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Transmission line transposition
The ACSR conductor 110 kV transmission line features complete transposition cycle at length of 120 kilometers.
Problem type:
Plane problem of AC magnetics.
Geometry:
Transmission line pole. All dimensions are in meters.
Aluminum Conductor Steel Reinforced (ACSR)
Scheme of transposition.
Transmission line length l = 120 km
Given:
Line rated voltage U_{line} = 110 kV
R_{load} = 100 Ohm, L_{load} = 0.23 H.
Problem:
Define transmission line phase inductance.
Solution:
At longer power lines wires are transposed according to the transposing scheme. Each of the three conductors must hang once at each position of the overhead line. On transmission lines of 110500 kV rate one complete cycle of a transposition should be carried out if the line length exceeds 100 km. The transposition should be carried out so that total lengths of transmission line parts were approximately equal.
The length of our line is 120 km. The distance between transposition points is 40 km.
The simulation model includes field and circuit parts. There are three encapsulated field parts connected one with another by the external circuit. Each conductor consists of aluminum and steel wires:
Full impedance of a line develops of separate parts impedances and can be found as total voltage drop divided by a current:
Z_{line} = (U1 + U2 + U3) / I.
Impedance of a line can be presented as the sum of active resistance (R_{line}) and inductive reactance (X_{line}):
Z_{line} = R_{line} + jX_{line}.
Line inductance can be calculated as:
L = X_{line} / 2 π f,
where X_{line}  line phase inductive reactance;
f  frequency of the alternating current.
Results:
Table of the measured currents and voltages for a phase conductors

Part 1 
Part 2 
Part 3 
Total 
Voltage U_{A}, V 
5676 + j2832 
5943 + j2800 
6142 + j2366 
17761 + j7998 
Voltage U_{B}, V 
5078 + j4213 
5292 + j3501 
5438 + j3671 
15808 + j11385 
Voltage U_{C}, V 
547  j6546 
1111  j6494 
297  j6331 
1955 + j19371 
Current I_{A}, A 
263  j270 
263  j270 
Current I_{B}, A 
102 + j376 
102 + j376 
Current I_{C}, A 
363  j93 
365  j93 
Resistance Z_{A}, Ohm 

17.7 + j48.6 
Resistance Z_{B}, Ohm 

17.7 + j48.6 
Resistance Z_{C}, Ohm 

17.7 + j48.6 
Inductance of a phase : L_{phase} = L_{A} = L_{B} =
L_{C} = 0.155 H (total length 120 km).
Transmission line magnetic field 
Download simulation files transposition.zip.
Video.
Watch online on YouTube.