User guide

PQA820
EN – 26
12.3. DEFINITIONS OF POWER AND POWER FACTOR
In a generic electrical system, powered by a sequence of sinusoidal voltages, the following
is defined:
Phase Active Power:
(n=1,2,3)
)cos(IVP
nnnNn




Phase Apparent Power:
(n=1,2,3)
nnNn
IVS 

Phase Reactive Power:
(n=1,2,3)
22
nnn
PSQ 
Phase Power Factor:
(n=1,2,3)
n
n
n
F
S
P
P 
Total Active Power:
321
PPPP
TOT


Total Reactive Power:
321
QQQQ
TOT


Total Apparent Power:
22
TOTTOTTOT
QPS 
Total Power Factor:
TOT
TOT
TOT
F
S
P
P 
where:
V
nN
= Efficient value of voltage between phase n and neutral.
I
n
= Efficient value of the current of phase n.
f
n
= Phase angle between voltage and current of phase n.
With distorted voltages and currents, the above-reported ratios change as follows:
Phase Active Power:
(n=1,2,3)
)(IVP
n
k
n
k
n
k
k
n
 cos
0




Phase Apparent Power:
(n=1,2,3)
nnNn
IVS 

Phase Reactive Power:
(n=1,2,3)
22
nnn
PSQ 
Phase Power Factor:
(n=1,2,3)
n
n
n
F
S
P
P 
Depurate Power Factor:
(n=1,2,3)
dPF
n
=cosf
1n
= phase angle between
the voltage and current
fundamentals of phase
n.
Total Active Power:
321
PPPP
TOT



Total Reactive Power:
321
QQQQ
TOT



Total Apparent Power:
22
TOTTOTTOT
QPS 
Total Power Factor:
TOT
TOT
TOT
F
S
P
P 
where:
V
kn
= Efficient value of the k-nth voltage harmonic between phase n and neutral.
I
kn
= Efficient value of the k-nth current harmonic of phase n.
f
kn
= Phase angle between the k-nth voltage harmonic and the k-nth current harmonic of
phase n