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Power lines are often placed in ground or sea water, which are weakly conductive media. In the paper, a new analytical formula, taking into account the proximity effect in a twin line placed in a weakly conductive medium, is derived, and the effect of the conductive medium is considered. In the first step, one of the wires is replaced by a current filament, and the solution is sought for magnetic vector potential around the filament. In the next step, an analytical formula for eddy currents induced in a long straight conductor of circular cross-section placed near to the current filament in the extensive conductive medium is found by using the method of separation of variables. The correctness of the formula is checked by comparison with the results obtained via other methods like finite and boundary element methods. Then, the effect of various parameters on the eddy current distribution is tested. Next, the proximity effect in a twin symmetrical line is considered, and the effect of the conductivity of the surrounding medium is investigated. The results indicate that the conductive medium weakens the proximity effect, but in typical cases (ground and sea water), the effect is very small.

The Proximity Effect in Twin Line with Round Conductors Placed in Conductive Medium