Measurement Algorithms for Digital Protection - Digital Signal Processing in Power System Protection and Control - page 138

(a),(b) (c)

u C (n)

FIR filter
cos window
N=10 - 12

FIR filter
cos window
N=10

u(n)

u(n) u C (n)

u C (n-2)

Time delay
k=2

FIR filter
sin window
N=10 - 12

u S (n)

u S (n)

FIR filter
sin window
N=10

u S (n-2)

i(n)

Time delay
k=2

FIR filter
cos window
N=10 - 12

i C (n)

i(n)

FIR filter
cos window
N=10

i C (n)

i S (n)

FIR filter
sin window
N=10 - 12

i C (n-2)

Time delay
k=2

FIR filter
sin window
N=10

i S (n)

(d)

i S (n-2)

Time delay
k=2

u(n) FIR filter

(sin, cos, Walsh)
N=10

u C (n)

Orthogonalization
by time delay
k=2

u S (n)

i(n) FIR filter

(sin, cos, Walsh)
N=10

i C (n)

Orthogonalization
by time delay
k=2

i S (n)

Fig. 8.6 Block schemes of signal orthogonalization for power measurement for the cases (a-d),
as in Example 8.9

¼ 0 : 512 þ sin ð 1 : 2p Þ
sin ð 0 : 1p Þ

¼ 3 : 06

F 1C ¼ 0 : 5 N þ sin ð NX 1 Þ
sin ð X 1 Þ

¼ 0 : 512 sin ð 1 : 2p Þ
sin ð 0 : 1p Þ

¼ 8 : 94

F 1S ¼ 0 : 5 N sin ð NX 1 Þ
sin ð X 1 Þ

and after substituting them to ( 8.48 ), ( 8.50 ) one gets:

Q 1 ¼ 0 : 0183 ½ u F1S ð n Þ i F1C ð n Þ u F1C ð n Þ i F1S ð n Þ;

where orthogonal components of voltage (similar for the current) are

obtained from