Thevenin's Theorem, Cramer's Rule, and Parameterized Systems: Some Connections

Autor(es)

Bhattacharyya, Shankar P. ^[1] ; Oliveira, Vilma A. ^[2] ; Magossi, Rafael F. Q. ^[3]

Afiliação do(s) autor(es)

^[1] Texas A&M Univ, Elect Engn, College Stn, TX - USA

^[2] Univ Sao Paulo, Dept Elect & Comp Engn, Sao Paulo - Brazil

^[3] Univ Sao Paulo, Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: IEEE CONTROL SYSTEMS MAGAZINE; v. 39, n. 2, p. 84-100, APR 2019.
• Citações Web of Science: 0

Resumo

The celebrated theorem by Thevenin is very useful in applications such as power system analysis because it states that it is possible to simplify a complex circuit to a much simpler equivalent circuit. Traditionally, it is accomplished by taking the power system to a short circuit that is a critical operating condition. This article, therefore, highlights the efficacy of using a proposed theorem that generalizes Thevenin's theorem and avoids submitting the system to critical operating conditions that differ from its conventional application. Additionally, this generalized Thevenin's theorem can be used in other fields, such as precision agriculture, to simplify complex interconnected systems. The connection between Thevenin's theorem and Cramer's rule in a parameterized state-space framework is also shown. The parameterized state-space solution is given in terms of parameters, which may include design parameters and unknown coefficients. Different problems in the agricultural, mechanical, and power electronic fields are used to illustrate practical applications of the theory presented. (AU)

• Processo FAPESP: 16/25017-1 - Controle baseado em medições e suas aplicações
• Beneficiário: Vilma Alves de Oliveira
• Linha de fomento: Auxílio à Pesquisa - Regular
• Processo FAPESP: 16/21120-2 - Sintonia de um controlador PID adaptativo obtido via otimização linear com restrições e equivalente de Thévenin pontual
• Beneficiário: Rafael Fernando Quirino Magossi
• Linha de fomento: Bolsas no Brasil - Mestrado
• Processo FAPESP: 14/50851-0 - INCT 2014: Instituto Nacional de Ciência e Tecnologia para Sistemas Autônomos Cooperativos Aplicados em Segurança e Meio Ambiente
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• Processo FAPESP: 17/21577-5 - Utilização dos conjuntos estabilizantes como restrições lineares para obtenção dos ganhos de um controlador PID obtido via otimização quadrática
• Beneficiário: Rafael Fernando Quirino Magossi
• Linha de fomento: Bolsas no Exterior - Estágio de Pesquisa - Mestrado