One major impediment to developing countries’ economic growth is the lack of access to affordable, sustainable, and reliable modern energy systems. Even today, hundreds of millions of people live in rural areas and do not have access to essential electricity services. In this study, we present a planar facility location–allocation problem for planning decentralized energy systems in rural development. We consider nano-grid and micro-grid systems to electrify rural households. While micro-grids serve multiple households with a common generation facility, nano-grids are small-scale systems serving individual consumers. The households served by micro-grids are connected to the generation facilities with low-voltage cables, for which we employ a distance limit constraint due to technical concerns, including power loss and allowable voltage levels. In this problem, we minimize the total investment cost that consists of the facility opening and the low-voltage cable costs. In order to capture the diversity of cost structures in renewable energy investments, we consider three versions of the objective function where we incorporate different combinations of fixed and variable cost components for facilities. For this problem, we provide mixed-integer quadratically constrained problem formulations and propose model-based and clustering-based heuristic approaches. Model-based approaches are multi-stage, in which we solve the discrete counterparts of the problem and employ alternative selection methods for the candidate facility locations. Clustering-based approaches utilize faster clustering techniques to identify the type and location of the facilities. We conduct computational experiments on real-life instances from villages in Sub-Saharan Africa and perform a comparative analysis of the suggested heuristic approaches.