Realization of Digital Differentiator Using Generalized Integrator For Power Converters

In power converters, the digital implementation of a differentiator is challenged by noise amplification and phase error. For example, the backward Euler differentiator loses its effectiveness at high frequency due to an introduced large-phase error. The Tustin differentiator, on the other hand, yields unacceptable noise amplification even though it produces the phase of an ideal differentiator perfectly. For an even more accurate performance, this letter proposes a new digital differentiator based on generalized integrator (GI). It will specifically be shown that the differentiation characteristic of a GI is an optimized compromise between those of backward Euler and Tustin differentiators. Several discretization techniques are then investigated for discretizing the GI-based differentiator. The effectiveness of the proposed differentiator has been verified by experimental results obtained with an LCL-filtered grid converter damped by feeding back the derivative of its capacitor voltage.