  Microgrid serves as a promising solution to integrate and manage distributed
renewable energy resources. In this paper, we establish a stochastic
multi-objective sizing optimization (SMOSO) model for microgrid planning, which
fully captures the battery degradation characteristics and the total carbon
emissions. The microgrid operator aims to simultaneously maximize the economic
benefits and minimize carbon emissions, and the degradation of the battery
energy storage system (BESS) is modeled as a nonlinear function of power
throughput. A self-adaptive multi-objective genetic algorithm (SAMOGA) is
proposed to solve the SMOSO model, and this algorithm is enhanced by
pre-grouped hierarchical selection and self-adaptive probabilities of crossover
and mutation. Several case studies are conducted to determine the microgrid
size by analyzing Pareto frontiers, and the simulation results validate that
the proposed method has superior performance over other algorithms on the
solution quality of optimum and diversity.
