This paper presents a new mixed-integer linear programming (MILP) model to solve the multistage long-term expansion planning problem of electrical distribution systems (EDSs) considering the following alternatives: increasing the capacity of existing substations, constructing new substations, allocating capacitor banks and/or voltage regulators, constructing and/or reinforcing circuits, and modifying, if necessary, the system's topology. The aim is to minimize the investment and operation costs of the EDS over an established planning horizon. The proposed model uses a linearization technique and an approximation for transforming the original problem into an MILP model. The MILP model guarantees convergence to optimality by using existing classical optimization tools. In order to verify the efficiency of the proposed methodology, a 24-node test system was employed.

Electrical distribution systems (EDSs) should be prepared to cope with demand growth in order to provide a quality service. The future increase in electric vehicles (EVs) represents a challenge for the planning of the EDS due to the corresponding increase in the load. Therefore, methods to support the planning of the EDS, considering the uncertainties of conventional loads and EV demand, should be developed. This paper proposes a mixedinteger linear programming (MILP) model to solve the robust multistage joint expansion planning of EDSs and the allocation of EV charging stations (EVCSs). Chance constraints are used in the proposed robust formulation to deal with load uncertainties, guaranteeing the fulfillment of the substation capacity within a specified confidence level. The expansion planning method considers the construction/reinforcement of substations, EVCSs, and circuits, as well as the allocation of distributed generation units and capacitor banks along the different stages in which the planning horizon is divided. The proposed MILP model guarantees optimality by applying classical optimization techniques. The effectiveness and robustness of the proposed method is verified via two distribution systems with 18 and 54 nodes. Additionally, Monte Carlo simulations are carried out, aiming to verify the compliance of the proposed chance constraint.

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