Mechanisms of air breakdown
SF 6 insulation systems and their monitoring
2.3 Breakdown mechanisms in low divergence fields
− B
where A= 27.7 kV−1and B= 2460 bar−1cm−1. The critical reduced field strength is therefore:
E p
crit
= Bp
A = 88.8 kV/cm bar
This simple relationship is useful in estimating onset voltages in SF6insulation.
2.3 Breakdown mechanisms in low divergence fields
As discussed above, the build-up of ionisation in SF6 is possible only under con-ditions where the (pressure-reduced) field exceeds a critical value (E/p)crit of
∼89 kV/cm bar.
For highly divergent fields (as, e.g., for the case of a sharp protrusion on a high voltage conductor) ionisation will be confined to a critically-stressed volume around the tip of the protrusion. In this situation localised PD, or corona, will be the first phenomenon observed as the applied voltage is increased. Breakdown under these conditions is a complex process, because of the effects of the space charge injected by the prebreakdown corona.
As any stress-raising defect in gas-insulated equipment will result in PD activity, it is important to understand non-uniform field discharge mechanisms. However, GIS
are designed for relatively low field divergence and it will be useful first to consider the simple case of breakdown in SF6under uniform field conditions, before reviewing the phenomena associated with particulate contamination or other defects.
2.3.1 Streamer breakdown
For a perfectly uniform field (plane–plane electrode geometry), no ionisation activity can occur for reduced fields less than the critical value. Above this level, ionisation builds up very rapidly and leads to complete breakdown of the insulation (formation of an arc channel).
The first stage of the breakdown involves the development of an avalanche of electrons. The growth of this avalanche from a single starter at the cathode can readily be found by computing the net electron multiplication. Considering a swarm that has grown to contain n(x) electrons at position x in a gap of width d; then, in travelling a further incremental discharge dx, these will generate a net new charge:
dn(x)= (α − η)n(x) dx = ¯αn(x) dx
as a result of ionising and attaching collisions with neutral molecules, where α is the net ionisation coefficient.
Integration over the interval 0 to x gives the number of electrons in the avalanche tip at that stage in its growth:
n(x)= exp
x
0
¯α dx
= exp( ¯αx)
In crossing the whole gap, an avalanche of exp(¯αd) electrons is created.
In itself, the occurrence of avalanches does not constitute breakdown. For exam-ple, if conditions were such that ¯α = 5 then, in a 1 cm gap at 1 bar, the current gain would be e5 ∼ 150. The normal low background conduction current density (due to collection of free charges present in the gap) would be increased as a result of ionisation from∼10−13A/cm2to∼10−11A/cm2, but the gap would still be a very good insulator. However, as illustrated in Figure 2.1, ¯α increases very quickly when the reduced field exceeds (E/p)crit and the multiplication can rapidly reach values of 106or greater, with most of the charge confined to a very small region at the head of the avalanche (approximately a sphere of typically∼10 μm radius).
The bipolar space charge generated by the ionisation process results in local distortion of the applied field such that ionisation activity ahead of, and behind, the avalanche tip is greatly enhanced. At a critical avalanche size (exp(¯αx) = Nc), the space charge field is high enough to generate rapidly moving ionisation fronts (streamers) which propagate at∼108cm/s towards the electrodes. When these bridge the gap, a highly conducting channel is formed within a few nanoseconds.
For pressures used in technical applications (p > 1 bar), the streamer process is the accepted breakdown mechanism in SF6under relatively uniform field conditions.
The critical avalanche size for streamer formation is found to be that for which the streamer constant k= nNcis approximately 12. The breakdown voltage is then
easily calculated using the linear relationship between¯α/p and E/p:
The minimum streamer inception or breakdown level will occur when the critical avalanche size is achieved at the anode. Thus:
¯αd = AEd − Bpd = k
The breakdown voltage Vs(=Ed) is then:
Vs =B
A(pd)+ k
A = 88.8 (pd) + 0.43 (kV) where pd is in bar cm.
Note that the breakdown voltage is a function only of the product (pressure x spacing). This is an example of the similarity relationship (Paschen’s Law) which allows gas-insulated equipment to be made more compact by increasing the pressure above atmospheric.
As indicated above, once the gap is bridged arc formation in SF6is extremely rapid. The voltage collapse time depends on the pressure (p), spacing (d) and geo-metry, and is typically∼10 d/p nanoseconds. In certain situations, this can present serious problems in GIS equipment. Sparking during closure of a disconnector switch, for example, can generate travelling waves in the GIS bus which have very fast rise times (up to 100 MV/μs). Doubling at open circuits elsewhere in the system can result in insulation being stressed with high amplitude (>2 p.u.) pulses with very short rise times (<10 ns). There are also problems with grounding and shielding, as very high fields (500 kV/m) can appear across parts of the grounded enclosure during the pulse transit.
2.3.2 Quasi-uniform fields (coaxial cylinders)
If the field is varying with position across the gap, the initial avalanche formation will occur within a critical volume for which (α− η) > 0 (i.e. E/p > 88.8 kV/cm bar).
Under these conditions, the streamer inception criterion is:
exp
xc
0 ¯α(x) dx
= N
where x is the distance from the inner electrode along a field line and xcis the position of the boundary of the ionisation region.
For coaxial electrode geometry (inner radius r0, outer r1) the field distribution is:
E(r)= V r ln
r1 r0
Also, at onset,¯α = 0 at position rc, so that:
E(rc)= Ecrit= Bp A
Using these relationships, together with the streamer criterion, it can easily be shown that the surface field at onset is:
E(r0)=Bp
With the above values of A and B, this yields:
E(r0)
For the large curvature electrodes and high pressures used in GIS, the field at the inner conductor at onset is therefore very close to the critical reduced field of
∼89 kV/cm bar.
Note that the streamer forms when the primary avalanche has developed a rela-tively short distance. For r0 = 8 cm, p = 4 bar, for example, xc will be∼1 mm.
The streamer will then propagate until the combination of the space charge field and the geometric field is unable to sustain further ionisation. In order for breakdown to occur, it will then be necessary to increase the surface field above the onset level.
In the relatively low divergence field in a (clean) GIS system only a small increase above the onset voltage is necessary to initiate breakdown.
2.3.3 Effect of surface roughness
Although laboratory measurements using polished coaxial electrodes are in agreement with the theoretical criterion that the inner surface field at breakdown should be close to the critical field of∼89 kV/cm bar, this value cannot be sustained in large scale equipment with a practical (machined) surface finish.
One reason for this is the fact that increased ionisation occurs in the vicinity of microscopic surface protrusions (surface roughness). This results in reduction of the breakdown field strength by a factor ζ . Figure 2.2 shows calculated values of the factor ζ as a function of the product ph (pressure× protrusion height) for a range of spheroidal protrusions [2].
It can be seen (a) that the breakdown voltage can be reduced to a low level and (b) that there is a critical protrusion size for the onset of roughness effects.
h
b
h/b 1 2
10 101
0.5 1.0
roughness factor,
102 103
ph (bar μm)
104
Figure 2.2 Roughness factor for uniform field breakdown in SF6
x
r E (x)
E0
Figure 2.3 Hemispherical protrusion on a uniform field electrode
The existence of a threshold value of ph can readily be demonstrated [2] for the hemispherical protrusion shown in Figure 2.3. For this case, the field at an axial distance x above the protrusion is given as:
E(x)= E0
1+ 2r3 (x+ r)3
For the protrusion to have no effect, E0(the macroscopic field) at onset must be equal to (E/p)crit(=Bp/A).
Also:
¯α(x) = AE(x) − Bp = Bp
1+ 2r3 (x+ r)3
− Bp = 2Bpr3 (x+ r)3 Breakdown occurs when:
xc
0 ¯α(x) dx = k
that is 2Bpr3
−12(x+ r)−2xc
0 = k therefore
1r2
(xc+ r)2 = k Bpr therefore
xc
r = 1 −
1
1− k/Bpr 1/2
With k= 12 and B = 0.246 bar−1μm−1: xc= r
1− (1 − 49/pr)−1/2
For xc to be real, pr must be >50 barμm. At a working pressure of 5 bar, surface roughness would therefore begin to affect the onset level for protrusion heights greater than∼10 μm.
Because of surface roughness effects (and other electrode phenomena such as micro discharges in charged oxide layers, etc.) practical SF6-insulated equipment is designed such that the maximum field is everywhere less than∼40 per cent of the critical value. In a typical GIS, for example, the basic insulation level (BIL) will correspond to a peak reduced field of only∼35 kV/cm bar.
With a good technical surface finish, streamers should not form in a clean coaxial electrode system under these conditions. Further, if a local defect does cause streamer formation, the streamer should not be able to propagate into the low field region of the gap. The fact that breakdown can occur, even at the lower reduced field associated with the AC working stress (∼15 kV/cm bar) indicates that an additional mechanism is operative. This is discussed in the following section on non-uniform field breakdown in SF6.