Date of Award

6-30-2021

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Systems Engineering

First Advisor

Hirak Patangia

Abstract

In this dissertation, we have investigated an analytical approach for solving a set of transcendental equations commonly encountered in Selective Harmonic Elimination (SHE). Generally, numerical solutions are used to solve the transcendental equations, which require guessing of an initial value and a valid value of modulation index m. Invalid initial values and an invalid m affect convergence. Such difficulties can be avoided with analytical solutions. The solution set will also determine the possible range of m valid for that modulation. Due to the complexity of solution that often requires computer algorithm to find a solution, we plan to develop design equation for various order of transcendental equations to find the switching angles. They are applicable to any type of optimal switching pattern. The investigated approach is suitable for real-time applications where a microcontroller/microprocessor can be programmed for the application making it attractive for low-cost real time applications. In this method, the transcendental equations (generated by Fourier expansion) are converted to power-sum non-linear polynomials using Chebyshev expansion. These non-linear polynomials are simplified using a successive polynomial reduction method. This leads to a solution set for elementary symmetric functions, which are used to generate a polynomial with roots containing the switching angles. The method is formulated for three types of modulation namely: bipolar, unipolar, and multilevel with contiguous and non-contiguous harmonic elimination. The solution trajectories as a function of m have been presented and valid possible range of m values have been determined. Simulation results verify the harmonic cancellations.

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