Insulation Strength
32 Chapter 2
criterion was simply to set the maximum stress or maximum switching overvoltage equal to the minimum insulation strength. Given the maximum switching overvolt- age, the next task was to find the SI strength of transmission tower insulation.
2 SWITCHING IMPULSE STRENGTH OF TOWERS
To determine the SI strength of a tower, a full-scale simulated tower is created in a high-voltage laboratory. This simulated tower shown in Fig. 1 is constructed of 1 inch angle iron covered with 1 inch hexagon wire mesh (chicken wire) to simulate the center phase of a transmission tower [17]. A two-conductor bundle is hung at the bottom of a 90-degree V-string insulator assembly. Switching impulses are then applied to the conductor with the tower frame grounded. First note the parameters of the test: (1) the strike distance, that is the clearance from the conductor to the tower side and the clearance from the yoke plate to the upper truss, (2) the insulator string length (or the number of insulators), (3) the SI waveshape (or actually the wavefront), and (4) wet or dry conditions.
Before proceeding to examine the test results, examine briefly the flashovers as shown in Figs. 2 to 5. These flashovers occurred under identical test conditions, i.e., dry, identical crest voltage, identical waveshape, and for the same strike distances and insulator length. The strike distance to the tower side and insulator length are approximately equal. First note that the flashover location is random, sometimes terminating on the right side of the tower (Fig. 2), sometimes on the left side (Fig. 3),
Figure 1 Tower test set-up.
Insulation Strength Characteristics
Figure 2 Switching impulse flashover.
Figure 3 Switching impulse flashover.
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Figure 4 Switching impulse flashover.
Figure 5 Switching impulse flashover.
Insulation Strength Characteristics
Figure 6 Lightning impulse flashover.
sometimes upward to the truss (Fig. 4), and sometimes part way up the insulator string and then over to the tower side (Fig. 5). Thus the tower is not simply a single gap but a multitude of air gaps plus two insulator strings, all of which are in parallel and any of which may flash over.
To develop fully the concepts and ideas, return to those early days of the 1960s when testing with switching impulses was new. Until this time, all testing knowledge was based on lightning impulses. For the lightning impulse, the concept in vogue was that there existed a critical voltage such that a slight increase in voltage would produce a flashover and a slight decrease in voltage would result in no flashover, i.e., a withstand. This critical voltage is called a critical flashover voltage or CFO. In testing with switching impulses, we were amazed to find that this same concept could not be applied. For example, apply a 1200kV impulse. A flashover occurs. Next decrease the voltage to 1100 kV. Another flashover occurs. Searching for that magi- cal CFO, decrease the voltage again to 1000 kV, and at last, a withstand. But now increase the voltage back to 1100 kV-and a withstand occurs whereas before a flashover occurred! Now, apply the 1200 kV 40 times, to get 8 flashovers and 32 withstands. That is 20% flashed over. And if the voltage is decreased and another 40 impulses are applied, a lower percentage flashed over.
Not to belabor the point, it was found that at any voltage level there exists a finite probability of flashover between 0 and 100 percent. If the percent flashover is now plotted as a function of the applied voltage, an S-shaped curve results as shown in Fig. 7 [9]. (In detail, the upper and lower data points are for 100 "shots"; or voltage applications, while the data points in the center of the curve are for 40 shots.)
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Figure 7 Best fit normal cumulative distribution curve for SI data points shown, center phase, positive, dry, 24 insulators [9].
When these data are plotted on normal or Gaussian probability paper, as shown by the upper curve of Fig. 8, the S-curve becomes a straight line, showing that the insulation strength characteristic may be approximated by a cumulative Gaussian distribution having a mean or 50% point that is called the CFO and a standard deviation or sigma of [9]. Usually the standard deviation is given in per unit or percentage of the CFO, which is formally known as the coefficient of variation. In engineering jargon, an engineer might state that the sigma is 5%, which is interpreted as 5% of the CFO.
FLASHOVER PROBABILITY
-
PERCENTFigure 8 Data of Figure 7 plotted on normal probability paper [9],
Insulation Strength Characteristics 37
This development was interesting and important, but it did not relieve the prob- lem of searching for the minimum insulation strength, since, as stated in section 1, the design criterion was to equate the minimum strength to the maximum stress. So a withstand or minimum strength was still required. In a somewhat arbitrary manner but realizing that a low probability value was necessary, the withstand, or perhaps better, the "statistical withstand" voltage for line insulation Vi, was set at 3 standard deviation below the CFO, or in equation form,
V3 = CFO - 3%) CFO
With the strength characteristic defined by two parameters, CFO and oc/CFO, investigation of the effect of other variables could proceed-testing to determine the effect of these other variables on the CFO or on the of/CFO. For completeness, the equation for the cumulative Gaussian distribution is
wherep or F ( V ) is the probability of flashover when V is applied to the insulation. In more condensed form,
where
V - CFO
z=
of
As noted in the above equations, the lower limit of integration is minus infi- nity-which is physically or theoretically impossible since this would mean that a probability of flashover existed for voltages less than zero. Detail tests on air- porcelain insulations have shown that the lower limit is equal to or less than about 4 standard deviations below the CFO [lo].
2.1 Wave Front
The effect of the wave front or time to crest on the CFO is shown in Fig. 9 for a strike distance of about 5 meters, for wet and dry conditions and for positive and negative polarity [ll]. First note the U-shaped curves showing that there exists a wave front that produces a minimum insulation strength. This is called the critical wave front or CWF. Next, wet conditions decrease the CFO, more for negative than for positive polarity. Also, positive polarity wet conditions are the most severe. In fact, for towers, the negative polarity strength is sufficiently larger than that for positive polarity that only positive polarity needs to be considered in design. Thus only positive polarity needs to be considered for further testing.
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Figure 9 Effect of wave front on the CFO [ll].
In immature EHV systems where switching of the EHV line is done from the low-voltage side of the transformer, the predominant wave front is not equal to the CWF but is much larger, of the order of 1000 to 2000 us. From the test results shown in Fig. 9 and from other tests, the CFO for these longer fronts is about 13% greater than the CFO for the CWF. As is discussed later, for application, this value of 13%
is reduced to 10% since the standard deviation also increases with the wave front.
Additional U-curves for other strike distances are shown in Fig. 10, where it is evident that the critical wave front increases with strike distance. Using these data, the CWF is plotted in Fig. 11 for positive polarity. Approximately, for positive polarity,
22 l- CWF