A Recursive Park Transformation to Improve the Performance of Synchronous Reference Frame Controllers in Shunt Active Power Filters

Load harmonic currents and load unbalances reduce power quality (PQ) supplied by electrical networks. Shunt active power filters (SAPFs) are a well-known solution that can be employed to enhance electrical PQ by injecting a compensation current at the point of common coupling (PCC) of the SAPF, the load, and the electrical grid. Hence, SAPF controllers must determine the instantaneous values of the compensation reference current, including nondesirable components of the load current. A family of SAPF controllers, which evaluates the compensation reference current using synchronous rotating frames (SRFs), employs a structure based on Park transformations: direct transform, low- pass filtering (LPF), and inverse transform. The cutoff frequency and the filter order of the LPF stage must be designed properly in order to obtain an accurate reference current and a fast dynamic response of these SAPF controllers. This paper proposes a recursive implementation of the direct Park transformation that avoids the filtering stage and allows accurate SRF controllers to be designed. Moreover, the proposed implementation is not dependent on PCC conditions. The proposed implementation is evaluated using a three-phase, three-wire SAPF and compared with LPF-based controllers by simulation and experiment.