Most Infinite Impulse Response (IIR) digital filter implementations in power electronic inverter applications are based on the time shift operator q and its associated z-transform. But for higher sampling frequencies where the sample period approaches zero for z-transform discrete systems, their dynamic response does not converge smoothly to the continuous counterpart, causing substantial implementation problems. In contrast, the response of filters based on the delta operator does converge to the continuous counterpart for smaller sample periods, and hence they are much better suited for digital control applications where sampling frequencies are much higher than the system poles. This paper presents a practical overview describing the use of the delta operator for IIR digital filter systems, and shows how the operator can be used in power electronic inverter applications to achieve substantial performance benefits compared to equivalent shift-based implementations. A transformation is presented to convert shift-based implementations to the delta form, and the specific examples of an active filter and a P+ Resonant current regulator are used to illustrate the improvements that can be expected. The superior performance of the delta operator for digital control of inverter applications has been verified in both simulation and experiment.
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