适用于CPU+GPU协同架构的大规模病态潮流求解方法
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摘要
随着电网规模不断扩大,负荷增长明显,快速、准确地进行大规模病态潮流求解具有重要的实用价值。将连续牛顿法(CNM)应用于大规模电力系统病态潮流求解中,将潮流方程的求解过程等效为常微分方程组积分计算过程。为了加速该计算过程,针对中央处理器(CPU)+图形处理器(GPU)协同计算架构,设计了基于GPU的不平衡功率快速计算方法,进而优化CNM算法并行实现所需软硬件配置,形成高效的大规模病态潮流求解方法。通过多个大规模病态潮流算例验证了所提CPU+GPU协同潮流计算方法的正确性和实用性。
With the growing size and increasing load of power systems,it has great significance in practice to solve the largescale ill-conditioned power flow problems accurately and efficiently.The continuous Newton's method(CNM)is applied to solve the ill-conditioned cases of large-scale power systems by equalizing the solving process of nonlinear equations to the numerical integration of ordinary differential equations.The coordination architecture of central processing unit(CPU)and graphics processing unit(GPU)is used to accelerate power flow calculations with CNM.Unbalanced power analysis is designed and implemented on GPU.Every part of the whole algorithm is optimized in consideration of characteristics of the coordination architecture to form an efficient solving method.Large-scale ill-conditioned cases are presented to verify the correctness and practicality of the proposed CPU and GPU coordinated power flow computation method.
With the growing size and increasing load of power systems,it has great significance in practice to solve the largescale ill-conditioned power flow problems accurately and efficiently.The continuous Newton's method(CNM)is applied to solve the ill-conditioned cases of large-scale power systems by equalizing the solving process of nonlinear equations to the numerical integration of ordinary differential equations.The coordination architecture of central processing unit(CPU)and graphics processing unit(GPU)is used to accelerate power flow calculations with CNM.Unbalanced power analysis is designed and implemented on GPU.Every part of the whole algorithm is optimized in consideration of characteristics of the coordination architecture to form an efficient solving method.Large-scale ill-conditioned cases are presented to verify the correctness and practicality of the proposed CPU and GPU coordinated power flow computation method.
引文
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[2]于宏文,郑春伟,汪洋,等.智能电网调度控制系统中历史数据服务优化方案[J].电力系统自动化,2016,40(19):113-118.DOI:10.7500/AEPS20150928001.YU Hongwen,ZHENG Chunwei,WANG Yang,et al.Historical data service optimization scheme for smart grid dispatching and control systems[J].Automation of Electric Power Systems,2016,40(19):113-118.DOI:10.7500/AEPS20150928001.
[3]IWAMOTO S,TAMURA Y.A load flow calculation method for ill-conditioned power systems[J].IEEE Transactions on Power Apparatus and Systems,1981,100(4):1736-1743.
[4]杜正春,周佃民,董继民.考虑负荷电压静特性的最佳乘子牛顿潮流算法[J].中国电机工程学报,2002,22(1):102-105.DU Zhengchun,ZHOU Dianmin,DONG Jimin.Optimal multiplier Newton method of load flow with static load characteristics[J].Proceedings of the CSEE,2002,22(1):102-105.
[5]胡泽春,王锡凡.基于最优乘子潮流确定静态电压稳定临界点[J].电力系统自动化,2006,30(6):6-11.HU Zechun,WANG Xifan.Determination of static voltage collapse critical point based on load flow method with optimal multiplier[J].Automation of Electric Power Systems,2006,30(6):6-11.
[6]张道天,严正,徐潇源,等.采用隐式Cholesky分解的大规模病态潮流计算[J].电网技术,2016,40(4):1197-1203.ZHANG Daotian,YAN Zheng,XU Xiaoyuan,et al.Largescale ill-conditioned power flow calculation using implicit Cholesky factorization method[J].Power System Technology,2016,40(4):1197-1203.
[7]SHAHRIARI A,MOKHLIS H,BAKAR A H A,et al.The calculation of low voltage solution based on state space search method in ill-conditioned system[J].Corrosion Science,2012,20(8/9):1059-1066.
[8]周佃民,廖培金.电力系统病态潮流的同伦方法求解[J].电力系统及其自动化学报,1999,11(5/6):67-71.ZHOU Dianmin,LIAO Peijin.Homotopy method for illconditioned power system load flow calculation[J].Proceedings of the CSU-EPSA,1999,11(5/6):67-71.
[9]MILANO F.Continuous Newton’s method for power flow analysis[J].IEEE Transactions on Power Systems,2009,24(1):50-57.
[10]RAMM A G,SMIRNOVA A B,FAVINI A.Continuous modified Newton’s-type method for nonlinear operator equations[J].Annali Di Matematica Pura Ed Applicata,2003,182(1):37-52.
[11]AIRAPETYAN R.Continuous Newton method and its modification[J].Applicable Analysis,1999,73(3/4):463-484.
[12]BUTCHER J C.The numerical analysis of ordinary differential equations:Runge-Kutta and general linear methods[J].Mathematics of Computation,1987,51(183):693.
[13]SCHENK O,GRTNER K,FICHTNER W.Efficient sparse LU factorization with left-right looking strategy on shared memory multiprocessors[J].Bit Numerical Mathematics,2000,40(1):158-176.
[14]FORD W.Chapter 11-Gaussian elimination and the LUdecomposition[M]//Numerical Linear Algebra with Applications,2015:205-239.
[15]CHEN X,WANG Y,YANG H.NICSLU:an adaptive sparse matrix solver for parallel circuit simulation[M].Piscataway,USA:IEEE Press,2013.
[16]SCHENK O,GRTNER K.PARDISO[M].Boston:Springer,2011:1458-1464.
[17]NVIDIA.CUDA toolkit documentation v8.0[EB/OL].[2017-06-23].http://docs.nvidia.com/cuda/index.html.