**6.1. Calculation of the electric field intensity at the edge of the insulation of the conductor**

Based on the measurements on figure 5, we calculated the maximum electric field intensity of the phase L1, using the computer program ELEFANT®. For the basic harmonic current this holds true when the voltage of the phase L1 is 326 kV and 163 kV for the phase L2 and L3. The phase to phase voltage from phase L1 to the other two phases is then at an amplitude value of 400 kV – 565.69 kV. From figure 20 you can see that the electric field intensity does not exceed the value of 0.1 MV/m, which is less than what we got from our analytical calculation (equation 22).

Polyurethane as an Isolation for Covered Conductors 403

**Figure 21.** Eef in the point of maximum sag, calculated with the computer program ELEFANT®

**Figure 22.** Comparison of *E*ef perpendicular to the conductors in the point of maximum sag calculated

with the programs Matlab and Elefant.

**Figure 20.** The electric field intensity calculated with the computer program ELEFANT®

#### **6.2. Calculation of the electric field intensity perpendicular to the conductor**

As a result, a figure is shown that depicts the calculation of the effective value of the electric field intensity perpendicular to the conductor in the point of the greatest sag (figure 21). The calculation results of the programs Matlab and Elefant are compared (figure 22).

In comparison, we see that both calculations give approximately the same result and that using both methods gives a value that is under the maximum allowed effective value permitted by the law.

With the use of the computer program we calculated the phase voltage of line conductors as a function of time (in a time period of 20 ms).

We calculated the potential coefficients of the capacitance (the inverse value of the matrix of potential coefficients), based on the geometry (arrangement of conductors and the insulation on them). We also calculated the current electric charge on the phase conductors based on the current values of voltage. With the known charges we calculated all three vectors of the electric field intensity, which are caused by the current values of charge on the individual line conductors in the point of interest. In the point of interest the current values of the vectors were added together, to get the total vector of electric field intensity. This total vector is dependent upon the three current values of charge on the line conductors. The resulting electric field intensity is not sinusoid quantity (figure 18) but it is a periodic quantity. We calculate the effective value in accordance with equation (31).

permitted by the law.

equation (31).

a function of time (in a time period of 20 ms).

**Figure 20.** The electric field intensity calculated with the computer program ELEFANT®

calculation results of the programs Matlab and Elefant are compared (figure 22).

**6.2. Calculation of the electric field intensity perpendicular to the conductor** 

As a result, a figure is shown that depicts the calculation of the effective value of the electric field intensity perpendicular to the conductor in the point of the greatest sag (figure 21). The

In comparison, we see that both calculations give approximately the same result and that using both methods gives a value that is under the maximum allowed effective value

With the use of the computer program we calculated the phase voltage of line conductors as

We calculated the potential coefficients of the capacitance (the inverse value of the matrix of potential coefficients), based on the geometry (arrangement of conductors and the insulation on them). We also calculated the current electric charge on the phase conductors based on the current values of voltage. With the known charges we calculated all three vectors of the electric field intensity, which are caused by the current values of charge on the individual line conductors in the point of interest. In the point of interest the current values of the vectors were added together, to get the total vector of electric field intensity. This total vector is dependent upon the three current values of charge on the line conductors. The resulting electric field intensity is not sinusoid quantity (figure 18) but it is a periodic quantity. We calculate the effective value in accordance with

**Figure 21.** Eef in the point of maximum sag, calculated with the computer program ELEFANT®

**Figure 22.** Comparison of *E*ef perpendicular to the conductors in the point of maximum sag calculated with the programs Matlab and Elefant.

Figure 22 shows the calculation for points 1 m above the ground transverse to the power line in the area of the maximum sag of the cable using the analytical method and the finite element method.

Polyurethane as an Isolation for Covered Conductors 405

this data we calculated the impact of non-ionizing radiation that over ground lines exert on

The installation of an over ground power line is disruptive to the environment. The frequency that we use for the transfer of electricity in the distribution network is 50 Hz, and it causes a magnetic field with the same frequency. This electromagnetic field falls in to the category of low frequency fields. As negotiated at an international level it actually belongs to electromagnetic fields with very low frequencies (ELFF), with frequencies ranging from 30-300 Hz. This is the range at which we talk about electric and magnetic fields separately, instead of electromagnetic fields. The electric field is the result of electric charge on the conductor and in the ground. It is also indirectly linked to the voltage between conductor and ground, the higher the voltage the higher the electric field is. If we look at the limit values that are determined in the Slovenian legislation the electric field is more problematic than the magnetic field. We calculated the electric field intensity in the critical points, and found that it is smaller than the value that is allowed under the regulation about non-ionizing radiation. We also calculated the electric field intensity perpendicular to the axis of the over ground conductor in the point of the greatest sag. It fall on the specified value determined by the regulation for new buildings in a distance of 75 m from the axis of the over ground conductor. We checked the

We found that the proposed covered conductor does not need a wider corridor as it is already set for the 220 kV overhead power line with bare conductors and allows the transfer

As future work we propose the construction of a prototype of such a conductor, laboratory experiment of these theoretical calculations and an economic analysis: cost of new conductors and the replacement of these on the existing transmission towers - the price of

R.J. Bacha, GPU/PENELEC Compact 115 kV Covered Conductor Study, Minutes of the

Manfred Beyer, Wolfram Boeck, Klaus Möller, Walter Zaengl, Hochspannungstechnik,

Ray Elford: Covered Conductors – making the right choice, Electrical engineer, februar 1995 Michèle Gaudry, Francis Chore, Claude Hardy, Elias Ghannoum: Increasing the ampacity of

Damjan Miklavčič: Vpliv elektromagnetnih polj na biološk esisteme, Zbornik 2, Konference slovenskega komiteja CIGRE, Maribor, 7. - 9. junij 1995: 445 -

Meeting – Pennsylvania Electric Association, Engineering Section, 1981

Theoretische und praktische Grundlagen; Springer-Verlag 1986.

overhead lines using homogeneous compact conductors, Pariz 1998

building the new above ground power line with all the necessary permits.

results with a calculation using the finite element method.

the environment.

of energy at 400 kV.

**Author details** 

**8. References** 

452

*University of Maribor, Slovenia* 

Žiga Voršič
