Análise comparativa de métodos de otimização para a solução do problema de reconfiguração de sistemas de distribuição de energia elétrica
Carregando...
Data
2020-07-31
Autores
Silveira, Christoffer Lucas Bezão
Título da Revista
ISSN da Revista
Título de Volume
Editor
Universidade Estadual Paulista (Unesp)
Resumo
O problema de reconfiguração de sistemas de distribuição de energia elétrica (RSDEE) consiste em modificar a topologia da rede para obter uma nova configuração radial sendo o mais comum, dentre uma diversidade de caracterizações, a função objetivo que busca minimizar as perdas de potência do sistema. Diversos métodos têm sido desenvolvidos para resolver o problema, podendo ser classificados em algoritmos heurísticos, metaheurísticos (e.g., algoritmos genéticos e busca tabu) e de otimização matemática (programação linear e programação não linear). Embora, muitos trabalhos informem o esforço computacional, nem sempre é possível fazer uma comparação direta do desempenho das distintas propostas devido às diferentes condições em que foram testados (e.g., diferentes sistemas teste, linguagem de modelamento e solvers, equipamento computacional). Esta Dissertação faz uma análise comparativa de diferentes métodos metaheurísticos e de otimização matemática aplicados na solução do problema de RSDEE, que permite classificar o desempenho dos métodos segundo a qualidade da solução e o esforço computacional. Em particular, é avaliado o desempenho de formulações matemáticas não lineares, cônicas, linearizadas e metaheurísticas. Também, a partir do estudo dessas diferentes propostas de modelamento matemático, será avaliada a aplicação de restrições substitutas para representar a restrição de radialidade de forma alternativa com o intuito de acelerar o processo de solução. As formulações matemáticas foram implementadas no ambiente de modelagem matemática AMPL e avaliadas sob as mesmas condições usando sistemas teste da literatura especializada de pequeno (33 e 69 barras), de médio (136 barras) e de grande porte (417 barras), segundo o número de combinações possíveis para a solução do problema. A análise feita permite concluir que as técnicas metaheurísticas são mais rápidas que os modelos matemáticos e, geralmente, obtém a solução ótima em sistemas de pequeno e grande porte. Embora as formulações matemáticas cônicas e linearizadas precisem de maior tempo para serem resolvidas, têm como vantagem a garantia de fornecer a solução ótima. Além disso, foi observada uma redução significativa no esforço computacional quando são adicionadas restrições substitutas nas formulações matemáticas para o problema de RSDEE.
The problem of reconfiguration of electrical energy distribution systems (RSDEE) consists of modifying the network topology to obtain a new radial configuration, the most common being, among a variety of characterizations, the objective function that seeks to minimize system power losses. . Several methods have been developed to solve the problem, which can be classified into heuristic, metaheuristic algorithms (e.g., genetic algorithms and taboo search) and mathematical optimization (linear programming and non-linear programming). Although, many works inform the computational effort, it is not always possible to make a direct comparison of the performance of the different proposals due to the different conditions in which they were tested (e.g., different test systems, modeling and solvers language, computational equipment). This Dissertation makes a comparative analysis of different metaheuristic and mathematical optimization methods applied in the solution of the RSDEE problem, which allows to classify the performance of the methods according to the quality of the solution and the computational effort. In particular, the performance of nonlinear, conical, linearized and metaheuristic mathematical formulations is evaluated. Also, from the study of these different proposals for mathematical modeling, the application of substitute restrictions to represent the radiality restriction in an alternative way will be evaluated in order to accelerate the solution process. The mathematical formulations were implemented in the AMPL mathematical modeling environment and evaluated under the same conditions using test systems from the specialized literature of small (33 and 69 buses), medium (136 buses) and large (417 buses), according to the number possible combinations to solve the problem. The analysis makes it possible to conclude that metaheuristic techniques are faster than mathematical models and, generally, obtain the optimal solution in small and large systems. Although conical and linearized mathematical formulations need more time to be solved, they have the advantage of being guaranteed to provide the optimal solution. In addition, a significant reduction in computational effort was observed when substitute restrictions are added in the mathematical formulations for the RSDEE problem.
The problem of reconfiguration of electrical energy distribution systems (RSDEE) consists of modifying the network topology to obtain a new radial configuration, the most common being, among a variety of characterizations, the objective function that seeks to minimize system power losses. . Several methods have been developed to solve the problem, which can be classified into heuristic, metaheuristic algorithms (e.g., genetic algorithms and taboo search) and mathematical optimization (linear programming and non-linear programming). Although, many works inform the computational effort, it is not always possible to make a direct comparison of the performance of the different proposals due to the different conditions in which they were tested (e.g., different test systems, modeling and solvers language, computational equipment). This Dissertation makes a comparative analysis of different metaheuristic and mathematical optimization methods applied in the solution of the RSDEE problem, which allows to classify the performance of the methods according to the quality of the solution and the computational effort. In particular, the performance of nonlinear, conical, linearized and metaheuristic mathematical formulations is evaluated. Also, from the study of these different proposals for mathematical modeling, the application of substitute restrictions to represent the radiality restriction in an alternative way will be evaluated in order to accelerate the solution process. The mathematical formulations were implemented in the AMPL mathematical modeling environment and evaluated under the same conditions using test systems from the specialized literature of small (33 and 69 buses), medium (136 buses) and large (417 buses), according to the number possible combinations to solve the problem. The analysis makes it possible to conclude that metaheuristic techniques are faster than mathematical models and, generally, obtain the optimal solution in small and large systems. Although conical and linearized mathematical formulations need more time to be solved, they have the advantage of being guaranteed to provide the optimal solution. In addition, a significant reduction in computational effort was observed when substitute restrictions are added in the mathematical formulations for the RSDEE problem.
Descrição
Palavras-chave
Análise comparativa, Metaheurísticas, Otimização clássica, Reconfiguração de sistemas de distribuição, Restrições substitutas, Classic optimization, Comparative analysis, Metaheuristics, Reconfiguration of distribution systems, Surrogate constraints