An analytical method of switching waveform design for selective harmonic elimination

The paper proposes an analytical approach to the design of switching waveforms to eliminate harmonics and thereby improve THD (Total Harmonic Distortion) in power converters. Generally, numerical solutions are used to obtain the switching angles to eliminate targeted harmonics and the solution requires guessing of an initial value and a valid modulation index, m (a ratio of the fundamental to the dc input). Both of these values affect solution convergence whereas, such difficulties do not arise in analytical solutions. The closed-form solutions obtained through the analytical approach also determine the valid range of m. Due to the closed form, this method is suitable for real-time applications where a microcontroller can be programmed, thus making it attractive for low-cost applications. A PWM (Pulse Width Modulation) signal with even–odd symmetry has been selected to minimize the complexity of the solution. The approach requires the solution of transcendental equations associated with Fourier coefficients of a periodic waveform. Chebyshev expansion is used to convert the transcendental equations to power-sum non-linear polynomials. A successive polynomial simplification method has been used that lead to a set of elementary functions in closed-form, which are used to generate a polynomial and its roots are the desired optimal switching angles. In this paper, the proposed approach has been examined through a fourth-order, three-phase system for bipolar and multistep waveforms. The approach is equally applicable to other types of PWM systems. Simulation results verify the harmonic cancellations.