Convex LMI optimization for the uncertain power flow analysis

TL;DR

This paper presents a novel convex LMI optimization approach for analyzing uncertain power flows in distribution networks with renewable energy sources, avoiding linearization of non-linear power flow equations.

Contribution

It introduces a new feasibility tool extending the $ ext{S}$-procedure, enabling polynomial constraint problems to be solved via LMIs without linearizing power flow equations.

Findings

LMI-based optimization effectively bounds worst-case voltages.

The method handles non-linear power flow equations directly.

Numerical examples demonstrate computational efficiency.

Abstract

This paper investigates the uncertain power flow analysis in distribution networks within the context of renewable power resources integration such as wind and solar power. The analysis aims to bound the worst-case voltage magnitude in any node of the network for a given uncertain power generation scenario. The major difficulty of this problem is the non-linear aspect of power flow equations. The proposed approach does not require the linearization of these equations and formulates the problem as an optimization problem with polynomial constraints. A new tool to investigate the feasibility of such problems is presented and it is obtained as an extension of the $\mathcal{S}-$procedure, a fundamental result in robustness analysis. A solution to the uncertain power flow analysis problem is proposed using this new tool. The different obtained results of this paper are expressed as LMI optimization problems which guaranties an efficient numerical resolution as it will be demonstrated through an illustrative example.