Optimal power flow calculation based on the holomorphic embedding method with adaptive initial value adjustment

YU Na; HUANG Xinxin; HUANG Dawei; LI Xue; SUN Lei

doi:10.19783/j.cnki.pspc.251374

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Optimal power flow calculation based on the holomorphic embedding method with adaptive initial value adjustment

更新时间：2026-07-27

- Optimal power flow calculation based on the holomorphic embedding method with adaptive initial value adjustment
- Power System Protection and Control Vol. 54, Issue 13, (2026)
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- DOI：10.19783/j.cnki.pspc.251374
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- Published：2026
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YU Na, HUANG Xinxin, HUANG Dawei, et al. Optimal power flow calculation based on the holomorphic embedding method with adaptive initial value adjustment[J]. Power System Protection and Control, 2026, 54(13).
DOI：

YU Na, HUANG Xinxin, HUANG Dawei, et al. Optimal power flow calculation based on the holomorphic embedding method with adaptive initial value adjustment[J]. Power System Protection and Control, 2026, 54(13). DOI： 10.19783/j.cnki.pspc.251374.

摘要

为解决全纯嵌入法 (holomorphic embedding method

HEM) 求解最优潮流 (optimal power flow

OPF) 时难以处理不等式 Karush-Kuhn-Tucker (KKT) 条件而引起的变量与乘子冲突的问题，提出一种基于 HEM 的 OPF 求解框架。该框架将不等式乘子以平方形式参数化以避免乘子取负时的路径失效，并将 KKT 变量划分为潮流物理变量与乘子变量。以直流最优潮流 (direct current optimal power flow

DC OPF) 解作为部分变量的预设初值，并由无功平衡关系确定无功变量的预设初值。提出基于惩罚机制的自适应不等式乘子初值调整策略，引导解析延拓过程。在 5 节点及 IEEE6/9/14/30 节点系统中与中心轨迹内点法进行对比，HEM 经较少次数的递归即可逼近 OPF 目标解。结果表明，该方法提升了 OPF 求解的准确性与可行性，为含有不等式约束的 OPF 计算提供一种解析化求解方法。

Abstract

To address the conflict between variables and multipliers caused by the difficulty of handling inequality-constrained Karush-Kuhn-Tucker (KKT) conditions in the solution of optimal power flow (OPF) problems using the holomorphic embedding method (HEM)

a novel HEM-based OPF solution framework is proposed. In this framework

inequality multipliers are parameterized in squared form to prevent path failure caused by negative multiplier values

and the KKT variables are partitioned into power-flow physical variables and multipliers. The direct current OPF solution is employed as the preset initial values for a subset of variables

while the preset initial values of reactive-power are derived from reactive power balance relations. Furthermore

an adaptive penalty-based initialization strategy adjusts inequality multipliers to guide analytical continuation toward the solution. Compared with the central-trajectory interior-point method on a 5-bus and the IEEE 6/9/14/30-bus systems

the proposed HEM approach can converge to the OPF solution with only a small number of recursive iterations. The results show that the proposed method improves the accuracy and feasibility of OPF computation

offering an analytical approach for OPF problems under inequality constraints.

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Keywords

references

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