Switched nonlinear DAEs in electrical circuit theory

Kuzmenko, Darina (2023) Switched nonlinear DAEs in electrical circuit theory. Bachelor's Thesis, Applied Mathematics.

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Abstract

Inconsistent initial conditions in RLC circuits with switches or faulty components can cause Dirac impulses in the solution. These electrical impulses can damage certain parts of the circuit, and thus warrant a study into the unique solvability of the circuit. However, the presence of nonlinear elements in such a circuit make this challenging. In this paper, the uniqueness and solvability of nonlinear RLC circuits is investigated through the framework of nonlinear switched DAEs. A theory developed by Kausar and Trenn in their 2017 paper "Impulses in structured nonlinear switched DAEs" is discussed and the extent to which it can be applied to DAE models of RLC circuits is investogated.Inconsistent initial conditions in RLC circuits with switches or faulty components can cause Dirac impulses in the solution. These electrical impulses can damage certain parts of the circuit, and thus warrant a study into the unique solvability of the circuit. However, the presence of nonlinear elements in such a circuit make this challenging. In this paper, the uniqueness and solvability of nonlinear RLC circuits is investigated through the framework of nonlinear switched DAEs. A theory developed by Kausar and Trenn in their 2017 paper "Impulses in structured nonlinear switched DAEs" is discussed and the extent to which it can be applied to DAE models of RLC circuits is investigated.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Trenn, S. and Waarde, H.J. van
Degree programme:	Applied Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	13 Jul 2023 10:54
Last Modified:	13 Jul 2023 10:54
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/30606

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