Power quality and the un-decimated wavelet transform: An analytic approach for time-varying disturbances

This paper introduces the un-decimated wavelet transform to compute power quantities using complex wavelet coefficients. The advantages and disadvantages of real and complex wavelets are first highlighted, then time–frequency formula for active, reactive and apparent power based on complex wavelet coefficients and with no decimation, are presented in light of Mallat's multi-resolution analysis (MRA). The performance of the proposed approach is evaluated using test cases incorporating time-variant and time-invariant power quality (PQ) disturbances. The results indicate that the use of the decimation-free complex wavelet coefficients in power quantities computation not only overcomes the limitations of other real wavelets but also assigns a direction for the flow of these power quantities by retaining the phase angle information at the approximation and detail levels which is not accessible in case of real wavelets or complex wavelets when used as stand-alone tools. The proposed approach can be useful in many applications involving challenging power quality event detection (high impedance faults, multi-stage PQ dips/swells, non-intentional islanding of distributed generation, etc.), non-intrusive load disaggregation in advanced metering infrastructure and wide area monitoring (WAM).

► A power quality analysis approach based on complex format of wavelet coefficients is presented.
► A decimation-free wavelet transform is used in conjunction with discrete Hilbert Transform to develop complex power quantities in time–frequency domain.
► The presented time–frequency phasor approach overcomes the limitations of existing power quality analysis approaches.
► The algorithm is tested in the presence of three phase time-varying power quality disturbances.
► Possible applications of the presented approach are highlighted.