Primal-Dual Logarithmic Barrier and Augmented Lagrangian Function to the Loss Minimization in Power Systems

Abstract

This article presents a new approach to minimize the losses in electrical power systems. This approach considers the application of the primal-dual logarithmic barrier method to voltage magnitude and tap-changing transformer variables, and the other inequality constraints are treated by augmented Lagrangian method. The Lagrangian function aggregates all the constraints. The first-order necessary conditions are reached by Newton's method, and by updating the dual variables and penalty factors. Test results are presented to show the good performance of this approach.

Loss minimization by the predictor–corrector modified barrier approach

“…The difference between the Newton's systems (21) and (16) is the addition of the nonlinear terms ( ) from the right-hand side of (21), which cannot be determined in advance. In order to estimate these nonlinear terms, Mehrotra [4] suggests solving two systems of linear equations within each iteration.…”

“…In the same year, the Primal-dual Interior Point algorithm with the predictor-corrector method [6] was used to accelerate the convergence of the problem. In recent years, most researches involving the OPF problem have been based on the variants of the IPM mainly with the predictor-corrector [7][8][9][10][11][12][13][14][15][16][17][18][19], and a few researches have been based on different approaches [20][21][22][23][24][25][26]. In [25] the modified barrier-augmented Lagrangian method [27], a variant of the modified barrier method [28], was used for the optimum selections of the transformers' tap positions and the voltage points of the generators, and in [26], the modified barrier (MB) method was used to establish the pricing mechanism for finding the equilibrium in an auction market.…”

Dimensionamento de Biodigestores Batelada através do Método Primal Dual Barreira Logarítmica

“…Com o uso do algoritmo PDBL de [1] e das ferramentas computacionais open source Java e NetBeans desenvolveu-se um software com o objetivo de resolver o modelo representado pela equação (6).…”

Uma Mistura De Funções Barreira E Barreira Modificada Na Resolução Do Fluxo De Potência Ótimo

“…Muitos trabalhos foram desenvolvidos na tentativa de resolvê-lo utilizando diferentes técnicas de Otimização Não-Linear, Linear e Métodos Heurísticos, entre eles citam-se: GRANVILLE [12], WU et al [22] e TORRES & QUINTANA [21] os quais aplicaram um algoritmo Primal-Dual Barreira Logarítmica na resolução do problema de Fluxo de Potência Ótimo e, as condições de Karush-Kuhn-Tuker (KKT) foram satisfeitas utilizando o método de Newton, sendo a maior dificuldade do algoritmo a escolha do parâmetro de Barreira; BAPTISTA et al [1][2][3] resolveram o problema utilizando uma função Lagrangiana Aumentada-Barreira Logarítmica; BAPTISTA et al [4] e SOUSA et al [18][19][20] utilizaram uma função Lagrangiana Barreira Modificada. Mais recentemente, lembra-se de CAPITANESCU et al [5][6][7] que analisa o desempenho de três algoritmos de pontos interiores e sua aplicação ao FPO.…”