Uma metodologia determinística à resolução de problemas multiobjetivo de despacho e de fluxo de potência
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Data
2019-07-16
Autores
Gonçalves, Elis
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Editor
Universidade Estadual Paulista (Unesp)
Resumo
O problema multiobjetivo de despacho econômico e ambiental com efeito de pontos de carregamento de válvula e com perdas de potência ativa, é um problema de otimização multiobjetivo, não convexo e não-diferenciável. Por apresentar tais características, normalmente, é resolvido na literatura, através de abordagens heurísticas de otimização. Com a inserção da representação da transmissão (fluxo de potência) ao problema multiobjetivo, o mesmo torna-se mais complexo de ser solucionado. Devido a estas dificuldades, são escassas as abordagens determinísticas de otimização para solução destes tipos de problemas, uma vez que elas necessitam do cálculo de derivadas parciais, enquanto que, as heurísticas não necessitam. Portanto, os principais objetivos deste trabalho são: propor uma abordagem determinística para a solução dos problemas em destaque e comparar com outros métodos disponíveis na literatura, principalmente os métodos heurísticos e meta-heurísticos. A abordagem determinística proposta tem as seguintes características: tratar a natureza multiobjetivo dos problemas através da estratégia de Restrições Canalizadas Progressivas (RCP); utilizar uma técnica de suavização de funções para lidar com a não diferenciabilidade e, por fim, utilizar um método de rescalamento não-linear, baseado na função barreira logarítmica modificada, com procedimento previsor-corretor e estratégia de correção de inércia para resolver os subproblemas resultantes da estratégia RCP. A metodologia proposta é aplicada aos sistemas testes com 2, 6, 10, 19 e 40 geradores para o problema multiobjetivo de despacho, e aos sistemas de 30, 57 e 118 barras para o problema multiobjetivo de fluxo de potência ótimo. De forma geral, os resultados mostram que as curvas de Pareto obtidas pelo método proposto têm boa qualidade quando comparadas às obtidas por outras abordagens de otimização.
The multiobjective economic and environmental dispatch problem with valve-point loading effects and losses is a multiobjective, non-convex and non-differentiable optimization problem. Due to these characteristics, it has been solved in the literature mainly by heuristic approaches. The addition of the network representation to the multiobjective problem makes it more complex to be solved. Due to these difficulties, there are few deterministic optimization approaches for solving these problems. While deterministic optimization approaches require the calculation of partial derivatives, heuristic approaches do not. Therefore, the main objective of this work is to propose a deterministic approach to solve these problems and compare it with other methods available in the literature, especially the heuristic and metaheuristic methods. The proposed deterministic approach has the following characteristics: the multiobjective nature of the problems is handled through the Progressive Bounded Constraint (PBC) strategy, a smoothing function technique is employed to deal with the cost function non-differentiability and, finally, the non-linear rescaling method, based on the modified logarithmic barrier function, with predictorcorrector procedure and inertia correction strategy, is applied to solve the single objective subproblems resulting from the PBC method. The proposed methodology is applied to the test systems with 2, 6, 10, 19 and 40 generators for the multiobjective dispatch problem, and the 30, 57 and 118 bus systems for the multiobjective optimal power flow problem. In general, the results show that the Pareto curves obtained by the proposed method have good quality when compared to those obtained by other optimization approaches. Keywords: dispatch multiobjective, optimal power flow multiobjective, progressive bounded constraint, smoothing function, nonlinear rescaling, modified logarithmic barrier function
The multiobjective economic and environmental dispatch problem with valve-point loading effects and losses is a multiobjective, non-convex and non-differentiable optimization problem. Due to these characteristics, it has been solved in the literature mainly by heuristic approaches. The addition of the network representation to the multiobjective problem makes it more complex to be solved. Due to these difficulties, there are few deterministic optimization approaches for solving these problems. While deterministic optimization approaches require the calculation of partial derivatives, heuristic approaches do not. Therefore, the main objective of this work is to propose a deterministic approach to solve these problems and compare it with other methods available in the literature, especially the heuristic and metaheuristic methods. The proposed deterministic approach has the following characteristics: the multiobjective nature of the problems is handled through the Progressive Bounded Constraint (PBC) strategy, a smoothing function technique is employed to deal with the cost function non-differentiability and, finally, the non-linear rescaling method, based on the modified logarithmic barrier function, with predictorcorrector procedure and inertia correction strategy, is applied to solve the single objective subproblems resulting from the PBC method. The proposed methodology is applied to the test systems with 2, 6, 10, 19 and 40 generators for the multiobjective dispatch problem, and the 30, 57 and 118 bus systems for the multiobjective optimal power flow problem. In general, the results show that the Pareto curves obtained by the proposed method have good quality when compared to those obtained by other optimization approaches. Keywords: dispatch multiobjective, optimal power flow multiobjective, progressive bounded constraint, smoothing function, nonlinear rescaling, modified logarithmic barrier function
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Palavras-chave
Despacho multiobjetivo, Fluxo de potência ótimo multiobjetivo, Restrições canalizadas progressivas, Suavização hiperbólica, Reescalamento não-linear, Barreira logarítmica modificada