Optimal Power Flow in Stand-Alone DC Microgrids

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 (OPF) of a stand-alone DC-MG is inherently non-convex. In this paper, the OPF of DC-MG is investigated considering convex relaxation based on second-order cone programming. Mild assumptions are proposed to guarantee the exactness of relaxation, which only require uniform nodal voltage upper bounds and positive network loss. It is revealed that the exactness of second-order conic (SOC) relaxation of DC networks does not rely on topology or operating mode of DC networks, and an optimal solution must be unique if it exists. If line constraints are considered, the exactness of SOC relaxation may not hold. In this regard, two heuristic methods are proposed to give approximate solutions. Numerical experiments confirm the theoretic results.