Sizing Renewable Generation and Energy Storage in Stand-Alone Microgrids Considering Distributionally Robust Shortfall Risk

Renewable generation has grown rapidly these years due to its advantages in low environmental impacts. Stand-alone microgrid with renewable generation and energy storage is a promising option in remote areas beyond the reach of an existing power grid. This paper proposes a multiobjective optimization model to co-optimize the sizes of renewable generation and energy storage in stand-alone microgrids, which minimizes the load shedding risk and the total investment cost. The load shedding degree is obtained by an optimal operation problem and measured by shortfall risk, considering the uncertainties of demand and renewable resources. To deal with the inaccurate empirical distribution, distributionally robust shortfall risk is further established under a Wasserstein-metric based ambiguity set, and an equivalent distributionally robust formulation is obtained. Then a conservative approximation is developed, and the resulting problem appears to be a bi-objective linear program. The Pareto frontier is proven to be piecewise linear, and the analytical expression of the Pareto frontier is derived. Case studies demonstrate the effectiveness and performance of the proposed method.