9

DIELECTRICS

Dielectrics are materials, which are generally non-metallic,

that have high resistivity, due to which the circulation of

current through them is very weak (forward or leakage current).

Taking advantage of this characteristic, they are used as

insulators to halt electrons, or to delimit the path they

should take.

9.1.1 WHAT ARE DIELECTRICS?

9.1.2 DIELECTRIC STRENGTH

This is the maximum voltage gradient that a material can withstand before being

destroyed by breakdown; it is expressed in kilowatts per millimetre. Its value is

influenced by the conditions of the test. Even supposing that a field free of

distortion (and consequently perfectly uniform) is obtained, and that the

properties of the materials to be assayed are stabilized by eliminating all

impurities and moisture, there is still the

influence of the time of the test. The

breakdown mechanism in long test times

is a thermal phenomenon (heating up due

to dielectric loss and charging currents),

while in short times, these phenomena do

not play a role and we find physical

breakdowns due to the electrical forces

that are present.

In general, dielectric strength decreases

as the test time increases, in accordance

with an approximately hyperbolic law.

• 80 •

9.1 DIELECTRICS

9.1.3 DIELECTRIC CONSTANT

This is the relation between the charge taken by a condenser with material

considered as dielectric and that which it would take if the dielectric were a

vacuum.

The phenomenon that is measured corresponds to the polarization of the unitary

particles that make up the structure of the dielectric. The greater the separation

between the elementary charges and their importance within the molecule, the

greater their influence over the electric field, and consequently, the higher the

dielectric constant will be.

The energy that is accumulated in a condenser is given by the following formula:

We= ----- C . U2 = ----- Co U2

Where: = -----------

• 81 •

C =

Co =

=

capacity of the dielectric in question

capacity with the dielectric being a vacuum

relative dielectric constant

1

2

1

2

C

Co

DIELECTRIC CONSTANTS OF

VARIOUS SUBSTANCES

SUBSTANCES

AIR

WATER

TRANSFORMER OIL

QUARTZ

POLYETHYLENE

NEOPRENE

PVC

EPR

XLPE (RETICULATEDPOLYETHYLENE)

CONDITIONS OF DIELECTRIC CONSTANT DIELECTRIC

GAS, 0º C, 1 ATMÓSFERA

LÍQUIDO, 20º C

LÍQUIDO, 20º C

CRISTAL, 20º C

SÓLIDO, 20º C

SÓLIDO, 20º C

SÓLIDO, 20º C

SÓLIDO, 20º C

SÓLIDO, 20º C

1,00059

80

2,24

4,27 - 4,34

2,25 - 2,3

4,1

6 - 8

3

2,5 - 3

9.2.1 RESISTIVITY (Insulators)

When a dielectric is subjected to a continuous voltage, the flow of current through

it is established by means of the few free charges that are present.

In conductors with a large number of free charges, the phenomenon

stabilizes for resistance values (ratio between applied voltages and

circulating intensity) and there is little variation over long intervals;

the same is not true for dielectrics, in which

temperature and impurities may significantly

modify the free charges present, and consequently

the response current.

Thus, resistivity can vary greatly according to the

condition of the test, and significant variations may easily result

from small modifications in the make up of the material.

Generally, resistivity decreases as temperature and moisture (in

oils) increase.

• 82 •

The resistivity measured with an alternating current is greater than

the value obtained with a direct current, since other phenomena

intervene in the transfer of charges.

9.2.2 SURFACE RESISTANCE

Very often the current can circulate on the surface of the dielectric instead of doing

so through the core. This phenomenon bears no relation with the resistance itself of

the dielectric; rather it is measured by surface resistance.

The quality of the surface and the presence of dust, moisture, etc., have a great

influence on this value. In cables, this phenomenon is of little interest, as it only has

an influence in terminals. It is fundamentally important in the design of insulators,

where surface discharges must be avoided.

9.2.3 ELECTRIC ABSORPTION

When a current is applied to a dielectric, in addition to the phenomena of

polarization, there is an absorption of electric charge which occurs during a certain

period (which may be important) and

then ceases, even if the current

persists. The dielectric will release

this charge if we cease to apply

vo l tage and shor t-c i rcu i t the

electrodes.

This phenomenon must be taken into

consideration, as it affects the

measurement of resistance, since the

presence of this current may alter

the values obtained.

• 83 •

When alternating voltage is applied to a dielectric, the following phenomena

will occur:

a) A current satisfying Ohm's Law will circulate. The value of this

current will depend on the resistivity of the insulation under

working conditions. Its passage will give rise to heating due to

the Joule effect.

b) There will also be a displacement current, /2 radians ahead

on the Gaussian plane with respect to the voltage applied. The

magnitude of this current will depend on the dielectric constant

of the material (which influences the capacity of the condenser

that is formed). Given that this is a displacement current, it will

not heat up the dielectric.

c) The pole pieces will vibrate with the excitation to which they

are subjected. Due to this phenomenon, the material will heat

up, and this will be reflected in the energetic process taking

place in its core. The measurement of this phenomenon cannot be distinguished

from that occurring in point a), except that the former is always present, while the

latter only occurs in the presence of alternating excitation.

LOSS ANGLES

Given that a cable is not an ideal condenser, there is an IR leakage current in the

dielectric in phase with the voltage U0

EQUIVALENT LAYOUT

9.2.4 DIELECTRIC LOSS

• 84 •

CONDUCTOR SHIELD

• 85 •

VECTORIAL DIAGRAM

The real current I in the dielectric forms an angle (of loss) with the reactive

current Ic which is dephased 90º from the voltage U, corresponding to an ideal

loss-free condenser. This is expressed by:

tg =R

The loss angle depends on the temperature, the material and the frequency.

Figure 1 shows the variation of tg with the temperature for the different types of

insulation.

Insulation Conductance (leakance)

The conductance G is defined and the inverse of the loss resistance of the

insulation.

c

= 2 f =

=

Co =

tg =

angular frequency

relative dielectric current

Capacity considering the dielectric as a vacuum

loss angle

The product “ . tg “ is called the loss factor.

9.2.5 LOSS FACTOR

In cables the value of the tangent (tg ) is measured, in order to give a quality

factor for the insulation. This value gives

us the ratio between the resistive

current and the capacitive current; this

must be as steady and as low as possible for

the optimal operation of the cable. An

increase in the value points to the possible

deterioration of the dielectr ic , as

currents that will give rise to heating

are circulating through it.

The dielectric losses per phase in three phase layout are given by the formula:

It can be seen that dielectric losses are proportional to the leakage, and the

square of the simple voltage. In simple low voltage cables. In low voltage cables

these losses are practically insignificant. They become more significant as the

voltage increases.

• 86 •

FIGURA 1

Uo =

C =

simple voltage, in V

capacity in µ F/Km

Variation of according to temperature. Variation of according to temperature.

9.2.6 CORONA EFFECT

If the electric field at a given point exceeds the disruptive voltage value for the

material present, ionization will take place, with the creation of free charges due

to the destruction of electrically balanced molecules.

It may come about that this value for the electric field only occurs at certain

points, either due to the concentration of the field owing to incorrect design, or

due to the presence of occlusions of different "epsilon" values (e.g. air

occlusions). Thus, this ionization is limited to this specific spot in the field. This

phenomenon is called the corona effect, and the limited discharge is called a

partial discharge.

There are dielectrics that demonstrate good resistance to high levels of partial

discharges, and others that degrade by decomposing in the presence of low levels

of ionization (many dry insulators are sensitive to these phenomena).

9.2.7 INSULATION RESISTANCE

The insulation resistance of cables is generally evaluated

in MΩ per kilometre. For the same resistivity in its

dielectric, the thicker the insulation is, and the smaller

the cross-section of conductor is, the higher the insulation

resistance will be.

The insulation resistance value for cables with one single

conductor with circular section is as follows:

R=0,367 ------- log ------l

d2

d1

• 87 •

=

d1 =

d2 =

l =

resistivity M per cubic centimetre

diameter of the conductor

diameter over insulation (expressed in the same units as d1)

length of the cable in kilometres

Definition of Ki

This is the insulation resistance expressed in MΩ of a

standard cable of 1 km in length with a diameter ratio

of 10 (d2 / d1 = 10). The Ki value is only a function of

the insulation.

Ki = 0,367. . 10-5 M Km

In this manner the insulation resistance of different cables can be compared by

calculating their Ki values.

R . l

Ki =

log d2

d1

the cables insulation resistance expressed in M .

Consequently, if we know the value of Ki at 20ºC for the most commonly used

polymeric insulations, we can easily deduce the insulation resistance in M Km.

using the above formula.

Type of Insulation Value of Ki at 20ºC

PVC

EPR

XLPE

PE

S (Silicone)

36,7

3.670

3.670

50.000

1.500

• 88 •

The capacitance of a cable depends on the dimensions of the cable and the

relative dielectric current of the insulation.

In cables with a radial field, the capacitance is calculated by considering the cable

as a cylindrical condenser.

CAPACITANCE

• 89 •

VOLTAGE DROP

In electric conductors, the presence of resistance and serial reactance gives rise

to a difference between the voltages at each end of the section being considered;

this difference is called the voltage drop. The nature and intensity of the current

in the line, its length, dimensions and layout of the conductors all play roles in its

calculation.

In lines made up of insulated cables the influence of the capacity between

conductor or between themselves and earth is not taken into account for the

purposes of voltage drop (except in cases of extreme lengths), which does not

mean, however, that it is not significant from other perspectives.

Similarly the insulation conduction or leakance is disregarded. The line may be

shown by means of an equivalent circuit (Fig. 2), in which R is the resistance of

the line, XL its inductive reactance, and in which we suppose that half of the

capacity of the line is concentrated at the ends.

=

D =

d =

relative dielectric current

diameter of insulation

diameter of the conductor, including the semiconductor layer

Figure 3 shows the equivalent vectorial diagram of voltages and currents.

However, given that in practice Ic1 and Ic2

are significantly lower than I1 and I

2 the

simplified diagram shown in Figure 4 is used.

In practice, the following formulae are used to calculate the voltage drop:

1) Three phase alternating current:

• 90 •

FIGURE 2

FIGURE 3 FIGURE 4

• 91 •

NOTE: In our catalogues and CD-ROM, voltage drops appear in V/A•Km with cos

0.8 and 1 for each of the sections in mm2. The resistance “R” of the

conductor, in ohms/km, refers to 90ºC alternating current.

Total resistance of a conductor

Resistance per unit of length

Total inductive reactance of a conductor

Reactance per unit of length

Length of line

Active power

Reactive power

Voltage drop between phases

Percentage voltage drop between phases

Compound voltage

total values for both conductors in the line.

R =

r =

XL =

x =

L =

P =

Q =

U =

U =

U =

1) Single phase alternating current:

R y X =