HT PQA400 - Power and Power Factor: Definitions

PQA400 - PQA823 - PQA824
EN - 136
10.7. POWER AND POWER FACTOR: DEFINITIONS
In a standard electrical installation powered by three sine voltages the following are to be
defined:
Phase Active Power:
(n=1,2,3)
)cos(
nnnNactn
IVP




Phase Apparent Power:
(n=1,2,3)
nnNappn
IVP 

Phase Reactive Power:
(n=1,2,3)
22
actnappnreactn
PPP 
Phase Power Factor:
(n=1,2,3)
appn
actn
n
F
P
P
P 
Total Active Power:
321 actactactact
PPPP 


Total Reactive Power:
321 reactreactreactreact
PPPP 


Total Apparent Power:
22
reactactapp
PPP 
Total Power Factor:
app
act
F
P
P
P 
where:
V
nN
= RMS value of voltage between phase n and Neutral.
I
n
= RMS value of n phase current.
f
n
= Phase angle between voltage and current of n phase.
In the presence of distorted voltages and currents the previous relations vary as follows:
Phase Active Power:
(n=1,2,3)
)(IVP
n
k
n
k
n
k
k
actn
 cos
0




Phase Apparent Power:
(n=1,2,3)
nnNappn
IVP


Phase Reactive Power:
(n=1,2,3)
22
actnappnreactn
PPP 
Phase Power Factor:
(n=1,2,3)
appn
actn
n
F
P
P
P 
Distorted Power Factor
(n=1,2,3)
dPF
n
=cosf
1n
= phase displacement between the
fundamentals of voltage and
current of n phase
Total Active Power:
321 actactactact
PPPP



Total Reactive Power:
321 reactreactreactreact
PPPP 


Total Apparent Power:
22
reactactapp
PPP 
Total Power Factor:
app
act
F
P
P
P 
where:
V
kn
= RMS value of kth voltage harmonic between n phase and Neutral.
I
kn
= RMS value of kth current harmonic of n phase.
f
kn
= Phase displacement angle between kth voltage harmonic and kth current harmonic of
n phase.
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