Convex LMI optimization for the uncertain power flow analysis
For power system operators, it provides a non-linear approach to assess voltage bounds under renewable uncertainty, though the method is incremental as it extends the S-procedure.
This paper addresses uncertain power flow analysis in distribution networks with renewable integration, bounding worst-case voltage magnitudes without linearizing power flow equations. The proposed method formulates the problem as an LMI optimization, enabling efficient numerical resolution.
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.