Sloped Multi-Level Selective Harmonic Elimination pulse-width modulation

Multi-Level Selective Harmonic Elimination (MSHE) offers tight control over the harmonic content of a multi-level inverter output signal. By employing Fourier series analysis and setting the appropriate initial conditions, a non-linear transcendental equation set is constructed. By turning inverter´s power switches on and off at exact instances defined by equation set solution, fundamental component can be adjusted within a range and the intrinsic harmonics selectively eliminated. Ideal by nature, MSHE does not account for the practical characteristics of power electronics switching devices. It assumes instantaneous switching transition and by that ignores the dynamic nature of switching process. In practice, output signal transitions between conduction state (on) and blocking state (off) and vice versa, do not occur instantaneously but change gradually over time, depending amongst others on switching device characteristics. Turning inverter power switches on and off according to switching sequence obtained using ideal MSHE while generating sloped-practical output signal, might alter its harmonic content. We provide a more practical model in terms of switching rise-time and fall-time parameters. As linear function approximation uses sloped (linear) function, we call this method Sloped Multi-Level Selective Harmonic Elimination or Sloped-MSHE. As shown, this new model does not increase the complexity of the solution process and can be solved using any known MSHE solution method. Theoretical results are validated by simulations. A quantitative comparison between ideal and practical method is made in terms of total harmonic distortion (THD) factor. Simulation results for various rise-time and fall-time durations, corresponding for both soft and hard switching techniques, are presented. Simulation results indicate Sloped-MSHE has slight advantage over MSHE which is prominent mainly with higher-order harmonics. These findings support the use of conventional MSHE methods- - in soft switching devices.