Transmission line magnetic coupling

QuickField simulation example

Two three phase power transmission lines go side by side for 10 km. Each transmission line is formed by 3 parallel aluminum conductors 1 cm diameter each placed on the same height above the ground (flat formation). Phase conductors in each line are separated by 1 m air clearance. Distance between the nearest conductors of two transmission lines is 18 meters.
Left transmission line is energized by three phase current system. Right line is under maintenance, it is grounded at the beginning of this segment and works are performed on another end. We need to make sure that the worker is not subjected to dangerous induced voltage on the right (victim) line at normal operating conditions of the energized line.

Problem Type
Plane-parallel problem of AC magnetics.

Geometry

Given
Left line current: 200 A, root mean square (r.m.s) value
Frequency f = 50 Hz
Ground electrical conductivity σ = 0.1 S/m
Transmission line length L_z= 10 km
Victim line grounding resistance R = 4 Ohm

Task
Find the electromagnetically induced voltages in the right (victim) transmission line at the ungrounded end of the 10 km segment.

Solution
In QuickField we should specify the peak values of currents that is √2 times more than r.m.s. value.

Results
Phase-to-ground inductively induced voltages for victim transmission line conductors
V_A = 12.2 V, V_B = 11.5 V, V_C = 10.8 V
Values are below the dangerous levels, so the worker is safe.

Magnetic field strength distribution in the vicinity of the victim line.

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