Application of flat-top windows for direct phasor estimation in electric power systems

W artykule przedstawiono wyniki zastosowania okna czasowego o płaskiej charakterystyce amplitudowej do obliczania fazora w sieciach elektroenergetycznych. Otrzymane wyniki porównano do wyników uzyskanych dla okna prostokątnego i okna Hanna. Do określenia właściwości porównywanych metod obliczeniowych wykorzystano niektóre z testów zgodności standardu IEEE Standard for Synchrophasor Measurements for Power Systems, oraz zdefiniowane tam błędy TVE (total vector error) i FE (frequency error). Otrzymane wyniki wskazują, że okna o płaskiej charakterystyce widmowej pozwalają istotnie poprawić dokładność estymacji fazora zwłaszcza w stanie ustalonym.This paper presents results of direct phasor estimation by DFT with application of flat-top windows. Results obtained with rectangular window and Hann window are also presented for comparison. The quality of the phasor estimation is evaluated by TVE (total vector error) and FE (frequency error) as defined in the IEEE Standard for Synchrophasor Measurements for Power Systems. The application of flat-top windows resulted in significant reduction of TVE in steadystate compliance tests. For actual frequency fin=50±2,5 Hz maximum TVE was reduced about 30 times as compare to Hann window. The smallest maximum FE errors were also obtained for flat-top window. In dynamic compliance tests flat-top windows performed only slightly better than Hann window and rectangular window in frequency estimation, and maximum TVE error is even slightly higher than for rectangular window for modulating frequency above 2,5 Hz. Straightforward computation of the phasor based on one DFT bin has computational complexity N. Application of FFT algorithms is not advised, because only one DFT bin is required. The phasor may be computed on sample by sample basis by discrete time convolution with FIR filter. In that case reporting frequency is the same as the sampling frequency of the signal