Main >> Applications >> Sample problems >> Transmission line transposition

transmission line impedance calculation, wires transposition, electromagnetic FEA finite element analysis of the transmission line

The ACSR conductor 110 kV transmission line features complete transposition cycle at length of 120 kilometers.

**Problem Type**

Plane-parallel problem of AC magnetics.

**Geometry**

Aluminum Conductor Steel Reinforced (ACSR)

Scheme of transposition, transmission line length *l* = 120 km:

**Given**

Line rated voltage *U _{line}* = 110 kV

**Task**

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 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:

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

**Results**

Table of the measured currents and voltages for 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 conductor : L_{phase} = L_{A} = L_{B} =
L_{C} = 0.155 H (total length 120 km).

Transmission line magnetic field

- Video: Transmission line transposition

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