− = ⋅ ⋅ + 1.2
PF RP
CFO 2 750 ln 1 0.55S (2.155)
where S is the strike distance, in m.
The CFO peak value under power-frequency voltage is about 20%–30% higher than the corresponding value under positive switching impulse at critical front time.
For gaps between 1 and 2 m, the above expression is a conservative approach. For gaps longer than 2 m, the strength (under dry conditions) could be evaluated as follows [2,162]:
( )
= − ⋅ − 2
PF PF RP g g
CFO CFO 1.35k 0.35k (2.156)
where kg is the gap factor.
By using this expression, the resulting power-frequency CFO can be greater than the switching impulse, positive-polarity CFO, for 3 m gaps and a gap factor larger than 1 [3].
Insulators may signifi cantly reduce the fl ashover voltage of the same gap but without insulators, especially in conditions of high humidity [2,162].
Several countermeasures can be applied to avoid or mitigate breakdowns caused by power-frequency voltages under contaminated conditions [161]: overinsulation by increas-ing the number of insulators, application of fog-type insulators, application of silicone grease, washing and cleaning of deenergized insulators, and use of semiconducting glazed insulators.
Although several models have been developed and tested to represent the perfor-mance of contaminated insulators under power frequency, they are not frequently used to predict fl ashover. A comprehensive survey of surface discharge models is presented in [163].
2.6.7 Atmospheric Effects
The fl ashover voltage of external insulation depends on atmospheric conditions. BILs and BSLs are specifi ed for standard atmospheric conditions. However, laboratory atmospheric conditions are rarely standard, and correlation factors are needed to determine the crest impulse voltage that should be applied so that the BIL and BSL will be valid for stan-dard conditions. It is necessary, therefore, to establish procedures by which it is possible to estimate fl ashover voltages at any atmospheric condition from those measured at another condition.
Usually, the fl ashover voltage for a given path in air is raised by an increase either in air density or the humidity [164]. Denoting the voltage measured under nonstandard atmo-spheric conditions as VA and the voltage for standard conditions as VS, the suggested rela-tionship is [1,3]
= δ
A m cw S
V H V (2.157)
where
δ is the relative air density
Hc is the humidity correction factor
m and w are constants dependent on the factor G0, which is defi ned as follows:
= S
0 CFO
G 500
S (2.158)
where
S is the strike distance in m
CFOS is the CFO under standard conditions
The values of m and w may be obtained from Table 2.19.
The standard atmospheric condition assumes an absolute humidity of 11 g moisture con-tent per cubic meter of air, 760 torr and 293 K (20°C).
Density effects: Breakdown voltages can be assumed to vary linearly with the density of the air, which is determined by temperature and pressure. The relative air density is defi ned as
δ = 0
0
PT
P T (2.159)
where
P0 and T0 are the standard pressure and temperature with the temperature in degrees Kelvin
P and T are the ambient pressure and temperature
Over the normal range of temperatures encountered in practice, the density correction factor is satisfactory. Values and curves of fl ashover voltages presented in the literature are usually described as uncorrected, for which δ = 1.
Since the relative air density is a function of pressure and temperature, it is also a func-tion of altitude. At any specifi c altitude, the air pressure and the temperature, and thus the relative air density, are not constant but vary with time. Therefore, the relative air density can be approximated by a Gaussian distribution [165]. The mean value of the relative air density is related to the altitude by the expression [1]
δ =e−A/8.6 (2.160)
where A is the altitude, in km.
Humidity effects: The effects of humidity on fl ashover are quite complex, but in general humidity has its strongest infl uence on the positive pre-breakdown discharge; it does not
TABLE 2.19 Values of m and w
G0 m w
G0 < 0.2 0 0
0.2 < G0 < 1.0 m = w = 1.25 G0 (G0 − 0.2)
1.0 < G0 < 1.2 1 1
1.2 < G0 < 2.0 1 w = 1.25 (2.2 − G0) (2 − G0)
G0 > 2.0 1 0
exhibit a signifi cant effect on the leader gradients, although it increases the leader velocity, and has not much infl uence on the negative fl ashover under lightning impulse. For wet or simulated rain conditions, Hc = 1.0.
Other atmospheric effects: Overhead lines must contend with atmospheric pollution, rain, ice, and snow. All of these can have a signifi cant effect on insulators. For further informa-tion see Refs. [166–168].
Improved correction factors were suggested in [169].
The conversion procedure can be used for impulse, alternating, and direct voltage mea-surements. It is also satisfactory for normal variations of pressure at altitudes up to 2000 m, although at greater altitudes (lower pressures) the linearity breaks down and a modifi ed procedure must be used [170].
By defi nition, Equation 2.157 can be applied to correct CFO, BIL, and BSL. That is,
= δ
= δ
= δ
A c S
A c S
A c S
CFO CFO
BIL BIL
BSL BSL
m w
m w
m w
H H
H (2.161)
Table 2.20 shows a summary of results for both lightning and switching impulses.
IEC Std 60071.2 proposes to account for nonstandard atmospheric conditions by means of the following relationship [2]:
=
A a S
V K V (2.162)
being the atmospheric correction factor Ka calculated from
= − ( /8.15)
a e m A
K (2.163)
where m = 1 for lightning impulse withstand voltages, while it depends on various param-eters (type of insulation, coordination switching impulse withstand voltage) for switching impulse withstand voltages.
TABLE 2.20
Correction for Nonstandard Atmospheric Conditions Impulse Type Atmospheric Conditions Correction Switching impulse Wet/rain conditions VA = δmVS
(Hc = 1) CFOA = δm CFOS
BSLA = δm BSLS
G0 is between 0.2 and 1.0 m = w = 1.25G0 (G0 − 0.2)
Lightning impulse Wet/rain conditions VA = δ VS
(Hc = 1) CFOA = δCFOS
BILA = δBILS
G0 is between 1.0 and 1.2 (m = 1, w = 1)
Standard correction factors for relative air density and humidity generally used for EHV design are not applicable to UHV tower design [132]. Tests on different gaps with varying atmospheric conditions show that a change of the relative air density and humidity had a smaller infl uence on the switching-surge fl ashover voltage at UHV spacings than at EHV spacings. Similarly, tests on various gaps in the UHV range show that the wet value of switching fl ashover voltage is very close to the dry value. The spread in fl ashover data in the total range of EHV and UHV spacings can be reduced if standard atmospheric correc-tion factors are applied to the air-gap clearance instead of to the fl ashover voltage. Because of the saturated fl ashover characteristics of UHV gap confi gurations, this approach pro-duces successively reduced effects of the atmospheric correction on the voltage as the spac-ings are increased. This method of correction has its experimental justifi cation in several works [171–173].
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