A Polynomial-Time Method for Testing Admissibility of Uncertain Power Injections in Microgrids

TL;DR

This paper presents a polynomial-time method for testing the admissibility of uncertain power injections in microgrids, ensuring secure and non-singular electrical states within specified uncertainty sets using convex optimization techniques.

Contribution

It introduces a novel framework for admissibility testing in microgrids, extending to multi-phase grids, with new theoretical results on voltage sets and load-flow solutions.

Findings

The method guarantees admissibility under certain convexity and nonsingularity conditions.

It provides a polynomial-time algorithm based on convex optimization infeasibility checks.

Numerical evaluations demonstrate the effectiveness of the proposed approach.

Abstract

We study the admissibility of power injections in single-phase microgrids, where the electrical state is represented by complex nodal voltages and controlled by nodal power injections. Assume that (i) there is an initial electrical state that satisfies security constraints and the non-singularity of load-flow Jacobian, and (ii) power injections reside in some uncertainty set. We say that the uncertainty set is admissible for the initial electrical state if any continuous trajectory of the electrical state is ensured to be secured and non-singular as long as power injections remain in the uncertainty set. We use the recently proposed V-control and show two new results. First, if a complex nodal voltage set V is convex and every element in V is nonsingular, then V is a domain of uniqueness. Second, we give sufficient conditions to guarantee that every element in some power injection set S has a load-flow solution in V, based on impossibility of obtaining load-flow solutions at the boundary of V. By these results, we develop a framework for the admissibility-test method; this framework is extensible to multi-phase grids. Within the framework, we establish a polynomial-time method, using the infeasibility check of convex optimizations. The method is evaluated numerically.