**Sergio Montoya-Bueno, Jose Ignacio Muñoz-Hernandez, Javier Contreras \* and Luis Baringo**

Department of Applied Mechanics and Project Engineering, University of Castilla-La Mancha, 13071 Ciudad Real, Spain; Sergio.Montoya@uclm.es (S.M.-B.); JoseIgnacio.Munoz@uclm.es (J.I.M.-H.); Luis.Baringo@uclm.es (L.B.)

**\*** Correspondence: Javier.Contreras@uclm.es

Received: 30 January 2020; Accepted: 21 February 2020; Published: 6 March 2020

**Abstract:** A model suitable to obtain where and when renewable energy sources (RES) should be allocated as part of generation planning in distribution systems is formulated. The proposed model starts from an existing two-stage stochastic mixed-integer linear programming (MILP) problem including investment and scenario-dependent operation decisions. The aim is to minimize photovoltaic and wind investment costs, operation costs, as well as total substation costs including the cost of the energy bought from substations and energy losses. A new Benders' decomposition framework is used to decouple the problem between investment and operation decisions, where the latter can be further decomposed into a set of smaller problems per scenario and planning period. The model is applied to a 34-bus system and a comparison with a MILP model is presented to show the advantages of the model proposed.

**Keywords:** Benders' decomposition; distributed generation planning (DGP); two-stage stochastic mixed-integer linear programming (MILP); renewable energy sources (RES)
