On the stability criteria for inverter current control loops with LCL output filters and varying grid impedance

The use of LC and LCL filters and grid impedance variations are creating new challenges on the controller design for current control loops of photovoltaic and wind turbine inverters. In the design process, stability criteria such as Bode and revised Bode are commonly used. This paper analyses the limitations of Bode and revised Bode criteria to reliably determine stability and proposes a sufficient and necessary stability criterion, based on the Nyquist criterion, but that makes use of the Bode diagram. The proposed criterion, named generalized Bode criterion, is always reliable and helps the controller design. Relative stability in complex control loops is also studied and a relative stability analysis is proposed. Finally, the generalized Bode criterion and the proposed relative stability analysis are illustrated with a practical example in which a PI is designed in order to guarantee stability and achieve relative stability.