1 ---#/WET
2.6 The Outside Phase
The CFO of the outside phase with V-string insulator strings should be expected to have a larger CFO than that of the center phase, since there exists only one tower side. From test data, the outside phase CFO is about 8% greater than that of the center phase, so multiply Eq. 7 by 1.08 [9, 11, 171.
2.7 V-Strings vs. Vertical or !-Strings
Only limited tests have been made on vertical or I-string insulators [17]. While dry tests showed consistent results, tests under wet conditions were extremely variable.
For insulators in vertical position, water cascades down them so much that it may be said that water and not insulators is being tested. Only when the string is moved about 20Â from the vertical position does water drip off each insulator so that test results become consistent. (The V-string is normally at a 45O angle.)
This should not be construed to mean that I-strings have a lower insulation strength than V-strings. Rather, the CFO of I-strings is difficult to measure for practical rain conditions. It is suggested that Eq. 7 multiplied by 1.08 be used to estimate the CFO. The strike distance S to be used is the smaller of the three distances as illustrated in Fig. 21: SH to the upper truss, Sv to the tower side, and s1/l.05, where SI is the insulator string length. The factor 1.05 is used for the insulator string since the insulator string length should be a minimum of 1.05 times the strike distances per Section 2.2. For practical designs, usually, the insulator string length is controlling.
3 SUMMARY-INSULATION STRENGTH OF TOWERS
Before proceeding to discuss SI insulation strength of other insulation structures, a summary of the insulation strength of towers followed by a sample design problem appears appropriate. The summary:
1. The insulation strength characteristic can be approximated by the equation for a Gaussian cumulative distribution having a mean denoted by the CFO and a standard deviation q. The statistical withstand voltage for line insulation V3 is defined as
Figure 21 Outside arm strike distances.
Chapter 2
V 3 = C F O - 3 ~ f = C F 0 1-3-
(
CFOwhere of/CFO is 5%.
2. The CFO for the center phase, dry conditions, positive polarity, and V-string insulators is
the critical wave front (CWF),
(10) where S is in meters, CFOs is the CFO in kV under standard atmospheric condi- tions, and
where h is the conductor height and W is the tower width.
3. For other conditions
Wet conditions decrease the CFOs by 4%, i.e., multiply Eq. 10 by 0.96.
Outside phase has an 8% higher CFOs, i.e., multiply Eq. 10 or Eq. 11 by 1.08.
The CFOs and V3 should be increased by 10% for wave fronts of 1000ps or longer, i.e., multiply Eq. 10 by 1.10.
The insulator string length should be a minimum of 1.05 times the strike distance.
For I-string insulators, the CFOs may be estimated by Eq. 10 multiplied by 1.08.
S is the minimum of the three distances (1) the strike distance to the tower side, (2) the strike distance to the upper truss, and (3) the insulator string length divided by 1.05.
4. The usual line design assumes thunderstorm or wet conditions. Also the line should be designed for its average altitude. Therefore the CFO under these condi- tions, CFOA, may be obtained by the equation from Chapter 1,
For application, the CFOs is changed to that for wet conditions. That is,
and therefore CFOa becomes
or if the strike distance is desired, then
Insulation Strength Characteristics
where
and the relative air density 8 is
8 = e-A'8-6 0.997 - 0.106.4 where A is the altitude in km.
4 DETERMINISTIC DESIGN OF TRANSMISSION LINES
Using the information and equations of the previous sections, a method called the deterministic method can now be developed. This method was employed to design the first 500 kV and 765 kV lines. Only during the last 10 years has the improved probabilistic method been adopted. This probabilistic method will be discussed in the next chapter.
To develop the simple deterministic design equations, assume that an EMTP or TNA study has been performed to determine the maximum switching surge Em. The design rule is to equate V3 to Em:
substituting V 3 ,
CFO -
A - 1 - 3(of/CFO) (19)
Thus from Em the CFOA and the strike distance can be determined. To illustrate, consider the following example.
Example. Determine the center phase strike distance and number of standard insulators for a 500 kV (550 kV max) line to be constructed at an altitude of 1000 meters. The maximum switching surge is 2.0 per unit (1 pu = 450 kV) and W = 1.5 meters and h = 15 meters. Assume that all surges have a front equal to the critical wave front. Design for wet conditions and let o f / C F O = 5%.
The CFOA, which is the CFO required at 1000 meters, is from Eq. 19, 90010.85 = 1059 kV. Also the relative air density from Eq. 17 is 0.890. Because the gap factor and Go are both functions of the strike distance, the strike distance cannot be obtained directly. Rather an iterative process is necessary. To calculate S , Eq. 15 is used, i.e.,
Chapter 2
(20)
As a first guess, let kg = 1.2 and m = 0.5 and therefore S = 3.2. Iterating on S ,
kg is obtained from Eq. 11, CFOs from Eq. 13, Go and m from Eq. 16, and finally S from Eq. 15 or 20. As noted, only two calculations are necessary. Usually no more than three iterations are required.
Therefore, for the center phase, the strike distance is 3.18 meters (10.4 feet) and the minimum insulator length is 5% greater or 3.34 meters, which translates to 23 insulators (5 x 10 inches).
The strike distance for the outside phase will be less than that for the center phase. Since the strength is 8% greater than that of the outside phase, the outside phase strike distance is approximately 3.1811.08 or 2.94 meters. However this assumes a linear relationship, which is untrue. The proper procedure is to perform the above calculation with kg = 1.08 times the value of kg for the center phase.
Performing this calculation results in a 2.91-meter strike distance for the outside phase, which in turn requires a minimum of 20 insulators.
5 SWITCHING IMPULSE STRENGTH OF POST INSULATORS
The CFO of station post insulators is presented in Fig. 22 for positive and negative polarity and dry conditions [18]. The parameter of the curves is the steel pedestal height, since at this time some authors suggested the use of a higher pedestal height to increase the SI strength. This suggestion prompted these tests.
As shown, as the pedestal height increases, the positive polarity strength increases but the negative polarity strength decreases. This implies the possibility that for some steel pedestal height, the positive and negative CFOs are equal. Per Fig. 22, this does not occur for practical pedestal heights. However, for a 1000 ps wave front, Fig. 23, the negative polarity CFO is only 3% above that for positive polarity for a pedestal height of 20 feet. (see also [19].)
For the CWF of about 120 ps used in these tests and a steel pedestal height of 8 feet (2.4meters), an approximated equation for the CFO is
CFO = k 3400 1
+
(81s)where kg = 1.4 for positive polarity and kg = 1.7 for negative polarity. The coeffi- cient of variation crf/CFO is about 7 % .
As for wet tests on the vertical insulator strings, wet tests on these vertical columns produced erratic results. Other investigations showed similar results in
Insulation Strength Characteristics
Figure 22 CFO of station posts [18].
this erratic behavior and indicated that the insulation strength is a function of the number of post units that compose the complete unit. That is, a post insulator column composed entirely of porcelain, i.e., without intervening metal caps, showed a higher CFO.
In 1988, IEC Technical Committee 36 proposed a revision of Publication 273 to provide a list of standard BILIBSLs of post insulators along with the height of the
Figure 23 Effect of steel pedestal height, post insulator height = 15ft [18].
2400
2
w I
:
2 0 0 0!i
> 0 0
1 6 0 0
-
1 1 1 1 1 1 1 1 1 1
- 1000-@s FRONT
-
----A
- - -
-
-- -
POS-
NEG
1 1 1 1 1 1 1 1 1 1
0 4 8 12 16 2 0 STEEL SUPPORT HEIGHT- FT.
Chapter 2
Table 1 BIL/BSLs of Post Insulators, IEC 273-1990
Creep distance, m Class I Class I1
column and creepage distances; see Table 1. These should be interpreted as BSLs under wet conditions.
The values in this table are ambiguous in that the same BSL is given for two different heights of insulators. Obviously, the BSL associated with the lower height would appear correct. These BSLs are plotted as a function of the height or strike distance S in Fig. 24. A regression line through the uppermost points results in the equation
or using a of/CFO of 7 %
where the BSLs and CFOs are the BSL and CFO at standard wet-weather condi- tions. As noted, the equation using the CFO provides a gap factor of 1.18 for wet conditions. From the test results presented previously, a gap factor of 1.40 was obtained for post insulators under dry conditions and positive polarity.
Comparing these gap factors indicates that wet conditions decrease the CFO by about 16%, a not unreasonable value. Also from Table 1, as shown by Fig. 24, the standard BILs is approximately 450 kV/m of insulator length, i.e.,
where S is the insulator height or strike distance in meters and the BILs is the BIL for standard atmospheric conditions in kV.
Insulation Strength Characteristics
0 1 2 3 4 5 6
S , meters
Figure 24 BSL of post insulators per Table 1.
0 1 2 3 4 5 6
S , meters
Figure 25 BIL of power insulators per Table 1.
52 Chapter 2
6 A GENERAL APPROACH TO THE SWITCHING IMPULSE STRENGTH
A general approach to the estimation of the positive polarity CFO for alternate gap configurations was suggested by Paris and Cortina in 1968 [13]. They noted that all curves of the CFO as a function of gap spacing S had essentially the same shape and that the rod-plane gap had the lowest CFO. For example, note the shapes of the rod-plane and tower curves of Fig. 14. Therefore, they proposed the following general equation for positive polarity and dry conditions:
CFO = 500k~sO'~ (25)
As before, S is the gap spacing or strike distance in meters with the CFO in kV. The parameter kg is the gap factor and is equal to 1 .OO for a rod-plane gap. For other gap configurations, the gap factor increases to a maximum of about 1.9 for a conductor- to-rod gap. To be carefully noted is that in developing the above equation, the authors used a 250-,us front-that is, it is not the critical wave front for all strike distances-so that the equation is not directly applicable to the minimum strength or minimum CFO.
Paris and Cortina suggested several gap factors, and in a 1973 ELECTRA paper, Paris et al. [20] proposed the gap factors shown in Table 2. As noted, the maximum gap factor of 1.9 is listed for a conductor-to-rod gap. From Table 2, two gap factors were selected for calculation of the phase-ground clearances in IEC Publication 71-2, 1976; (1) kg = 1.30 for a conductor-to-structure gap, where, for example, the structure is a tower leg, and (2) kg = 1.10 as a conservative gap factor for a rod-structure gap, where, for example, the gap configuration could be consid- ered as the top of an apparatus bushing with a small or no grading ring to a tower leg. These clearances are given as a function of the BSL using a or/CFO of 6%.
(This will be more fully discussed and used in Chapter 5 concerning substation insulation coordination.)
Subsequently, Gallet et al. [12] further investigated the gap factor concept. They realized that the Paris-Cortina equation was valid only for a 250-ps wave front, and therefore they sought an alternate equation to express the CFO for the critical wave front, that is, an equation for the minimum CFO. Their proposed equation, which is now used exclusively, is
CFO = k 3400 1
+
(815)which again is valid for positive polarity and is normally applied only for dry con- ditions. As is recognized, this form of the equation was used for the tower insulation strength, where kg was normally 1.2, and was also used for the post insulator.
Using the Gallet equation, the gap factors of Table 3 apply and as noted they do not differ greatly from those of Table 2. With further study, it became obvious that the gap factor was not simply a specific number but did vary with the specific parameters of the gap configuration. For example, note the equation of a rod-rod or conductor-rod gap of Table 3. Most recently, a CIGRE working group published a guide [15] in which general equations are presented for gap factors. But before
Insulation Strength Characteristics
Table 2 Gap Factors Proposed in Ref. 11 for Use with the Paris-Cortina Equation
Electrode configurations Diagram k g
Rod-plane
Rod-structure (under) Conductor-plane Conductor-window
Conductor-structure (under) Rod-rod (h = 6 m, under)
Conductor-structure (over and laterally) Conductor-rope
Conductor-crossarm end Conductor-rod (h = 3 m, under) Conductor-rod (h = 6 m, under) Conductor-rod (over)
examining these equations, consider the Gallet equation and note that as S approaches infinity, for a rod-plane gap, the CFO approaches 3400 kV, which would seem to indicate that a maximum CFO exists for any gap configuration.
This is totally untrue and points out the limit of the equation. In general, the Gallet equation appears valid for a gap spacing in the range of about 15 meters.
Beyond this spacing, Pigini, Rizzi, and Bramilla [21] proposed the following equation for a rod-plane gap for S in the range of 13 to 30 meters:
CFO = 1400
+
555' (27)Comparing at a gap spacing of 15,20, and 25 meters, for a rod-plane gap, the Gallet equations gives CFOs of 2217 kV, 2429 kV, and 2579 kV, whereas Eq. 27 results in 2225 kV, 2500 kV, and 2775 kV.
Another equation for the CFO, positive polarity, appears in IEC Publication 71 [41], which is stated to be applicable for rod-plane gaps up to 25m:
CFO = 1080kg ln(0.46S
+
1) (28)54 Chapter 2
Table 3 Gap Factors for Gallet Equation
Configuration Diagram he
Conductor-structure 0.3
1 - w à ‘
Conductor-large structure 1.30
Conductor-guy wire
I
The standard deviation is stated to be about 5% to 6% of the CFO.
For negative polarity, Publication 71 provides the following equation applicable for spacing from 2 to 14m, which is stated to have a standard deviation of about 8%
of the CFO:
CFO = 1 180kg~0.45 (29)
Comparing the CFO as determined by Eqs. 28 and 26, Eq. 28 results in essentially the same CFO as Eq. 26 for an S of 3 m and a CFO that is about 1.8% greater than that of Eq. 26 for an S of 6 m. Therefore there exists little reason to alter the equation for the basic rod-plane gap. That is, Eq. 26 is valid.