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Power transmission line transposition - QuickField simulation example

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.

Engineering question

How to find effect of conductor transposition in three phase transmission line?

Answer
Set up a plane-parallel QuickField AC Magnetics problem for a three-phase transmission line and evaluate conductor transposition effects from computed field results.

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Typical applications
overhead transmission lines, transposed conductors, three-phase line corridors

Power transmission line transposition

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Simulation problem

Problem Type
Plane-parallel problem of AC magnetics.

Geometry
The length of transmission line is 120 km. The distance between transposition points is 40 km.
Transmission line transposition The length of transmission line is 120 km. The distance between transposition points is 40 km. C A B Soil 2 m 3.5 m 2 m 3 m 14.5 m 3 m Steel Steel Aluminum Aluminum 91.92 mm² 103 mm² Aluminum Conductor Steel Reinforced (ACSR) Simplified ACSR model

Given
ACSR conductor* consists of 19 steel wires width diameter of 2.482 mm and 16 aluminum wires with diameter is 2.863 mm.
Aluminum conductivity is 33.5 MS/m; steel core permeability 200, steel core conductivity is 5.9 MS/m.
Rated current I = 300 A (r.m.s.), frequency f = 50 Hz.

Task
Calculate transmission line phase inductance.

Solution
The are three 40km-long sections. In each section the phase conductors occupy different position on the tower.
In section #2 conductor A occupies the place of conductor B : ZA(#2) = ZB(#1).
In section #3 conductor A occupies the place of conductor C : ZA(#3) = ZC(#1).
Total impedance of conductor A is: ZA(#1) + ZA(#2) + ZA(#3) = ZA(#1) + ZB(#1) + ZC(#1).
So we model only section #1 and calculate impedance of each phase conductor ZA(#1), ZB(#1), ZC(#1).
Transmission line full transposition Transmission line transposition scheme A B C C A B B C A Section #1 Section #2 Section #3

Each conductor consists of aluminum and steel wires. We do not draw individual wires and represent conductors by solid blocks.

Results

Table of the measured currents and voltages for phase conductors of section #1 (40 km)
Phase Current, A Voltage drop, V Impedance, Ohm =
= Voltage drop / Current
A 300∠0° 5785.4∠58.588° 19.28∠58.588°
B 300∠120° 6138.8∠174.17° 20.46∠54.17°
C 300∠-120° 6051.2∠-62.101° 20.17∠57.899°

Phase conductor impedance is 19.28∠58.588° + 20.46∠54.17° + 20.17∠57.899° = 59.87 Ohm ∠57.18°
Phase conductor inductance is LA = LB = LC = 59.87*sin(57.18°) / 2πf = 0.160 H per 120 km of the transmission line length.
Power transmission line transposition

* Reference
Brahma, ACSR Aluminum Conductor Steel Reinforced

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