Design Procedure of Current Controllers for LCL-filtered Grid-Tied Inverters with Robust Stability Certification

  • Caio R. D. Osório Federal University of Santa Maria
  • Gustavo G. Koch Federal University of Santa Maria
  • Pablo García University of Oviedo
  • Vinicius F. Montagner Federal University of Santa Maria
Keywords: Active damping, Direct pole placement, Grid-tied inverter, LCL filter, Robust control


This paper proposes an alternative design procedure for current control of LCL-filtered grid-tied inverters, taking into account robustness against uncertain and possibly timevarying grid inductances. The control strategy is developed in stationary reference frame, and is based on a partial state feedback, including an active damping scheme of the LCL filter resonance. From the system parameters and the design specifications, analytical expressions for the calculation of the control gains are provided, oriented by a pole placement in discretetime domain. These expressions are obtained neglecting the dynamics of the filter capacitor, including resonant controllers to track sinusoidal references, and taken into account the delay due to digital implementation. To certicate robust stability of the closed-loop system under time-varying grid inductances, a theoretical analysis based on a Lyapunov function is provided. Time and frequency domain results are presented for a case study, illustrating that the proposed design strategy is able to provide robust control gains leading to grid-injected currents with suitable responses for the entire range of grid inductances considered in the design.