Considering the aim of having low switching losses, especially in medium-voltage and high-power converters, the pre-programmed pulse width modulation technique is very useful because the generated harmonic content can be known in advance and optimized. Among the different low switching frequency techniques, the Selective Harmonics Elimination (SHE) modulation method is most suitable because of its direct control over the harmonic spectrum. This paper proposes a method for obtaining multiple solutions for selectively eliminating specific harmonics in a wide range of modulation indices by using modified Newton–Raphson (NR) and pattern generation techniques. The different pattern generation and synthesis approach provide more degrees of freedom and a way to operate the converter in a wide range of modulation. The modified Newton–Raphson technique is not complex and ensures fast convergence on a solution. Moreover, multiple solutions are obtained by keeping a very small increase in the modulation index. In the previous methods, solutions were not obtainable at all modulation indices. In this paper, only exact solutions to the low-order harmonics elimination for Cascaded H-bridge inverter are reported for all modulation indices. Analytical and simulation results prove the robustness and correctness of the technique proposed in this paper.

Pulse width modulation (PWM) control for power converters have been vastly investigated and used in many industrial application. For medium voltage and high power applications, low switching frequency PWM techniques are preferred over high switching frequency-based PWM techniques. The preprogrammed low switching frequency-based PWM technique known as selective harmonics elimination (SHE) gives the better quality waveform at a lower switching frequency. The main difficulty in applying SHE PWM is in solving of non-linear transcendental equations for obtaining switching angles. Several methods have been proposed for computation of switching angles that include numerical techniques, optimization techniques, and algebraic techniques. However, the computation of switching angles is still a challenging task in the application of SHE PWM. In this paper, a novel fast convergent homotopy perturbation method (HPM) is proposed to compute switching angles for a multilevel inverter at a faster rate. The solutions obtained by the proposed technique is as accurate as obtained by the algebraic methods with no dependency on the initial guess. The proposed technique can compute the higher number of switching angles with multiple solutions in some modulation index range. A prototype is developed and the computed switching angles have been verified using field-programmable gate arrays (FPGA) controller to validate the results for practical applications.