Optimal sizing of microgrids: On the design equivalences of different objective functions

Decentralized energy systems have risen attention of policy makers and academia for their potentiality to improve the electricity service, reduce costs and foster the rural electrification in developing countries. Several design methodologies have been proposed to optimize the size of different components, which is crucial especially in off-grid configurations. Given the interests of private companies, profitability aspects are becoming the major focus; nevertheless, there is no general agreement on the best indicator to use to assess if and how much the microgrid is cost effective. Moreover, different economic indicators can correspond to several sizing solutions, which makes the selection of the objective function a very critical aspect. In this study, we propose a comparison between main indicators used to optimize off-grid microgrids, including theoretical and numerical comparisons. Equivalences and inequalities among typical economic criteria are considered, including formulations accounting for the cost of the energy-not-served. Numerical case studies supporting the analysis are provided.