Passivity enforcement via chordal methods

Orientador: Prof. Dr. Gustavo Henrique da Costa OliveiraTese (doutorado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Engenharia Elétrica. Defesa : Curitiba, 27/08/2019Inclui referências: p. 164-175Resumo: Neste documento são propostos três algoritmos inéditos associados aos problemas subsequentes de aferição e imposição da passividade, a qual é uma propriedade qualitativa, geral e fundamental na modelagem matemática de transitórios eletromagnéticos de sistemas elétricos passivos, como transformadores. Esses algoritmos baseiam-se numa combinação de teoria dos grafos e otimização convexa. O primeiro deles consiste na aferição de subsistemas passivos contidos num sistema não passivo, intuitivamente busca-se partes passivas contidas num todo não passivo. Já na etapa de imposição de passividade, o segundo algoritmo é consequência natural do primeiro: retendo apenas os parâmetros associados às partes passivas e descartando os demais, parte-se de um sistema passivo parcialmente especificado para se determinar novos parâmetros em substituição àqueles descartados de modo que o sistema como um todo seja passivo. A possibilidade de determinação dos novos parâmetros depende de uma propriedade topológica de um grafo associado às matrizes de parâmetros do modelo, tal propriedade é denominada cordalidade. O terceiro algoritmo aborda novamente a questão de imposição da passividade e também faz uso da cordalidade, não mais como condição de existência de solução, mas sim como uma forma de explorar a esparsidade das matrizes de parâmetros. O problema de imposição da passividade encerra dois desafios no seu processo de solução, a saber: (i) compensação de parâmetros resultando na degradação do modelo bem como (ii) longos tempos de solução. Os algoritmos ora propostos são uma resposta a essas questões e os resultados obtidos demonstraram-se comparáveis àqueles já existentes na literatura especializada, em alguns casos apresentando melhorias, seja em termos de aproximação ou tempo computacionais. Os algoritmos foram testados a partir de dados de medição de um Transformador de Potencial Indutivo bem como de um Transformador de Potência. Palavras-chave: Macro-modelagem Passiva. Teoria de Sistemas. Álgebra Linear Aplicada. Análise de Transitórios. Transformadores.Abstract: Three novel algorithms are herein proposed to solve passivity assessment and enforcement problems. Passivity is a general, qualitative and fundamental property pertaining to the modeling associated with electromagnetic transients in passive power systems, such as transformers. These algorithms make combined use of Graph Theory and Convex Optimization. The first algorithm is concerned with passivity assesment. In particular, it searches for passive subsystems embedded into a larger nonpassive system and eventually specifies a partially specified passive system. Focusing on the subsequent step, algorithm two is a natural consequence of the preceeding one: retaining only the parameter set associated with passive subsystems as determined before, this partially specified passive system is used to further determine the remaining parameters so that the entire system be fully specified and passive. The existence condition for finding a fully specified system hinges on the fulfillment of a topological property of the graph associated the parameter matrices, namely chordality. The third algorithm also solves the passivity enforcement problem by making use of chordality, not as an existence condition, but rather by exploiting chordal sparsity patterns obtained with the parameter matrices. Solving passivity enforcement problems entails two persisting challenges, namely: (i) passivity compensations to parameters prompting increased model degradation as well as (ii) large computation times. The algorithms herein proposed tackle these issues and yield results comparable to those already in use, sometimes resulting in improved performance in terms of either approximation accuracy or runtime. These results herein reported entail data from actual measurements of an Inductive Voltage Transformer and a Power Transformer. Keywords: Passive Macromodeling. System Theory. Applied Linear Algebra. Transient Analysis. Transformers

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