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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-parallel problem of AC magnetics.

Transmission line pole Tangent tower design, 110kV A B C Soil 2 m 3.5 m 2 m 3 m 14.5 m 3 m

Aluminum Conductor Steel Reinforced (ACSR)
Aluminum Conductor Steel Reinforced (ACSR) ACSR conductor for HV transmission line Steel Aluminum

Scheme of transposition, transmission line length l = 120 km:
Transmission line full transposition Transmission line transposition scheme A B C C A B B C A 40 km 40 km 40 km

Line rated voltage Uline = 110 kV
Rload = 100 Ohm, Lload = 0.23 H.
Line to phase voltage Three phase system line and phase voltages A B C Uphase Uline Uphase =Uline / √3

Define transmission line phase inductance.

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 110-500 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:

transmission line simulation model

transmission line electric circuit

Full impedance of a line develops of separate parts impedances and can be found as total voltage drop divided by a current:
Zline = (U1 + U2 + U3) / I.

Impedance of a line can be presented as the sum of active resistance (Rline) and inductive reactance (Xline):
Zline = Rline + jXline.

Line inductance can be calculated as:

L = Xline / 2 π f,
where Xline - line phase inductive reactance;
f - frequency of the alternating current.

Table of the measured currents and voltages for phase conductors


Part 1

Part 2

Part 3


Voltage UA, V

5676 + j2832

5943 + j2800

6142 + j2366

17761 + j7998

Voltage UB, V

-5078 + j4213

-5292 + j3501

-5438 + j3671

-15808 + j11385

Voltage UC, V

-547 - j6546

-1111 - j6494

-297 - j6331

-1955 + j19371

Current IA, A

263 - j270

263 - j270

Current IB, A

102 + j376

102 + j376

Current IC, A

-363 - j93

-365 - j93

Resistance ZA, Ohm


17.7 + j48.6

Resistance ZB, Ohm


17.7 + j48.6

Resistance ZC, Ohm


17.7 + j48.6

Inductance of a phase : Lphase = LA = LB = LC = 0.155 H (total length 120 km).

Transmission line magnetic field

3 phase transmission line magnetic field lines

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