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

Author(s)

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

Affiliation

^[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

• Document type: Journal article
• Source: IEEE CONTROL SYSTEMS MAGAZINE; v. 39, n. 2, p. 84-100, APR 2019.
• Web of Science Citations: 0

Abstract

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)

• FAPESP's process: 16/25017-1 - Measurement-Based Control and Its Applications
• Grantee: Vilma Alves de Oliveira
• Support Opportunities: Regular Research Grants
• FAPESP's process: 17/21577-5 - Use of stabilizers sets as linear constraints to obtain the gains of a PID controller obtained via quadratic optimization
• Grantee: Rafael Fernando Quirino Magossi
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree
• FAPESP's process: 14/50851-0 - INCT 2014: National Institute of Science and Technology for Cooperative Autonomous Systems Applied in Security and Environment
• Grantee: Marco Henrique Terra
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 16/21120-2 - Tuning an adaptive PID controller obtained via linear optimization with constraints and pointwise Thévenin equivalent
• Grantee: Rafael Fernando Quirino Magossi
• Support Opportunities: Scholarships in Brazil - Master