Low Cost and Precise Frequency Estimation in Unbalanced Three Phase Power Systems

Monitoring the voltage frequency is of great significance in power systems. In this paper we propose two novel frequency estimators, namely the unbalanced HAM-WLS (UHW) estimator and the weighted least squares fusion (WLSF) estimator, to identify the voltage frequency in unbalanced three-phase power systems. The UHW method modifies both the coarse search and the weighted least squares (WLS) post-processing step of our previous HAM-WLS algorithm, and thus removes the spectrum leakage caused by the fluctuant maxima of the signal periodogram in phase unbalanced grids. Meanwhile, a new alternative is used in the WLSF estimator to aggregate the signal information in three difference phases. Compared with the Clarke's transformation that merely maximizes signal to noise ratios (SNRs), the proposed WLSF assigns different weights to the single-phase estimates according to their estimation variances, leading to improved accuracy and higher reliability. Both proposed estimation algorithms employ the Fourier coefficient interpolation and the iterative leakage subtraction in the frequency domain to lower the computation complexity as well as the WLS technique as a post-processing step to enhance the estimation precision. Therefore, both estimators realize accurate estimates with low computational cost. The complexity calculation, simulations and experiments for various scenarios all support the analysis. The results also show that the WLSF estimator exhibits more precise and stable performance than the UHW estimator at the cost of requiring relatively higher computational effort.