergence by Newton Raphson with a LevenbergMarquardt method[C]//IEEE Power and Energy Society General Meeting,July 20-24,2008,Pittsburgh,USA:1-6.
[16]严正,范翔,赵文恺,等.自适应Levenberg-Marquardt方法提高潮流计算收敛性[J].中国电机工程学报,2015,35(8):1909-1918.YAN Zheng,FAN Xiang,ZHAO Wenkai,et al.Improving the convergence of power flow calculation by a self-adaptive Levenberg-Marquardt method[J].Proceedings of the CSEE,2015,35(8):1909-1918.
[17]曹佳,徐潇源,严正,等.几种高阶收敛的Levenberg-Marquardt方法在潮流计算中的应用[J].电网技术,2017,41(4):1181-1187.CAO Jia,XU Xiaoyuan,YAN Zheng,et al.Application of several Levenberg-Marquardt methods with higher-order convergence in power flow calculation[J].Power System Technology,2017,41(4):1181-1187.
[18]李智欢,朱乔木,苏寅生,等.几种提高牛顿法潮流收敛性的初值给定方法研究[J].电工电气,2015(10):1-5.LI Zhihuan,ZHU Qiaomu,SU Yinsheng,et al.Research on several initial value methods of improved Newton-Raphson power flow convergence[J].Electrotechnics Electric,2015(10):1-5.
[19]唐坤杰,董树锋,宋永华.基于不完全LU分解预处理迭代法的电力系统潮流算法[J].中国电机工程学报,2017,37(增刊1):55-62.TANG Kunjie,DONG Shufeng,SONG Yonghua.Power flow algorithm based on an iterative method with incomplete LUdecomposition preconditioning[J].Proceedings of the CSEE,2017(Supplement 1):55-62.
[20]唐坤杰,董树锋,宋永华.一种GPU-CPU异构运算框架加速的实时N-1交流潮流计算方法[J].中国电机工程学报,2018,38(15):4329-4338.TANG Kunjie,DONG Shufeng,SONG Yonghua.A real-time N-1AC power flow calculation method based on GPU-CPUheterogeneous computing framework[J].Proceedings of the CSEE,2018,38(15):4329-4338.
[21]BARAN M E,WU F F.Optimal capacitor placement on radial distribution systems[J].IEEE Transactions on Power Delivery,2002,4(1):725-734.
[22]ZHANG D,FU Z,ZHANG L.An improved TS algorithm for loss-minimum reconfiguration in large-scale distribution systems[J].Electric Power Systems Research,2007,77(5/6):685-694.
[23]孙秋野,陈会敏,杨家农,等.牛顿类潮流计算方法的收敛性分析[J].中国电机工程学报,2014,34(13):2196-2200.SUN Qiuye,CHEN Huimin,YANG Jianong,et al.Analysis on convergence of Newton-like power flow algorithm[J].Proceedings of the CSEE,2014,34(13):2196-2200.
[24]谷同祥.迭代方法和预处理技术(下册)[M].北京:科学出版社,2015:159-232.GU Tongxiang.Iterative methods and preprocessing techniques(PartⅡ)[M].Beijing:Science Press,2015:159-232.
[25]SAUER T.Numerical analysis[M].Cambridge:Pearson Publishing Ltd,2016:235-236.
[26]张朝晖,刘俊起,徐勤建.GPU并行计算技术分析与应用[J].信息技术,2009(11):86-89.ZHANG Chaohui,LIU Junqi,XU Qinjian.Analysis and application of the GPU parallel computing technology[J].Information Technology,2009(11):86-89.
[27]COOK S.CUDA programming:a developer’s guide to parallel computing with GPUs[M].Amsterdam:Elsevier,2012.
[28]LAGACE P J.Power flow methods for improving convergence[C]//IEEE Annual Conference on IEEE Industrial Electronics Society,October 25-28,2012,Montreal,Canada:1387-1392.
[2]刘涛,米为民,陈郑平,等.适用于大运行体系的电网模型一体化共享方案[J].电力系统自动化,2015,39(1):36-41.LIU Tao,MI Weimin,CHEN Zhengping,et al.Integrated sharing scheme for grid model and graphics applicable to grand operation system[J].Automation of Electric Power Systems,2015,39(1):36-41.
[3]郑宗强,韩冰,闪鑫,等.输配电网高级应用协同运行关键技术分析[J].电力系统自动化,2017,41(6):122-128.DOI:10.7500/AEPS20161212003.ZHENG Zongqiang,HAN Bing,SHAN Xin,et al.Analysis on key technologies for coordinated operation of advanced application software in transmission and distribution network[J].Automation of Electric Power Systems,2017,41(6):122-128.DOI:10.7500/AEPS20161212003.
[4]闪鑫,王轶禹,金一丁,等.特高压互联电网一体化监视和故障协同处置方案及应用[J].电力系统自动化,2018,42(2):84-91.DOI:10.7500/AEPS20170230005.SHAN Xin,WANG Yiyu,JIN Yiding,et al.Scheme and application of integrated monitoring and fault co-disposal technology of UHV interconnected power grid[J].Automation of Electric Power Systems,2018,42(2):84-91.DOI:10.7500/AEPS20170230005.
[5]郭健,周京阳,李强,等.高性能在线分析计算现状与协同计算关键技术[J].电力系统自动化,2018,42(3):149-159.DOI:10.7500/AEPS20170230007.GUO Jian,ZHOU Jingyang,LI Qiang,et al.Current status of high-performance on-line analysis computation and key technologies for cooperating computation[J].Automation of Electric Power Systems,2018,42(3):149-159.DOI:10.7500/AEPS20170230007.
[6]许洪强,姚建国,南贵林,等.未来电网调度控制系统应用功能的新特征[J].电力系统自动化,2018,42(1):1-7.DOI:10.7500/AEPS20170518001.XU Hongqiang,YAO Jianguo,NAN Guilin,et al.New features of application function for future dispatching and control systems[J].Automation of Electric Power Systems,2018,42(1):1-7.DOI:10.7500/AEPS20170518001.
[7]JAIN H,RAHIMI K,TBAILEH A,et al.Integrated transmission&distribution system modeling and analysis:need&advantages[C]//IEEE Power and Energy Society General Meeting,July 17-21,2016,Boston,USA:1-5.
[8]郭志红,韩学山,李文博,等.适应分布式电源的输配电网协调潮流算法[J].山东电力技术,2014(1):1-6.GUO Zhihong,HAN Xueshan,LI Wenbo,et al.Acoordination power flow algorithm for power transmissiondistribution grid accommodate distributed generations[J].Shandong Electric Power,2014(1):1-6.
[9]MARINHO J M T,TARANTO G N.A hybrid three-phase single-phase power flow formulation[J].IEEE Transactions on Power Systems,2008,23(3):1063-1070.
[10]SUN Hongbin,GUO Qinglai,ZHANG Boming,et al.Masterslave-splitting based distributed global power flow method for integrated transmission and distribution analysis[J].IEEETransactions on Smart Grid,2015,6(3):1484-1492.
[11]孙宏斌,郭烨,张伯明.含环状配电网的输配全局潮流分布式计算[J].电力系统自动化,2008,32(13):11-15.SUN Hongbin,GUO Ye,ZHANG Boming.Distributed global power flow calculation for whole transmission and looped distribution networks[J].Automation of Electric Power Systems,2008,32(13):11-15.
[12]CHEN Ying,SHEN Chen.A Jacobian-free Newton-GMRES(m)method with adaptive preconditioner and its application for power flow calculations[J].IEEE Transactions on Power Systems,2006,21(3):1096-1103.
[13]HUANG W T,YAO K C.New network sensitivity-based approach for real-time complex power flow calculation[J].IETGeneration Transmission and Distribution,2012,6(2):109-120.
[14]YANG H,WEN F,WANG L.Newton-Raphson on power flow algorithm and Broyden method in the distribution system[C]//IEEE Power and Energy Conference,December 1-3,2008,Johor Bahru,Malaysia:1613-1618.
[15]LAGACE P J,VUONG M H,KAMWA I.Improving power flow convergence by Newton Raphson with a LevenbergMarquardt method[C]//IEEE Power and Energy Society General Meeting,July 20-24,2008,Pittsburgh,USA:1-6.
[16]严正,范翔,赵文恺,等.自适应Levenberg-Marquardt方法提高潮流计算收敛性[J].中国电机工程学报,2015,35(8):1909-1918.YAN Zheng,FAN Xiang,ZHAO Wenkai,et al.Improving the convergence of power flow calculation by a self-adaptive Levenberg-Marquardt method[J].Proceedings of the CSEE,2015,35(8):1909-1918.
[17]曹佳,徐潇源,严正,等.几种高阶收敛的Levenberg-Marquardt方法在潮流计算中的应用[J].电网技术,2017,41(4):1181-1187.CAO Jia,XU Xiaoyuan,YAN Zheng,et al.Application of several Levenberg-Marquardt methods with higher-order convergence in power flow calculation[J].Power System Technology,2017,41(4):1181-1187.
[18]李智欢,朱乔木,苏寅生,等.几种提高牛顿法潮流收敛性的初值给定方法研究[J].电工电气,2015(10):1-5.LI Zhihuan,ZHU Qiaomu,SU Yinsheng,et al.Research on several initial value methods of improved Newton-Raphson power flow convergence[J].Electrotechnics Electric,2015(10):1-5.
[19]唐坤杰,董树锋,宋永华.基于不完全LU分解预处理迭代法的电力系统潮流算法[J].中国电机工程学报,2017,37(增刊1):55-62.TANG Kunjie,DONG Shufeng,SONG Yonghua.Power flow algorithm based on an iterative method with incomplete LUdecomposition preconditioning[J].Proceedings of the CSEE,2017(Supplement 1):55-62.
[20]唐坤杰,董树锋,宋永华.一种GPU-CPU异构运算框架加速的实时N-1交流潮流计算方法[J].中国电机工程学报,2018,38(15):4329-4338.TANG Kunjie,DONG Shufeng,SONG Yonghua.A real-time N-1AC power flow calculation method based on GPU-CPUheterogeneous computing framework[J].Proceedings of the CSEE,2018,38(15):4329-4338.
[21]BARAN M E,WU F F.Optimal capacitor placement on radial distribution systems[J].IEEE Transactions on Power Delivery,2002,4(1):725-734.
[22]ZHANG D,FU Z,ZHANG L.An improved TS algorithm for loss-minimum reconfiguration in large-scale distribution systems[J].Electric Power Systems Research,2007,77(5/6):685-694.
[23]孙秋野,陈会敏,杨家农,等.牛顿类潮流计算方法的收敛性分析[J].中国电机工程学报,2014,34(13):2196-2200.SUN Qiuye,CHEN Huimin,YANG Jianong,et al.Analysis on convergence of Newton-like power flow algorithm[J].Proceedings of the CSEE,2014,34(13):2196-2200.
[24]谷同祥.迭代方法和预处理技术(下册)[M].北京:科学出版社,2015:159-232.GU Tongxiang.Iterative methods and preprocessing techniques(PartⅡ)[M].Beijing:Science Press,2015:159-232.
[25]SAUER T.Numerical analysis[M].Cambridge:Pearson Publishing Ltd,2016:235-236.
[26]张朝晖,刘俊起,徐勤建.GPU并行计算技术分析与应用[J].信息技术,2009(11):86-89.ZHANG Chaohui,LIU Junqi,XU Qinjian.Analysis and application of the GPU parallel computing technology[J].Information Technology,2009(11):86-89.
[27]COOK S.CUDA programming:a developer’s guide to parallel computing with GPUs[M].Amsterdam:Elsevier,2012.
[28]LAGACE P J.Power flow methods for improving convergence[C]//IEEE Annual Conference on IEEE Industrial Electronics Society,October 25-28,2012,Montreal,Canada:1387-1392.