Reformulação das restrições de complementaridade em problemas de fluxo de potência ótimo
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Data
2019-06-05
Autores
Alencar, Marina Valença
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Universidade Estadual Paulista (Unesp)
Resumo
Neste trabalho duas abordagens de resolução são propostas para tratar restrições de complementaridade que modelam a atuação de dispositivos de controle de tensão no problema de fluxo de potência ótimo reativo, uma proposta de reformulação das restrições via programação inteira e a outra via desigualdades válidas. Este problema é modelado matematicamente como um problema de programação não linear inteira mista com variáveis discretas e restrições de complementariedade. As restrições de complementaridade na atuação dos dispositivos de controle de tensão (tap dos transformadores em fase e bancos de capacitores e reatores shunt) têm por objetivo viabilizar a implementação das soluções obtidas em sistemas elétricos de grande porte, para que eles operem apenas quando um dos limites de tensão da barra, por ele controlada, for atingido, restringindo o número de ajustes. Serão obtidas soluções para que o sistema elétrico opere de maneira ótima, com mínimas perdas, tensões nas barras dentro de limites rigorosamente fixados e com números mínimos de ajustes nos dispositivos controláveis. Testes numéricos com os sistemas elétricos IEEE 14, 30, 118 barras foram realizados para validar as abordagens propostas. Também foram realizados testes com outra reformulação das restrições de complementaridade proposta na literatura e com o problema de fluxo de potência ótimo reativo clássico para análise de resultados.
In this paper two approaches of resolution are proposed to treat complementarity constraints that model the performance of voltage control devices in the reactive optimal power flow problem, a proposal of reformulation of the restrictions through integer programming and the other via valid inequalities. This problem is mathematically modeled as a mixed integer nonlinear programming problem with discrete variables and complementarity constraints. The complementarity constraints in the performance of the voltage control devices (tap of the phase transformers and banks of capacitors and shunt reactors) has the objective of making feasible the implementation of the solutions obtained in large electrical systems, so that they operate only when one of the voltage limits of the bus controlled by it is reached, restricting the number of adjustments. Solutions will be obtained so that the electrical system operates optimally, with minimum losses, voltages in the buses within bounds strictly fixed and with minimum numbers of adjustments in controllable devices. Numerical tests with the electrical systems IEEE 14, 30, and 118 buses were carried out to validate the proposed approaches. We also performed tests with another reformulation of the complementarity constraints proposed in the literature and with the classical reactive optimal power flow problem for results analysis
In this paper two approaches of resolution are proposed to treat complementarity constraints that model the performance of voltage control devices in the reactive optimal power flow problem, a proposal of reformulation of the restrictions through integer programming and the other via valid inequalities. This problem is mathematically modeled as a mixed integer nonlinear programming problem with discrete variables and complementarity constraints. The complementarity constraints in the performance of the voltage control devices (tap of the phase transformers and banks of capacitors and shunt reactors) has the objective of making feasible the implementation of the solutions obtained in large electrical systems, so that they operate only when one of the voltage limits of the bus controlled by it is reached, restricting the number of adjustments. Solutions will be obtained so that the electrical system operates optimally, with minimum losses, voltages in the buses within bounds strictly fixed and with minimum numbers of adjustments in controllable devices. Numerical tests with the electrical systems IEEE 14, 30, and 118 buses were carried out to validate the proposed approaches. We also performed tests with another reformulation of the complementarity constraints proposed in the literature and with the classical reactive optimal power flow problem for results analysis
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Palavras-chave
Restrições de complementaridade, Fluxo de potência ótimo reativo, Variáveis discretas, Complementarity constraints, Reactive optimal power flow, Discrete variables