Recursive convex approximations for optimal power flow solution in direct current networks

The optimal power flow problem in direct current (DC) networks considering dispersal generation is addressed in this paper from the recursive programming point of view. The nonlinear programming model is transformed into two quadratic programming approximations that are convex since the power balance constraint is approximated between affine equivalents. These models are recursively (iteratively) solved from the initial point vt equal to 1.0 pu with t equal to 0, until that the error between both consecutive voltage iterations reaches the desired convergence criteria. The main advantage of the proposed quadratic programming models is that the global optimum finding is ensured due to the convexity of the solution space around vt. Numerical results in the DC version of the IEEE 69-bus system demonstrate the effectiveness and robustness of both proposals when compared with classical metaheuristic approaches such as particle swarm and antlion optimizers, among others. All the numerical validations are carried out in the MATLAB programming environment version 2021b with the software for disciplined convex programming known as CVX tool in conjuction with the Gurobi solver version 9.0; while the metaheuristic optimizers are directly implemented in the MATLAB scripts.