Low-Complexity Least-Squares Dynamic Synchrophasor Estimation Based on the Discrete Fourier Transform

In this paper the expressions for the phasor parameter estimates returned by the Taylor-based Weighted Least Square (TWLS) approach, achieved using either complex-valued or real-valued variables, are derived. In particular, the TWLS phasor estimator and its derivatives are expressed as weighted sums of the Discrete Time Fourier Transform (DTFT) of the analyzed waveform and its derivatives. The derived expressions show that the TWLS algorithm is sensitive to lower order harmonics and inter-harmonics located close to the waveform frequency when few waveform cycles are analyzed. Also, the algorithm sensitivity to wideband noise is explained. The relationship between the TWLS phasor estimator and the waveform DTFT is then specifically analyzed when either a static or a second-order dynamic phasor model is assumed. Moreover, a simple and accurate procedure for evaluating the TWLS estimator of the dynamic phasor parameters is proposed. The derived expressions for the real-valued version are then approximated in order to reduce the required computational burden so achieving the Simplified TWLS (STWLS) procedure. That procedure can be advantageously employed in real-time low-cost applications when the reference frequency used in the TWLS approach is estimated run-time to improve estimation accuracy. Finally, computer simulations show that the phasor parameter estimates returned by the STWLS procedure when the waveform frequency is estimated by the Interpolated Discrete Fourier Transform method comply with the M-class of performance if an appropriate number of waveform cycles is considered.