Mathematical model of quadratic approximation for optimal power flow in electrical distribution systems (Ciencias de la Ingeniería y Aplicadas, 2021)
The purpose of this document is the development of a mathematical model that allows obtaining a global optimal value and eliminating the interaction process, making its convergence faster, because traditional methods for the power flows of the transmission system are not reliable. , when applied to distribution networks, and these in turn increase their complexity as their number of nodes is greater, giving as a solution to this problem the development of the mathematical model based on the quadratic approximation in the complex plane with Taylor series. Obtaining as a result of the mathematical model carried out an error percentage of 5% with a voltage of 0.8 pu, which determines that its linearization is optimal for the development of power flows in radial systems, finally the validation of the OPF was carried out with a comparison of the results obtained with the developed model applied to the IEEE test systems, these being compared with the results presented by traditional methods such as Gauss Seidel and Newton Raphson, thus demonstrating that this mathematical model can be considered as an optimal solution for the calculation of the OPF of distribution systems due to its rapid convergence, its calculation time and its adaptation for distribution systems.
Keywords: Quadratic Approximation; OPF; Objective Function; Restrictions; CVX