8)
In symmetrical three-phase system, the phase voltages are rotated 120° against each oth-
er.Page 21
Applications
U3N
U2N
U1N
C C
LP
IP
IC2
IC3
N
U1E
U2E
U3E
UNE
earth
IF
G G
GP
I1
I2
I3
ΔG ΔC
Figure simplified equivalent circuit
For the equivalent circuit Figure the following equations can formulated:
1 3
1
1 1
2
2 2
3
3 3
0
( )
( )
( )
P
P
NE P
N NE
N NE
N NE
I I
U I
U I
U I
U I
(1.
2
0 a
applies.1) yields:
2
1 3
1
0 )
P
ne
U aY
(1.8) yields:
2
1 3
1 )
Y C
Y C
(1.11)
Using equations (1.4)
(1.9)
Using equation (1.6) (1. This can used the rotation operator
120
j
a
clearly display the equations.1)
(1.10)
or equivalently
2
1 3
1
1 3
ne
P
Y aY
U U
Y Y
(1.2)
(1.3)
(1.
P P
P
Y G
j L
Y C
Y C
(1.12)
(1.6)
(1.13)
Used equation (1. For voltages and this results the following expressions:
2
2 1
U U
and 1
U aU
(1.11) yields:
.5)
The conductances yield:
1
2 3
1
( )
.7)
(1
