Specialized models for the long-term transmission network expansion planning problem
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Data
2018-12-10
Autores
Escobar Vargas, Laura Mónica
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Editor
Universidade Estadual Paulista (Unesp)
Resumo
A análise de sistemas altamente complexos quando e analizado o problema de planejamento de expansão de redes de transmissão de longo prazo, é o foco principal deste trabalho. Os modelos e metodos propostos são aplicados ao problema de planejamento estático tradicional, que é um problema de otimização matemática classificado como NP-completo, não-linear inteiro misto. O qual envolve no investimento, variáveis operacionais contínuas e variáveis inteiras. O comportamento normal de cada sistema pode conter informação essencial para a criação de novos métodos, como os planos de corte baseados em cortes de diferença de ângulos para problemas de grande escala, o que é a base é o ponto de partida deste trabalho, derivando em desigualdades válidas é ciclos críticos. Os cortes angulares básicos reduzem o espaço de busca do problema e o tempo total de cálculo deste problema, enquanto ao método de inequações válidas que pode ser usado para fornecer limites inferiores sólidos no investimento ótimo do planejamento de transmissão, já que a diferença entre o modelo DC (modelo exato) e o modelo de transporte (modelo mais relaxado) são as restrições angulares. Os ciclos críticos têm sido desenvolvidos para melhoraralguns dos modelos tradicionais do problemas de planejamento da expansão da rede de transmissão de longo prazo. A razão por trás disso é a ausência da segunda lei de Kirchhoff, que completa a representação do sistema, mas aumenta a complexidade. Para resolver os problemas resultantes, este trabalho usa a linguagem de modelagem AMPL com o solver CPLEX. Assim, este trabalho apresenta um método novo e mais eficiente para reduzir o espaço de busca do problema, a fim de melhorar o processo de solução através de diferentes tipos de desigualdades válidas e a combinação de ciclos com modelos tradicionais. Por ultimo, uma heurística de baixo esforço é proposta para permitir que o modelo identifique as opções de investimento mais atraentes, que devem ser consideradas no processo de otimização que descartará as opções de investimentos pouco promissoras que complicarão o problema sem contribuir para a solução final. Os testes fazem uso de quatro sistemas clássicos da literatura especializada: o sistema sul-brasileiro, o sistema colombiano, e o sistema norte-nordeste brasileiro.
The analysis of highly complex systems when solving the long-term transmission network expansion planning problem is the main focus of this work. The proposed improved models and methodology are applied to the traditionalstatic planning problem, which is a mathematical optimization problem classified as NP-complete and mixed-integer nonlinear problem. It involves continuousoperating variables and integer investment variables. The normal behavior of each system can be shown essential information to the creation of new methods, as the cutting-planes based in bus-angle difference cuts for large-scale problems which were the starting point of this work, deriving in valid inequalities and critic cycles. The angular cuts aim to reduce the search space of the problem and the total computation time of this NP-hard problem as for the valid inequalities methodthat can be used to provide strong lower bounds on the optimal investment of the transmissionplanning, since the difference between the DC model (exact model) and the transport model (more relaxed model) are the angular constraints. Critic cycles has been develop in order to improve some of the traditional long-term transmission network expansion planning problem models. The reason behind it is the absence of second Kirchhoff’s law which completes the representationof the system, but increase the complexity. In order to solve the resulting problems, this work uses the modeling language AMPL with the solver CPLEX. In test systems with many variables and constraints, Hence, this work presents a new, more efficient method to reduce the search space of the problem in order to improve the solution process through different types of valid inequalities and the combination of cycles with traditionalmodels. Lastly, a low effort heuristic is proposed to allow the model to identify the most attractive investment options, which should be considered in the optimization process which will discard the unpromisinginvestment options that will complicate the problem without contributing to the final solution. The tests make use of four classic systems in the specialized literature: the Southern Brazilian system, the Colombian system, and the Brazilian north-northeastsystem.
The analysis of highly complex systems when solving the long-term transmission network expansion planning problem is the main focus of this work. The proposed improved models and methodology are applied to the traditionalstatic planning problem, which is a mathematical optimization problem classified as NP-complete and mixed-integer nonlinear problem. It involves continuousoperating variables and integer investment variables. The normal behavior of each system can be shown essential information to the creation of new methods, as the cutting-planes based in bus-angle difference cuts for large-scale problems which were the starting point of this work, deriving in valid inequalities and critic cycles. The angular cuts aim to reduce the search space of the problem and the total computation time of this NP-hard problem as for the valid inequalities methodthat can be used to provide strong lower bounds on the optimal investment of the transmissionplanning, since the difference between the DC model (exact model) and the transport model (more relaxed model) are the angular constraints. Critic cycles has been develop in order to improve some of the traditional long-term transmission network expansion planning problem models. The reason behind it is the absence of second Kirchhoff’s law which completes the representationof the system, but increase the complexity. In order to solve the resulting problems, this work uses the modeling language AMPL with the solver CPLEX. In test systems with many variables and constraints, Hence, this work presents a new, more efficient method to reduce the search space of the problem in order to improve the solution process through different types of valid inequalities and the combination of cycles with traditionalmodels. Lastly, a low effort heuristic is proposed to allow the model to identify the most attractive investment options, which should be considered in the optimization process which will discard the unpromisinginvestment options that will complicate the problem without contributing to the final solution. The tests make use of four classic systems in the specialized literature: the Southern Brazilian system, the Colombian system, and the Brazilian north-northeastsystem.
Descrição
Palavras-chave
Planejamento da expansão de redes de transmissão, Cortes de diferença de ângulo, Ciclos críticos, Desigualdades válidas, Otimização, Modelo de transmissão de baixo esforço, Modelo de transporte disjuntivo melhorado, Segunda lei de Kirchhoff, Transmission network expansion planning, Bus-angle difference cuts, Critic cycles, Valid inequalities, Optimization, Low effort transmission model, Improv ed disjunctive transportation model, Second Kirchhoff law