A least squares enhanced smart DFT technique for frequency estimation of unbalanced three-phase power systems

Abstract

The problem of off-nominal frequency estimation in unbalanced three-phase power systems is addressed from the frequency domain perspective. It is first established that the original Smart discrete Fourier transform (SDFT) technique designed for real-valued single-phase voltage can be extended to deal with complex-valued αβ transformed voltage. By observing that the underlying time series relationship among the consecutive DFT fundamental components employed by SDFT technique does not hold when noise or unexpected higher order harmonics are present, resulting in suboptimal estimation performances, the least squares framework is then built upon the underlying relationship among the consecutive DFT fundamental components to minimise the mean square model error. The benefits of the proposed LS-SDFT over the time-domain widely linear least squares (WL-LS) frequency estimator are verified by simulations for unbalanced power system conditions in the presence of noise and higher order harmonic pollution, as well as for real-world measurements.