BREAKDOWN OF THE AIR INSULATION

Basic insulation breakdown process

3.1 BREAKDOWN OF THE AIR INSULATION

CHAPTER 3

takes place depends entirely on how much energy the electron gains before it makes contact with a neutral atom.

For a given volume of gas within which these free electrons and the molecules exist, the typical distance an electron can travel before colliding with another molecule is known as the mean free path.

The energy gained by an electron over the mean free path, is given by

,1.W=eEA_e (1)

where A.e is the mean free path in the direction dictated by an electric field of strength E. The electron charge, e, is -1.6 x 10-¹⁹ coulombs. Ionisation will take place when ,1.W is at least equal to the ionisation energy of the molecule with which the electron is colliding, which is eViwhere Vi is the ionisation potential. In addition to the electric field, the mean free pathA.e is therefore also an influencing parameter and is directly proportional to temperature (T) and inversely proportional to the gas pressure(P)[13]:

,l(p,T)

~ A,( _~ g)

⁽²⁾

where

1..0,

po and To are constants. Hence A.e is inversely proportional to the density of the gas.

Any fires under the power lines can be expected to both increase the temperature of the air about the conductors and decrease the gas density (or air density), hence the mean free path of electrons in the air about the conductors can be expected to be longer. Therefore a larger value of energy /). W gained by the electron as a direct result of the fires under the conductors, can be expected. However, ionisation by collision or electron impact, as are all other processes in gas discharges, is a probability phenomenon usually expressed in terms of cross-section for ionisation, denoted by cri which can be defined as the product ofPi, the probability of ionisation on impact, andcr, the molecular cross-sectional area of intersection or simply the collision cross- section. That is:

where the collision cross-section is:

1

( J = -

NA

(3)

(4)

and N is the number of particles per unit volume of gas. Therefore the event of a fire under a power line will increase the probability of an increase in corona activity which should be measurable. In order to develop a high 1evel0 f confidence in results, the number0 f samples must be as high as is reasonably possible.

Since A is proportional to lip in equation (2), then from equation (1) ~W is proportional to E/p.

Decreases in gas pressure as previously stated and increases in electric field (gradient), will increase the energy gained by an electron. The gradient on a conductor or conductor bundle is dependent on the applied voltage on the conductors

E=-VV (5)

wherenabla V, is a vector operator differentiating V in the x, y and z directions. Increasing the applied voltage on a conductor or conductor bundle will increase the gradient on the conductors and increase the energy~W gained by the electron.

The gradient⁰ n a conductor⁰r conductor bundle is a Iso dependent⁰ n the dimensions of the conductors or of the overall conductor bundle. From fundamental electromagnetic theory [14]

the analysis of point charges can be used for the influence of conductor dimensions

(6)

(7) where for a given point charge Ql in medium with permittivityE, the electric field in direction of the unit vector is inversely proportional to the square of the distance from that charge. The dielectric constant or permittivity is often conveniently expressed as the relative permittivity Er

which is the ratio of the medium's permittivity and that of a vacuum. This is confirmed by work done by Peek [20], [22], [26].

e_v g = ---'---

v s

rlog_e^- r

where gy is the visual critical gradient on the conductor before ionisation starts, ey is the visual critical voltage, r is the conductor radius and s is the separation between conductors. T he air density factor 8, was taken here as 1. That is, the barometric pressure was 76 cm0 fHg and ambient air temperature was 25 QC [from equation (16)]. Therefore the larger the radius of the conductor or conductor bundle is, the smaller the field will be for the same applied voltage and the lower the energy~W gained by the electron.

Insummary of the above statements, increasing the applied voltage on a given conductor bundle will increase the extent· to which ionisation is occurring and likewise decreasing the conductor and/or conductor bundle' diameter for a given applied voltage will also increase the electric field and hence the probability of ionisation occurring. Townsend [15] found that when gas is under a sufficiently high electric field, the current in the gas increases proportionately with the applied voltage, then at some voltage (A) in figure 3.1 below, remains constant and again at some higher voltage (B) the gas current increases exponentially.

Current flow between two plates

-

^t:_~... ^{Stage 1 Stage 2 smg. )}

::3 ()

(

^{A B}

Voltage

Figure 3.1: Current flow between two plates due to applied voltage (and electric field)

This final exponential increase in stage 3 is as a result of ionisation of the gas by electron collision. Townsend introduced the first ionisation coefficient a, to explain this increase in current. Where a is the number of ion pairs (new electron and the remaining positive ion) produced by an electron per unit length of path in the direction of the applied electric field:

~=~~

W

where n is the number of electrons at a distancex from the cathode. These electrons increase by dn at a distance x+dx from the cathode.

oil

E

,,,,

K ^!

^:

^{: A}

^~~

i

^,_,

~

^,_,

, ,

, ,

I--_~X'---+i:

dx!

~'.. .'

,--_--',t ,.L-t -,

I

^Initial

I

Initial electron

electron +arlx electrons

+arlx positive ions

Figure 3. 2: Electron collisions with stationary molecules producing electrons and ions.

Ifno is the primary number of electrons generated at the cathode (at x=O), then at x=d:

The discharge current to distancex is then

1= Ioe^ad

(9)

(10) Here e^ad represents the number of electrons produced by one electron travelling in an electric field with a separation of d between electrodes and 10 is the current leaving the cathode. A second ionisation coefficient y, was introduced for cathode secondary processes. The electrode current at the anode becomes

(11) Mathematically, the first ionisation coefficient can be described as follows [g]

(12) with dependence on E and p. Similarlyy is dependent on E and p. The ionisation by electron impact results in an avalanche as more collisions generate more ions and electrons. As the applied voltage increases, the ratio E/p increases and so Cl and 'Y also increase. Therefore the

[g] Seep 279 [15].

denominator in equation (11) will decrease and I will increase. For breakdown to occur, I becomes self-sustaining and indeterminate. The criteria for self-sustained discharge (current flow tends to infinity) is when the denominator will be zero and is

y(e^ad -1)=1 (13)

Provided the local electric field continues to be greater than the critical field for ionisation, further ionisation will occur at greater distances from the cathode resulting in streamers occurring. This is the development of additional avalanches at the "head" of the previous avalanche due to a high local field still present. From equation (9), the number of electrons is dependent on e^ux where x is the distance from the cathode to the streamer head. The criteria for the initiation of streamers were initially developed, independently, by Raether [16] and Meek [17] and as a result of subsequent research, they have been merged into the formulation:

X.\"Jrealllcr

J(a - 'l)dx= 18 (14)

where 11 represents the attachment of electrons in the path. The above criterion will be met when a sufficiently high applied voltage increases the local electric field Eloeal to exceed Eerit in the volume of air about the conductors. Eerit could be defined as that field at which the probability of ionisation by electron impact is high. The avalanche process will result in filamentary streamers propagating beyond the limits of the critical volume. Excitation and recombination by the initial avalanches generate photo-ionising quanta triggering streamers at other locations about the conductors. A web of streamers then develops out of the critical volume into the "first corona"

region. As the "tip" of the streamers move further from the conductor, Eloeal decreases until Eroea)<Eerit ·and the streamers halt. The electrons from the streamers then rapidly combine to produce a channel of positive and negative ions. During the corona propagation phase (streamers) the channels have experienced thermal expansion and the positive and negative ions generated then drift apart and generate space charge filaments in the field.