A comparison of convex formulations for the joint planning of microgrids

Martin, Benoît [UCL] De Jaeger, Emmanuel [UCL] Glineur, François [UCL]

Planning of autonomous microgrids differs from traditional distribution planning because of the need to plan investments not only in the network but also in generation capacity. Generation and distribution planning, traditionally performed separately should be done simultaneously in this case to provide a cost-effective planning solution. Joint planning of generation and distribution can be cast as mixed-integer non-linear integer program and is difficult to solve due to the presence of both integer variables and non-linear constraints. In this study, we use the framework of convex programming to tackle the joint planning problem. The study presents four different convex relaxations of this problem, with different levels of accuracy. We compare their results in terms of computation time and solution quality in order to determine the most relevant formulation to use in function of the problem size.