Renewable energy (RE) microgrids are considered one solution for solving the increasing electricity demand and environmental pollution problem. Selecting RE sources for a microgrid plays a crucial role in determining the performance of the microgrid. Illustrated with an empirical study on a city’s microgrid project, this article proposes a new evaluation approach with a bi-capacity based multi-criteria decision making method called Bi-ELECTRE to evaluate and select RE source alternatives based on interacting performance indicators with bipolar measurement. With the novelty of the Bi-ELECTRE method, this article addresses the questions of (a) how to measure interactions between bipolar-scaled indicators when evaluating the RE source alternatives of a microgrid, and (b) how to determine the optimal combination of RE sources for a microgrid. The results from the empirical study suggest that a microgrid with a single RE source has the worst performance, compared with multi-source alternatives. In the empirical study conducted, the microgrid using a RE source combination of 20% wind, 30% solar, and 50% biomass has the best overall performance. By considering interactions between bipolar-scaled indicators and various combinations of RE sources, the proposed approach contributes to MCDM research methodologically and to the RE source selection problem for a microgrid practically.