Optimal expansion planning in distribution networks with distributed generation

This paper addresses the multistage expansion planning problem of a distribution system where investments in the distribution network and in distributed generation are jointly considered. Network expansion comprises several alternatives for feeders and transformers. Analogously, the installation of distributed generation takes into account several alternatives for conventional and wind generators. Unlike what is customarily done, a set of candidate nodes for generator installation is considered. Thus, the optimal expansion plan identifies the best alternative, location, and installation time for the candidate assets. The model is driven by the minimization of the net present value of the total cost including the costs related to investment, maintenance, production, losses, and unserved energy. The costs of energy losses are modeled by a piecewise linear approximation. As another distinctive feature, radiality conditions are specifically tailored to accommodate the presence of distributed generation in order to avoid the isolation of distributed generators and the issues associated with transfer nodes. The resulting optimization problem is a mixed-integer linear program for which finite convergence to optimality is guaranteed and efficient off-the-shelf software is available. Numerical results illustrate the effective performance of the proposed approach.