**Author details**

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through magnetic (inductive) coupling in the disconnected circuits of 220 kV power lines with double circuit from the Banat area – Romania. The results are presented in Table 5, in com‐

This case brings about an important observation. Considering phase shift φ, between voltages and currents, through which the charging with power of the inductor circuit is indirectly expressed, the mathematical model has required the representation of the currents through momentary values instead of effective ones. But this leads to an additional unknown, which is time, *t*, namely the measuring moment of the voltages induced for each phase. It means that this case also requires the digitization of period *T = 0.02* seconds in 100 time intervals, *Δt<sup>k</sup>*

*0.0002* seconds and the search of the moment in which the measurement of the voltage induced through magnetic coupling for each of the phases of the disconnected circuit was performed.

Comparing the measured values of the voltages induced through magnetic (inductive) coupling with the calculated ones there has been observed a very good concordance, which demonstrates an appropriate mathematical approach of the physical phenomena which lead to the magnetic (inductive) coupling between the conductors of the high voltage overhead

**a.** In all of the cases, the middle phase of the disconnected circuit of the high voltage overhead power lines with double circuit has got the lowest value for the voltage induced. It has been proved by both the measurements on the ground and the mathematical modeling. The explanation for the electric coupling lies in the longest distance between the phases of the active circuit and the middle phase of the disconnected circuit. As to the magnetic (inductive) coupling, the effect is due to the vector summation of the intensities of the

**b.** In the case of the power lines where the transposition of the phases has not been per‐ formed, the voltage induced through magnetic (inductive) coupling is the highest on the upper phase. This phenomenon is explained by the fact that the respective conductor – earth loop has the largest surface. This means that if all the protection conductors of each of the pillars were grounded there would be realized a large number of conductor – earth loops (equal with the number of openings) which would capture a part of the inductor magnetic flux, particularly that of the upper phase, thereby reducing the voltages induced

**c.** All the voltages induced through electric (capacitive) coupling have got very high values, which are dangerous for the operating staff. By being grounded, the power lines are discharged of this high potential, but there appear voltages induced through magnetic (inductive) coupling, they being high enough to be dangerous, too. Therefore, we consider that, in the case of circuits separated from the ground in a galvanic way, the operating

staff have to obey the protection rules regarding working under high voltage.

parison with the values of the voltages measured on the ground..

power lines.

**4. Conclusions**

364 Computational and Numerical Simulations

inductor magnetic fields..

through magnetic (inductive) coupling.

Flavius Dan Surianu

Politechnica University of Timisoara, Romania
