Optimal allocation of active and reactive generation in power systems using Zbus matrix and first-order conditions

Abstract

This work proposes an algorithm to reduce total losses in electric power transmission systems. The reduction is caused by the optimization of the active power dispatch in system generating units, and/or the injection of reactive power in substations. Until the end of the 1980s, optimal power flows were based on deterministic methods usually based on derivatives, such as the Gradient method and Newton's method. In the 1990s, the first metaheuristic-based methods such as Genetic Algorithms and Ant Colony Optimization emerged. This paper aims to rescue the deterministic methods, but using Z <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">bus</inf> matrix to determine the gradient and the first order condition (Δf(X)=0), together with Gauss Method to reach the optimal point. Thus, there will be no need to calculate the gradient vector at each iteration, as well also step size nor assembly the Hessian matrix, representing a saving of processing time. This is due the used of Z <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">bus</inf> matrix.