Measurement Algorithms for Digital Protection - Digital Signal Processing in Power System Protection and Control - page 152

And when algorithms of impedance components calculation are utilized, one
can measure phase shift as follows:

X
R

u ¼ arctg

ð 8 : 136 Þ

Applying these two equations one can get many particular algorithms for dif-
ferent orthogonalization methods.

Example 8.14 Propose a method for measurement of the mutual-phase dis-
placement between voltage and current signals. Sampling frequency is equal to
1000 Hz.

Solution For the measurement of phase shift one can apply either Eq. 8.135 or
8.136 , that are in fact equivalent when the impedance components are calculated
with use of active and reactive power values obtained for example according to
( 8.80 ) and ( 8.82 ). Assuming that the orthogonal components of voltage and current
are calculated with use of full-cycle sin, cos filters, the following equation for the
phase shift measurement holds:

!

¼ arctg

1

F 1C F 1S ½ u 1S ð n Þ i 1C ð n Þ u 1C ð n Þ i 1S ð n Þ
1

Q ð n Þ
P ð n Þ

u ¼ arctg ¼;

F 1C u 1C ð n Þ i 1C ð n Þþ F 1 u 1S ð n Þ i 1S ð n Þ

u 1S ð n Þ i 1C ð n Þ u 1C ð n Þ i 1S ð n Þ
u 1C ð n Þ i 1C ð n Þþ u 1S ð n Þ i 1S ð n Þ

¼ arctg

where suitable cancelling of the filter gain coefficients was possible due to
application of appropriate filters (identical for voltage and current, with the same
gain values for 50 Hz). The orthogonal components of current/voltage signal are
here defined by:

x 1C ð n Þ¼ X

19

x ð n k Þ cos ½ 0 : 1p ð 9 : 5 k Þ;

k ¼ 1

x 1S ð n Þ¼ X

19

x ð n k Þ sin ½ 0 : 1p ð 9 : 5 k Þ:

k ¼ 1

8.2.5 Measurement of Frequency

The power system frequency is almost constant at normal operating conditions.
The frequency deviation from 50 Hz is then very small. If this deviation increases
it could inform that some troubles appeared in the system and that is why it is
important problem to measure frequency or frequency deviation with very high
accuracy.

Higher deviations of frequency may appear during high-power