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The lack of access to electricity in developing countries necessitates spatial electricity planning for guiding sustainable electrification projects that evaluate the costs of centralized systems vis-a-vis decentralized systems. Heuristic approaches have been widely used in such electrification problems to find feasible, cost effective solutions; however, most of the time global optimality of these solutions is not guaranteed. Our paper through its modeling approach provides a new methodology to find the least cost solution to this electrification problem. We model the spatial network planning problem as Prize Collecting Steiner Tree problem, which would be a base for a decision support tool for rural electrification. This new method is systematically assessed using both randomly generated data and real data from rural regions across Sub-Saharan Africa. Comparative results for the proposed approach and a widely used heuristic method are presented based on computational experiments. [ABSTRACT FROM AUTHOR]