Measurement Algorithms for Digital Protection - Digital Signal Processing in Power System Protection and Control - page 126

P 1 ¼ 0 : 05 X

19

u 1 ð n k Þ i 1 ð n k Þ;

k ¼ 0

Q 1 ¼ 0 : 05 X

19

u 1 ð n k Þ i 1 ð n k 5 Þ:

k ¼ 0

Among the four algorithms, both in half- and full-cycle versions, the accuracy of
measurement does not depend on sampling frequency for averaging of samples
squared. In the case of summing of absolute values the results depend on f s value,
and for full-cycle algorithm (N ¼ N 1 ¼ 20) the following error value can be derived:

DS ¼ S max S av
S max

¼ 0 : 5 ½ 1 cos ð p = N 1 Þ ¼ 6 10 3

From the above one can arrive at a formula for determination of the required
number of samples (per cycle) that assures given level of error. Here, for the
assumed maximum error at the level of 0.1% one gets:

p
arccos ð 1 2DS Þ ¼ 49 : 6 50 :

N [

To achieve required accuracy level 50 samples of signal are needed. It means that
either the measurement should last for five half-cycles (by sampling at 1000 Hz) or
the sampling rate should be increased to 50 9 50 Hz = 2500 Hz.

8.1.3 Measurement with Use of Orthogonal Components

The most important and the most frequently used algorithms of measurement of
criterion values use orthogonal signal components [ 6 , 8 - 10 ]. The components can
be obtained in various ways, as it was described above. They can be divided in
general for such obtained from rotating phasor, as in the case when we use digital
filters, and the ones resulting from standing phasor, as in case of correlation. The
first case is more general since AC is more adequate for further processing. That is
why mainly the first one is considered here.

8.1.3.1 Measurement of Sinusoidal Signal Magnitude

It is assumed that having on disposal current or voltage samples a pair of
orthogonal components given by the equations can be produced:

x 1C ð n Þ¼ X 1m cos ð nX 1 þ u 1 Þ; ð 8 : 47a Þ