Clustering approaches to select Multiple Design Options in multi-objective optimization: an application to rural microgrids

The sizing of off-grid systems in developing countries can be very challenging and rarely mathematical modelling techniques are able to account for their multifaceted nature, even when using multi-objective optimization to capture economic, social and environmental aspects. To overcome that, developers perform sensitivity analyses to test whether different configurations, here denoted as Multiple Design Options (MDOs), may lead to acceptable economic performances, yet slightly more costly than the theoretical mathematical optimum. In this study, we propose a methodology to provide developers with a manageable number of design options that map the design space close to the Pareto frontier. First, we employ MDO - Multi Objective Particle Swarm Optimization (MDOMOPSO) algorithm to identify the Pareto frontier with respect to Net Present Cost and CAPEX. Then, all the explored configurations in the nearby of the Pareto frontier are stored, and a novel clustering methodology, namely Peripheral Mapping by Receding Nearest Neighbor (PM-RNN), based on hierarchical clustering, is used to reduce the selected space to a handy number of MDOs. The proposed approach is compared to the standard k-means to highlight benefits of the proposed method. Results of a numerical case study regarding a Kenyan hybrid minigrid support the findings.