GE Multilin PQM - Page 323

APPENDIX A: APPLICATION NOTES PHASORS IMPLEMENTATION
PQM POWER QUALITY METER – INSTRUCTION MANUAL A–11
Let k
1
= cos(π/8), k
2
= cos(π/4), k
3
= cos(3π/8); the equations for the real and imaginary
components are reduced to:
The number of subtractions can be reduced between the calculations of real and
imaginary components by not repeating the same subtraction twice. The following
subtractions are repeated:
Substituting in the above ‘delta’ values results in the form of the equations that will be used
to calculate the phasors:
Re g()
1
8
-- -
k
1
g
1
g
7
– g
9
– g
15
g
17
g
23
– g
25
– g
31
++ +()k
2
g
2
g
6
– g
10
– g
14
+
+
(
k
3
g
3
g
5
– g
11
– g
13
g
19
g
21
– g
27
– g
29
++ +()g
0
g
8
– g
16
g
24
–+()
+
+
(
)
=
Im g()
1
8
---
k
1
g
3
g
5
g
11
– g
13
– g
19
g
21
g
27
– g
29
–+++()k
2
g
2
g
6
g
10
– g
14
–+
+
(
k
3
g
1
g
7
g
9
– g
15
– g
17
g
23
g
25
– g
31
–+++()g
4
g
12
– g
20
g
28
–+()
+
+
(
)
=
Δ
0
g
0
g
8
–=
Δ
4
g
4
g
12
==
Δ
8
g
16
g
24
–=
Δ
12
g
20
g
28
–=
Δ
1
g
1
g
9
–=
Δ
5
g
5
g
13
–=
Δ
9
g
17
g
25
–=
Δ
13
g
21
g
29
–=
Δ
2
g
2
g
10
–=
Δ
6
g
6
g
14
–=
Δ
10
g
18
g
26
–=
Δ
14
g
22
g
30
–=
Δ
3
g
3
g
11
–=
Δ
7
g
7
g
15
–=
Δ
11
g
19
g
27
–=
Δ
15
g
23
g
31
–=
Re g()
1
8
-- -
Δ
0
Δ
8
k
1
Δ
1
Δ
7
– Δ
9
Δ
15
–+()k
3
Δ
3
Δ
5
– Δ
11
Δ
13
–+()++ +()=
Im g()
1
8
-- -
Δ
4
Δ
12
k
1
Δ
3
Δ
5
Δ
11
Δ
13
++ +()k
2
Δ
1
Δ
7
Δ
9
Δ
15
+++()++ +()=
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