Optimal Power Flow in Stand-alone DC Microgrids

TL;DR

This paper investigates the optimal power flow problem in stand-alone DC microgrids, proposing convex relaxation methods, analyzing their exactness, and providing heuristics for cases with line constraints, supported by simulations.

Contribution

It introduces conditions for the exactness of SOCP relaxation in stand-alone DC microgrids and proposes heuristic methods when line constraints affect relaxation accuracy.

Findings

SOCP relaxation is exact under mild assumptions.

Exactness does not depend on topology or mode.

Heuristics provide approximate solutions with line constraints.

Abstract

Direct-current microgrids (DC-MGs) can operate in either grid-connected or stand-alone mode. In particular, stand-alone DC-MG has many distinct applications. However, the optimal power flow problem of a stand-alone DC-MG is inherently non-convex. In this paper, the optimal power flow (OPF) problem of DC-MG is investigated considering convex relaxation based on second-order cone programming (SOCP). Mild assumptions are proposed to guarantee the exactness of relaxation, which only require uniform nodal voltage upper bounds and positive network loss. Furthermore, it is revealed that the exactness of SOCP relaxation of DC-MGs does not rely on either topology or operating mode of DC-MGs, and an optimal solution must be unique if it exists. If line constraints are considered, the exactness of SOCP relaxation may not hold. In this regard, two heuristic methods are proposed to give approximate solutions. Simulations are conducted to confirm the theoretic results.