Calculations:
2
/
1
2
2
2
/
1
)
(
)
2
(
1
+
=
∑
n
vn
vn
rms
b
a
V
Vt(FDRMS) – RMS voltage computed using all
harmonics which pass the user definable filter.
1
2
/
1
2
2
2
/
1
)
(
)
2
(
1
+
=
∑
n
in
in
rms
b
a
I
It(FDRMS) – RMS current computed using all
harmonics which pass the user definable filter.
1
∑
∑
∑
=
+
=
•
=
n
n
n
n
n
vn
in
in
vn
n
n
n
I
V
b
b
a
a
I
V
Pt
)
cos(
)
(
θ
Pt(FD) – Active power computed by summing the
vector dot products of each of the harmonics
1
∑
∑
∑
=
−
=
×
=
n
n
n
n
n
vn
in
in
vn
n
n
n
I
V
b
a
b
a
I
V
Qt
)
sin(
)
(
θ
Qt(FD) – Reactive power computed by summing
the vector dot products of each of the harmonics
1
2
/
1
2
2
2
2
)
)(
(
2
1
+
+
=
∑
n
in
in
vn
vn
b
a
b
a
St
St(FD) – Apparent power computed by summing
the Vrms times Irms for each harmonic.
St
Pt
PFt
=
Power Factor (PFt)
Note:
1
The
0
a
component is not included in numbers reported by the PowerMaster
®
.
2
Normalization constants have been omitted for simplicity
FUNDAMENTAL ONLY
For Fundamental Only, the PowerMaster
®
uses a subset calculation from the Frequency Domain.
In this case, harmonics are
not
included in the analysis.
Calculations:
[
]
2
/
1
2
1
2
1
2
/
1
)
2
(
1
1
v
v
b
a
V
+
=
V1(FDRMS) – RMS voltage for the fundamental
frequency only.
[
]
2
/
1
2
1
2
1
2
/
1
)
2
(
1
1
i
i
b
a
I
+
=
I1(FDRMS) – RMS current for the fundamental
frequency only.
)
cos(
1
1
1
1
1
1
1
1
1
1
θ
I
V
b
b
a
a
I
V
P
i
v
i
v
=
+
=
•
=
P1(FD) - Active power for the fundamental only
)
sin(
1
1
1
1
1
1
1
1
1
1
θ
I
V
b
a
b
a
I
V
Q
v
i
i
v
=
−
=
×
=
P1(FD) - Reactive power for the fundamental only
2
/
1
2
1
2
1
2
/
1
2
1
2
1
)
(
)
(
2
1
1
i
i
v
v
b
a
b
a
S
+
+
=
S1t(FD) – Apparent power computed as Irms times
Vrms for the fundamental only.
1
1
1
S
P
PF
=
Power Factor (PF1)
Rev 1.5
133
