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(3
π
/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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