A Holomorphic Embedded Method for Solving Power Flow in Hybrid AC-DC Power System
Jiang Tao, Zhang Yong, Li Xue, Li Guoqing, Chen Houhe
Key Laboratory of Modern Power System Simulation and Control & Renewable Energy Technology Ministry of Education Northeast Electric Power University Jilin 132012 China
Abstract：In order to address the initial value selection and large calculation amount when Newton Raphson(NR) method is used to calculate AC-DC power flow, this paper proposes a holomorphic embedding method for AC-DC power flow calculation. Firstly, according to the construction principle of holomorphic function, the holomorphic AC-DC power flow model and converter station control model are constructed by embedding parameters. Then, based on the Taylor series expansion characteristics of the holomorphic function, the problem of solving nonlinear power flow equations is transformed into an explicit problem of implicit holomorphic functions. Moreover, according to the principle that the same power coefficient is equal, the power series coefficient of Taylor series expansion term is obtained, and the explicit holomorphic function is completed, and then the embedded parameters are assigned to realize the fast solution of AC-DC power flow. Finally, it is analyzed and verified through modified IEEE 5 node AC-DC system, RTS-96 AC-DC system and Polish power grid 3012wp AC-DC test system. The results show that the proposed method can quickly and accurately calculate the power flow of AC-DC power system without relying on the initial value, and has strong robustness, which provides a new idea for power flow calculation of large-scale AC-DC power grid.
姜涛, 张勇, 李雪, 李国庆, 陈厚合. 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.
Jiang Tao, Zhang Yong, Li Xue, Li Guoqing, Chen Houhe. A Holomorphic Embedded Method for Solving Power Flow in Hybrid AC-DC Power System. Transactions of China Electrotechnical Society, 2021, 36(21): 4429-4443.
[1] 朱介北, 周小尧, 曾平良, 等. 英国交直流输电网规划方法及对中国电网规划的启示[J]. 全球能源互联网, 2020, 3(1): 59-69. Zhu Jiebei, Zhou Xiaoyao, Zeng Pingliang, et al.UK AC-DC power grid planning method and its implications for China power grid planning[J]. Global Energy Internet, 2020, 3(1): 59-69. [2] 骆悦, 姚骏, 张田, 等. 大规模风电直流外送系统单极闭锁场景下送端系统协调控制策略[J]. 电工技术学报, 2019, 34(19): 4108-4118. Luo Yue, Yao Jun, Zhang Tian, et al.Coordinated control strategy of sending-end system in the single-pole blocking scenario of large-scale wind power DC transmission system[J]. Transactions of China Electrotechnical Society, 2019, 34(19): 4108-4118. [3] 李岩, 滕云, 冷欧阳, 等. 含多端柔性直流互联的交直流电力系统静态安全分析[J]. 电力系统自动化, 2019, 43(10): 155-163. Li Yan, Teng Yun, Leng Ouyang, et al.Static security analysis of AC-DC power system with multi-terminal flexible DC interconnection[J]. Automation of Electric Power Systems, 2019, 43(10): 155-163. [4] 李国庆, 边竞, 王鹤, 等. 适用于直流电网的环流式线间直流潮流控制器[J]. 电工技术学报, 2020, 35(5): 1118-1127. Li Guoqing, Bian Jing, Wang He, et al.Circulating line-to-line DC power flow controller for DC power grids[J]. Transactions of China Electrotechnical Society, 2020, 35(5): 1118-1127. [5] 周晓风, 付艳, 崔晨, 等. 提高分接开关可靠性的直流输电控制策略优化[J]. 电气技术, 2020, 21(9): 54-58. Zhou Xiaofeng, Fu Yan, Cui Chen, et al.The optimization of high voltage direct current control strategy to improve on-load tap changer reliability[J]. Electrical Engineering, 2020, 21(9): 54-58. [6] 王浩翔, 赵冬梅, 陶然, 等. 基于分解的多目标进化算法的含MMC-HVDC交直流混合系统最优潮流研究[J]. 电工技术学报, 2020, 35(17): 3691-3702. Wang Haoxiang, Zhao Dongmei, Tao Ran, et al.Research on optimal power flow of MMC-HVDC AC-DC hybrid system based on decomposition-based multi-objective evolutionary algorithm[J]. Transac-tions of China Electrotechnical Society, 2020, 35(17): 3691-3702. [7] 陈厚合, 黄亚磊, 姜涛, 等. 含VSC-HVDC的交直流系统电压稳定分析与控制[J]. 电网技术, 2017, 41(8): 2429-2438. Chen Houhe, Huang Yalei, Jiang Tao, et al.Voltage stability analysis and control of AC-DC system with VSC-HVDC[J]. Power System Technology, 2017, 41(8): 2429-2438. [8] 杜萍静, 杨明, 曹良晶, 等. 含电压源换流器交直流系统的仿射潮流算法[J]. 电工技术学报, 2020, 35(5): 1106-1117. Du Pingjing, Yang Ming, Cao Liangjing, et al.Affine power flow algorithm for AC-DC system with voltage source converter[J]. Transactions of China Electrotechnical Society, 2020, 35(5): 1106-1117. [9] 郑超, 周孝信, 李若梅, 等. VSC-HVDC稳态特性与潮流算法的研究[J]. 中国电机工程学报, 2005, 25(6): 1-5. Zheng Chao, Zhou Xiaoxin, Li Ruomei, et al.Study on VSC-HVDC steady-state characteristics and power flow algorithm[J]. Proceedings of the CSEE, 2005, 25(6): 1-5. [10] Lei Jingting, An Ting, Du Zhengchun, et al.A general unified AC-DC power flow algorithm with MTDC[J]. IEEE Transactions on Power Systems, 2017, 32(4): 2837-2846. [11] Beerten J, Cole S, Belmans R.Generalized steady-state VSC MTDC model for sequential AC-DC power flow algorithms[J]. IEEE Transactions on Power Systems, 2012, 27(2): 821-829. [12] 郑超, 盛灿辉. 含VSC-HVDC的交直流混合系统潮流统一迭代求解算法[J]. 中国电力, 2007(7): 65-69. Zheng Chao, Sheng Canhui.A uniform iterative algorithm for power flow solution of AC-DC hybrid system with VSC-HVDC[J]. China Electric Power, 2007(7): 65-69. [13] 陈谦, 唐国庆, 王浔. 多端VSC-HVDC系统交直流潮流计算[J]. 电力自动化设备, 2005(6): 1-6. Chen Qian, Tang Guoqing, Wang Xun.AC-DC power flow calculation for multi-terminal VSC-HVDC system[J]. Electric Power Automation Equipment, 2005(6): 1-6. [14] Beerten J, Cole S, Belmans R.A sequential AC-DC power flow algorithm for networks containing multi-terminal VSC-HVDC systems[C]//IEEE PES General Meeting, Providence, RI, 2010: 1-7. [15] Beerten J, Belmans R.Development of an open source power flow software for high voltage direct current grids and hybrid AC-DC systems: MATACDC[J]. IET Generation, Transmission and Distribution, 2015, 9(7): 966-974. [16] 李雪, 刘烨, 姜涛, 等. 电力系统负荷裕度的并行计算方法研究[J]. 中国电机工程学报, 2019, 39(14): 5105-5117. Li Xue, Liu Ye, Jiang Tao, et al.Research on the parallel calculation method of load margin in power system[J]. Proceedings of the CSEE, 209, 39(14): 5105-5117. [17] Marcos T, Kamel S, Jurado F.Robust and efficient approach based on richardson extrapolation for solving badly-initialized/ill-conditioned power flow problems[J]. IET Generation Transmission & Distribution, 2019, 13(13): 3524-3533. [18] Trias A.The holomorphic embedding load flow method[C]//IEEE Power and Energy Society General Meeting, San Diego, 2012: 1-8. [19] Shruti R, Yang Feng, Daniel J, et al.The holomorphic embedding method applied to the power flow problem[J]. IEEE Transactions on Power Systems, 2016, 31(5): 3816-3828. [20] Muthu K, Yang Feng, Daniel T.PV bus modeling in a holomorphically embedded power-flow formulation[C]// North American Power Symposium (NAPS), Manhattan, KS, 2013: 1-6. [21] Jonckheere EA, Ke NP.Complex-analytic theory of the μ-function*[C]//Proceedings of the 1997 American Control Conference, Albuquerque, NM, USA, 1997: 366-371. [22] Liu Chengxi, Wang Bin, Hu Fengkai, et al.Online voltage stability assessment for load areas based on the holomorphic embedding method[J]. IEEE Transactions on Power Systems, 2018, 33(4): 3720-3734. [23] 徐经民, 徐在德, 童超. 基于模糊下垂控制的VSC-HVDC交直流系统潮流计算方法[J]. 电力系统保护与控制, 2019, 47(20): 50-57. Xu Jingmin, Xu Zaide, Tong Chao.VSC-HVDC AC-DC system power flow calculation method based on fuzzy droop control[J]. Power System Protection and Control, 2019, 47(20): 50-57. [24] 陈厚合, 李国庆, 姜涛. 控制方式转换策略下的改进交直流系统潮流算法[J]. 电网技术, 2011, 35(8): 93-98. Chen Houhe, Li Guoqing, Jiang Tao.Improved AC-DC power flow algorithm under control mode switching strategy[J]. Power System Technology, 2011, 35(8): 93-98. [25] 刘英培, 解赛, 梁海平, 等. 计及换流站间电压误差的VSC-MTDC系统自适应下垂控制[J]. 电工技术学报, 2020, 35(15): 3270-3280. Liu Yingpei, Xie Sai, Liang Haiping, et al.Adaptive droop control of VSC-MTDC system considering voltage error between converter stations[J]. Transactions of China Electrotechnical Society, 2020, 35(15): 3270-3280.
2021, Vol. 36 
