PowerMetrix PowerMaster 3 Series - Page 133

Calculations:
2/
1
2
2
2/1
)
(
)2(
1






+
=
∑
n
vn
vnrms
ba
V
Vt(FDRMS) – RMS voltage computed using all
harmonics which pass the user definable filter.
1
2/1
22
2/1
)(
)2(
1






+=
∑
n
ininrms
baI
It(FDRMS) – RMS current computed using all
harmonics which pass the user definable filter.
1
∑
∑∑
=
+=•=
n
nnn
n
vnininvn
n
nn
IV
bbaaIVPt
)cos(
)(
θ

Pt(FD) – Active power computed by summing the
vector dot products of each of the harmonics
1
∑
∑∑
=
−=×=
n
nnn
n
vnininvn
n
nn
IV
babaIVQt
)sin(
)(
θ

Qt(FD) – Reactive power computed by summing
the vector dot products of each of the harmonics
1
2
/1
2
22
2
))((
2
1






++=
∑
n
ininvnvn
babaSt
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
vv
baV +=
V1(FDRMS) – RMS voltage for the fundamental
frequency only.
[ ]
2/1
2
1
2
1
2/1
)2(
1
1
ii
baI +=
I1(FDRMS) – RMS current for the fundamental
frequency only.
)cos(1
111111111
θ IVbbaaIVP
iviv
=+=•=

P1(FD) - Active power for the fundamental only
)sin(1
1111
11111
θ IV
babaI
VQ
viiv
=−=×=


P1(FD) - Reactive power for the fundamental only
2
/12
1
2
1
2/
12
1
2
1
)()
(
2
1
1
iiv
v
baba
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