Optimal Multi-Scenario, Multi-Objective Allocation of Fault Indicators in Electrical Distribution Systems Using a Mixed-Integer Linear Programming Model

In this paper, a mixed-integer nonlinear programming (MINLP) model for the optimal multiscenario allocation of fault indicators (FIs) in electrical distribution systems (EDS) is presented. The original MINLP model is linearized to obtain an equivalent mixed-integer linear programming (MILP) model. The proposed MILP formulation is a precise, flexible, and scalable optimization model whose optimal solution is guaranteed by commercial solvers. In order to improve the practicality and scope of the proposed method, different demand levels, topologies, and N - 1 contingencies are included as scenarios within the proposed model. The flexibility of the model is also emphasized by adding a custom noncontinuous interruption cost function. The objective function minimizes the average cost of energy not supplied and the present value of the overall investments made over a discrete planning horizon. Since the proposed model is convex, other conflicting objectives can be considered using a simple step-by-step approach to construct the optimal Pareto front. In order to demonstrate the efficiency and scalability of the proposed method, two different EDS are tested: a 69-node RBTS4 benchmark and a real Brazilian distribution system. Results show the efficiency of the proposed method to improve the overall reliability of the system even when few FIs are installed.