Spherical Search based constrained optimization algorithm for power flow analysis of islanded microgrids

Conventional power flow (PF) algorithms are ineffective in the droop-regulated islanded microgrids as the slack bus voltage and system operating frequency are presumed constant parameters. Such assumptions are not applicable in the operation of the droop-regulated islanded microgrid. We formulate a novel formulation for islanded microgrids to solve the PF problem as a constrained optimization problem. Non-linear and linear constraints are developed to model the power balance and the various modes of Distributed Generation units (DGs). In islanded microgrids, DGs can be operated in PQ, PV, and droop mode. We propose an optimization algorithm named SS-NR (Spherical Search with Newton–Raphson based repair) for solving the formulated problem. We employ Spherical Search (SS) as a base optimizer to minimize the objective function in this algorithm. Moreover, Newton–Raphson based repair operator is also used within the framework of SS to handle non-linear equality constraints of a PF problem. Then, we compare the performance of the proposed algorithm with the state-of-the-art algorithms of global optimization. The experimental results show that the proposed algorithm performs better than the other contenders in convergence and accuracy. Furthermore, to validate the proposed formulation, we compare SS-NR results with the results of a time-domain simulator and other PF tools. This comparative analysis presents the efficacy of the proposed formulation as well as the proposed algorithm.