Accuracy Analysis and Enhancement of DFT-Based Synchrophasor Estimators in Off-Nominal Conditions

Synchrophasor estimation accuracy is a well-known critical issue in systems for smart grid monitoring and control. This paper deals with an in-depth analysis of the effect of both steady-state and dynamic disturbances on single-cycle and multicycle windowed discrete Fourier transform (DFT)-based synchrophasor estimators. Unlike other qualitative or simulation-based results found in the literature, this work provides two accurate and easy-to-use analytical expressions that can be used to determine the worst case range of variation of the total vector error (TVE) due to off-nominal frequency deviations. In such conditions, estimation accuracy is limited by two factors, i.e., the infiltration caused by the input signal image frequency and the scalloping loss associated with the spectrum main lobe of the chosen window. Starting from the aforementioned general analysis, a new two-term window minimizing the detrimental effects of image frequency tone is proposed. The accuracy of the related DFT-based synchrophasor estimator is evaluated under both static and dynamic conditions, which is the most interesting scenario for future smart grids. Moreover, the effect of waveform frequency measurement uncertainty on scalloping loss compensation is quantified. Several simulation results (including the effects of noise, harmonic distortion, and amplitude and phase modulation) confirm that the proposed window can significantly improve the accuracy achievable with a simple single-cycle DFT estimator. Indeed, TVE values much smaller than 1% can be achieved even in the worst case conditions reported in the standard IEEE C37.118.1-2011, when the frequency waveform deviations are within ±4% of the nominal value. In addition, the proposed solution could be useful to improve the performance of more complex dynamic phasor estimators, e.g., those in which the first- and second-order terms of the phasor Taylor series expansion result from the differences of consecutive DFT-based phasor estimates.