Characteristics of Measurement of Criterion Values and Adaptive - Digital Signal Processing in Power System Protection and Control - page 178

Fig. 9.4 Signal magnitude
measurement with correction
acc. to ( 9.11 ); standard
algorithm (dashed line), alg.
with correction (solid line)

1

I m

0.8

0.6

0.4

0.2

0

0 5 10 15 20 25

n

Output signals of orthogonal filters of voltage and current during transients can
be written similarly to ( 9.7a , b ) in the form:

u F1C ð n Þ¼ d CC ð n Þ u C ð n Þþ d CS ð n Þ u S ð n Þ
u F1S ð n Þ¼ d SC ð n Þ u C ð n Þþ d SS ð n Þ u S ð n Þ
i F1C ð n Þ¼ d CC ð n Þ i C ð n Þþ d CS ð n Þ i S ð n Þ
i F1S ð n Þ¼ d SC ð n Þ i C ð n Þþ d SS ð n Þ i S ð n Þ;

ð 9 : 14 Þ

where

u C ð n Þ¼ U m cos ½ð n þ 0 : 5 Þ X 1 þ u U ;

u S ð n Þ¼ U m sin ½ð n þ 0 : 5 Þ X 1 þ u U ;

i C ð n Þ¼ I m cos ½ð n þ 0 : 5 Þ X 1 þ u I ;

i S ð n Þ¼ I m sin ½ð n þ 0 : 5 Þ X 1 þ u I ;

u U is an initial phase shift of voltage, and u I is an initial phase shift of current.
Substituting the values into ( 9.13 ) after simple rearrangements yields:

Q 1 ð n Þ¼ d SS ð n Þ d CC ð n Þ d CS ð n Þ d SC ð n Þ
2F 1C F 1S

Q ; ð 9 : 15 Þ

where

Q ¼ 0 : 5U m I m sin ð u U u I Þ:
Assuming application of sine, cosine full-cycle orthogonal FIR filters one
obtains values of reactive power during transient period: