**2. A practical method for measuring on the ground the voltages induced by the overhead power lines**

In the case of high voltage overhead power lines with double circuit having one of the electrical circuits disconnected for maintenance or repair, the active electrical circuit will induce electromotive voltages and will force the electric currents induced in the disconnected electric circuit, threatening the technical staff working on the respective line [3-5,7].

Considering this phenomenon, between years 2006 - 2009, the author measured on the ground the voltages induced in the 220 kV power lines with double circuit from the Banat area - Romania. These measurements were aimed at determining the level of electromagnetic stress which appears in a disconnected circuit, when in parallel with it there is the second circuit which is operating in normal regime. Experimentally, there has been established that imme‐ diately after disconnecting the circuit, although it is disconnected and insulated from the earth, the voltages induced through electric (capacitive) coupling appear on each phase and at the moment when the short-circuit devices are closed, the voltages induced through electric coupling become null and voltages induced through magnetic (inductive) coupling appear and they force the appearance of currents induced in the loops formed by each of the three phases of the disconnected circuit and the earth.

Given the appearance of two types of disturbances affecting the disconnected power line, the measurements must firstly take into account the determination of the voltages induced through electric (capacitive) coupling on each of the three phases, and then, that of the voltages induced by magnetic (inductive) coupling in the three loops of the disconnected circuit and connected to the ground through short-circuit devices, at one of its ends.

There are several methods of determining the induced voltages, but we have opted for using classical measurement apparatuses accessible to everybody, namely an electrostatic voltmeter, with a scale of up to 30 kV, a common voltmeter with a scale up to 2.5 kV and Ditz pliers ammeter, which is sensitive enough.

For measuring the voltages induced electrically and magnetically by the active circuit into the power lines of the disconnected circuits, the following two methods have been adopted [6]:

**a.** If the three-phase circuit conductors of the disconnected lines are not grounded through short-circuit devices, thus they being insulated from the ground, the disconnected circuit conductors will have a much lower potential than the active circuit conductor placed in close proximity. In this case, between the active circuit conductors and the disconnected circuit conductors there will take place electric (capacitive) couplings, the conductors playing the role of armature of the huge condenser having the air as a dielectric medium. Depending on the intensity of the electric coupling (depending on the distance between the conductor and the length of parallel lines), the potentials of the disconnected circuit phases will change when compared with the ground potential. A possible measurement of these potentials (voltages induced through capacitive coupling) is shown in figure 1.

**Figure 1.** Measuring the voltages induced by the electric (capacitive) coupling in the disconnected circuit conductors of a high voltage overhead power line with double circuit.

disconnected circuit both through electric and magnetic coupling, and these voltages must be known. The worst cases are those in which the active circuit is very long and supplies con‐

**Figure 3.** Measuring the voltages induced by the magnetic (inductive) coupling in the disconnected circuit of a high

Experimental Determinations and Numerical Simulations of the Effects of...

http://dx.doi.org/10.5772/57044

349

In figure 4 there is presented the configuration of 220 kV overhead power lines with double

**Figure 4.** Configuration of 220 kV overhead power lines from the Banat area - Romania

Since the metal supporting pillars for most of the lines have the same configuration, in Table 1 there are given their main geometrical parameters corresponding to the generalized geo‐

sumers requiring high power consumption.

circuit, from the Banat area – Romania.

voltage overhead power line with double circuit.

metrical distances presented in figure 5.

**b.** If the disconnected three-phase circuit conductors are grounded at both ends through short-circuit devices, three loops are basically being formed, in which the intense electro‐ magnetic fields of the load currents of the active circuit will induce electromotive voltages, forcing the closing of the induced currents, this coupling being magnetic (figure 2).

**Figure 2.** The magnetic coupling between the active circuit and the disconnected circuit of a high voltage overhead power line with double circuit.

In this situation, in order to measure the induced voltages in the three phases of the discon‐ nected circuit, there need to be opened the short-circuit devices from one of the ends of the line and install a voltmeter, as shown in figure 3.

In the Banat area- Romania, which consists of four districts, there are several overhead lines of 220 kV, which operate in parallel on a structure of double circuit metal pillars, on different distances supplying many consumers of different types. Depending on the power transferred on these lines, if there is a disconnected circuit, there will appear voltages induced in the

phases will change when compared with the ground potential. A possible measurement of these potentials (voltages induced through capacitive coupling) is shown in figure 1.

**Figure 1.** Measuring the voltages induced by the electric (capacitive) coupling in the disconnected circuit conductors

**b.** If the disconnected three-phase circuit conductors are grounded at both ends through short-circuit devices, three loops are basically being formed, in which the intense electro‐ magnetic fields of the load currents of the active circuit will induce electromotive voltages, forcing the closing of the induced currents, this coupling being magnetic (figure 2).

**Figure 2.** The magnetic coupling between the active circuit and the disconnected circuit of a high voltage overhead

In this situation, in order to measure the induced voltages in the three phases of the discon‐ nected circuit, there need to be opened the short-circuit devices from one of the ends of the

In the Banat area- Romania, which consists of four districts, there are several overhead lines of 220 kV, which operate in parallel on a structure of double circuit metal pillars, on different distances supplying many consumers of different types. Depending on the power transferred on these lines, if there is a disconnected circuit, there will appear voltages induced in the

of a high voltage overhead power line with double circuit.

348 Computational and Numerical Simulations

power line with double circuit.

line and install a voltmeter, as shown in figure 3.

**Figure 3.** Measuring the voltages induced by the magnetic (inductive) coupling in the disconnected circuit of a high voltage overhead power line with double circuit.

disconnected circuit both through electric and magnetic coupling, and these voltages must be known. The worst cases are those in which the active circuit is very long and supplies con‐ sumers requiring high power consumption.

In figure 4 there is presented the configuration of 220 kV overhead power lines with double circuit, from the Banat area – Romania.

**Figure 4.** Configuration of 220 kV overhead power lines from the Banat area - Romania

Since the metal supporting pillars for most of the lines have the same configuration, in Table 1 there are given their main geometrical parameters corresponding to the generalized geo‐ metrical distances presented in figure 5.


necessary measures to be taken in case of working under voltage and it was spread out over

Experimental Determinations and Numerical Simulations of the Effects of...

http://dx.doi.org/10.5772/57044

351

**a.** Specification of the initial state of the overhead high voltage power line with double circuit, on which measurements are to be carried out, indicating the exact situation of the

**•** Circuit B – non- operating, grounded through short-circuit devices at both ends.

protective helmet and high voltage electro-insulated gloves.

**b.** For each measurement, the following conditions of protection must be respected:

**•** The leader of the team must be equipped with overalls, high voltage electro-insulated boots,

**•** The modification of the measuring range of the apparatus is made only after disconnecting the measuring circuit by removing the electro-insulated rod from the circuit being meas‐

**•** The reading of the measuring apparatus is done remotely by an operator equipped accord‐

**c.** The measurement of the voltages induced through the two types of coupling into the conductors of the disconnected circuit is realized according to the following procedures:

**•** Connect to the ground the cable of the electrostatic voltmeter and then connect it to the

**•** Connect one end of the active cable to the measuring clamp of the electrostatic voltmeter;

**•** For measuring the voltages induced by electric coupling, the short-circuit devices of the disconnected circuit of the power lines have to be open at both ends and for measuring the voltage induced by magnetic coupling, the short-circuit devices of the disconnected circuit

**•** The voltages induced on the three-phase disconnected circuit are measured successively by touching, with the electro-insulated rod the connections of the phase conductors to the short-

Based on the diagram shown in Fig. 4, there have been determined sub stations in which the measures are performed, according to the number of the outputs of 220 kV lines, with double

**•** Connect the other end of the active cable to the electro-insulated rod

are opened only at the end where the measuring is performed.

**•** Substation 11 – with connections to substation 7, 8 and 12;

**•** Substation 2 - with connections to substation 3 and 1; **•** Substation 4 - with connections to substation 5, 1 and 6;

**•** The cables of the measuring apparatus will be placed at a distance from the operator.

the following steps:

ured;

two circuits of the power lines, namely:

**•** Circuit A – set into operation;

ingly (work under high voltage).

grounding clamp of the apparatus;

circuit devices.

circuit:

**Table 1.** The dimensions of the supporting pillars for 220 kV overhead power lines with double circuit.

**Figure 5.** Schematic geometrical representation of a supporting pillar

The active conductors of the power lines are steel-aluminium with standard sections of 400 mm2 or 450 mm2 , these being specified for each power line separately.

In order to perform measurements of the voltages induced there was previously required to establish the measuring program, with well defined steps, to be able to protect the operating staff against the exposure to the high voltage effects. This program has included all the necessary measures to be taken in case of working under voltage and it was spread out over the following steps:


**Nr.**

350 Computational and Numerical Simulations

mm2

or 450 mm2

**crt. Pillar type H (m) a1 (m) h1(m) h2 (m) d1 (m) d2 (m)**

c 1

c 2

**Figure 5.** Schematic geometrical representation of a supporting pillar

c 3

 Sn 220.201 41,4 6,4 6,5 6,5 5,0 8,0 5,0 2,541 14,0 5,459 Sn 220.202 41,4 6,4 6,5 6,5 5,0 8,0 5,0 2,541 14,0 5,459 Sn 220.204 42,5 5,5 6,5 6,5 4,5 8,0 5,0 2,541 14,0 7,459 Sn 220.205 42,5 5,5 6,5 6,5 4,5 8,0 5,0 2,541 14,0 7,459 Ss 220.205 44,9 6,9 8,0 8,0 5,5 9,5 5,5 2,541 14,0 5,459 Ss 220.206 46,0 6,0 8,0 8,0 4,75 9,25 5,25 2,541 14,0 7,459

> a1

> a2

a3

liz

a

f max

hg

The active conductors of the power lines are steel-aluminium with standard sections of 400

In order to perform measurements of the voltages induced there was previously required to establish the measuring program, with well defined steps, to be able to protect the operating staff against the exposure to the high voltage effects. This program has included all the

, these being specified for each power line separately.

**Table 1.** The dimensions of the supporting pillars for 220 kV overhead power lines with double circuit.

**d3 (m)**

**λiz (m) fmax (m) hg (m)**


Based on the diagram shown in Fig. 4, there have been determined sub stations in which the measures are performed, according to the number of the outputs of 220 kV lines, with double circuit:


The results of the measurements carried out according to the program described above are synthetically, presented in Table 2, for the voltages induced through electric (capacitive) coupling and in Table 3, for the voltages induced by the magnetic (inductive) coupling.


**Table 2.** The voltages induced through electric (capacitive) coupling in 220 kV overhead power lines, with double circuit, having circuit B disconnected.

**•** All the voltages induced by capacitive coupling are very high and dangerous for the

**Table 3.** Voltages induced through magnetic (inductive) coupling in 220 kV overhead power lines, with double circuit,

**•** The length of the parallel distance between the active line (inductor) and the disconnect‐ ed one (armature) influences the values of the voltage induced, regardless of the type of electromagnetic coupling. To observe this phenomenon, there have been drawn the curves of the voltages induced, depending on the length of their parallel portions; there have been drawn curves for voltages induced both through electric (capacitive) coupling, UE = f(l) and for magnetic (inductive) coupling, UM = f(l). The resulted curves are shown in

operating staff.

with circuit B disconnected.

**Overhead power line**

8 - 9 maximum load

**Length of A circuit [km]**

4 - 6 116.550 116.550

1 - 2 53.719 24.620

2 - 3 53.719 55.173

**Length of B circuit [km]**

**Active circuit voltage**

> **U [kV]**

228 225 232

230 235 225

230 235 225

**Active circuit current**

> **I [A]**

440 480 460

212 237 218

212 237 218

**UR [V]**

7 - 11 49.876 25.455 237.5 265.75 320 21 120 107 22 0.9795 0.2028

8 - 9 25.455 11.249 236.9 74.826 34 10.2 18.5 24.9 17.9 0.812 0.6232 11 - 12 16.688 43.897 225 181.68 120 26 122 5 5 0.707 0.7855 9 - 11 25.455 7.422 236.8 92.542 11 4.3 13.2 28.5 25 0.7518 0.72

7 - 8 18.675 18.675 237 71.77 63.6 13 42 29 5 0.985 0.1734 4 - 5 30.730 30.730 226.5 14.54 20.8 3.6 17 0 5.7 0 1.57 4 - 1 72.867 72.867 234 497.03 1020 400 940 200 22 0.988 0.155

**Magnetically induced voltage measured in the disconnected B circuit**

**US [V]**

25.455 11.249 236.9 156.9 68 10.2 39 50 40 0.781 0.6745

**UT [V]**

Experimental Determinations and Numerical Simulations of the Effects of...

**P [MW]**

1400 400 1440 182 7.354 0.98 0.2003

180 71 1260 50 10.15 0.98 0.2003

310 80 270 50 10.15 0.98 0.2003

**Transferred power and voltage – current phase shift**

http://dx.doi.org/10.5772/57044

**φ [rad]** 353

**Q [MVar] cos φ**

fig. 6 and fig. 7.

Observing Table 2 and Table 3 there has been stated that:



**•** Substation 7 - with connections to substation 1, 8, 10 and 11;

The results of the measurements carried out according to the program described above are synthetically, presented in Table 2, for the voltages induced through electric (capacitive) coupling and in Table 3, for the voltages induced by the magnetic (inductive) coupling.

> **Active circuit voltage**

7 - 11 49.876 25.455 237.5 8.87 2.7 4.4

8 - 9 25.455 11.249 236.9 12.7 20.2 12.3 11 - 12 16.688 43.897 225 1.9 3.35 2.35 9 - 11 25.455 7.422 236.8 19.4 23.4 18.2

> 228 225 232

7 - 8 18.675 18.675 237 8.9 4.42 6.25 4 - 5 30.730 30.730 226.5 3.03 7.94 5.9 4 - 1 72.867 72.867 234 11.1 3.7 5.4

> 230 235 225

> 230 235 225

**Table 2.** The voltages induced through electric (capacitive) coupling in 220 kV overhead power lines, with double

**•** In the case of the lines where no phase transposition has been performed, the voltage induced through magnetic (inductive) coupling is the largest on the phase placed the highest

**•** In the case of the middle phase, at most of the lines, the induced voltage is the lowest;

25.455 11.249 236.9 12.7 20.2 18.3

**Voltage induced electrically (capacitive) measured in the disconnected circuit**

10.4 3.6 5.1

6.55 5.82 5.41

8.2 2.8 4.2

**U [kV] UR [kV] US [kV] UT [kV]**

**•** Substation 9 - with connections to substation 8 and 11.

**Circuit A [km]**

4 - 6 116..550 116..550

1 - 2 53.719 24.620

2 - 3 53.719 55.173

Observing Table 2 and Table 3 there has been stated that:

circuit, having circuit B disconnected.

from the ground;

**Circuit B [km]**

**Overhead power line**

352 Computational and Numerical Simulations

8 - 9 maximum load

> **Table 3.** Voltages induced through magnetic (inductive) coupling in 220 kV overhead power lines, with double circuit, with circuit B disconnected.


From the analysis of figures 6 and 7 there has been observed that on small distances, of up to about 20 km, where there is parallelism between the two electric circuits located on the same pillars of the double-circuit, the length influences very little the induced volt‐ age. On these distances, a number of other causes are more important. At distances longer than 20 km, the value of the voltage induced by both the electric (capacitive) and magnet‐ ic (inductive) coupling has a linear increasing trend along with the increasing of the length

Experimental Determinations and Numerical Simulations of the Effects of...

http://dx.doi.org/10.5772/57044

355

**3. The mathematical models for determining the induced voltages**

The data obtained from measurements on the ground represent an advantage for conceiv‐ ing mathematical models, because the results obtained through mathematical modeling can be managed comparing with the real ones. This fact has lain at the basis of designing the mathematical models, trying to imitate, as realistically as possible, the physical phenom‐

It should also be mentioned that, at low frequencies, the couplings of the electromagnetic interferences between sources and victims can be separated, through different experi‐ ments, into electric couplings and magnetic couplings, respectively. Mathematical model‐ ing should take into account this observation that leads to achieving, separately, two

But regardless of the type of electromagnetic coupling, the values of induced voltages are dependent on both the geometry of the power lines and the power running on these lines and therefore the mathematical models must include, primarily, the geometric calculation of the supporting pillars of the high voltage overhead power lines with double circuit and the determination of their capacities and, respectively, the mutual inductances between the conductors of the power line with double circuit. The geometric, electric and magnetic parameters represent equation coefficients through which there are determined the voltages induced electrically and magnetically in the conductors of the disconnected circuit of the

**3.1. Determination of the geometric parameters of the supporting pillars of the high voltage**

The calculation of the geometrical parameters of the supporting pillars of the high voltage overhead power lines with double circuit must consider the distances between the conductors of the double circuit, the distances between conductors and their images in the earth and the maximum arrow formed by the conductors of the power line in a standard

different models, one for electric and one for magnetic phenomena [8, 9].

of the parallel distance.

ena that occur in nature.

high voltage power line with double circuit.

**overhead power lines with double circuit**

horizontal opening, as shown in Fig.8, a and b.

**Figure 6.** The variation of the voltages induced through capacitive coupling depending on the length of their parallel portions.

**Figure 7.** The variation of the voltages induced through inductive coupling depending on the length of their parallel portions.

From the analysis of figures 6 and 7 there has been observed that on small distances, of up to about 20 km, where there is parallelism between the two electric circuits located on the same pillars of the double-circuit, the length influences very little the induced volt‐ age. On these distances, a number of other causes are more important. At distances longer than 20 km, the value of the voltage induced by both the electric (capacitive) and magnet‐ ic (inductive) coupling has a linear increasing trend along with the increasing of the length of the parallel distance.
