KMB SMC 144, Operating Manual

Page: 18 / 23

Current (RMS):
I
1
=
v
u
u
t
1
n
n
X
i =1
I
2
1 i
where: i ............................. sample index
n ............................ number of samples per cycle of measurement (128)
U
1 ,i
, U
2 ,i
, I
1 ,i
........ individual samples of voltage and current
3.3.3 Evaluation of Powers and Power Factor (PF)
Powers and power factors are evaluated by the following relations. The formulas apply to the star type of
connection.
Active power:
P
1
=
1
n
n
X
i =1
U
1 i
×
I
1 i
Reactive power:
Q
1
=
N
X
k =1
U
1 ,k
× I
1 ,k
× sin 4 ϕ
1 ,k
where: k ................... index of the order of each harmonic
N .................. highest harmonic (63)
U
1 ,k
, I
1 ,k
....... k-th harmonic of voltage and current (1
st
phase)
∆ ϕ
1 ,k
............ angle between U
1 ,k
, I
1 ,k
(1
st
phase)
Apparent power:
S
1
= U
1
×
I
1
Distortion power:
D
1
=
q
S
2
1
−
P
2
1
−
Q
2
1
Power factor:
P F
1
=
|
P
1
|
S
1
Three-phase active power:
3 P = P
1
+ P
2
+ P
3
Three-phase reactive power:
3 Q = Q
1
+ Q
2
+ Q
3
Three-phase apparent power:
3 S = S
1
+ S
2
+ S
3
Three-phase distortion power:
3 D =
p
3 S
2 −
3 P
2 −
3 Q
2
Three-phase power factor:
3 P F =
|
3 P
|
3 S
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