Novas modelagens matemáticas para otimização do problema de restauração em sistemas de distribuição de energia elétrica radiais
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Data
2018-03-16
Autores
Souza, Eliane Silva de
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Universidade Estadual Paulista (Unesp)
Resumo
Novas modelagens matemáticas são propostas para a otimização do problema de restauração em sistemas de distribuição radiais balanceados. O problema de restauração consiste em estratégias de reconfiguração topológica para o restabelecimento ótimo do fornecimento de energia elétrica para áreas desatendidas após interrupção permanente. A reconfiguração consiste na definição de operações de chaveamento para estabelecer a nova configuração operacional e requer a definição de uma sequência factível para essas operações. Neste trabalho, são propostos dois modelos matemáticos para a otimização do problema de reconfiguração restaurativa, um modelo de programação cônica de segunda ordem inteira mista (PCSOIM) e outro de programação linear inteira mista (PLIM) e é proposto um modelo matemático de PCSOIM para a otimização do problema de sequenciamento de operações de chaveamento. Os modelos matemáticos de reconfiguração ótima e de sequenciamento ótimo são independentes. No primeiro caso, resolve-se apenas o problema de definir a topologia ótima e, no segundo caso, resolve-se apenas o problema de definir a sequência ótima de operações de chaveamento. Assim, o problema de sequenciamento formulado consiste em definir a sequência ótima de operação do conjunto de chaves indicadas em uma proposta de reconfiguração previamente obtida e essa proposta de reconfiguração pode ser em contexto de operação normal ou restaurativo. Os modelos de reconfiguração restaurativa são formulados com o objetivo de minimizar a demanda não suprida no sistema e minimizar o número de chaveamentos nessa proposta que maximiza o atendimento e o modelo de sequenciamento ótimo de operações de chaveamento é formulado com o objetivo de minimizar a energia não suprida durante o processo de transição topológica. Todos os modelos propostos estão sujeitos a um conjunto de restrições topológicas e operacionais do sistema elétrico de distribuição. Nos dois modelos de PCSOIM, essas restrições representam satisfatoriamente a operação de um sistema elétrico de distribuição e, no modelo de PLIM, algumas restrições operacionais estão relaxadas e, por isso, são menos representativas, assim, a qualidade e a factibilidade das soluções propostas por esse modelo devem ser avaliadas. O propósito do modelo de PLIM é simplificar a resolução do problema de reconfiguração restaurativa e apresentar soluções com menor tempo de resolução que o correspondente modelo de PCSOIM. Os modelos matemáticos são completos e foram resolvidos através de técnicas exatas de otimização usando softwares comerciais de programação matemática. Foram realizados testes que definem propostas de reconfiguração restaurativa em um sistema de distribuição de 53 barras e em um sistema de distribuição de 417 barras. Os testes que definem a sequência ótima de operações de chaveamento foram realizados em propostas de reconfiguração restaurativa para o sistema de 53 barras. Os resultados mostraram que os modelos matemáticos são eficientes e robustos na otimização desses problemas. Na literatura, esses problemas são resolvidos principalmente por técnicas heurísticas, portanto, neste trabalho, são apresentados modelos matemáticos inovadores.
New mathematical models are proposed for the optimization of the restoration problem in balanced radial distribution systems. The restoration problem consists in topological reconfiguration strategies for the optimal restoration of the electric power supply to unattended areas after a permanent interruption. The reconfiguration consists in the definition of switching operations to establish the new operational configuration and requires the definition of a feasible sequence for these operations. In this work, two mathematical models for the optimization of the restorative reconfiguration problem, a mixed-integer second order conic programming (MISOCP) model and a mixed-integer linear programming (MILP) model are proposed. Additionally, a MISOCP mathematical model for the optimization of the switching operations sequencing problem is proposed. The mathematical models for optimal reconfiguration and optimal sequencing are independent. In the first case, only the problem of defining the optimum topology is solved and, in the second case, only the problem of defining the optimum sequence of switching operations is solved. Thus, the formulated sequencing problem consists in defining the optimum operations sequence of the set of indicated switches in a previously obtained proposal of reconfiguration and this proposal of reconfiguration may be in the normal or restorative operation context. The restorative reconfiguration models are formulated with the objective of minimizing the demand not supplied in the system and minimizing the number of switching operations in this proposal that maximizes the supply service. The optimal switching operations sequencing model is formulated with the objective of minimizing the energy not supplied during the topological transition process. All the proposed models are subject to a set of topological and operational constraints of the electric distribution system. In the two MISOCP models, these constraints represent satisfactorily the operation of an electrical distribution system and, in the MILP model, some operational constraints are relaxed and, therefore, the quality and the feasibility of the proposed solutions should be evaluated. The purpose of the MILP model is to simplify the resolution of the restorative reconfiguration problem and to present solutions with a shorter time than the corresponding MISOCP model. The mathematical models are complete and have been solved through exact optimization techniques using commercial mathematical programming software. Tests were carried out to define restorative reconfiguration proposals using a 53-bus distribution system and a 417-bus distribution system. The tests that define the optimal switching operations sequence were performed in restorative reconfiguration proposals for the 53-bus system. The results demonstrated that the mathematical models are efficient and robust in optimizing these problems. In the literature, these problems are solved mainly by heuristic techniques, therefore, in this work, innovative mathematical models are presented.
New mathematical models are proposed for the optimization of the restoration problem in balanced radial distribution systems. The restoration problem consists in topological reconfiguration strategies for the optimal restoration of the electric power supply to unattended areas after a permanent interruption. The reconfiguration consists in the definition of switching operations to establish the new operational configuration and requires the definition of a feasible sequence for these operations. In this work, two mathematical models for the optimization of the restorative reconfiguration problem, a mixed-integer second order conic programming (MISOCP) model and a mixed-integer linear programming (MILP) model are proposed. Additionally, a MISOCP mathematical model for the optimization of the switching operations sequencing problem is proposed. The mathematical models for optimal reconfiguration and optimal sequencing are independent. In the first case, only the problem of defining the optimum topology is solved and, in the second case, only the problem of defining the optimum sequence of switching operations is solved. Thus, the formulated sequencing problem consists in defining the optimum operations sequence of the set of indicated switches in a previously obtained proposal of reconfiguration and this proposal of reconfiguration may be in the normal or restorative operation context. The restorative reconfiguration models are formulated with the objective of minimizing the demand not supplied in the system and minimizing the number of switching operations in this proposal that maximizes the supply service. The optimal switching operations sequencing model is formulated with the objective of minimizing the energy not supplied during the topological transition process. All the proposed models are subject to a set of topological and operational constraints of the electric distribution system. In the two MISOCP models, these constraints represent satisfactorily the operation of an electrical distribution system and, in the MILP model, some operational constraints are relaxed and, therefore, the quality and the feasibility of the proposed solutions should be evaluated. The purpose of the MILP model is to simplify the resolution of the restorative reconfiguration problem and to present solutions with a shorter time than the corresponding MISOCP model. The mathematical models are complete and have been solved through exact optimization techniques using commercial mathematical programming software. Tests were carried out to define restorative reconfiguration proposals using a 53-bus distribution system and a 417-bus distribution system. The tests that define the optimal switching operations sequence were performed in restorative reconfiguration proposals for the 53-bus system. The results demonstrated that the mathematical models are efficient and robust in optimizing these problems. In the literature, these problems are solved mainly by heuristic techniques, therefore, in this work, innovative mathematical models are presented.
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Palavras-chave
Modelagem matemática, Reconfiguração de sistemas elétricos de distribuição radiais, Restauração do serviço de fornecimento de energia elétrica, Sequenciamento ótimo de operações de chaveamento, Mathematical modeling, Reconfiguration of electrical distribution systems, Service restoration problem, Optimal switching operations sequencing