An Optimal Dispatch Model for Stand-Alone Microgrids Convexifying Operational Constraints of Distributed Generation

Solving optimal dispatch problems in stand-alone microgrids aims to ensure reliable power supplies feeding the majority of customers by distributed generations (DGs) and curtailing controllable loads (CLs), in case of critical generation shortage. Theoretically, the optimal dispatch problem belongs to the category of mixed-integer non-convex programming (MINCP) which is a non-deterministic polynomial time (NP) problem and has no accurate solving approach. In practice, the phase unbalance in stand-alone microgrids should be limited within specified levels to prevent DGs from tripping to enhance operational reliability, yet is not considered in most existing literature. To bridge the two gaps, this paper proposes convex envelopes to enclose non-convex operational constraints of three-phase DGs to restrict the current unbalance ratio (CUR), integrated with a three-phase power flow model and CL constraints. The overall problem is reformulated as a mixed-integer second-order cone programming (MISOCP) which enables applying off-the-shelve commercial solvers. Simulation results based on the IEEE-34 bus system demonstrate accuracy, effectiveness and computational efficiency of the proposed dispatch model.