Recursive Convex Model for Optimal Power Flow Solution in Monopolar DC Networks

This paper presents a new optimal power flow (OPF) formulation for monopolar DC networks using a recursive convex representation. The hyperbolic relation between the voltages and power at each constant power terminal (generator or demand) is represented as a linear constraint for the demand nodes and generators. To reach the solution for the OPF problem a recursive evaluation of the model that determines the voltage variables at the iteration t + 1 ( v t + 1 ) by using the information of the voltages at the iteration t ( v t ) is proposed. To finish the recursive solution process of the OPF problem via the convex relaxation, the difference between the voltage magnitudes in two consecutive iterations less than the predefined tolerance is considered as a stopping criterion. The numerical results in the 85-bus grid demonstrate that the proposed recursive convex model can solve the classical power flow problem in monopolar DC networks, and it also solves the OPF problem efficiently with a reduced convergence error when compared with semidefinite programming and combinatorial optimization methods. In addition, the proposed approach can deal with radial and meshed monopolar DC networks without modifications in its formulation. All the numerical implementations were in the MATLAB programming environment and the convex models were solved with the CVX and the Gurobi solver.