Planejamento ótimo de microrredes usando aritmética afim
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Data
2022-02-24
Autores
Peñaloza Morán, John Eugenio
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Editor
Universidade Estadual Paulista (Unesp)
Resumo
Neste trabalho apresenta-se uma formulação matemática baseada na Aritmética Afim para resolver o problema do Sistema de Gerenciamento de Energia para microrredes trifásicas considerando as incertezas na carga e nas fontes de geração renováveis. A formulação matemática resultante é decomposta em dois subproblemas de otimização, sendo o primeiro, um modelo de programação linear inteiro misto que representa o problema Unit Commitment baseado na Aritmética Afim e, o segundo, um modelo de programação não linear que estabelece a formulação para o problema de despacho econômico. O problema de Unit Commitment baseado na Aritmética Afim é resolvido através do solver comercial CPLEX e fornece como resultado os estados para as variáveis binárias, bem como as formas afins das variáveis contínuas para todo o horizonte de otimização. Em seguida, a solução do problema de despacho econômico é calculada com base na determinação dos valores dos símbolos de ruído das formas afins obtidas no problema de Unit Commitment. Os problemas de otimização são escritos na linguagem de modelagem algébrica AMPL, enquanto o processo heurístico, que integra os subproblemas, é resolvido no Matlab2018b através da interface AMPL-API. Finalmente, a eficiência do trabalho proposto é avaliada e analisada num sistema de distribuição IEEE de 19 barras trifásico presente na literatura, onde os resultados obtidos mostraram soluções robustas sem precisar de um grande esforço computacional, atingindo uma operação econômica da micorrede.
This work presents a mathematical formulation based on Affine Arithmetic to solve the problem of the Energy Management System for three-phase microgrids considering the uncertainties in the load and the renewable generation sources. The resulting mathematical formulation is decomposed into two optimization subproblems, the first being a mixed integer linear programming model that represents the Unit Commitment problem based on Affine Arithmetic and, the second, a nonlinear programming model that establishes the formulation for the economic dispatch problem. The Unit Commitment problem based on Affine Arithmetic is solved using the commercial solver CPLEX and provides as a result the states for the binary variables, as well as the affine forms of the continuous variables for the entire optimization horizon. Then, the solution of the economic dispatch problem is calculated based on the determination of the values of the noise symbols of the affine forms obtained in the Unit Commitment problem. The optimization problems are written in the algebraic modeling language AMPL, while the heuristic process, which integrates the subproblems, is solved in Matlab2018b through the AMPL-API interface. Finally, the efficiency of the proposed work is evaluated and analyzed in a three-phase IEEE 19-bus distribution system present in the literature, where the results obtained showed robust solutions without requiring a great computational effort, reaching an economic operation of the microgrid.
This work presents a mathematical formulation based on Affine Arithmetic to solve the problem of the Energy Management System for three-phase microgrids considering the uncertainties in the load and the renewable generation sources. The resulting mathematical formulation is decomposed into two optimization subproblems, the first being a mixed integer linear programming model that represents the Unit Commitment problem based on Affine Arithmetic and, the second, a nonlinear programming model that establishes the formulation for the economic dispatch problem. The Unit Commitment problem based on Affine Arithmetic is solved using the commercial solver CPLEX and provides as a result the states for the binary variables, as well as the affine forms of the continuous variables for the entire optimization horizon. Then, the solution of the economic dispatch problem is calculated based on the determination of the values of the noise symbols of the affine forms obtained in the Unit Commitment problem. The optimization problems are written in the algebraic modeling language AMPL, while the heuristic process, which integrates the subproblems, is solved in Matlab2018b through the AMPL-API interface. Finally, the efficiency of the proposed work is evaluated and analyzed in a three-phase IEEE 19-bus distribution system present in the literature, where the results obtained showed robust solutions without requiring a great computational effort, reaching an economic operation of the microgrid.
Descrição
Palavras-chave
Microrrede, Incertezas, Microgrid, Uncertainties, Geração distribuída, Sistemas de distribuição, Otimização robusta, Sistema de gerenciamento de energia, Distributed generation, Distribution systems, Robust optimization, Energy management system, Aritmética afim, Affine arithmetic