Generalization of Optimal Modulation Control for 3φ VSI Through Solving of Transcendent Equations

Pulse width modulation (PWM) techniques are primordial to high performance and great efficiency of inverters. The Selective Harmonic Elimination (SHE) technique determines in advance the switching angles, by taking into account the desired output voltage amplitude and harmonics to be eliminated. Thus, resolution of non-linear equation systems to set the switching angles poses crucial problem for the initial values choice. So, to remedy this problem, we propose in this work to formulate initial conditions by linear mathematical approximations, in order to approximate them to exact values that define pulse-width modulation. This formulation allows gain on the one hand the harmonics eliminated number (N) which will increase and on the other hand the computation time, which is often important. In this paper, we present transcendental equations resolution for switching angles (even or odd) and for two types of control patterns, namely: \({\uptheta }_{{\text{N}}} < {60}{^\circ }\) and \({\uptheta }_{{\text{N}}} < {90}{^\circ }\) . In order to validate our study, we demonstrated switching angles variation law as a function of modulation index using MATLAB simulation.