Characteristics of Measurement of Criterion Values and Adaptive - Digital Signal Processing in Power System Protection and Control - page 195

(a)

R, X, Z

1.4

1.3

Z

1.2

1.1

1

f
R

0.9

0.8

0.7

X

0.6

100 125 150 175 t [ms]

(b)

R, X, Z

Z

1

0.9

f

0.8

R

0.7

X

100 125 150 175

t [ms]

Fig. 9.17 Impedance measurement with a standard and b adaptive algorithms; signals

contaminated by noise, step change of frequency from 50 to 40 Hz

From the filter features (sine, cosine full-cycle filters) it is known that filters
having window length N 0 have a gain for frequency 2p = N 0 equal to N 0 = 2 : It means
that knowing signals frequency it is possible to realize adaptive procedure and
calculate new filter gains immediately.
Calculation of frequency deviation can be realized in many ways. Observing the
methods described in Sect. 8.2.5 devoted to frequency measurement one can
derive the following frequency dependent equation:

cos ð kX Þ¼ 0 : 5 u ð n 2k Þ u ð n k Þ u ð n Þ u ð n 3k Þ
u ð n k Þ u ð n k Þ u ð n Þ u ð n 2k Þ

: ð 9 : 42 Þ