A new multi-objective microgrid restoration via semidefinite programming

This paper presents a new multi-objective microgrid reconfiguration problem formulation. Unlike existing distribution system or microgrid reconfiguration algorithms, we consider the effect of uncertainty arising from the renewable energy generation and investigate the tradeoff between the invented index measuring the reliability of reconfiguration and the total load served. The resulting optimization problem is computationally prohibitive due to the binary circuit breaker variables and the probability constraint accounting for the uncertainty of renewable generation. Nevertheless, a semidefinite programming (SDP) reformulation is developed based on convex relaxation techniques and the scenario-based approximation. Furthermore, weighted-sum method is applied in the reformulation and we eventually obtain the Pareto solution points of the microgrid reconfiguration. Numerical tests validate the intrinsic tradeoff between the two objectives and demonstrate the effectiveness of the proposed solution methodology.