Accuracy of DFT-based synchrophasor estimators at off-nominal frequencies

An improved dynamic synchrophasor estimator

“…It is well known that the estimator (6) returns inaccurate results when off-nominal frequency offsets occur [5]. Also, the estimation error quickly increases under dynamic conditions [6].…”

“…In steadystate conditions the waveform frequency, amplitude and phase parameters can be considered constant during the whole observation interval and the phasor measurement accuracy is mainly affected by the off-nominal frequency offset [5]. However, in a more realistic scenario we need to consider the effect of both amplitude and phase variations produced by power oscillations.…”

“…The residual estimation uncertainty depends on how well the actual synchrophasor variations are described by (5). The phasor derivative required by (7) can be estimated, for instance, by using the difference between subsequent pairs of computed one-cycle DFTs.…”

“…It provides very accurate results in steady-state conditions as long as the waveform frequency is equal, or very close, to its nominal value. However, its sensitivity to both off-nominal frequency offsets and power system oscillations limits its applicability in actual operating conditions [5], [6]. In order to tackle this problem, different algorithms are focused on the improvement of the performances of the classic DFT estimator have been proposed in the literature [7], [8].…”

“…APPENDIX -DERIVATION OF 4PM(N/2) ESTIMATOR Assuming an input sine wave with nominal frequency and evaluating its DFT related to the one-cycle record centred in the r-th time-instant, we have [& and ;& are the signal synchrophasor and its derivative at the r-th instant, respectively. According to(5), the signal phasor and its derivative at the (r-N/2)-th time-instant are given by respectively. Thus, by considering the DFT related to the one-cycle length record centered in the (r-N/2)-th time-instant, it follows that:…”