A Recursive Conic Approximation for Solving the Optimal Power Flow Problem in Bipolar Direct Current Grids

This paper proposes a recursive conic approximation methodology to deal with the optimal power flow (OPF) problem in unbalanced bipolar DC networks. The OPF is formulated through nonlinear programming (NLP) representation, where objective function corresponds minimization of expected grid losses for particular load scenario. NLP formulation has non-convex structure due hyperbolic equality constraints that define current injection/absorption constant terminals as powers and voltages. To obtain an approximate convex model represents asymmetric distribution networks, relation associated product two positive variables applied all nodes loads. In case dispersed generation, direct replacement voltage their operating point used. An iterative solution procedure implemented order minimize error introduced by linearization generation sources. 21-bus employed numerical validations. validate effectiveness proposed model, solved, considering neutral wire floating grounded, obtaining same results traditional methods (successive approximations, triangular-based, Taylor-based approaches): 95.4237 91.2701 kW, respectively. solving problem, three combinatorial optimization are implemented: sine-cosine algorithm (SCA), black-hole optimizer (BHO), vortex search (VSA). Numerical show finds global value 22.985 followed VSA 22.986 kW. At time, BHO SCA stuck locally solutions (23.066 23.054 respectively). All simulations were carried out MATLAB environment.