Impedance /2 Shunt /2 Shunt Admittance FIGURE 61.3 Generalized conductor model TABLE 61.2 Standard System Voltage, kv Category 4.5 15的2 tra-high voltage(EHV) 345 (principally in Europe) 765 Ultra-high voltage(UHV) 1100 transmission lines are divided into two halves and lumped at buses connecting the lines(Fig. 61.3). More discussion on the transmission line models can be found in El-Hawary [1995 Standard Voltages Standard transmission voltages are established in the United States by the American National Standards Institute (ANSI). There is no clear delineation between distribution, subtransmission, and transmission voltage levels Table 61.2 shows the standard voltages listed in ANSI Standard C84 and C92. 2, all of which are in use at present. Insulators The electrical operating performance of a transmission line depends primarily on the insulation Insulators not only must have sufficient mechanical strength to support the greatest loads of ice and wind that may be reasonably expected, with an ample margin, but must be so designed to withstand severe mechanical abuse, lightning, and power arcs without mechanically failing. They must prevent a flashover for practically any frequency operation condition and many transient voltage conditions, under any conditions of humidity, temperature, rain, or snow, and with accumulations of dirt, salt, and other contaminants which are not periodically washed off by The majority of present insulators are made of glazed porcelain Porcelain is a ceramic product obtained by the high-temperature vitrification of clay, finely ground feldspar, and silica. Porcelain insulators for transmission may be disks, posts, or long-rod types. Glass insulators have been used on a significant proportion of trans- mission lines. These are made from toughened glass and are usually clear and colorless or light green. For transmission voltages they are available only as disk types. Synthetic insulators are usually manufactured long-rod or post types. Use of synthetic insulators on transmission lines is relatively recent, and a few questions c 2000 by CRC Press LLC
© 2000 by CRC Press LLC transmission lines are divided into two halves and lumped at buses connecting the lines (Fig. 61.3). More discussion on the transmission line models can be found in El-Hawary [1995]. Standard Voltages Standard transmission voltages are established in the United States by the American National Standards Institute (ANSI). There is no clear delineation between distribution, subtransmission, and transmission voltage levels. Table 61.2 shows the standard voltages listed in ANSI Standard C84 and C92.2, all of which are in use at present. Insulators The electrical operating performance of a transmission line depends primarily on the insulation. Insulators not only must have sufficient mechanical strength to support the greatest loads of ice and wind that may be reasonably expected, with an ample margin, but must be so designed to withstand severe mechanical abuse, lightning, and power arcs without mechanically failing. They must prevent a flashover for practically any powerfrequency operation condition and many transient voltage conditions, under any conditions of humidity, temperature, rain, or snow, and with accumulations of dirt, salt, and other contaminants which are not periodically washed off by rains. The majority of present insulators are made of glazed porcelain. Porcelain is a ceramic product obtained by the high-temperature vitrification of clay, finely ground feldspar, and silica. Porcelain insulators for transmission may be disks, posts, or long-rod types. Glass insulators have been used on a significant proportion of transmission lines. These are made from toughened glass and are usually clear and colorless or light green. For transmission voltages they are available only as disk types. Synthetic insulators are usually manufactured as long-rod or post types. Use of synthetic insulators on transmission lines is relatively recent, and a few questions FIGURE 61.3 Generalized conductor model. TABLE 61.2 Standard System Voltage, kV Rating Category Nominal Maximum 34.5 36.5 46 48.3 69 72.5 115 121 138 145 161 169 230 242 Extra-high voltage (EHV) 345 362 400 (principally in Europe) 500 550 765 800 Ultra-high voltage (UHV) 1100 1200
TABLE 61.3 Typical Line Insulation Line Voltage, kV No of Standard Disks Controlling Parameter(Typical Lightning or contamination 2306 Lightning, switching surge, or contamination 24-26 Switching surge or contamination Switching surge or contamination about their use are still under study. Improvements in design and manufacture in recent years have made synthetic insulators increasingly attractive since the strength-to-weight ratio is significantly higher than that of porcelain and can result in reduced tower costs, especially on EHV and UHV transmission lines. NEMA Publication"High Voltage Insulator Standard"and AIEE Standard 41 have been combined in ANSI Standards C29.1 through C29. 9. Standard C29.1 covers all electrical and mechanical tests for all types of insulators. The standards for the various insulators covering flashover voltages(wet, dry, and impulse; radio influence; leakage distance; standard dimensions; and mechanical-strength characteristics)are addressed. These standards should be consulted when specifying or purchasing insulators The electrical strength of line insulation may be determined by power frequency, switching surge, or lightning typical line insulation levels and the controlling ges, different parameters tend to dominate. Table 61.3 shows performance requirements. At different li Defining Term Surge impedance loading(SIL): The surge impedance of a transmission line is the characteristic impedance with resistance set to zero(resistance is assumed small compared to reactance). The power that flows in a lossless transmission line terminated in a resistive load equal to the lines surge impedance is denoted as the surge impedance loading of the line. Related Topics 3.5 Three-Phase Circuits 55.2 Dielectric Losses References Aluminum Electrical Conductor Handbook, 2nd ed. Aluminum Association, 1982. J.R. Carson, Wave propagation in overhead wires with ground return, " Bell System Tech J, vol 5, Pp. 539-554 S. Chen and w. E. Dillon,"Power system modeling, Proc. IEEE, vol 93, no. 7, Pp. 901-915, 1974. E. Clarke, Circuit Analysis of A-C Power Systems, vols. I and 2, New York: Wiley, 1943. Electrical Transmission and Distribution Reference Book, Central Station Engineers of the Westinghouse Electric Corporation, East Pittsburg .E. El-Hawary, Electric Power Systems: Design and Analysis, revised edition, Piscataway, N J. IEEE Press, 199 Further Information Other recommended publications regarding EHV transmission lines include Transmission Line Refe 345 and Above 2nd ed. 1982. from Electric Power Research Institute, Palo Alto, Calif and the ieee Group on Insulator Contamination publication "Application guide for insulators in a contaminated ment, IEEE Trans. Power Appar Syst, September/October 1979 Research on higher voltage levels has been conducted by several organizations: Electric Power Research Institute, Bonneville Power Administration, and others. The use of more than three phases for electric transmission has been studied intensively by sponsors such as the U.S. Department of Energy c 2000 by CRC Press LLC
© 2000 by CRC Press LLC about their use are still under study. Improvements in design and manufacture in recent years have made synthetic insulators increasingly attractive since the strength-to-weight ratio is significantly higher than that of porcelain and can result in reduced tower costs, especially on EHV and UHV transmission lines. NEMA Publication “High Voltage Insulator Standard” and AIEE Standard 41 have been combined in ANSI Standards C29.1 through C29.9. Standard C29.1 covers all electrical and mechanical tests for all types of insulators. The standards for the various insulators covering flashover voltages (wet, dry, and impulse; radio influence; leakage distance; standard dimensions; and mechanical-strength characteristics) are addressed. These standards should be consulted when specifying or purchasing insulators. The electrical strength of line insulation may be determined by power frequency, switching surge, or lightning performance requirements. At different line voltages, different parameters tend to dominate. Table 61.3 shows typical line insulation levels and the controlling parameter. Defining Term Surge impedance loading (SIL): The surge impedance of a transmission line is the characteristic impedance with resistance set to zero (resistance is assumed small compared to reactance). The power that flows in a lossless transmission line terminated in a resistive load equal to the line’s surge impedance is denoted as the surge impedance loading of the line. Related Topics 3.5 Three-Phase Circuits • 55.2 Dielectric Losses References Aluminum Electrical Conductor Handbook, 2nd ed., Aluminum Association, 1982. J. R. Carson, “Wave propagation in overhead wires with ground return,” Bell System Tech. J., vol. 5, pp. 539–554, 1926. M. S. Chen and W. E. Dillon, “Power system modeling,” Proc. IEEE, vol. 93, no. 7, pp. 901–915, 1974. E. Clarke, Circuit Analysis of A-C Power Systems, vols. 1 and 2, New York: Wiley, 1943. Electrical Transmission and Distribution Reference Book, Central Station Engineers of the Westinghouse Electric Corporation, East Pittsburgh, Pa. M. E. El-Hawary, Electric Power Systems: Design and Analysis, revised edition, Piscataway, N.J.: IEEE Press, 1995. Further Information Other recommended publications regarding EHV transmission lines include Transmission Line Reference Book, 345 kV and Above, 2nd ed., 1982, from Electric Power Research Institute, Palo Alto, Calif., and the IEEE Working Group on Insulator Contamination publication “Application guide for insulators in a contaminated environment,” IEEE Trans. Power Appar. Syst., September/October 1979. Research on higher voltage levels has been conducted by several organizations: Electric Power Research Institute, Bonneville Power Administration, and others. The use of more than three phases for electric power transmission has been studied intensively by sponsors such as the U.S. Department of Energy. TABLE 61.3 Typical Line Insulation Line Voltage, kV No. of Standard Disks Controlling Parameter (Typical) 115 7–9 Lightning or contamination 138 7–10 Lightning or contamination 230 11–12 Lightning or contamination 345 16–18 Lightning, switching surge, or contamination 500 24–26 Switching surge or contamination 765 30–37 Switching surge or contamination
61.2 Alternating Current Underground: Line Parameters, Models Standard Voltages. Cables Mo-Shing Chen and K.C. Lai Although the capital costs of an underground power cable are usually several times those of an overhead line ual capacity, installation of undergroun is continuously increasing for reasons of safety, security reliability, aesthetics, or availability of right-of-way. In heavily populated urban areas, underground cable ystems are mostly preferred. Two types of cables are commonly used at the transmission voltage level: pipe-type cables and self-contained oil-filled cables. The selection depends on voltage, power requirements, length, cost, and reliability. In the United States, over 90% of underground cables are pipe-type design. Cable parameters A general formulation of impedance and admittance of single-core coaxial and pipe-type cables was proposed by Prof. Akihiro Ametani of Doshisha University in Kyoto, Japan [Ametani, 1980]. The impedance and adm tance of a cable system are defined in the two matrix equations d(v) =-[Z]·(D) 61.13) d(D)=-y]·(V) 61.14) where(V)and(n) are vectors of the voltages and currents at a distance x along the cable and [z and [y are square matrices of the impedance and admittance. For a pipe-type cable, shown in Fig. 61.4, the impedance and admittance matrices can be written as Eqs. (61. 15)and(61. 16) by assuming: 1. The displacement currents and dielectric losses are negligible. 2. Each conducting medium of a cable has constant permeability. 3. The pipe thickness is greater than the penetration depth of the pipe wall. [Z=[Z]+[zp (61.15) [Y=jo[P]-1 (61.16) [P]=[P]+[P where [P] is a potential coefficient matrix. [Zl= single-core cable internal impedance matrix Za O 0] [Zil (61.17) [O][0 [ZI I impedance mat c 2000 by CRC Press LLC
© 2000 by CRC Press LLC 61.2 Alternating Current Underground: Line Parameters, Models, Standard Voltages, Cables Mo-Shing Chen and K.C. Lai Although the capital costs of an underground power cable are usually several times those of an overhead line of equal capacity, installation of underground cable is continuously increasing for reasons of safety, security, reliability, aesthetics, or availability of right-of-way. In heavily populated urban areas, underground cable systems are mostly preferred. Two types of cables are commonly used at the transmission voltage level: pipe-type cables and self-contained oil-filled cables. The selection depends on voltage, power requirements, length, cost, and reliability. In the United States, over 90% of underground cables are pipe-type design. Cable Parameters A general formulation of impedance and admittance of single-core coaxial and pipe-type cables was proposed by Prof. Akihiro Ametani of Doshisha University in Kyoto, Japan [Ametani, 1980]. The impedance and admittance of a cable system are defined in the two matrix equations (61.13) (61.14) where (V) and (I) are vectors of the voltages and currents at a distance x along the cable and [Z] and [Y] are square matrices of the impedance and admittance. For a pipe-type cable, shown in Fig. 61.4, the impedance and admittance matrices can be written as Eqs. (61.15) and (61.16) by assuming: 1. The displacement currents and dielectric losses are negligible. 2. Each conducting medium of a cable has constant permeability. 3. The pipe thickness is greater than the penetration depth of the pipe wall. [Z] = [Zi ] + [Zp] (61.15) [Y] = jw[P]–1 (61.16) [P] = [Pi ] + [Pp] where [P] is a potential coefficient matrix. [Zi ] = single-core cable internal impedance matrix (61.17) [Zp] = pipe internal impedance matrix d V dx Z I ( ) = × –[ ] ( ) d I dx Y V ( ) = × –[ ] ( ) = ××× ××× ××× È Î Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] Z Z Z i i in 1 2 0 0 0 0 0 0 M M O M
FIGuRE 61.4 A pipe-type cable system FIGURE 61.5 A single-core cable cross section. mll…pl (61.18) Lz21z1…zn The diagonal submatrix in [Z] expresses the self-impedance matrix of a single-core cable. When a single core cable consists of a core and sheath( Fig. 61.5), the self-impedance matrix is given by [Z= where Zssi= sheath self-impedance sheath-outt sheath/pipe-insulation (61.20) Zsi= mutual impedance between the core and sheath 'sheath-mutual (61.21) Zoi= core self-impedance (Zcore Zcorelsheath-insulation Zsheath-in )+ Z-Z 'sheath-mutu (61.2) where pm Io(mr) I1(m)
© 2000 by CRC Press LLC (61.18) The diagonal submatrix in [Zi ] expresses the self-impedance matrix of a single-core cable. When a singlecore cable consists of a core and sheath (Fig. 61.5), the self-impedance matrix is given by (61.19) where Zssj = sheath self-impedance = Zsheath-out + Zsheath/pipe-insulation (61.20) Zcsj = mutual impedance between the core and sheath = Zssj – Zsheath-mutual (61.21) Zccj = core self-impedance = (Zcore + Zcore/sheath-insulation + Zsheath-in) + Zcsj – Zsheath-mutual (61.22) where (61.23) (61.24) FIGURE 61.4 A pipe-type cable system. FIGURE 61.5 A single-core cable cross section. = ××× ××× ××× È Î Í Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ ˙ [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] Z Z Z Z Z Z Z Z Z p p p n p p p n p n p n pnn 11 12 1 12 22 2 1 2 M M O M [Z ] Z Z Z Z ij ccj csj csj ssj = È Î Í Í ˘ ˚ ˙ ˙ Z m r I mr I mr core = r 2p 1 0 1 1 1 ( ) ( ) Z j r r core/sheath-insulation = wm p 1 2 1 2 ln
sheath-in [o(mr2)K,(mr,)+ Ko(mr,)I(mr) (61.25) sheath-mutual (61.26) 2Tr,,D Lo(mr3)K,(mr,)+ Ko(mr)I(mr2) (61.27) joHo. cos -{+R-4 sheath/pipe-insulation (61.28) where p= resistivity of conductor, D=I(mr3)K,(mT2)-I(mr2)K,(mr3),Y= Eulers constant =1.7811, I modified Bessel function of the first kind of order K= modified Bessel function of the second kind of order jou/p= reciprocal of the complex depth of penetration A submatrix of [Zp] is given in the following form ZniI (61.29) Zpit in Eq(61.29)is the impedance between the jth and kth inner conductors with respect to the pipe inn surface. When j= k, Zpik= Zpipe-in otherwise Zpit is given in Eq (61.31) =pmkm)+y‖ Kn(mq) (61.30) 2πaK,(m q)nu, Kn(mq)-mqKn(mq) In 4+H Ko( mq) K(mq) (61.31) d k cos(nek) 2u nu, K, (mq)-mgkn(mg) n where q is the inside radius of the pipe(Fig. 61.4) The formulation of the potential coefficient matrix of a pipe-type cable is similar to the impedance matrix. 0][P2l 00:P c 2000 by CRC Press LLC
© 2000 by CRC Press LLC (61.25) (61.26) (61.27) (61.28) where r = resistivity of conductor, D = I1(mr3)K1(mr2) – I1(mr2)K1(mr3), g = Euler’s constant = 1.7811, Ii = modified Bessel function of the first kind of order i, Ki = modified Bessel function of the second kind of order i, and m = = reciprocal of the complex depth of penetration. A submatrix of [Zp] is given in the following form: (61.29) Zpjk in Eq. (61.29) is the impedance between the jth and kth inner conductors with respect to the pipe inner surface. When j = k, Zpjk = Zpipe-in; otherwise Zpjk is given in Eq. (61.31). (61.30) (61.31) where q is the inside radius of the pipe (Fig. 61.4). The formulation of the potential coefficient matrix of a pipe-type cable is similar to the impedance matrix. (61.32) Z m r D I mr K mr K mr I mr sheath-in = + r 2p 2 0 2 1 3 0 21 3 [ ( ) ( ) ( ) ( )] Z rrD sheath-mutual = r 2p 2 3 Z m r D I mr K mr K mr I mr sheath-out = + r 2p 3 0 3 1 2 0 31 2 [ ( ) ( ) ( ) ( )] Z j qRd qR i i i sheath/pipe-insulation = Ê + - Ë Á ˆ ¯ ˜ wm - p 0 1 2 22 2 2 cosh jw r m/ [ ] Z Z Z Z Z pjk pjk pjk pjk pjk = È Î Í Í ˘ ˚ ˙ ˙ Z m q K mq K mq j d q K mq n K mq mqK mq i n n n rn n pipe-in = + Ê Ë Á ˆ ¯ ˜ ¢ È Î Í Í ˘ ˚ ˙ ˙ = • Â r p wm 2 p m 0 1 2 1 ( ) ( ) ( ) ( )– ( ) Z j q S mq K mq K mq d d q n K mq n K mq mqK mq n pjk jk r j k n jk r n n rn n = + + Ê Ë Á ˆ ¯ ˜ ¢ È Î Í ˘ ˚ ˙ Ï Ì Ô Ô Ó Ô Ô ¸ ˝ Ô Ô ˛ Ô Ô = • Â wm p m q m m 0 0 1 2 1 2 2 1 ln ( ) ( ) cos( ) ( ) ( )– ( ) – [ ] [ ] [] [] [] [ ] [] [] [] [ ] P P P P i i i in = ××× ××× ××× È Î Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ 1 2 0 0 0 0 0 0 M MOM