Measurement Algorithms for Digital Protection - Digital Signal Processing in Power System Protection and Control - page 155

( a ) (b)

M 0.5 * T S

1

1

0.8

0.5

0.6

0

0.4

0.2

-0.5 u k +1

u k u m u m +1

0

M 0.5

-0.2

-1

0

t b 1

t a 1 0.5 T m

t

t b 2 a 2

Fig. 8.8 Frequency measurement with counting of impulses: a standard version, b version with
zero crossing determination

where subscripts p þ 1 ; p denote zero crossings: the last and before last and sub-
scripts of samples with +1 denote the first sample after changing the sign.
Applying the method one can reduce errors substantially and it is possible to get
good results even for small sampling frequencies. Using 1000 Hz sampling fre-
quency for instance the highest zero crossing error is equal to 0.16 percent. This
results in 80 mHz error of measured frequency (nominal, i.e. 50 Hz). This is really
small error for such sampling frequency and substantial improvement of the
method. Additional burden are two divisions performed once at half period.

8.2.5.2 Measurement of Frequency Deviations Applying Zero-Order
Walsh Function

The idea of convolution of the signal and zero-order Walsh function (averaging)
results from simple observation of zero average value over one period of AC
signal. If that averaging period is kept constant but the frequency changes then
calculated average value is no longer equal to zero and can be the measure of
frequency deviation from its nominal value. Let the signal samples on disposal be
given by the equation u ð n Þ¼ U m cos ð nX 1 þ u Þ:
Let all the samples be summed during one period of nominal frequency (20 ms
for 50 Hz signal, N 1 —number of samples for that period):

y ð n Þ¼ X

N 1 1

u ð n k Þ:

k ¼ 0

Output signal of such filter is equal to zero for nominal frequency, according to
Chap. 6 (i.e. X ¼ X 1 and X 1 ¼ 2p = N 1 ). If the frequency is different, one observes
non-zero output signal of the filter. The signal can be given by the equation: