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.
张逸, 蓝天, 李传栋, 蔡伟杰, 王建明. 基于功率重启动的全纯嵌入潮流算法[J]. 电工技术学报, 2025, 40(21): 7046-7061.
Zhang Yi, Lan Tian, Li Chuandong, Cai Weijie, Wang Jianming. A Holomorphic Embedding Power Flow Algorithm Based on Power Restart. Transactions of China Electrotechnical Society, 2025, 40(21): 7046-7061.
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