Direct Realization of Digital Differentiators in Discrete Domain for Active Damping of LCL -Type Grid-Connected Inverter

To damp the LCL-filter resonance in a grid-connected inverter, the feedback of capacitor current is usually adopted, and it can be replaced by the feedback of capacitor voltage as a low-cost solution, if an accurate digital differentiator can be made. The best way for realizing such a differentiator has so far proved to be an indirect nonideal generalized integrator (GI). As a simple alternative, this paper proposes two digital differentiators, which are directly developed in the discrete domain. They are a first-order differentiator based on backward Euler plus digital lead compensator and a second-order differentiator based on Tustin plus digital notch filter. The basic idea of the proposed methods is to correct their frequency responses to match the ideal differentiator with embedded digital filters. It is shown that the proposed differentiators exhibit the same derivative performance as the nonideal-GI differentiator, and they are more attractive for digital implementations due to their direct discrete natures, compact expressions, and easy algebraic manipulations. In particular, the proposed first-order differentiator is most competitive for its general representation and simplest implementation. Finally, a 12-kW prototype is built, and experiments are performed to verify the theoretical analysis.