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 Uline = 110 kV
Rload = 100 Ohm, Lload = 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 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:
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.
Results: Table of the measured currents and voltages for a phase conductors
Part 1
Part 2
Part 3
Total
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).
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