Sizing Renewable and Energy Storage in Fully Renewable Stand-Alone Microgrids

This chapter studies the optimal sizing of renewable and storage capacities in a stand-alone microgrid powered by renewable energy. It proposes a bi-objective optimization model to minimize load shedding Shortfall risk and total investment cost, taking into account the uncertainty of renewable energy generation and load. To account for the inaccuracy of empirical probability distributions, an ambiguity set of probability distributions is constructed based on the Wasserstein distance, and a distributionally robust Shortfall risk model of load shedding is constructed. It is equivalently transformed into a worst-case expectation form and further conservatively approximated using a method based on the Lipschitz constant, transforming the problem into bi-objective linear programming (LP). According to the theory of parametric LP, it is explained that the Pareto frontier is piecewise affine, and an algorithm for solving the analytical expression of the Pareto frontier is proposed. This chapter introduces the work in Xie et al. (2022).