A planar facility location-allocation problem with fixed and variable cost structures for rural electrification

Abstract

One of the major impediments to the economic development of developing coun-tries is the lack of access to affordable, sustainable, and reliable modern energy systems. Even today, hundreds of millions of people, most of whom live in ru-ral areas, do not have access to essential electricity services. In this study, we present a planar facility location-allocation problem for the planning of decentral-ized energy systems in the context of rural development. We consider nano-grid and micro-grid systems to electrify the 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-grid fa-cilities are connected to the generation point with low voltage cables, for which we employ a distance limit constraint due to the technical concerns, including the 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 connec-tion costs. Additionally, given the diversity of cost structures in the renewable energy investments, we provide three different formulations where we incorpo-rate different combinations of fixed and variable cost components for facilities. For this problem, we provide a mixed integer quadratically constrained problem formulation and propose six heuristic approaches. The three of these heuristic methods are multi-stage approaches in which we solve optimization models, while the other methods utilize faster clustering techniques that have been extensively studied in the literature. We conduct computational experiments on the synthetic data and real life instances from the small villages in Sub-Saharan Africa, and perform a comparative analysis of the suggested heuristic approaches.