|
|
|
| A Holomorphic Embedding Power Flow Algorithm Based on Power Restart |
| Zhang Yi1, Lan Tian1, Li Chuandong2, Cai Weijie1, Wang Jianming3 |
1. School of Electrical Engineering and Automation Fuzhou University Fuzhou 350108 China;
2. School of Mechanical and Electrical Engineering Fujian Agriculture and Forestry University Fuzhou 350100 China;
3. Energy Economics Institute of CNOOC Beijing 100013 China |
|
|
|
Abstract Compared with Newton Raphson (NR) power flow algorithm, holomorphic embedding (HE) power flow algorithm has the advantages of not relying on the initial value selection and obtaining the analytical solution. However, in the actual power flow calculation of large power grids and heavy loads, the power series order required by the algorithm is high, resulting in poor convergence. In view of the above problems, this paper proposes a power restart holomorphic embedded (PRHE) power flow algorithm.
Firstly, based on the initial value flexibility of the flexible holomorphic embedding power flow algorithm, the proposed method defines the initial power state Si0(Pi0) and the target power state Si(Pi) in the power injection space to characterize the physical space relationship between the initial solution and the target solution. The direction correction power Sid(Pid) is used to characterize the analytical continuation direction of the HE power flow algorithm. The restart mechanism and power relaxation method are introduced to perform holomorphic embedding analytical reconstruction of the power flow model in the power injection space, and the model is simplified to obtain a linear recursive calculation matrix model.
On the basis of the above model, this paper introduces the restart mechanism. In the power injection space, the position of the initial state power Si0(Pi0) is continuously updated by each restart to shorten its distance from Si(Pi). Each power restart can also achieve the purpose of correcting the direction and step size of the analytical continuation by updating Sid(Pid), so as to ensure the stable convergence of the system power flow model. In the recursive operation of the model, for each higher power series coefficient calculated, the numerical solution of the obtained analytical expression is obtained at s=1, and the maximum power residual ΔS of the model is calculated by using the obtained numerical solution. The change trend of ΔS reflects the change of the power injection space in the analytic continuation of the holomorphic embedding model to a certain extent, which can be used as a criterion for whether to continue the recursive calculation or whether to restart the power. The control conditions are shown in Equ. (7).
The proposed dynamic restart mechanism Equ. (7) is based on the quotient convergence theorem. Therefore, when (ΔSn-ε)/(ΔSn-1-ε) is closer to 0 (i. e., when (ΔSn-1-ΔSn)/(ΔSn-1-ε) is larger and closer to 1), the proposed method is closer to superlinear convergence and the convergence speed is faster. And considering that the approximation effect of the HE method is most obvious in the first recursive calculation to the second recursive calculation, the proposed restart mechanism sets (ΔS1-ΔS2)/(ΔS1-ε) as the critical value of the convergence speed restart constraint. (ΔS1-ΔS2)/(ΔS1-ε) can have different values according to different operating conditions of different systems. After each restart, (ΔS1-ΔS2)/(ΔS1-ε) will change, which can make the constraint condition Equ. (7) more universal.
Finally, the proposed algorithm is compared with HE power flow algorithm, NR power flow algorithm and CHELM on the IEEE 9, case 2868rte and East China regional networking system, it is verified that the proposed algorithm can effectively deal with the problem of poor convergence of HE power flow algorithm under actual large power grid and heavy load conditions, and improve the computational efficiency of the method.
|
|
Received: 17 October 2024
|
|
|
|
|
|
[1] 陈彬彬, 孙宏斌, 吴文传, 等. 综合能源系统分析的统一能路理论(三): 稳态与动态潮流计算[J]. 中国电机工程学报, 2020, 40(15): 4820-4831.
Chen Binbin, Sun Hongbin, Wu Wenchuan, et al.Energy circuit theory of integrated energy system analysis (Ⅲ): steady and dynamic energy flow calculation[J]. Proceedings of the CSEE, 2020, 40(15): 4820-4831.
[2] 杨浩, 朱宇迪, 刘铖, 等. 基于MLSSVR数据驱动的潮流非线性回归及其灵敏度解析[J]. 中国电机工程学报, 2022, 42(21): 7706-7719.
Yang Hao, Zhu Yudi, Liu Cheng, et al.Data-driven nonlinear power flow regression and analytical sensitivity calculation using MLSSVR[J]. Proceedings of the CSEE, 2022, 42(21): 7706-7719.
[3] Zhang Fan, Cheng C S.A modified Newton method for radial distribution system power flow analysis[J]. IEEE Transactions on Power Systems, 1997, 12(1): 389-397.
[4] 王宪荣, 包丽明, 柳焯, 等. 快速解耦牛顿法最优潮流[J]. 中国电机工程学报, 1994, 14(4): 26-32.
Wang Xianrong, Bao Liming, Liu Zhuo, et al.Fast decoupled Newton optimal power flow[J]. Procee- dings of the CSEE, 1994, 14(4): 26-32.
[5] 周亦尧, 王强钢, 匡江锋, 等. 基于功率注入潮流模型的双极直流配电网的电压不平衡分析及传递计算[J]. 电工技术学报, 2025, 40(8): 2656-2667.
Zhou Yiyao, Wang Qianggang, Kuang Jiangfeng, et al.Voltage unbalance analysis and transfer calculation of bipolar DC distribution network based on power injection power flow model[J]. Transactions of China Electrotechnical Society, 2025, 40(8): 2656-2667.
[6] 王淏, 谢开贵, 邵常政, 等. 柔性互联输配一体化电网有损潮流的精细化建模及应用[J]. 电工技术学报, 2024, 39(9): 2593-2607.
Wang Hao, Xie Kaigui, Shao Changzheng, et al.Precise lossy power flow modeling and application of integrated transmission and distribution grids with multi-terminal flexible interconnected[J]. Transactions of China Electrotechnical Society, 2024, 39(9): 2593-2607.
[7] 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.
[8] 周涛, 陈中, 戴中坚, 等. 含VSC-MTDC的交直流系统潮流算法[J]. 中国电机工程学报, 2019, 39(11): 3140-3149.
Zhou Tao, Chen Zhong, Dai Zhongjian, et al.An AC-DC system power flow algorithm with VSC- MTDC[J]. Proceedings of the CSEE, 2019, 39(11): 3140-3149.
[9] Trias A.The holomorphic embedding load flow method[C]//2012 IEEE Power and Energy Society General Meeting, San Diego, CA, USA, 2012: 1-8.
[10] 邵振国, 李壹民, 颜熙颖, 等. 基于全纯嵌入的电力系统不确定性仿射潮流方法[J]. 中国电机工程学报, 2024, 44(1): 105-117.
Shao Zhenguo, Li Yimin, Yan Xiying, et al.Affine power flow algorithm for power system based on holomorphic embedding method[J]. Proceedings of the CSEE, 2024, 44(1): 105-117.
[11] 陈飞雄, 吴鸿斌, 邵振国, 等. 电力系统仿射潮流多场景不确定性分析方法[J]. 电网技术, 2025, 49(1): 252-262.
Chen Feixiong, Wu Hongbin, Shao Zhenguo, et al.Affine power flow multi-scenario uncertainty analysis method for power system[J]. Power System Technology, 2025, 49(1): 252-262.
[12] 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): 4210-4227.
Li Xue, Li Bo, Jiang Tao, et al.A holomorphic embedding power flow algorithm for active distribution network[J]. Proceedings of the CSEE, 2024, 44(11): 4210-4227.
[13] Morgan M Y, Shaaban M F, Sindi H F, et al.A holomorphic embedding power flow algorithm for islanded hybrid AC-DC microgrids[J]. IEEE Trans- actions on Smart Grid, 2022, 13(3): 1813-1825.
[14] 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 Electro-technical Society, 2021, 36(21): 4429-4443, 4481.
[15] 李雪, 付云跃, 姜涛, 等. 基于多项式混沌展开的交直流系统全纯嵌入概率潮流计算方法[J]. 电力系统自动化, 2024, 48(18): 177-188.
Li Xue, Fu Yunyue, Jiang Tao, et al.Holomorphic embedding probabilistic power flow calculation method for AC/DC system based on polynomial chaos expansion[J]. Automation of Electric Power Systems, 2024, 48(18): 177-188.
[16] 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.
[17] Rao S, Feng Yang, Tylavsky D J, et al.The holomorphic embedding method applied to the power- flow problem[J]. IEEE Transactions on Power Systems, 2016, 31(5): 3816-3828.
[18] 黄莹. 全纯嵌入理论在新形态电力系统潮流计算中的应用研究[D]. 武汉: 华中科技大学, 2022.
Huang Ying.Application of holomorphic embedding theory in power flow calculation of new-pattern power grids[D]. Wuhan: Huazhong University of Science and Technology, 2022.
[19] 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.
[20] Wang Tao, Chiang H D.On the holomorphic and conjugate properties for holomorphic embedding methods for solving power flow equations[J]. IEEE Transactions on Power Systems, 2020, 35(4): 2506-2515.
[21] 李雪, 高翔, 姜涛, 等. 电力系统全纯嵌入潮流的并行计算[J]. 电工技术学报, 2024, 39(18): 5839-5854.
Li Xue, Gao Xiang, Jiang Tao, et al.Parallel computing method of power system holomorphic embedded power flow[J]. Transactions of China Electrotechnical Society, 2024, 39(18): 5839-5854.
[22] 张逸, 蓝天, 李传栋, 等. 基于全纯嵌入法的三相潮流通用算法[J]. 中国电机工程学报, 2024, 44(20): 8024-8039.
Zhang Yi, Lan Tian, Li Chuandong, et al.A general three-phase power flow algorithm based on holo- morphic embedding method[J]. Proceedings of the CSEE, 2024, 44(20): 8024-8039.
[23] 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.
[24] 李思儒. 全纯嵌入法潮流与暂态稳定计算原理与应用[D]. 杭州: 浙江大学, 2021.
Li Siru.Principle and application of holomorphic embedding load flow and transient stability calcula- tion[D]. Hangzhou: Zhejiang University, 2021.
[25] Beckermann B, Matos A C.Algebraic properties of robust Padé approximants[J]. Journal of Approxima- tion Theory, 2015, 190: 91-115.
[26] Hopkins T R.On the sensitivity of the coefficients of Padé approximants with respect to their defining power series coefficients[J]. Journal of Computational and Applied Mathematics, 1982, 8(2): 105-109.
[27] 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.
[28] Freitas F D, Santos A C, Fernandes L F J, et al. Restarted holomorphic embedding load-flow model based on low-order Padé approximant and estimated bus power injection[J]. International Journal of Electrical Power & Energy Systems, 2019, 112: 326-338.
[29] Domínguez Á B, Echavarren Cerezo F M, Rouco Rodríguez L. A convergence control scheme for multi- stage holomorphic embedding load-flow method[J]. IEEE Transactions on Power Systems, 2025, 40(1): 286-298.
[30] 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 Electro- technical Society, 2023, 38(11): 2870-2882.
[31] Trias A. Fundamentals of the holomorphic embedding load-flow method[J/OL]. ArXiv, 2015: 1509.02421v1 [2024-10-15]. https://doi.org/10.48550/arXiv.1509.02421.
[32] 冯卓诚, 姜彤, 万凯遥, 等. 基于功率下垂节点与两步式分析的扩展潮流计算模型[J]. 电工技术学报, 2023, 38(9): 2335-2349.
Feng Zhuocheng, Jiang Tong, Wan Kaiyao, et al.An extended power flow calculation model based on power droop bus and two-step analysis[J]. Trans- actions of China Electrotechnical Society, 2023, 38(9): 2335-2349.
[33] Dronamraju A, Li Songyan, Li Qirui, et al.Implications of Stahl's theorems to holomorphic embedding part II: numerical convergence[J]. CSEE Journal of Power and Energy Systems, 2021, 7(4): 773-784.
[34] Li Songyan, Tylavsky D, Shi Di, et al.Implications of Stahl's theorems to holomorphic embedding part I: theoretical convergence[J]. CSEE Journal of Power and Energy Systems, 2021, 7(4): 761-772.
[35] Ortega J M, Rheinboldt W C.Iterative Solution of Nonlinear Equations in Several Variables[M]. Philadelphi: Academic Press, 1970. |
|
|
|
2025, Vol. 40 
