Measurement Algorithms for Digital Protection - Digital Signal Processing in Power System Protection and Control - page 133

Solution Parameters of the equations result from the sampling frequency and are
equal:

N 1 ¼ f S = f 1 ¼ 1000 = 50 ¼ 20 ;

X 1 ¼ 2p = N 1 ¼ 2p = 20 ¼ p = 10 ;

cos ð X 1 Þ¼ cos ð p = 10 Þ¼ 0 : 951 ;

sin ð X 1 Þ¼ sin ð p = 10 Þ¼ 0 : 309 :

Substituting the values to the general equations one obtains specific algorithms
for magnitude measurement, and for:
• orthogonalization by single delay, k ¼ 1( 8.73 )

x 1 ð n Þþ x 1 ð n k Þ cos ð kX 1 Þ x 1 ð n Þ

s

2

X 1m ¼

sin ð kX 1 Þ

s

x 1 ð n Þþ x 1 ð n 1 Þ 0 : 951x 1 ð n Þ

2

¼ ;

0 : 309

• orthogonalization by double delay, k = 1( 6.41 )

s

x 1 ð n k Þþ x 1 ð n 2k Þ x 1 ð n Þ

2

X 1m ¼

2 sin ð kX 1 Þ

s

x 1 ð n 1 Þþ x 1 ð n 2 Þ x 1 ð n Þ
0 : 618

2

¼ ;

• orthogonalization by single delay, k ¼ N 1 = 4 ;

q

x 1 ð n Þþ x 1 ð n N 1 = 4 Þ

q

x 1 ð n Þþ x 1 ð n 5 Þ X 1m ¼ ¼ :

Example 8.7 Provide full-cycle magnitude measurement algorithms with appli-
cation of Walsh filters of I and II order. Assume sampling rate f S = 1000 Hz.
Solution For the sampling frequency f S = 1000 Hz the number of samples per
cycle is N 1 ¼ 20 : Thus the output signals y ð n Þ of respective Walsh filters are
produced according to the following equations processing input values x ð n Þ; ( 6.22 ),
( 6.25 ):

y 1C ð n Þ¼ X x ð n k Þþ X x ð n k Þ X

4 14 19

x ð n k Þ;

k ¼ 0 k ¼ 5 15