Closed-Form Harmonic Compensation Using Resonant Controllers Applied to Four-Leg VSI

Harmonic compensation employing resonant controllers applied to voltage source inverters (VSIs) generally requires complex techniques or a trial-and-error process to design the controller parameters. This article proposes a closed-form solution for designing digital proportional-resonant controllers applied to three-phase four-leg (TP4L) inverters. The proposal presents a sequential procedure that uses closed-form expressions to establish the harmonic frequencies at which resonant stages must be added to comply with individual voltage harmonic distortion standards. The method eliminates the need for a trial-and-error process and ensures compliance with total harmonic distortion (THD) and individual harmonic distortion limits. The frequencies that require compensation and the gains of the resonant controllers are determined by evaluating the difference that presents the output harmonic impedance of the inverter concerning normalized three-phase harmonic impedance limits defined in this work. Furthermore, this article adopts the harmonic distortion restrictions imposed by the Standard IEC 61000-2-2, allowing the harmonic impedance limits to be defined for the reference nonlinear (RNL) load indicated in IEC 62040-3. Experimental results are presented to validate the proposed design using a 5-kVA four-leg inverter, feeding balanced, unbalanced, linear, and nonlinear loads.