Sub-Cycle Dynamic Phasors with Adjustable Transient Response

We extend in several directions the study of our fast sparse alternative to the standard (FFT-based) evaluation of dynamic phasors. We present analysis for an arbitrary shift between the waveform samples used to construct sub-cycle dynamic phasors. Next, we show that the transient response of sub-cycle dynamic power metrics can be improved by using a small number of waveform samples and adjusting the uniform inter-sample shift. Our real-life examples demonstrate that reduction of the inter-sample shift can be quite effective in the presence of fast transients (wide-band in frequency). We use a synthetic example to demonstrate that a metric obtained from a sub-cycle scheme provides surprisingly accurate information about the duration and onset-time of a transient. We also identify a range of shift values for which the steady-state error remains near-optimal, and we derive conditions for a superior performance for slow transients. Finally, our results suggest that in practical real-time implementations it may be advantageous to calculate at least two sets of phasors to cover both slow and fast transients: the computational cost of such a scheme is still significantly lower than that of a standard full-cycle calculation.