Método direto para localizar soluções de baixa tensão no problema de fluxo de potência

Abstract

In the current context, Distributed Generators are progressively increasing their importance in the operation of distribution systems, and, consequently, the study of voltage stability increases their importance in these systems as well. Since Low-voltage Solutions (LVS) of the power flow equations are an important information for voltage stability analyzes, the need arises for a specialized method to locate LVS in distribution systems. This need can be divided into two sub-problems: first, the development of a power flow method with the capability to calculate LVS in distribution systems, and lastly, the specialization of this power flow method to locate LVS. In this work, it is proposed to solve both sub-problems. For the first, a three-phase power flow method for distribution systems with the capability to calculate LVS is proposed, which is based on an innovative formulation written in complex numbers. This formulation is solved by Newton’s method using Wirtinger calculus. For the second sub-problem, three formulations are proposed to locate LVS directly, called: basic formulation, alternative basic, and SBT-RCF formulation. The three are based on a characteristic of the generalized eigenvalues of the power flow, which indicates that when a normal operating solution occurs, all eigenvalues are complex, and when an LVS occurs, there is a pair of pure real eigenvalues. In the convergence analysis of the proposals, the power flow method has better computational performance when compared to a typical method of distribution systems, the backward-forward sweep method. In addition, the proposed method can converge in an LVS, being an essential feature in analysis of voltage stability. In relation to formulations to locate LVS, Newton's method fails to try to solve the basic formulation due to the poor global convergence of this method in this formulation. In the alternative basic formulation, Newton's method shows slight improvement, however, false convergences can happen due to the formulation being based on the gradient of a merit function. Nevertheless, for the SBT-RCF formulation, an equivalent optimization problem was developed, in which a relaxation of the equation was performed. The problem was solved using the interior points method, presenting convergence characteristics superior to Newton's method when solving the previous formulations, being able to calculate LVS in systems of 2, 4, 34 and 123 buses without problems.