Characteristics of Measurement of Criterion Values and Adaptive - Digital Signal Processing in Power System Protection and Control - page 184

Fig. 9.9 Algorithms spectra
for additive distortions;
algorithms as in Fig. 9.8

2.5

U , P , Q

2

U

1.5

1

P

0.5

0

Q

-0.5

-1

0 1 2 3 4 5

f f

1

susceptible to frequency deviations, both of the changing fundamental frequency
component and oscillating distortion components. This feature significantly
decreases general good opinion about the algorithms, whose undisputed advantage
is their numerical simplicity.
For frequency analysis of the measurement algorithms applying orthogonal
filters one can utilize current and voltage signals of the form:
u FC
F C

¼ h C cos ð nX þ u U Þþ g Ck cos ð nX k þ u Uk Þ; ð 9 : 24a Þ

u Fc
F S

¼ h S sin ð nX þ u U Þþ g Sk sin ð nX k þ u Uk Þ; ð 9 : 24b Þ

i FC
F C

¼ h C cos ð nX þ u I Þ; ð 9 : 25a Þ

i FS
F S

¼ h S sin ð nX þ u I Þ; ð 9 : 25b Þ

where

H C ð jX Þ
H C ð jX 1 Þ

h C ¼

;

H S ð jX Þ
H S ð jX 1 Þ

h S ¼ ;

g Ck ¼ H C ð jX k Þ
H C ð jX 1 Þ

U km
U 1m ;

g Sk ¼ H S ð jX k Þ
H S ð jX 1 Þ

U km
U 1m ;