电力系统全纯嵌入潮流的并行计算

doi:10.19595/j.cnki.1000-6753.tces.231195

Abstract
Figure/Table
References
Related Citation (15)

Download: PDF (28831 KB) HTML (1 KB)
Export: BibTeX | EndNote (RIS)

Abstract Power flow calculation is the foundation of power system analysis and control. At present, the Newton-Raphson (NR) method is still the most widely used, and its convergence depends on the initial values election. When the power flow is overloaded, the Jacobian matrix of the NR method is prone to singularity, resulting in divergence of the power flow calculation, making it difficult to meet the efficiency and robustness requirements of complex power flow calculation. Unlike the NR method, the holomorphic embedded power flow (HELM) is a recursive rather than an iterative process. This method fixes the center of the expansion at the initial point and expands the power series term to obtain the target solution. Accordingly, the initial value is no longer to be set, ensuring convergence to the power flow solution and providing a clear signal when there is no power flow solution. However, when solving large-scale power flow, HELM requires multiple solutions to high-dimensional power series coefficient linear equations and Padé approximation, and its computational efficiency is lower than the NR method. Therefore, improving the computational efficiency of HELM is crucial.
This paper proposes a power system holomorphic embedded power flow parallel calculation method based on stable bi-conjugate gradient stabilized (BICGSTAB) and Aitken difference. The BICGSTAB method is used to solve high-dimensional power series coefficient linear equations iteratively. A sparse matrix approximate inverse preprocessor is constructed based on the coefficient matrix of the equation system to improve the convergence effect of the BICGSTAB method and quickly obtain the coefficients of each order of the voltage power series. Then, based on the traditional Aitken difference method, a new Aitken difference calculation for solving voltage is constructed to rapidly calculate rational approximation values of power series of voltage. Next, with the CPU-GPU heterogeneous computing platform, the large-scale matrix vector in the BICGSTAB method is calculated using the GPU, and the logical judgment part of BICGSTAB is achieved using the CPU. Then, an adaptive thread calling method using GPU threads and voltage one-to-one correspondence automatically calls the same thread number as the number of nodes when solving power flow of different scales. Approximation values of voltage power series for all nodes can be calculated in parallel. Furthermore, combined with the above parallel computing based on the CPU-GPU heterogeneous computing platform, the overall parallel computing process is proposed. Finally, the proposed power flow holomorphic embedded parallel calculation method is analyzed and validated through different power system test examples with node sizes ranging from 1 354 to 13 802.

Key words： Holomorphic embedding method (HEM) power flow calculation Aitken difference method CPU-GPU heterogeneous platform preconditioner

Received: 24 July 2023

PACS:

TM744

	Service

	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors
	Li Xue
	Gao Xiang
	Jiang Tao
	Wang Changjiang
	Li Guoqing

Cite this article:

Li Xue,Gao Xiang,Jiang Tao等. Parallel Computing Method of Power System Holomorphic Embedded Power Flow[J]. Transactions of China Electrotechnical Society, 2024, 39(18): 5839-5854.

URL:

https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.231195 OR https://dgjsxb.ces-transaction.com/EN/Y2024/V39/I18/5839

[1] 柴润泽, 张保会, 薄志谦. 含电压源型换流器直流电网的交直流网络潮流交替迭代方法[J]. 电力系统自动化, 2015, 39(7): 7-13.
Chai Runze, Zhang Baohui, Bo Zhiqian.Alternating iterative power flow algorithm for hybrid AC/DC networks containing DC grid based on voltage source converter[J]. Automation of Electric Power Systems, 2015, 39(7): 7-13.
[2] 刘洪, 赵晨晓, 葛少云, 等. 基于精细化热网模型的电热综合能源系统时序潮流计算[J]. 电力系统自动化, 2021, 45(4): 63-72.
Liu Hong, Zhao Chenxiao, Ge Shaoyun, et al.Sequential power flow calculation of power-heat integrated energy system based on refined heat network model[J]. Automation of Electric Power Systems, 2021, 45(4): 63-72.
[3] 刘承锡, 徐慎凯, 赖秋频. 基于全纯嵌入法的非迭代电力系统最优潮流计算[J]. 电工技术学报, 2023, 38(11): 2870-2882.
Liu Chengxi, Xu Shenkai, Lai Qiupin.Non-iterative optimal power flow calculation based on holomorphic embedding method[J]. Transactions of China Elec- trotechnical Society, 2023, 38(11): 2870-2882.
[4] 姜涛, 张勇, 李雪, 等. 电力系统交直流潮流的全纯嵌入计算[J]. 电工技术学报, 2021, 36(21): 4429-4443, 4481.
Jiang Tao, Zhang Yong, Li Xue, et al.A holomorphic embedded method for solving power flow in hybrid AC-DC power system[J]. Transactions of China Electrotechnical Society, 2021, 36(21): 4429-4443, 4481.
[5] 王紫瑶, 廖进贤, 杨家豪, 等. 计及功率控制模式的VSC-MTDC交直流并列运行系统概率潮流计算[J]. 电气技术, 2019, 20(2): 12-17.
Wang Ziyao, Liao Jinxian, Yang Jiahao, et al.Pro- babilistic load flow calculation of VSC-MTDC AC/DC parallel operation system considering power control mode[J]. Electrical Engineering, 2019, 20(2): 12-17.
[6] 李雪, 姚超凡, 姜涛, 等. 基于常项值和先验节点的全纯嵌入潮流计算方法[J]. 电力自动化设备, 2023, 43(2): 142-150.
Li Xue, Yao Chaofan, Jiang Tao, et al.Constant values and priori buses based holomorphic embedding load flow method[J]. Electric Power Automation Equipment, 2023, 43(2): 142-150.
[7] Trias A.The holomorphic embedding load flow method[C]//2012 IEEE Power and Energy Society General Meeting, San Diego, CA, USA, 2012: 1-8.
[8] Liu Chengxi, Wang Bin, Hu Fengkai, et al.Online voltage stability assessment for load areas based on the holomorphic embedding method[C]//2018 IEEE Power & Energy Society General Meeting (PESGM), Portland, OR, USA, 2018: 1.
[9] Wu Dan, Wang Bin.Holomorphic embedding based continuation method for identifying multiple power flow solutions[J]. IEEE Access, 2019, 7: 86843-86853.
[10] Liu Chengxi, Wang Bin, Xu Xin, et al.A multi- dimensional holomorphic embedding method to solve AC power flows[J]. IEEE Access, 2017, 5: 25270-25285.
[11] Liu Chengxi, Sun Kai, Wang Bin, et al.Probabilistic power flow analysis using multi-dimensional holomorphic embedding and generalized cumulants[C]// 2019 IEEE Power & Energy Society General Meeting (PESGM), Atlanta, GA, USA, 2019: 1.
[12] 张勇. 含VSC: MTDC的交直流电力系统潮流全纯嵌入计算方法研究[D]. 吉林: 东北电力大学, 2021.
Zhang Yong.Research on pure embedding calculation method of power flow in AC/DC power system with VSC--MTDC[D]. Jilin: Northeast Dianli University, 2021.
[13] 李建斌, 王鹏程, 傅侃, 等. 基于预处理共轭梯度迭代法的电力系统状态估计算法[J]. 电力系统自动化, 2021, 45(14): 90-96.
Li Jianbin, Wang Pengcheng, Fu Kan, et al.State estimation algorithm of power system based on preconditioned conjugate gradient iteration[J]. Auto- mation of Electric Power Systems, 2021, 45(14): 90-96.
[14] 唐灿, 董树锋, 任雪桂, 等. 用于迭代法潮流计算的改进Jacobi预处理方法[J]. 电力系统自动化, 2018, 42(12): 81-86.
Tang Can, Dong Shufeng, Ren Xuegui, et al.Improved Jacobi pre-treatment method for solving iterative power flow calculation[J]. Automation of Electric Power Systems, 2018, 42(12): 81-86.
[15] 刘珊瑕, 靳松, 王文琛, 等. 基于变量相关性分解方法的稀疏线性方程组并行求解算法[J]. 清华大学学报(自然科学版), 2020, 60(4): 312-320.
Liu Shanxia, Jin Song, Wang Wenchen, et al.Parallel algorithm for solving sparse linear equations based on variable correlation decomposition[J]. Journal of Tsinghua University (Science and Technology), 2020, 60(4): 312-320.
[16] 蔡大用, 陈玉荣. 用不完全LU分解预处理的不精确潮流计算方法[J]. 电力系统自动化, 2002, 26(8): 11-14.
Cai Dayong, Chen Yurong.Solving power flow equationswith inexact Newton methodspreconditioned by incomplete LU factorization with partially fill-in[J]. Automation of Electric Power Systems, 2002, 26(8): 11-14.
[17] 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 LU decomposition preconditioning[J]. Proceedings of the CSEE, 2017, 37(S1): 55-62.
[18] 林亚君, 陈学军, 陈越. 基于雅可比矩阵逆预处理的快速潮流计算方法[J]. 计算技术与自动化, 2019, 38(2): 72-75.
Lin Yajun, Chen Xuejun, Chen Yue.Fast flow calculation method with Jacobian matrix inverse preconditions[J]. Computing Technology and Auto- mation, 2019, 38(2): 72-75.
[19] Li Xue, Li Fangxing, Yuan Haoyu, et al.GPU-based fast decoupled power flow with preconditioned iterative solver and inexact Newton method[J]. IEEE Transactions on Power Systems, 2017, 32(4): 2695-2703.
[20] Chiang H D, Wang Tao, Sheng Hao.A novel fast and flexible holomorphic embedding power flow method[J]. IEEE Transactions on Power Systems, 2018, 33(3): 2551-2562.
[21] Trias A, Marín J L.A Padé-Weierstrass technique for the rigorous enforcement of control limits in power flow studies[J]. International Journal of Electrical Power & Energy Systems, 2018, 99: 404-418.
[22] 李雪, 李博, 姜涛, 等. 主动配电网潮流的全纯嵌入计算方法[J]. 中国电机工程学报, 2024, 44(11): 4210-4226.
Li Xue, Li Bo, Jiang Tao, et al.A holomorphic embedding power flow algorithm for active dis- tribution network[J]. Proceedings of the CSEE, 2024, 44(11): 4210-4226.
[23] 宋晓喆, 魏国, 李雪, 等. 基于预处理BICGSTAB法的电力系统潮流并行计算方法[J]. 电力系统保护与控制, 2020, 48(20): 18-28.
Song Xiaozhe, Wei Guo, Li Xue, et al.Parallel power flow computing in power grids based on a preconditioned BICGSTAB method[J]. Power System Protection and Control, 2020, 48(20): 18-28.
[24] 冯金超, 李祎楠, 李哲, 等. 结合预处理BiCGStab和CUDA的BLT快速并行前向方法[J]. 北京工业大学学报, 2017, 43(11): 1658-1665.
Feng Jinchao, Li Yinan, Li Zhe, et al.Fast parallel forward method of BLT combining preconditioned Bi CGStab and CUDA[J]. Journal of Beijing University of Technology, 2017, 43(11): 1658-1665.
[25] Rao S D.Exploration of a scalable holomorphic embedding method formulation for power system analysis applications[D]. Arizona: Arizona State University. 2017.
[26] Rao S D, Tylavsky D J.Theoretical convergence guarantees versus numerical convergence behavior of the holomorphically embedded power flow method[J]. International Journal of Electrical Power & Energy Systems, 2018, 95: 166-176.
[27] 邱智勇, 周越德, 刘中平. CPU+GPU架构下节点阻抗矩阵生成及节点编号优化方法[J]. 电力系统自动化, 2020, 44(2): 215-221.
Qiu Zhiyong, Zhou Yuede, Liu Zhongping.Optimal methods of node impedance matrix construction and node numbering based on CPU and GPU collaborative architecture[J]. Automation of Electric Power Systems, 2020, 44(2): 215-221.
[28] 姜涛, 张道远, 李雪, 等. 基于自适应幂级数初始点的电力系统全纯嵌入潮流并行计算[J]. 电力自动化设备, 2023, 43(10): 208-216.
Jiang Tao, Zhang Daoyuan, Li Xue, et al.Adaptive power series initial points based holomorphic embedding load flow parallel calculation for power system[J]. Electric Power Automation Equipment, 2023, 43(10): 208-216.
[29] 李雪, 张琳玮, 姜涛, 等. 基于CPU-GPU异构的电力系统静态电压稳定域边界并行计算方法[J]. 电工技术学报, 2021, 36(19): 4070-4084.
Li Xue, Zhang Linwei, Jiang Tao, et al.CPU-GPU heterogeneous computing for static voltage stability region boundary in bulk power systems[J]. Transa- ctions of China Electrotechnical Society, 2021, 36(19): 4070-4084.
[30] Zimmerman R D, Murillo-Sánchez C E, Thomas R J. MATPOWER: steady-state operations, planning, and analysis tools for power systems research and education[J]. IEEE Transactions on Power Systems, 2011, 26(1): 12-19.