**5. The electric field in the surrounding of a 400 kV PUAC 2150/490/65 power line**

We deal with electric field in the surroundings of electrically charged bodies, for example in the vicinity of electric energy transmission lines, transmission antennas of telecommunications equipment. Electric fields are everywhere, where electric charge is present. Every electric conductor under voltage creates an electric field around itself. The field exists even when no current is flowing through the conductor, so even when the power line is not laden with users. The higher the voltage is the greater the electric field. Electric fields have the highest intensity close to the source and decrease very rapidly with distance. Metal shields them very well, but other material weaken it as well. The intensity of electric fields of power lines is greatly reduced by walls, buildings and trees. The electric fields of underground cables are also reduced by the soil.

We have determined that with the use of insulation made from polyurethane we can reduce the electric field intensity on the surface of covered conductors and that it is possible to operate at 400 kV. Due to the increased voltage it is necessary to examine the impact of such above ground power lines on the environment in accordance with our regulations.

#### **5.1. Electromagnetic radiation**

392 Polyurethane

**4. The mechanics of the PUAC 2150/490/65 power line** 

impact of power lines by means of non-ionizing radiation.

**Figure 10.** Cross section of the proposed covered conductor

**Figure 11.** The calculated sag of the power line PUAC 2150/490/65

Mechanical calculations showed that the proposed cable (figure 10) meets the requirements. With the calculation of the formed catenary we get the height at which the conductor needs to be over the ground (figure 11) and thus the input data to determine the environmental

> Exposure to electromagnetic radiations is not something new. It accompanies us from the very beginning of human existence. Here we think of natural sources of radiation. Another story is artificially generated sources, which are much stronger in intensity and more recently also increased in number. Man is now, unlike in the past, at home and at work, exposed to a complex mix of electric and magnetic fields.

> The main sources of electric and magnetic fields of low frequencies 50 Hz are artificial sources of electromagnetic radiations, namely those caused by man, which are devices for transmitting and distributing electricity, electrical substations, and all devices that use electricity for their operation. The intensity of electromagnetic radiations emitted by artificial sources, in comparison with natural resources (the Earth's static magnetic field, electric field caused by the discharge in the atmosphere - lightning) is much higher. When an electrical device is plugged in, an electric field is generated in its surroundings. The higher the voltage, the stronger the electric field at a certain distance from the device. The electric field is present even when the device is not working because there is no need for the electric current to flow to create voltage. The magnetic field on the other hand requires a flow of electrons, so it occurs only when the device is plugged in and the current is flowing. Under these conditions both fields exist in the room. The greater the power consumption and thus the electric current, the stronger the magnetic field is.

#### **5.2. Evaluation of electromagnetic fields in the Slovenian legislation**

The Slovenian government adopted a regulation on electromagnetic radiations in the natural and living environment, which specifies the maximum allowed threshold of radiations. The regulation protects the most sensitive areas (EMR protection zone I, which

includes living environment, schools, kindergartens, hospitals) with an additional preventive factor.

These areas demand increased protection against radiation therefore they are subject to ten times more severe limitations than in the European Union. For EMR protection zone II (areas with no residential building), the restrictions for magnetic fields are the same as in the European Union but for the intensity of the electric field two times higher values are allowed.

The maximum levels of radiation for networks with a frequency of 50 Hz are 500 V/m and 10 µT for EMR protection zones I and 10000 V/m and 100 µT for EMR protection zones II. Radiation with frequencies of 50 Hz includes electromagnetic fields from distribution substations, over ground and underground power lines, high voltage transformers and others. This is described under the Slovenian Regulation (2nd paragraph of article 2). At this frequency we distinguish two fields:


When calculating the effects of electromagnetic radiation we have to consider the most unfavorable impact on nature that can occur in normal operations.

#### **5.3. Electric field intensity in the vicinity of an overhead power line**

For the straight infinitely long conductor we assume that the electric charge is evenly distributed over the whole surface (uniform linear charge density). The charge on such a conductor can be described with an infinite line charge, which in any given point of T (x, y) (Fig. 12) leads to the following vector of electric field intensity:

$$
\bar{E} = \bar{1}\_{\text{r}} \cdot \frac{q\_{+}}{2 \cdot \pi \cdot \varepsilon\_{0}} \cdot \frac{1}{\left| \overline{r\_{+}} \right|} \tag{23}
$$

Polyurethane as an Isolation for Covered Conductors 395

where:

[ ] *q* is the columnar vector of positive charge, *V* is the columnar vector of conductor potentials,

*C* is the square matrix of the capacitance.

**Figure 12.** Electric field of a line charge

To determine the electric field intensity we have to determine the charge on the phase conductors. These are obtained from the current values of the voltage taking into account the capacitance. In Figure 13 current value of tension on the 400 kV overhead line are shown.

**Figure 13.** Current values of voltage in each phase of a three-phase conductor

*5.3.1. Voltage on conductors* 

Where:


To calculate the electric field intensity of a conductor above a conductive surface we use the method of equivalent charges. Its main idea is the exchange of the surface charge near a conductive surface (in our case soil) with a charge opposite in sign but equal in quantity that is projected over a conductive surface.

$$
\begin{bmatrix} q\_+ \end{bmatrix} = \begin{bmatrix} \mathbf{C} \end{bmatrix} \cdot \begin{bmatrix} V \end{bmatrix}\_{\prime\prime}
$$

**Figure 12.** Electric field of a line charge

#### *5.3.1. Voltage on conductors*

394 Polyurethane

Where: 1r

*r*

0 

preventive factor.

frequency we distinguish two fields:

is the unit vector of distance,

is the vacuum permittivity.

is projected over a conductive surface.

point of observation and

*q* is the positive value of the line charge,

includes living environment, schools, kindergartens, hospitals) with an additional

These areas demand increased protection against radiation therefore they are subject to ten times more severe limitations than in the European Union. For EMR protection zone II (areas with no residential building), the restrictions for magnetic fields are the same as in the European Union but for the intensity of the electric field two times higher values are allowed. The maximum levels of radiation for networks with a frequency of 50 Hz are 500 V/m and 10 µT for EMR protection zones I and 10000 V/m and 100 µT for EMR protection zones II. Radiation with frequencies of 50 Hz includes electromagnetic fields from distribution substations, over ground and underground power lines, high voltage transformers and others. This is described under the Slovenian Regulation (2nd paragraph of article 2). At this

 The electric field, which is described with the effective value of the electric field intensity *E* [V/m] and depends on the voltage of the radiation source or the element The magnetic field, which is described with the Magnetic flux density *B* [T] which depends on the electric current passing through the source of radiation or the element.

When calculating the effects of electromagnetic radiation we have to consider the most

For the straight infinitely long conductor we assume that the electric charge is evenly distributed over the whole surface (uniform linear charge density). The charge on such a conductor can be described with an infinite line charge, which in any given point of T (x, y)

> 0 <sup>1</sup> <sup>1</sup> 2 *<sup>q</sup> <sup>E</sup>*

(23)

 *r* 

is the absolute value of the distance vector between the electric charge and the

To calculate the electric field intensity of a conductor above a conductive surface we use the method of equivalent charges. Its main idea is the exchange of the surface charge near a conductive surface (in our case soil) with a charge opposite in sign but equal in quantity that

*q CV* ,

unfavorable impact on nature that can occur in normal operations.

(Fig. 12) leads to the following vector of electric field intensity:

**5.3. Electric field intensity in the vicinity of an overhead power line** 

r

To determine the electric field intensity we have to determine the charge on the phase conductors. These are obtained from the current values of the voltage taking into account the capacitance. In Figure 13 current value of tension on the 400 kV overhead line are shown.

**Figure 13.** Current values of voltage in each phase of a three-phase conductor

#### *5.3.2. Charge on conductors*

We get the matrix of capacitance *C* by first determining the elements of the potential coefficients of the conductor *p* (Tičar I., Zorič T., 2003):

$$p\_{\rm ii} = 18 \cdot 10^9 \cdot \ln \frac{H\_{\rm ii}}{r} \qquad \left[\frac{\rm m}{\rm F}\right] \tag{24}$$

Polyurethane as an Isolation for Covered Conductors 397

L1

*H*L1L1'

**Figure 14.** Mirror projections over the conductive surface plane

**Figure 15.** Current values of electric charge on the conductor

*d*L1L2

*d*L2L3

*H*L1L3'

*y* 

*H*L2L1'

*H*L1L2'

L1' L3'

L2

L3

*H*L3L3'

*x* 

*d*L1L2

*H*L2L2'

*H*L3L2'

*<sup>H</sup>*L2L3' *<sup>H</sup>*L3L1'

L2'

$$p\_{\rm ii} = 18 \cdot 10^9 \cdot \ln \frac{H\_{\rm ii}}{d\_{\rm ii}} \qquad \left[ \frac{\rm m}{\rm F} \right] \text{.} \tag{25}$$

where:


Distances established like that apply to bare conductors (line charge) in the air with a constant relative permittivity ε0. In our case, where we are dealing with insulation around the conductors, the electric charge gathers on the edge of the insulation and we have to consider that the distance between conductors is reduced by the thickness of the insulation. So when we consider these reductions in distance and the designations on figure 14 we get the new:

»Individual« potential coefficient:

$$p\_{ii} = \frac{\frac{1}{\mathcal{E}\_{r2}} \cdot \ln \frac{r\_2}{r\_1} + \ln \frac{H\_{ii}}{r\_2}}{2 \cdot \pi \cdot \varepsilon\_0} \tag{26}$$

»Mutual« potential coefficient

$$p\_{ij} = \frac{\frac{1}{\mathcal{E}\_{r2}} \cdot \ln \frac{r\_2}{r\_1} + \ln \frac{H\_{ij}}{d}}{2 \cdot \pi \cdot \varepsilon\_0} \tag{27}$$

We deal with three potential of conductors, four line charges and nine potential coefficients, which we can combine into a matrix.

$$
\begin{bmatrix} V\_{\rm L1} \\ V\_{\rm L2} \\ V\_{\rm L3} \end{bmatrix} = \begin{bmatrix} p\_{\rm L11,1} & p\_{\rm L11,2} & p\_{\rm L11,3} \\ p\_{\rm L21,1} & p\_{\rm L21,2} & p\_{\rm L21,3} \\ p\_{\rm L31,1} & p\_{\rm L31,2} & p\_{\rm L31,3} \end{bmatrix} \cdot \begin{bmatrix} q\_{\rm L1} \\ q\_{\rm L2} \\ q\_{\rm L3} \end{bmatrix} \tag{28}
$$

**Figure 14.** Mirror projections over the conductive surface plane

where:

*5.3.2. Charge on conductors* 

coefficients of the conductor *p* (Tičar I., Zorič T., 2003):

*p*ii is the individual potential coefficient, *p*ij is the mutual potential coefficient,

*d*ij is the distance between multi-phase conductors,

*ε*0 is the vacuum permittivity,

other multi-phase conductors.

»Individual« potential coefficient:

»Mutual« potential coefficient

which we can combine into a matrix.

ii

ij

*p*

We get the matrix of capacitance *C* by first determining the elements of the potential

9 ii

9 ij

*H*ii is the distance between the multi-phase conductors ant there mirror projections, *H*ij is the distance between the multi-phase conductors and the mirror projections of

Distances established like that apply to bare conductors (line charge) in the air with a constant relative permittivity ε0. In our case, where we are dealing with insulation around the conductors, the electric charge gathers on the edge of the insulation and we have to consider that the distance between conductors is reduced by the thickness of the insulation. So when we

> 2 r2 1 2 0

 

2 2 1

> 

<sup>1</sup> ln ln

2

We deal with three potential of conductors, four line charges and nine potential coefficients,

L1 L1L1 L1L2 L1L3 L1 L2 L2L1 L2L2 L2L3 L2 L3 L3L1 L3L2 L3L3 L3

*V ppp q V ppp q V ppp q* 

*r*

0

*r H r d*

*r H r r*

*ii*

*ij*

(26)

(27)

(28)

<sup>1</sup> ln ln

2

*ii*

*ij*

*p*

*p*

consider these reductions in distance and the designations on figure 14 we get the new:

*<sup>p</sup> <sup>d</sup>*

<sup>m</sup> 18 10 ln

*H*

*r* 

ij <sup>m</sup> 18 10 ln , <sup>F</sup> *H*

F

(25)

(24)

**Figure 15.** Current values of electric charge on the conductor

From the equation <sup>1</sup> *C p* and by considering the geometry on figure 15 we get the current value of the electric charge on the conductors:

$$
\begin{bmatrix} q \ \end{bmatrix} = \begin{bmatrix} p \ \end{bmatrix}^{-1} \cdot \begin{bmatrix} \mathcal{U} \ \end{bmatrix} \tag{29}
$$

Polyurethane as an Isolation for Covered Conductors 399

**Figure 17.** The electric field intensity on the edge of the insulation of the conductor L2

**Figure 18.** The electric field intensity on the edge of the insulation of the conductor L3

#### *5.3.3. Electric field intensity*

With the current values of electric charge on the conductor we calculated the components of the electric field intensity that exists because of the charge on all three phases.

We get the greatest electrical field intensity in the substance 2 at a radius *r*2 (figure 4):

$$E\_{2\max} = \frac{q}{2 \cdot \pi \cdot \varepsilon\_0 \cdot \varepsilon\_{t2}} \cdot \frac{1}{r\_2} = \frac{U \cdot \frac{1}{r\_2}}{\varepsilon\_{t2} \cdot \left(\frac{1}{\varepsilon\_{t1}} \cdot \ln\frac{r\_2}{r\_1} + \frac{1}{\varepsilon\_{t2}} \cdot \ln\frac{r\_3}{r\_2}\right)} \tag{30}$$

We calculated the electric field intensity in several points of the space around the conductor. The points were selected at the edge of the insulation (at the radius *r*2) of the multi-phase conductors. The radius was chosen so that the distance to the neighbouring conductors was as small as possible. As seen in figure 5, the point for the phase L1 is at (4.6785; 27.9785), for the phase L2 at (3.9215; 30.9785) and for the phase L3 at(5.4785; 25.0215). We got the electric field intensity at the edge of the insulation for each individual phase conductor (figure 16, figure 17 and figure 18) with vector addition of the contribution of all the electric charges (equation 23). The geometric sum of the current values (the current value of the electric field intensity) is a periodic quantity, but not a sinus one.

**Figure 16.** Electric field intensity on the edge of the insulation of the conductor L1 in the point (-4.6785; 27.9785)

**Figure 17.** The electric field intensity on the edge of the insulation of the conductor L2

27.9785)

From the equation <sup>1</sup> *C p* and by considering the geometry on figure 15 we get the

With the current values of electric charge on the conductor we calculated the components of

the electric field intensity that exists because of the charge on all three phases.

*<sup>q</sup> <sup>r</sup> <sup>E</sup>*

 

We get the greatest electrical field intensity in the substance 2 at a radius *r*2 (figure 4):

<sup>1</sup> *qp U* (29)

2

 

1

*U*

*r r r*

r1 1 r2 2

 

*r r*

(30)

0 r2 2 2 3

<sup>1</sup> , <sup>2</sup> 1 1 ln ln

r2

We calculated the electric field intensity in several points of the space around the conductor. The points were selected at the edge of the insulation (at the radius *r*2) of the multi-phase conductors. The radius was chosen so that the distance to the neighbouring conductors was as small as possible. As seen in figure 5, the point for the phase L1 is at (4.6785; 27.9785), for the phase L2 at (3.9215; 30.9785) and for the phase L3 at(5.4785; 25.0215). We got the electric field intensity at the edge of the insulation for each individual phase conductor (figure 16, figure 17 and figure 18) with vector addition of the contribution of all the electric charges (equation 23). The geometric sum of the current values (the current value of the electric field

**Figure 16.** Electric field intensity on the edge of the insulation of the conductor L1 in the point (-4.6785;

current value of the electric charge on the conductors:

2 max

intensity) is a periodic quantity, but not a sinus one.

*5.3.3. Electric field intensity* 

**Figure 18.** The electric field intensity on the edge of the insulation of the conductor L3

We get the effective value of the electric field intensity by summing over the whole period. By definition, the effective value of the periodic quantity is the one which makes the same effect as the corresponding one-way quantity. In our case the effective value of the electric field intensity is as follows.

$$E\_{\rm ef} = \frac{1}{T} \cdot \int\_0^T E^2(t) \cdot \mathbf{d}t \tag{31}$$

Polyurethane as an Isolation for Covered Conductors 401

**Figure 19.** The electrical field intensity perpendicular to the bisector of the span in the point of the

distance of 30 m away from the bisector of the power line.

The value of the electric field intensity falls under the permitted limit of the regulation at a

**6. The calculation of the electric field intensity with the finite element** 

The planned covered conductor does not float in the air by itself, but is mounted in a threephase electric system and hanged on a steel construction. Because of that, an analytical approach is not sufficient and the approximate results have to be checked with the finite

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

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

greatest sag.

**method** 

element method.

analytical calculation (equation 22).

**conductor** 

here:

*E*ef is the effective value of the electric field intensity, *T* is the period,

*E* is the vector sum of all the contributing charges.

#### *5.3.4. The electric field intensity on the edge of the insulation*

The highest current value of the electric field intensity in the point (-4.6785; 27.9785) – on the edge of the insulation of the conductor L1 is 24.366e+003 V/m with the effective value of 17.235e+003 V/m.

The highest current value of the electric field intensity in the point (3.9215; 30.9785) – on the edge of the insulation of the conductor L2 is 19.865e+003 V/m with the effective value of 14.287e+003 V/m.

The highest current value of the electric field intensity in the point (5.4785; 25.0215) – on the edge of the insulation of the conductor L3 je 33.813e+003 V/m with the effective value of 24.023e+003 V/m.

From the calculations and figures, we see that the electrical field intensity at the edge of the insulation of any of these three conductors does not exceed the critical dielectric strength of air.
