Measurement Algorithms for Digital Protection - Digital Signal Processing in Power System Protection and Control - page 135

For the sampling frequency 1600 Hz the number of samples per cycle (also
number of coefficients of the filters' impulse responses) amounts to 1600/50 = 32,
and then the respective filtration and magnitude measurement equations are:

y 1C ð n Þ¼ X

31

x ð n k Þ cos ½ð 15 : 5 k Þ p = 16 ;

k ¼ 0

y 1S ð n Þ¼ X

31

x ð n k Þ sin ½ð 15 : 5 k Þ p = 16 ;

k ¼ 0

F 1C ¼ F 1S ¼ F ¼j A C ð jX 1 Þj ¼ j A S ð jX 1 Þj ¼ N 1 = 2 ¼ 16 ;

q

y 1C ð n Þþ y 1S ð n Þ

q

y 1C ð n Þþ y 1S ð n Þ X 1 ¼ 1

F

¼ 1
16

:

8.2.2 Measurement of Power

Fundamental equations of power measurement with application of orthogonal
components are given in Sect. 8.1.3.2 . Required orthogonal components can be
produced from signals on disposal, according to methods described in Chap. 6 .Let
us assume they are given in the form:

u 1 ð n Þ¼ U 1m cos ð nX 1 þ u 1U Þ ð 8 : 78a Þ

i 1 ð n Þ¼ I 1m cos ð nX 1 þ u 1I Þ ð 8 : 78b Þ

When orthogonal components from rotating phasor, applying, for instance,
digital filters are used, the signal components have the form:

u F1C ð n Þ¼ F 1C U 1m cos ð nX 1 þ u 1U þ b Þ; ð 8 : 79a Þ

u F1S ð n Þ¼ F 1S U 1m sin ð nX 1 þ u 1U þ b Þ; ð 8 : 79b Þ

i F1C ð n Þ¼ F 1C I 1m cos ð nX 1 þ u 1I þ b Þ; ð 8 : 79c Þ

i F1S ð n Þ¼ F 1S I 1m sin ð nX 1 þ u 1I þ b Þ: ð 8 : 79d Þ

One can notice that the components were obtained using the same orthogonal
filters for current and voltage, which leads to simpler form of final algorithm (in
general we may use different filters for voltage and current). Substituting the
components to Eq. 8.60 the active power value is reached:

u F1C ð n Þ i F1C ð n Þ
F 1C

þ u F1S ð n Þ i F1S ð n Þ
F 1S

P 1 ¼ 1
2

ð 8 : 80 Þ