DOI
https://doi.org/10.11606/T.18.2019.tde-08102019-153756
Documento
Autor
Nome completo
Diego Nunes da Silva
Área do Conhecimento
Data de Defesa
Imprenta
São Carlos, 2019
Costa, Geraldo Roberto Martins da (Presidente)
Andretta, Marina
Mantovani, José Roberto Sanches
Soler, Edilaine Martins

Título em português
Novas abordagens determinísticas de otimização para resolução do problema de fluxo de potência ótimo
Palavras-chave em português
Fluxo de Potência Ótimo
Newton-PL
Pontos Interiores
Região de Confiança
Rescalamento Não-Linear
Resumo em português

Título em inglês
New Deterministic Optimization Approaches to Solve the Optimal Power Flow Problem
Palavras-chave em inglês
Interior Point
LP-Newton
Nonlinear Rescaling
Optimal Power Flow
Trust Region
Resumo em inglês
In an Optimal Power Flow problem (OPF), the goal is to determine a power system operating point that satisfies its physical and operating constraints and, at the same time, optimizes a network performance measure. The mathematical model for the Optimal Power Flow problem is a Mixed Integer Nonlinear Programming problem (MINLP). The goal of this work is to investigate and propose new approaches to solve the Reactive Optimal Power Flow (ROPF) problem, in order to minimize the active power losses. Three deterministic approaches, based on methods with well-established convergence theories, were investigated, modified and applied. In the first approach, the constrained nonlinear system of equations that arises from the KKT necessary optimality conditions is solved by a Newton-type method which has been recently proposed in the literature. In contrast with the classical Newtons method, this approach, called Linear Programming Newtons method (LP-Newton), is able to solve constrained nonlinear systems of equations which include complementarity equations. The numerical results for this approach were obtained only for the continuous relaxation of the ROPF problem, but a possible modification to deal with discrete variables is presented. In the second and third approaches, the discrete variables are treated as continuous by introducing sinusoidal penalty functions in the objective function, penalizing it when discrete variables assume non-discrete values. These two proposals differ by the continuous optimization approach employed to solve the penalty subproblems. In the second approach, inequality constraints are treated by means of a nonlinear rescaling function, based on the modified logarithmic barrier function with quadratic extrapolation. The sequence of nonlinear rescaling penalty problems is solved by a sequential quadratic programming method with a trust region, whose trial step is decomposed in a normal step, that tries to satisfy the linearized constraints as best as possible, and a tangential step, which seeks to minimize the objective function model. In the third approach, each penalty problem is solved by a trust region primal-dual interior point method. However, this approach is conceptually different of the classical trust region methods, because the trial step is not obtained by solving a quadratic subproblem. Instead, the trial step is obtained as the convex combination of a Newtons direction and a reference steepest descent direction, which are calculated from linear systems that are similar to those of standard interior point methods. Numerical experiments with IEEE 14, 30, 57, 118 and 300-bus test systems were performed, and the results show that the proposed approaches are robust.

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Diego.pdf (2.70 Mbytes)
Data de Publicação
2019-12-02

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