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Insulators
CHAPTER
INSULATORS
4
Insulators of various types are used to support overhead conductors at poles or towers. These insulators are generally made of porcelain. Porcelain is a ceramic material. It is made from a wet mixture of kaolin with other materials such as quartz (silica), feldspar, steatite, and bone ash. The mixture is molded to the required shape and heated in a kiln to a temperature of 1200 C1400 C and then glazed. Glazing porcelain gives moisture and dust-free surface. It has good dielectric strength of about 40280 V/mil and a relative permittivity of 5.15.9. Glass is another material used sometimes for voltages below 25 kV. The advantages of glass are that it is cheaper and flaws in molding, if any, can be detected easily. Some synthetic resins made of silicon compounds are also used sometimes as insulator materials. Where greater thickness is needed, porcelain insulators are manufactured in two or more pieces of the required shape and cemented together to form a single monolithic piece. Porcelain is mechanically stronger than glass, and less affected by temperature changes. Furthermore the leakage resistance can be increased by suitable design of the pieces. Porcelain is the most widely used insulator material.
4.1 TYPES OF INSULATORS Insulators are classified into three categories: 1. Pin type 2. Suspension type 3. Strain type
4.2 PIN TYPE INSULATORS Pin type insulators of single piece type are used for voltage up to 25 kV. For higher voltages up to 66 kV and even beyond, two, three, and four piece constructions are used. However, as the number of pieces increase, its weight also increases and the bending moment on the pin will become more. The pin type insulator is fixed to the crossarm on the pole with a bolt. Since this type of insulator is fixed rigidly on to the crossarm, the mechanical stress must be evenly balanced. Fig. 4.1 shows two-piece and three-piece construction of pin insulators. Pin insulators perform well under pollution conditions. They provide natural cleaning by wind and rain. They are mechanically strong and possess good flash over characteristics. Electrical Power Systems. DOI: http://dx.doi.org/10.1016/B978-0-08-101124-9.00004-8 Copyright © 2017 BSP Books Pvt. Ltd. Published by Elsevier Ltd. All rights reserved.
61
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CHAPTER 4 INSULATORS
FIGURE 4.1 Pin insulators. (A) 11 kV and (B) 33 kV.
4.3 SUSPENSION TYPE OR DISC INSULATORS There are two types of construction in disc insulators (1) Cemented cap type and (2) Hewlett or interlinking type With a pin insulator the conductor is connected to the insulator and is above the crossarm. In case of suspension insulators, the conductor is below the crossarm connected and suspended from the disc insulator. As the conductor is suspended freely, the stress on the insulator body is minimal. These insulators are made available as discs of about 26 cm diameter. Several discs are connected in series to form a string. Line voltage gets distributed over the number of discs connected in series, so that based on the design, suitable number of discs can be selected to form a string. In the cemented cap type there is a metal cap at the top and a metal pin underneath. To form a string, the cap is so recessed that it can take the pin of another unit. Such a disc is shown in Fig. 4.2. The upper surface of all types of insulators are so shaped that water will drop down from the surface easily.
4.5 VOLTAGE DISTRIBUTION IN STRING INSULATORS
63
FIGURE 4.2 Disc insulator in section.
In the Hewlett type of design each disc has two curved tunnels lying in planes at right angles to each other. Steel U-shaped links covered with lead are threaded into these tunnels. They are fastened to similar links to other discs in the string. The Hewlett type insulator is more reliable than the cemented cap type, but the porcelain in this case is subjected to higher electrostatic stress and hence liable to puncture more than the cemented cap type.
4.4 STRAIN INSULATORS Wherever transmission lines take a turning or at dead ends where the lines start-up or end, the pull of the conductors on the string becomes uneven. The tension becomes more for large spans encountered, such as at river crossings. For such cases special mechanically strong insulators are used. They are called strain insulators. For even distribution of tension, two or more strings of insulators may be used in parallel. This is shown in Fig. 4.3.
4.5 VOLTAGE DISTRIBUTION IN STRING INSULATORS If several disc insulators are connected in series to withstand a higher voltage, ideally they should share the total potential from line to ground equally. But, in practice, since the tower is in the vicinity of the insulator and because the tower is at earth potential, each metal joint of the string has capacitance to earthed tower. These capacitances alter the potential distribution across the string
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CHAPTER 4 INSULATORS
FIGURE 4.3 String insulator and arrangements.
from uniform to nonuniform. The potential across the disc nearest to the line conductor will be the maximum while the potential across the unit nearest to the crossarm end will be the least. Let the self-capacitance of each unit be mc and the capacitance of each metal link to earth (tower) be C. V 5 Total line voltage to ground 5 V1 1 V2 1 V3 1 V4
(4.1)
This is shown in Fig. 4.4 At junction 1 I2
5 I1 1 i 1 5 V1 mcw 1 V1 cw 5 V1 ½1 1 mcw
V2 mcw 5 V1 cw½1 1 m
V2 5 V1
cwð1 1 mÞ ð1 1 mÞ 1 5 V1 5 V1 1 1 mcw m m
(4.2)
At junction 2 I3 5 I2 1 i2 5 ðI1 1 i1 Þ 1 i2 5 V1 mcw 1 V1 cw 1 ðV1 1 V2 Þcw ð1 1 mÞ cw m ð1 1 mÞ V1 ð1 1 mÞ 1 1 V1 5 V1 m m2 m 2 3 ½m2 1 3m 1 1 3 1 5 V1 5 V1 41 1 1 2 5 m2 m m
V3 mcw 5 V1 ð1 1 mÞcw 1 V1 cw 1 Vi V3
Similarly at junction 4 I4 5 I3 1 i3 5 V3 mwc 1 ðV1 1 V2 1 V3 Þwc
(4.3)
4.5 VOLTAGE DISTRIBUTION IN STRING INSULATORS
65
FIGURE 4.4 Voltage distribution.
V4 mwc
5 V3 mwc 1 V1 wc 1 V2 wc 1 V3 wc ðm 1 1Þ ðm2 1 3m 1 1Þ wc 1 V3 mwc 5 V1 wc 1 V1 wc 1 V1 m m2 2 3 2 2 ðm 1 1Þ ðm 1 3m 1 1Þ ðm 1 3m 1 1Þm 5wc 1 1 5 V1 41 1 m m2 m2
1 m2 1 m2 1 m 1 m2 1 3m 1 1 1 m3 1 3m2 1 m m m2 3 ðm 1 m2 1 5m 1 1Þ 6 5 1 5 V 1 1 1 V4 5 V1 1 1 m3 m m2 m3 V4 5
Proceeding to junction 5,
V5 mwc
I5 5 V5 mwc 5 I4 1 i4 5 V4 mwc 1 ðV1 1 V2 1 V3 1 V4 Þwc 2 3 2 3 2 ðm 1 1Þ ðm 1 3m 1 1Þ V ðm 1 6m 1 5m 1 1Þ 1 5wc 5 4V1 1 V1 1 1 V1 m m2 m3 2 3 3 2 ðm 1 6m 1 5m 1 1Þ 5mwc 1 V1 4 m3
(4.4)
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CHAPTER 4 INSULATORS
V5
2 3 1 4m4 1 6m3 1 15m2 1 7m 1 15 5 V1 m m3 2 3 4 3 2 m 1 6m 1 15m 1 7m 1 1 5 5 V1 4 m4 2 3 6 15 7 1 5 V1 41 1 1 2 1 3 1 4 5 m m m m
(4.5)
In this manner the potential distribution can be computed for any number of discs.
4.6 STRING EFFICIENCY It is seen that the presence of crossarm and tower which are at earth potential in the proximity of the line conductor introduced additional capacitances providing leakage paths and this has altered the uniform potential distribution across the units into nonuniform distribution. This results in the unit nearest to the line carrying the maximum potential. The efficacy of the units is progressively reduced as the top is reached. The ratio Flash over voltage of a string of n units is called string efficiency n 3 Flash over voltage of unit nearest to line
Various methods are there to improve the nonuniform distribution.
4.7 METHODS FOR IMPROVING STRING EFFICIENCY From the equations derived for potential distribution across the various discs of a string, it can be concluded that potential across the unit near the line end is maximum. To make potential distribution uniform, several methods exist. They are briefly discussed in the following.
4.7.1 SELECTION OF M The ratio of the self-capacitance to capacitance to earth of links m can be properly chosen. A high value of m will have the effect of equalizing the potential distribution across the units. However, a large m means a longer crossarm and large tower which proves uneconomical. In general, a value of m equal to about 10 is considered as reasonable.
4.7.2 GRADING OF UNITS The voltage across any disc is related to capacitance C by I 5 VwC
(4.6)
4.7 METHODS FOR IMPROVING STRING EFFICIENCY
67
To maintain constant voltage, since a part of the current is leaking to earth, in proportion to this the value of the capacitance can be changed by selecting different types of insulator units. Since I is maximum at the line end, the capacitance of unit near the line conductor should be selected high, and progressively as the top (crossarm) is reached, the capacitances should be reduced. This enables to make the potential more uniform. However, this requires storing large quantities of insulator discs of different sizes and is not practical. The principle of grading of insulators can be explained as follows: Let C be the capacitance of the metal links to earth. Let mc be the capacitance of the top most unit of the string insulator nearest to the crossarm. The voltage is uniformly distributed across each disc as v. At junction 1, with the current distribution as assumed in Fig. 4.5 I2 5 I1 1 Ia
Let X, Y, Z, U, . . . be the capacitances of the discs graded to have uniform voltage. vX 5 vmc 1 vc 5 v½c 1 mc
FIGURE 4.5 Insulator grading.
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CHAPTER 4 INSULATORS
X 5 1c 1 mc
(4.7)
At junction 2 I3 5 Ib 1 I2 5 Ib 1 Ia 1 I1 vY 5 2cv 1 vc 1 mcY Y 5 ð1 1 2Þc 1 mc
(4.8)
Similarly, it can be obtained that I4 5 ic 1 I3 5 ic 1 ib 1 I2 5 ic 1 ib 1 ia 1 I1 vZ 5 3vC 1 2vcCc 1 vc 1 mcv Z 5 ð3 1 2 1 1Þc 1 mc
(4.9)
U 5 ð4 1 3 1 2 1 1Þc 1 mc
(4.10)
and Capacitance of the p-th link from the bottom is given by pðp 1Þ c cp 5 m 1 2
(4.11)
where m is the ratio of mutual capacitance of the top (nearest to tower) unit to the capacitance of each link to earth.
4.7.3 STATIC SHIELDING OR GRADING RING A large metal ring surrounding the bottom unit is connected to the line. This ring is also called guard ring. This metal piece introduces capacitances between different insulator links and the line. The effective capacitance of the bottom unit is raised. If, in addition, an arcing horn is used at the top of the string, then, in case of an over voltage, the arcing horn and the guard ring constitute a flash over path through air for the surge taking it away from the string, thus preventing damage to the insulator string. The basic principle involved in static shielding can be explained as follows. Consider Fig. 4.6, where C is the capacitance to earth of each metal link, m c mutual capacitance between discs. The guard ring connected to the line is assumed to have capacitance to the links A, B, C, D, E, F . . . . These capacitances are so selected that the leakage currents Ia, Ib, Ic, . . . are neutralized by currents flowing from shield to links IA, IB, IC, ID, etc. This is shown in Fig. 4.6. At junction 1 Ia 1 I1 5 I2 1 iA
For uniform potential distribution across the discs I1 5 I2
Therefore Ia 5 IA EC 5 ðn 1ÞECA
4.7 METHODS FOR IMPROVING STRING EFFICIENCY
69
FIGURE 4.6 Static shielding.
where n is the number of discs in the string. Then CA 5
C n21
(4.12)
At junction 2, in a similar way Ib 5 iB since I2 5 I3 CU2E 5 ðn 2ÞEUCB CB 5
2C n22
(4.13)
CC 5
3C n23
(4.14)
Likewise,
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CHAPTER 4 INSULATORS
Capacitance of guard ring to p-th link Cp 5
pc n2p
(4.15)
In this way, by selecting the static shield connected to the line conductor, neutralization of the capacitance currents to earth from links can be achieved. In practice, a grading ring is used but no care is taken to achieve exact neutralization of the earth leakage currents.
4.8 TESTING OF INSULATORS Insulators are tested as per I.S. 731 (1971) so that they withstand both electrically and mechanically field conditions or equivalent standards adopted. Electrical Tests: They include: 1. Power frequency dry flashover test 2. Power frequency wet flashover test 3. Impulse voltage flashover test. These tests are intended to examine the capability of the insulator to withstand both normal and storm weather conditions. On few pieces of every batch of manufactured units break down test till puncture are carried and under specified conditions. Mechanical Tests: Since the insulators support the line conductors which are both heavy and are subjected to large tension, it is mandatory to subject insulators for: 1. 2. 3. 4. 5.
tensile strength test, compression strength test, torsional strength test, vibration test, and bending test (for pin insulators only).
Porosity test is also performed by injecting a dye under pressure to examine the penetration into the insulator body. Pollution tests and other environmental tests are also needed depending upon the climatic and other conditions of the areas where insulators are used.
WORKED EXAMPLES E.4.1 Calculate the maximum voltage that a string of three disc insulators can withstand, if the maximum voltage per disc unit cannot exceed 17.4 kV. Given the ratio of mutual capacitance to earth capacitance is 8.
WORKED EXAMPLES
Solution: v3 5 17.4 kv
FIGURE E.4.1
c 5 8c1 ; m 5 8 v2 5
ðm 1 1Þ v1 and m
v3 5 v1 5
ðm2 1 3m 1 1Þ m2
Therefore, 17:4 3 64 5 v1 5 12:512 kV 64 1 24 1 1 ð8 1 1Þ 5 14:07 kV v2 5 12:512 8 Total voltage
5 17:4 1 14:07 1 12:512 5 43:988 5 44 kV
E.4.2 Each conductor of a three-phase 33-kV system is suspended by a string of three similar insulators, the mutual capacitance of which across units is 9 times the shunt capacitance between unit and earthed frame work. Calculate the voltage across each insulator. Also, calculate the string efficiency. Solution: m 5 9; v 5 p33ffiffi3 5 19 kV v1 1 v2 1 v3 5 19 kV v2 5 v1
v1 5 v1 2 m11 m 1 3m 1 1 and v3 5 v1 m m2
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CHAPTER 4 INSULATORS
Hence,
2
19
0 1 0 13 9 1 1 81 1 27 1 1 A1@ A5 5 v1 41 1 @ 9 81 2 3 10 109 5 5 3:456v1 1 5 v1 41 1 9 81 v1 5 5:497 kv 10 5 6:108 kV v2 5 5:497 9
v3 5 19 6:108 5:497 5 7:395 kV Flashover voltage of string of n units 3 100 String efficiency 5 n 3 Flashover voltage of one unit 5
19 19 3 100 5 3 100% 5 85:64% 3 3 7:395 22:185
E.4.3 A string of six suspension insulators is to be fitted with a grading ring. If the pin to earth capacitances are equal to c, determine the line-to-pin capacitances that would give a uniform distribution of potential over the string. Solution: cp 5
pc ; np
c1 5
c2 5
n56
c c 5 61 5
2c 2c 1 5 5 c 62 4 2
c3 5
3c 3c 5 5c 63 3
c4 5
4c 4c 5 5 2c 64 2
c5 5
4c 5c 5 5 5c 65 1
E.4.4 A string of eight suspension insulators is to be graded to obtain uniform potential distribution across each unit. Given that the pin-to-earth capacitance c is the same for all links and the mutual capacitance of the top insulator disc is 9c. Find the mutual capacitance of each unit in terms of c.
WORKED EXAMPLES
73
Solution: m 5 9; n 5 8; p 5 7
pðp 2 1Þ c cp 5 m 1 2 7ð7 1Þ c7 5 c 9 1 5 c½9 1 21 5 30c 2 6ð6 1Þ c6 5 c 9 1 5 c½9 1 15 5 24c 2 5ð5 1Þ 5 c½9 1 10 5 19c c5 5 c 9 1 2 4ð4 1Þ c4 5 c 9 1 5 c½9 1 6 5 15c 2 3ð3 1Þ c3 5 c 9 1 5 c½9 1 3 5 12c 2 2ð2 1Þ c2 5 c 9 1 5 10c 2 1ð1 1Þ 5 9c c1 5 c 9 1 2
E.4.5 A three-disc suspension insulator string is used for a three-phase, 50-Hz system for a length of 75 km. Each disc has a self-capacitance c (F). The shunt capacitance of metal work of each insulator to earth is 0.25c and 0.16c to line. If a guard ring is fitted to increase the shunt capacitance to line of metal work for the bottom most unit to 0.36c, determine the string efficiency. Solution: At A wcv2 5 wcv1 1 0:25wcv1 0:16wcðv2 1 v3 Þ
FIGURE E.4.5
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CHAPTER 4 INSULATORS
v2 5 1:25v1 0:16v2 0:16v3 1:16v2 5 1:25v1 0:16v3
(i)
At B wcv3 5 wcv2 1 0:25wcðv1 1 v2 Þ 0:36wcv3 v3 1 0:36v3 5 1:25v2 1 0:25v1
(ii)
From (i) substituting (ii) for v3 1:16v2
5 1:25v1
0:16 ½1:25v2 1 0:25v1 1:36
5 1:25v1 0:147v2 0:0294v1 1:307v2 5 1:2206v1 ; Again from ðiiÞ v3
5
v2 5 0:9339v1
1:25v2 1 0:25v1 5 0:919v2 1 0:1838v1 1:36
5 ð0:919 3 0:9339Þv1 1 0:1838v1 5 0:857v1 1 0:1838v3 5 1:04v1 String efficiency
5
v1 1 0:9339v1 1 1:04v1 2:973 5 3:12 3 3 1:04v1
5 95:28%
PROBLEMS P.4.1 A string of five insulator units has mutual capacitance 9 times the capacitance to earth. Determine the voltage across each unit as a ratio of the operating voltage. What is the string efficiency? P.4.2 A suspension insulator has three discs. The capacitance of each metal part to ground is 11% of the capacitance of each unit. The voltage across each unit or disc should not exceed 11 kV. Find the operating voltage for the string. P.4.3 A three-unit suspension insulator string is used to support the conductors for a three-phase system. If the voltage across the line unit is not to exceed 18 kv, calculate the line-to-line voltage. Given that the shunt capacitance between each unit to earth is one-ninth of the capacitance of the insulator unit. Find also the string efficiency.
QUESTIONS
75
QUESTIONS Q.4.1 Explain why the voltage is not uniformly distributed across a string of disc insulators. Q.4.2 A three-unit string insulator has mutual capacitances mc and shunt capacitance to earth of c. Determine the potential distribution across each unit. Q.4.3 Explain how the string efficiency can be improved in practice. Q.4.4 What do you understand by grading of insulators? Explain. Q.4.5 Explain static shielding method of improving string efficiency. Q.4.6 What are the various tests performed on insulators? Explain the significance of each test.
INSULATORS
4
Insulators of various types are used to support overhead conductors at poles or towers. These insulators are generally made of porcelain. Porcelain is a ceramic material. It is made from a wet mixture of kaolin with other materials such as quartz (silica), feldspar, steatite, and bone ash. The mixture is molded to the required shape and heated in a kiln to a temperature of 1200 C1400 C and then glazed. Glazing porcelain gives moisture and dust-free surface. It has good dielectric strength of about 40280 V/mil and a relative permittivity of 5.15.9. Glass is another material used sometimes for voltages below 25 kV. The advantages of glass are that it is cheaper and flaws in molding, if any, can be detected easily. Some synthetic resins made of silicon compounds are also used sometimes as insulator materials. Where greater thickness is needed, porcelain insulators are manufactured in two or more pieces of the required shape and cemented together to form a single monolithic piece. Porcelain is mechanically stronger than glass, and less affected by temperature changes. Furthermore the leakage resistance can be increased by suitable design of the pieces. Porcelain is the most widely used insulator material.
4.1 TYPES OF INSULATORS Insulators are classified into three categories: 1. Pin type 2. Suspension type 3. Strain type
4.2 PIN TYPE INSULATORS Pin type insulators of single piece type are used for voltage up to 25 kV. For higher voltages up to 66 kV and even beyond, two, three, and four piece constructions are used. However, as the number of pieces increase, its weight also increases and the bending moment on the pin will become more. The pin type insulator is fixed to the crossarm on the pole with a bolt. Since this type of insulator is fixed rigidly on to the crossarm, the mechanical stress must be evenly balanced. Fig. 4.1 shows two-piece and three-piece construction of pin insulators. Pin insulators perform well under pollution conditions. They provide natural cleaning by wind and rain. They are mechanically strong and possess good flash over characteristics. Electrical Power Systems. DOI: http://dx.doi.org/10.1016/B978-0-08-101124-9.00004-8 Copyright © 2017 BSP Books Pvt. Ltd. Published by Elsevier Ltd. All rights reserved.
61
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CHAPTER 4 INSULATORS
FIGURE 4.1 Pin insulators. (A) 11 kV and (B) 33 kV.
4.3 SUSPENSION TYPE OR DISC INSULATORS There are two types of construction in disc insulators (1) Cemented cap type and (2) Hewlett or interlinking type With a pin insulator the conductor is connected to the insulator and is above the crossarm. In case of suspension insulators, the conductor is below the crossarm connected and suspended from the disc insulator. As the conductor is suspended freely, the stress on the insulator body is minimal. These insulators are made available as discs of about 26 cm diameter. Several discs are connected in series to form a string. Line voltage gets distributed over the number of discs connected in series, so that based on the design, suitable number of discs can be selected to form a string. In the cemented cap type there is a metal cap at the top and a metal pin underneath. To form a string, the cap is so recessed that it can take the pin of another unit. Such a disc is shown in Fig. 4.2. The upper surface of all types of insulators are so shaped that water will drop down from the surface easily.
4.5 VOLTAGE DISTRIBUTION IN STRING INSULATORS
63
FIGURE 4.2 Disc insulator in section.
In the Hewlett type of design each disc has two curved tunnels lying in planes at right angles to each other. Steel U-shaped links covered with lead are threaded into these tunnels. They are fastened to similar links to other discs in the string. The Hewlett type insulator is more reliable than the cemented cap type, but the porcelain in this case is subjected to higher electrostatic stress and hence liable to puncture more than the cemented cap type.
4.4 STRAIN INSULATORS Wherever transmission lines take a turning or at dead ends where the lines start-up or end, the pull of the conductors on the string becomes uneven. The tension becomes more for large spans encountered, such as at river crossings. For such cases special mechanically strong insulators are used. They are called strain insulators. For even distribution of tension, two or more strings of insulators may be used in parallel. This is shown in Fig. 4.3.
4.5 VOLTAGE DISTRIBUTION IN STRING INSULATORS If several disc insulators are connected in series to withstand a higher voltage, ideally they should share the total potential from line to ground equally. But, in practice, since the tower is in the vicinity of the insulator and because the tower is at earth potential, each metal joint of the string has capacitance to earthed tower. These capacitances alter the potential distribution across the string
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CHAPTER 4 INSULATORS
FIGURE 4.3 String insulator and arrangements.
from uniform to nonuniform. The potential across the disc nearest to the line conductor will be the maximum while the potential across the unit nearest to the crossarm end will be the least. Let the self-capacitance of each unit be mc and the capacitance of each metal link to earth (tower) be C. V 5 Total line voltage to ground 5 V1 1 V2 1 V3 1 V4
(4.1)
This is shown in Fig. 4.4 At junction 1 I2
5 I1 1 i 1 5 V1 mcw 1 V1 cw 5 V1 ½1 1 mcw
V2 mcw 5 V1 cw½1 1 m
V2 5 V1
cwð1 1 mÞ ð1 1 mÞ 1 5 V1 5 V1 1 1 mcw m m
(4.2)
At junction 2 I3 5 I2 1 i2 5 ðI1 1 i1 Þ 1 i2 5 V1 mcw 1 V1 cw 1 ðV1 1 V2 Þcw ð1 1 mÞ cw m ð1 1 mÞ V1 ð1 1 mÞ 1 1 V1 5 V1 m m2 m 2 3 ½m2 1 3m 1 1 3 1 5 V1 5 V1 41 1 1 2 5 m2 m m
V3 mcw 5 V1 ð1 1 mÞcw 1 V1 cw 1 Vi V3
Similarly at junction 4 I4 5 I3 1 i3 5 V3 mwc 1 ðV1 1 V2 1 V3 Þwc
(4.3)
4.5 VOLTAGE DISTRIBUTION IN STRING INSULATORS
65
FIGURE 4.4 Voltage distribution.
V4 mwc
5 V3 mwc 1 V1 wc 1 V2 wc 1 V3 wc ðm 1 1Þ ðm2 1 3m 1 1Þ wc 1 V3 mwc 5 V1 wc 1 V1 wc 1 V1 m m2 2 3 2 2 ðm 1 1Þ ðm 1 3m 1 1Þ ðm 1 3m 1 1Þm 5wc 1 1 5 V1 41 1 m m2 m2
1 m2 1 m2 1 m 1 m2 1 3m 1 1 1 m3 1 3m2 1 m m m2 3 ðm 1 m2 1 5m 1 1Þ 6 5 1 5 V 1 1 1 V4 5 V1 1 1 m3 m m2 m3 V4 5
Proceeding to junction 5,
V5 mwc
I5 5 V5 mwc 5 I4 1 i4 5 V4 mwc 1 ðV1 1 V2 1 V3 1 V4 Þwc 2 3 2 3 2 ðm 1 1Þ ðm 1 3m 1 1Þ V ðm 1 6m 1 5m 1 1Þ 1 5wc 5 4V1 1 V1 1 1 V1 m m2 m3 2 3 3 2 ðm 1 6m 1 5m 1 1Þ 5mwc 1 V1 4 m3
(4.4)
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CHAPTER 4 INSULATORS
V5
2 3 1 4m4 1 6m3 1 15m2 1 7m 1 15 5 V1 m m3 2 3 4 3 2 m 1 6m 1 15m 1 7m 1 1 5 5 V1 4 m4 2 3 6 15 7 1 5 V1 41 1 1 2 1 3 1 4 5 m m m m
(4.5)
In this manner the potential distribution can be computed for any number of discs.
4.6 STRING EFFICIENCY It is seen that the presence of crossarm and tower which are at earth potential in the proximity of the line conductor introduced additional capacitances providing leakage paths and this has altered the uniform potential distribution across the units into nonuniform distribution. This results in the unit nearest to the line carrying the maximum potential. The efficacy of the units is progressively reduced as the top is reached. The ratio Flash over voltage of a string of n units is called string efficiency n 3 Flash over voltage of unit nearest to line
Various methods are there to improve the nonuniform distribution.
4.7 METHODS FOR IMPROVING STRING EFFICIENCY From the equations derived for potential distribution across the various discs of a string, it can be concluded that potential across the unit near the line end is maximum. To make potential distribution uniform, several methods exist. They are briefly discussed in the following.
4.7.1 SELECTION OF M The ratio of the self-capacitance to capacitance to earth of links m can be properly chosen. A high value of m will have the effect of equalizing the potential distribution across the units. However, a large m means a longer crossarm and large tower which proves uneconomical. In general, a value of m equal to about 10 is considered as reasonable.
4.7.2 GRADING OF UNITS The voltage across any disc is related to capacitance C by I 5 VwC
(4.6)
4.7 METHODS FOR IMPROVING STRING EFFICIENCY
67
To maintain constant voltage, since a part of the current is leaking to earth, in proportion to this the value of the capacitance can be changed by selecting different types of insulator units. Since I is maximum at the line end, the capacitance of unit near the line conductor should be selected high, and progressively as the top (crossarm) is reached, the capacitances should be reduced. This enables to make the potential more uniform. However, this requires storing large quantities of insulator discs of different sizes and is not practical. The principle of grading of insulators can be explained as follows: Let C be the capacitance of the metal links to earth. Let mc be the capacitance of the top most unit of the string insulator nearest to the crossarm. The voltage is uniformly distributed across each disc as v. At junction 1, with the current distribution as assumed in Fig. 4.5 I2 5 I1 1 Ia
Let X, Y, Z, U, . . . be the capacitances of the discs graded to have uniform voltage. vX 5 vmc 1 vc 5 v½c 1 mc
FIGURE 4.5 Insulator grading.
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CHAPTER 4 INSULATORS
X 5 1c 1 mc
(4.7)
At junction 2 I3 5 Ib 1 I2 5 Ib 1 Ia 1 I1 vY 5 2cv 1 vc 1 mcY Y 5 ð1 1 2Þc 1 mc
(4.8)
Similarly, it can be obtained that I4 5 ic 1 I3 5 ic 1 ib 1 I2 5 ic 1 ib 1 ia 1 I1 vZ 5 3vC 1 2vcCc 1 vc 1 mcv Z 5 ð3 1 2 1 1Þc 1 mc
(4.9)
U 5 ð4 1 3 1 2 1 1Þc 1 mc
(4.10)
and Capacitance of the p-th link from the bottom is given by pðp 1Þ c cp 5 m 1 2
(4.11)
where m is the ratio of mutual capacitance of the top (nearest to tower) unit to the capacitance of each link to earth.
4.7.3 STATIC SHIELDING OR GRADING RING A large metal ring surrounding the bottom unit is connected to the line. This ring is also called guard ring. This metal piece introduces capacitances between different insulator links and the line. The effective capacitance of the bottom unit is raised. If, in addition, an arcing horn is used at the top of the string, then, in case of an over voltage, the arcing horn and the guard ring constitute a flash over path through air for the surge taking it away from the string, thus preventing damage to the insulator string. The basic principle involved in static shielding can be explained as follows. Consider Fig. 4.6, where C is the capacitance to earth of each metal link, m c mutual capacitance between discs. The guard ring connected to the line is assumed to have capacitance to the links A, B, C, D, E, F . . . . These capacitances are so selected that the leakage currents Ia, Ib, Ic, . . . are neutralized by currents flowing from shield to links IA, IB, IC, ID, etc. This is shown in Fig. 4.6. At junction 1 Ia 1 I1 5 I2 1 iA
For uniform potential distribution across the discs I1 5 I2
Therefore Ia 5 IA EC 5 ðn 1ÞECA
4.7 METHODS FOR IMPROVING STRING EFFICIENCY
69
FIGURE 4.6 Static shielding.
where n is the number of discs in the string. Then CA 5
C n21
(4.12)
At junction 2, in a similar way Ib 5 iB since I2 5 I3 CU2E 5 ðn 2ÞEUCB CB 5
2C n22
(4.13)
CC 5
3C n23
(4.14)
Likewise,
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CHAPTER 4 INSULATORS
Capacitance of guard ring to p-th link Cp 5
pc n2p
(4.15)
In this way, by selecting the static shield connected to the line conductor, neutralization of the capacitance currents to earth from links can be achieved. In practice, a grading ring is used but no care is taken to achieve exact neutralization of the earth leakage currents.
4.8 TESTING OF INSULATORS Insulators are tested as per I.S. 731 (1971) so that they withstand both electrically and mechanically field conditions or equivalent standards adopted. Electrical Tests: They include: 1. Power frequency dry flashover test 2. Power frequency wet flashover test 3. Impulse voltage flashover test. These tests are intended to examine the capability of the insulator to withstand both normal and storm weather conditions. On few pieces of every batch of manufactured units break down test till puncture are carried and under specified conditions. Mechanical Tests: Since the insulators support the line conductors which are both heavy and are subjected to large tension, it is mandatory to subject insulators for: 1. 2. 3. 4. 5.
tensile strength test, compression strength test, torsional strength test, vibration test, and bending test (for pin insulators only).
Porosity test is also performed by injecting a dye under pressure to examine the penetration into the insulator body. Pollution tests and other environmental tests are also needed depending upon the climatic and other conditions of the areas where insulators are used.
WORKED EXAMPLES E.4.1 Calculate the maximum voltage that a string of three disc insulators can withstand, if the maximum voltage per disc unit cannot exceed 17.4 kV. Given the ratio of mutual capacitance to earth capacitance is 8.
WORKED EXAMPLES
Solution: v3 5 17.4 kv
FIGURE E.4.1
c 5 8c1 ; m 5 8 v2 5
ðm 1 1Þ v1 and m
v3 5 v1 5
ðm2 1 3m 1 1Þ m2
Therefore, 17:4 3 64 5 v1 5 12:512 kV 64 1 24 1 1 ð8 1 1Þ 5 14:07 kV v2 5 12:512 8 Total voltage
5 17:4 1 14:07 1 12:512 5 43:988 5 44 kV
E.4.2 Each conductor of a three-phase 33-kV system is suspended by a string of three similar insulators, the mutual capacitance of which across units is 9 times the shunt capacitance between unit and earthed frame work. Calculate the voltage across each insulator. Also, calculate the string efficiency. Solution: m 5 9; v 5 p33ffiffi3 5 19 kV v1 1 v2 1 v3 5 19 kV v2 5 v1
v1 5 v1 2 m11 m 1 3m 1 1 and v3 5 v1 m m2
71
72
CHAPTER 4 INSULATORS
Hence,
2
19
0 1 0 13 9 1 1 81 1 27 1 1 A1@ A5 5 v1 41 1 @ 9 81 2 3 10 109 5 5 3:456v1 1 5 v1 41 1 9 81 v1 5 5:497 kv 10 5 6:108 kV v2 5 5:497 9
v3 5 19 6:108 5:497 5 7:395 kV Flashover voltage of string of n units 3 100 String efficiency 5 n 3 Flashover voltage of one unit 5
19 19 3 100 5 3 100% 5 85:64% 3 3 7:395 22:185
E.4.3 A string of six suspension insulators is to be fitted with a grading ring. If the pin to earth capacitances are equal to c, determine the line-to-pin capacitances that would give a uniform distribution of potential over the string. Solution: cp 5
pc ; np
c1 5
c2 5
n56
c c 5 61 5
2c 2c 1 5 5 c 62 4 2
c3 5
3c 3c 5 5c 63 3
c4 5
4c 4c 5 5 2c 64 2
c5 5
4c 5c 5 5 5c 65 1
E.4.4 A string of eight suspension insulators is to be graded to obtain uniform potential distribution across each unit. Given that the pin-to-earth capacitance c is the same for all links and the mutual capacitance of the top insulator disc is 9c. Find the mutual capacitance of each unit in terms of c.
WORKED EXAMPLES
73
Solution: m 5 9; n 5 8; p 5 7
pðp 2 1Þ c cp 5 m 1 2 7ð7 1Þ c7 5 c 9 1 5 c½9 1 21 5 30c 2 6ð6 1Þ c6 5 c 9 1 5 c½9 1 15 5 24c 2 5ð5 1Þ 5 c½9 1 10 5 19c c5 5 c 9 1 2 4ð4 1Þ c4 5 c 9 1 5 c½9 1 6 5 15c 2 3ð3 1Þ c3 5 c 9 1 5 c½9 1 3 5 12c 2 2ð2 1Þ c2 5 c 9 1 5 10c 2 1ð1 1Þ 5 9c c1 5 c 9 1 2
E.4.5 A three-disc suspension insulator string is used for a three-phase, 50-Hz system for a length of 75 km. Each disc has a self-capacitance c (F). The shunt capacitance of metal work of each insulator to earth is 0.25c and 0.16c to line. If a guard ring is fitted to increase the shunt capacitance to line of metal work for the bottom most unit to 0.36c, determine the string efficiency. Solution: At A wcv2 5 wcv1 1 0:25wcv1 0:16wcðv2 1 v3 Þ
FIGURE E.4.5
74
CHAPTER 4 INSULATORS
v2 5 1:25v1 0:16v2 0:16v3 1:16v2 5 1:25v1 0:16v3
(i)
At B wcv3 5 wcv2 1 0:25wcðv1 1 v2 Þ 0:36wcv3 v3 1 0:36v3 5 1:25v2 1 0:25v1
(ii)
From (i) substituting (ii) for v3 1:16v2
5 1:25v1
0:16 ½1:25v2 1 0:25v1 1:36
5 1:25v1 0:147v2 0:0294v1 1:307v2 5 1:2206v1 ; Again from ðiiÞ v3
5
v2 5 0:9339v1
1:25v2 1 0:25v1 5 0:919v2 1 0:1838v1 1:36
5 ð0:919 3 0:9339Þv1 1 0:1838v1 5 0:857v1 1 0:1838v3 5 1:04v1 String efficiency
5
v1 1 0:9339v1 1 1:04v1 2:973 5 3:12 3 3 1:04v1
5 95:28%
PROBLEMS P.4.1 A string of five insulator units has mutual capacitance 9 times the capacitance to earth. Determine the voltage across each unit as a ratio of the operating voltage. What is the string efficiency? P.4.2 A suspension insulator has three discs. The capacitance of each metal part to ground is 11% of the capacitance of each unit. The voltage across each unit or disc should not exceed 11 kV. Find the operating voltage for the string. P.4.3 A three-unit suspension insulator string is used to support the conductors for a three-phase system. If the voltage across the line unit is not to exceed 18 kv, calculate the line-to-line voltage. Given that the shunt capacitance between each unit to earth is one-ninth of the capacitance of the insulator unit. Find also the string efficiency.
QUESTIONS
75
QUESTIONS Q.4.1 Explain why the voltage is not uniformly distributed across a string of disc insulators. Q.4.2 A three-unit string insulator has mutual capacitances mc and shunt capacitance to earth of c. Determine the potential distribution across each unit. Q.4.3 Explain how the string efficiency can be improved in practice. Q.4.4 What do you understand by grading of insulators? Explain. Q.4.5 Explain static shielding method of improving string efficiency. Q.4.6 What are the various tests performed on insulators? Explain the significance of each test.