Solution Method of SHEWPM for Neutral-point-clamped Inverter Based on Improved Levenberg-Marquardt Method

Abstract

It is difficult to choose the iterative initial values in Newton-Raphson(N-R) method for solving the non-linear equations of selective harmonic elimination pulse width modulation(SHEPWM) for neutral-point-clamped(NPC) inverter. To this end, we proposed an improved Levenberg-Marquardt(L-M) method. By introducing the damping factor in the inverse matrix, the proposed method avoided the disadvantages of singular or pathological in Jacobi matrix of N-R method. In order to effectively overcome the strict requirements of the iterative initial selection, the relaxation parameter was adaptively adjusted, so that the trial-and-error processes could be significantly reduced. When the modulation degree m was 0.85, taking the SHEPWM of NPC inverter of nine switching angles for example, we randomly selected six initial sets and obtained the required six numerical solutions by selecting reasonable damping factor and adaptively adjusting the relaxation parameter. The results showed that the convergence domain of the proposed method was wider than that in N-R method. Then we analyzed the six groups of solution trajectories and their differences in harmonic characteristics at the modulation index of m∈[0.7, 1.15], which provided more choices in practical use. Finally, we verified the correctness of the solutions obtained from the new method by using a single-phase laboratory prototype.