Affine Optimization Method for Probability Interval Power Flow of Distribution Network Based on Holomorphic Embedding

LIAO Xiaobing; 1; WEI Hanqi; 1; LI Zicheng; 1; ZHANG Yiming; 1; YANG Jie; 2; YANG Meng; 2

doi:10.13335/j.1000-3673.pst.2025.0262

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Affine Optimization Method for Probability Interval Power Flow of Distribution Network Based on Holomorphic Embedding

更新时间：2026-03-13

- Affine Optimization Method for Probability Interval Power Flow of Distribution Network Based on Holomorphic Embedding
- Vol. 49, Issue 12, Pages: 5166-5175(2025)
- 作者机构：
  
  武汉工程大学电气信息学院,湖北省,武汉市,430205
- 作者简介：
- 基金信息：
- DOI：10.13335/j.1000-3673.pst.2025.0262
  CLC： TM744
- Published：2025
- 稿件说明：
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LIAO Xiaobing, 1, WEI Hanqi, et al. Affine Optimization Method for Probability Interval Power Flow of Distribution Network Based on Holomorphic Embedding[J]. 2025, 49(12): 5166-5175.
DOI：

LIAO Xiaobing, 1, WEI Hanqi, et al. Affine Optimization Method for Probability Interval Power Flow of Distribution Network Based on Holomorphic Embedding[J]. 2025, 49(12): 5166-5175. DOI： 10.13335/j.1000-3673.pst.2025.0262.

摘要

为了准确模拟分布式光伏接入对配电网不确定性潮流分布的影响，提出了基于全纯嵌入的配电网概率区间潮流仿射优化方法。首先，建立系统节点电压和功率的仿射模型并引入嵌入因子，构建全纯嵌入仿射优化潮流模型；接着，建立分布式光伏的出力焦元模型，将基于焦元模型的概率区间潮流模型转化为全纯嵌入仿射优化潮流模型；然后，建立混合盒式-椭球集合的区间变量相关性模型，将其转化为仿射约束条件在全纯嵌入仿射优化潮流模型中进行联立求解；最后根据证据理论得到配电网概率区间潮流解的概率边界。算例仿真结果表明，全纯嵌入仿射优化潮流算法的保守性更低，更适用于较大波动区间下的不确定性潮流分析，同时混合盒式-椭球集合相关性模型比其他相关性模型更准确，能反映相关性系数对计算结果的影响。

Abstract

To accurately simulate the impact of distributed photovoltaic (PV) integration on the uncertain power flow distribution in distribution networks

an affine optimization method for the probability interval power flow of the distribution network based on holomorphic embedding is proposed. First

an affine model for bus voltages and power is established

and an embedding factor is introduced to construct the holomorphic embedded affine optimization power flow model. A focal element model for distributed PV output is developed

transforming the probabilistic interval power flow model based on focal elements into the holomorphic embedded affine optimization power flow model. A hybrid box-ellipsoidal uncertainty set model is established to capture the correlation between interval variables

which is then converted into affine constraints and solved simultaneously within the holomorphic embedded affine optimization power flow model. Finally

the probability bounds of the probabilistic interval power flow solution for the distribution network are obtained based on evidence theory. Case study results demonstrate that the holomorphic embedded affine optimization power flow algorithm exhibits lower conservatism and is more suitable for uncertainty analysis under larger fluctuation intervals. Additionally

the hybrid box-ellipsoidal uncertainty set model is more accurate than other correlation models and can effectively reflect the influence of correlation coefficients on the computational results.

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