Pu [ pul [P [Pp12][P2 IP [Pmn [Pp2nl The diagonal submatrix in[Pi expresses the potential coefficient matrix of a single-core cable. When a single core cable consists of a core and sheath(Fig. 61.5), the submatrix is given by IP I Pa Psi In 4 P In (61.36) Eo= absolute permittivity of free space, Es= relative permittivity of insulation outside sheath, and Eg= relative permittivity of insulation outside core. [Prik of [p,] is given by (61.37) Ppit in Eq(61. 37)is the potential coefficient between the jth and kth inner conductors with respect to the pipe inner surface. When j=k, Ppie= Ppipe-in otherwise Ppil is given in Eq (61.39) d EPO d dk cos(ne, Pik where E, is the relative permittivity of insulation inside the pipe; R; is the outer radius of cable i and d, d and
© 2000 by CRC Press LLC (61.33) The diagonal submatrix in [Pi ] expresses the potential coefficient matrix of a single-core cable. When a singlecore cable consists of a core and sheath (Fig. 61.5), the submatrix is given by (61.34) where (61.35) (61.36) e0 = absolute permittivity of free space, esj = relative permittivity of insulation outside sheath, and ecj = relative permittivity of insulation outside core. Submatrix [Ppjk] of [Pp] is given by (61.37) Ppjk in Eq. (61.37) is the potential coefficient between the jth and kth inner conductors with respect to the pipe inner surface. When j = k, Ppjk = Ppipe-in; otherwise Ppjk is given in Eq. (61.39). (61.38) (61.39) where ep is the relative permittivity of insulation inside the pipe; Ri is the outer radius of cable i; and di , dj , and dk are the inner radii of cables i, j, and k. [ ] [ ][ ] [ ] [ ][ ] [ ] [ ][ ] [ ] P PP P PP P PP P p p p pn p p pn p n p n pnn = ××× ××× ××× È Î Í Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ ˙ 11 12 1 12 22 2 1 2 M MOM [ ] P P P P P P ij cj sj sj sj sj = È + Î Í Í ˘ ˚ ˙ ˙ P r r sj sj = Ê Ë Á ˆ ¯ ˜ 1 2 0 4 3 pe e ln P r r cj cj = Ê Ë Á ˆ ¯ ˜ 1 2 0 2 1 pe e ln [ ] P P P P P pjk pjk pjk pjk pjk = È Î Í Í ˘ ˚ ˙ ˙ P q R d q i i p pipe-in = Ê Ë Á ˆ ¯ ˜ È Î Í Í ˘ ˚ ˙ ˙ Ï Ì Ô Ó Ô ¸ ˝ Ô ˛ Ô ln –1 2 2 pe e0 p q S d d q n n pjk p jk j k n jk n = Ê Ë Á ˆ ¯ ˜ × È Î Í Í Í ˘ ˚ ˙ ˙ ˙ = • Â 1 2 0 2 1 pe e q ln – cos( )
Models Refer to "Models" in Section 61.1 Standard Voltages In the United States, the underground transmission cables are rated 69 to 345 kv(refer to Table 61. 2 in Section 61. 1). Cables rated 550 kV are used commercially in Japan. In the United States, cables installed at the 550-kV level are used in relatively short distances, for example, at the grand Coulee Dam Cable standards The most universal standardizing authority for cables is the International Electrotechnical Commission(IEC) The IEC standards cater to a large variety of permissible options and serve mainly as a basis for the preparation of national standards. In the United States, in addition to national standards for materials and components, there are cable standards in widespread use by industry issued by four bodies: Underwriter's Laboratories (UL) Association of Edison Illuminating Companies(AEIC), and jointly by the Insulated Power Cables Engineers Association and the National Electrical Manufacturers Association(IPCEA/NEMA) Related Topic 55.5 Dielectric Materials References A. Ametani, "A general formulation of impedance and admittance of cables, IEEE Trans. Power Syst., vol. PAs- 9,no.3,Pp.902-910,1980 P. Graneau, Underground Power Transmission, New York: Wiley, 1979 D. McAllister, Electric Cables handbook. New York: granada Technical Books, 1982 B M. Weedy, Underground Transmission of Electric Power, New York: Wiley, 1980 Further Information The development of advanced cable systems is continuously supported by government and utilities. Information and reports regarding these activities are available from two principal funding agencies, the Electric Power Research Institute(EPRI)and the U.S. Department of Energy 61.3 High- Voltage direct- Current Transmission hallam The first commercial high-voltage direct-current(HVDC) power transmission system was commissioned in 1954, with an interconnection between the island of gotland and the swedish mainland. it was an undersea able, 96 km long, with ratings of 100 kV and 20 MW. There are now more than 50 systems operating throughout the world, and several more are in the planning, design, and construction stages. HVDC transmission has ecome acceptable as an economical and reliable method of power transmission and interconnection. It offers advantages over alternating current(ac) for long-distance power transmission and as asynchronous intercon- nection between two ac systems and offers the ability to precisely control the power flow without inadvertent loop flows in an interconnected ac system. Table 61.4 lists the hvDC projects to date(1995), their ratings, year commissioned (or the expected year of commissioning), and other details. The largest system in operation, Itaipu HVDC transmission, consists of two t600-kV, 3150-MW-rated bipoles, transmitting a total of 6300 Mw power from the Itaipu generating station to the Ibiuna(formerly Sao Roque) converter station in southeastern Brazil over a distance of 800 kn c 2000 by CRC Press LLC
© 2000 by CRC Press LLC Models Refer to “Models” in Section 61.1. Standard Voltages In the United States, the underground transmission cables are rated 69 to 345 kV (refer to Table 61.2 in Section 61.1). Cables rated 550 kV are used commercially in Japan. In the United States, cables installed at the 550-kV level are used in relatively short distances, for example, at the Grand Coulee Dam. Cable Standards The most universal standardizing authority for cables is the International Electrotechnical Commission (IEC). The IEC standards cater to a large variety of permissible options and serve mainly as a basis for the preparation of national standards. In the United States, in addition to national standards for materials and components, there are cable standards in widespread use by industry issued by four bodies: Underwriter’s Laboratories (UL), Association of Edison Illuminating Companies (AEIC), and jointly by the Insulated Power Cables Engineers Association and the National Electrical Manufacturers’ Association (IPCEA/NEMA). Related Topic 55.5 Dielectric Materials References A. Ametani, “A general formulation of impedance and admittance of cables,” IEEE Trans. Power Syst., vol. PAS- 99, no. 3, pp. 902–910, 1980. P. Graneau, Underground Power Transmission, New York: Wiley, 1979. D. McAllister, Electric Cables Handbook, New York: Granada Technical Books, 1982. B. M. Weedy, Underground Transmission of Electric Power, New York: Wiley, 1980. Further Information The development of advanced cable systems is continuously supported by government and utilities. Information and reports regarding these activities are available from two principal funding agencies, the Electric Power Research Institute (EPRI) and the U.S. Department of Energy. 61.3 High-Voltage Direct-Current Transmission Rao S. Thallam The first commercial high-voltage direct-current (HVDC) power transmission system was commissioned in 1954, with an interconnection between the island of Gotland and the Swedish mainland. It was an undersea cable, 96 km long,with ratings of 100 kV and 20 MW. There are now more than 50 systems operating throughout the world, and several more are in the planning, design, and construction stages. HVDC transmission has become acceptable as an economical and reliable method of power transmission and interconnection. It offers advantages over alternating current (ac) for long-distance power transmission and as asynchronous interconnection between two ac systems and offers the ability to precisely control the power flow without inadvertent loop flows in an interconnected ac system. Table 61.4 lists the HVDC projects to date (1995), their ratings, year commissioned (or the expected year of commissioning), and other details. The largest system in operation, Itaipu HVDC transmission, consists of two ±600-kV, 3150-MW-rated bipoles, transmitting a total of 6300 MW power from the Itaipu generating station to the Ibiuna (formerly Sao Roque) converter station in southeastern Brazil over a distance of 800 km
TABLE 61.4 HVDC Projects Data HVDC DC Volts, Line/Cable Suppliert Commissioned Rating, Mw Location Mercury Arc valves Moscow- kashira Gotland ia olgograd-Donbass' FAAFAAA 00000000 00005 Konti-Skan I Sakuma ardisia Pacific Intertie 0 1440 USA Nelson River I< Canada 1975 england Thyristor Valves oland Extension A B anada Skagerrak I 240 Norway- Denmark skagerrak II 240 Norway-Denmark skagerrak Ill orway.Denmark ouver II 2×125 B 3 Butte Cahora b Bassa 1978 1920 lozambique-S. Africa River ll 1978 900 800 C-U 3 1000 Hokkaido. Honshu DccJJAEEGFF 55 Acaray B-B Paraguay 551×170(±85)B- B Russia( tie with finland) 3×170 Duernrohr 1983 Austria oland ll 35 130 veden oland Ill ±150 40 B anada lannion B 1985 Pac Intertie Upgrade 1362 B 1985 B 200 Madawaska BBB anada 2 australia Intermountain 784 USA Thyristor Valves(continued c 2000 by CRC Press LLC
© 2000 by CRC Press LLC TABLE 61.4 HVDC Projects Data HVDC Year Power DC Volts, Line/Cable, Supplier† Commissioned Rating, MW kV km Location Mercury Arc Valves Moscow-Kashiraa F 1951 30 ±100 100 Russia Gotland Ia A 1954 20 ±100 96 Sweden English Channel A 1961 160 ±100 64 England-France Volgograd-Donbassb F 1965 720 ±400 470 Russia Inter-Island A 1965 600 ±250 609 New Zealand Konti-Skan I A 1965 250 250 180 Denmark-Sweden Sakuma A 1965 300 2125 B-Bf Japan Sardinia I 1967 200 200 413 Italy Vancouver I A 1968 312 260 69 Canada Pacific Intertie JV 1970 1440 ±400 1362 USA 1982 1600 Nelson River Ic I 1972 1620 ±450 892 Canada Kingsnorth I 1975 640 ±266 82 England Thyristor Valves Gotland Extension A 1970 30 ±150 96 Sweden Eel River C 1972 320 2 ¥ 80 B-B Canada Skagerrak I A 1976 250 250 240 Norway-Denmark Skagerrak II A 1977 500 ±250 240 Norway-Denmark Skagerrak III A 1993 440 ±350 240 Norway-Denmark Vancouver II C 1977 370 –280 77 Canada Shin-Shinano D 1977 300 2 ¥ 125 B-B Japan 1992 600 3 ¥ 125 Square Butte C 1977 500 ±250 749 USA David A. Hamil C 1977 100 50 B-B USA Cahora Bassa J 1978 1920 ±533 1360 Mozambique-S. Africa Nelson River II J 1978 900 ±250 930 Canada 1985 1800 ±500 C-U A 1979 1000 ±400 710 USA Hokkaido-Honshu E 1979 150 125 168 Japan E 1980 300 250 1993 600 ±250 Acaray G 1981 50 25.6 B-B Paraguay Vyborg F 1981 355 1 ¥ 170 (±85) B-B Russia (tie with Finland) F 1982 710 2 ¥ 170 1065 3 ¥ 170 Duernrohr J 1983 550 145 B-B Austria Gotland II A 1983 130 150 100 Sweden Gotland III A 1987 260 ±150 103 Sweden Eddy County C 1983 200 82 B-B USA Chateauguay J 1984 1000 2 ¥ 140 B-B Canada Oklaunion C 1984 200 82 B-B USA Itaipu A 1984 1575 ±300 785 Brazil A 1985 2383 A 1986 3150 ±600 A 1987 6300 2 ¥ ±600 Inga-Shaba A 1982 560 ±500 1700 Zaire Pac Intertie Upgrade A 1984 2000 ±500 1362 USA Blackwater B 1985 200 57 B-B USA Highgate A 1985 200 ±56 B-B USA Madawaska C 1985 350 140 B-B Canada Miles City C 1985 200 ±82 B-B USA Broken Hill A 1986 40 2 ¥ 17(±8.33) B-B Australia Intermountain A 1986 1920 ±500 784 USA Thyristor Valves (continued)
TABLE 61.4(continued) HVDC Projects Data HVDC DC Volts, Line/Cable Suppliert Commissioned Rating, Mw Location H france 72 England Canada- US H Urguaiana Freq Conv 0070 B-B Brazil (tie with Uruguay) Virginia Smith(Sidney) +G China Pac Intertie Expansion McNeill Fenno- Skan 00 Finland-Sweden Sileru- Barsoor Rihand- Delhi 750 1991 Quebec-New Eng 200 00 Canada-USA Etzenricht th Czech) Vienna South- East G Bm由 Hungary) DC Hybrid Link 992 New zealand 900 India -B India 440 Philippines Haenam-Cheju I 100 South Kore Baltic Cable Project Victoria-Tasmania Australia Kontek hvdc intercon Denmark Scotland-N. Ireland United Kingdon 1800 03 China -B India Thailand-Malaysia 110 Malaysia-Thailand River 70 B-B Urguay H-CGEE Alsthom: B-Brown boveri I-GEC(formerly Eng Elec ) -General Electric; J-HVDC W.G. (AEG, BBC, Siemens); -Toshi AB-ABB F-Russian; /V-Joint Venture(GE and aSEA) Retired from service b2 valve groups replaced with thyristors in 1977. 2 valve groups in Pole I replaced with thyristors by gEC in 1991 50-MW thyristor tap. Uprate with thyristor valves. I Back-to-back HVDC system. Multiterminal system. Largest terminal is rated 2250 MW Source: Data compiled by D J. Melvold, Los Angeles Department of Water and Power. c 2000 by CRC Press LLC
© 2000 by CRC Press LLC Cross-Channel Les Mandarins H 1986 2000 ±270 72 France Sellindge I 1986 2000 ±270 72 England Descantons-Comerford C 1986 690 ±450 172 Canada-USA SACOId H 1986 200 200 415 Corsica Island SACOIe 1992 300 Italy Urguaiana Freq. Conv. D 1987 53.7 17.9 B-B Brazil (tie with Uruguay) Virginia Smith (Sidney) G 1988 200 55.5 B-B USA Gezhouba-Shanghai B+G 1989 600 500 1000 China 1990 1200 ±500 Konti-Skan II A 1988 300 285 150 Sweden-Denmark Vindhyachal A 1989 500 2 ¥ 69.7 B-B India Pac Intertie Expansion B 1989 1100 ±500 1362 USA McNeill I 1989 150 42 B-B Canada Fenno-Skan A 1989 500 400 200 Finland-Sweden Sileru-Barsoor K 1989 100 +100 196 India 200 +200 400 ±200 Rihand-Delhi A 1991 750 +500 910 India 1991 1500 ±500 Hydro Quebec-New Eng. A 1990 2000g ±450 1500 Canada-USA Welch-Monticello 1995 300 B-B USA 1998 600 Etzenricht 1993 600 160 B-B Germany (tie with Czech) Vienna South-East G 1993 600 160 B-B Austria (tie with Hungary) DC Hybrid Link AB 1993 992 +270/–350 617 New Zealand Chandrapur-Padghe 1997 1500 ±500 900 India Chandrapur-Ramagundam 1996 1000 2 ¥ 205 B-B India Leyte-Luzun 1997 1000 350 440 Philippines Haenam-Cheju I 1997 300 ±180 100 South Korea Baltic Cable Project 1994 600 450 250 Sweden-Germany Victoria-Tasmania 1995 300 300 Australia Kontek HVDC Intercon 1995 600 600 Denmark Scotland-N. Ireland 1998 250 150 60 United Kingdom Greece-Italy 1998 500 Italy Tiang-Guang 1998 1800 500 903 China Visakhapatnam I 1998 500 205 B-B India Thailand-Malaysia 1998 300 300 110 Malaysia-Thailand Rivera 1998 70 B-B Urguay †A–ASEA; H–CGEE Alsthom; B–Brown Boveri; I–GEC (formerly Eng. Elec.); C–General Electric; J–HVDC W.G. (AEG, BBC, Siemens); D–Toshiba; K–(Independent); E–Hitachi; AB–ABB Brown Boveri; F–Russian; JV–Joint Venture (GE and ASEA). G–Siemens; a Retired from service. b 2 valve groups replaced with thyristors in 1977. c 2 valve groups in Pole 1 replaced with thyristors by GEC in 1991. d 50-MW thyristor tap. e Uprate with thyristor valves. f Back-to-back HVDC system. g Multiterminal system. Largest terminal is rated 2250 MW. Source: Data compiled by D. J. Melvold, Los Angeles Department of Water and Power. TABLE 61.4 (continued) HVDC Projects Data HVDC Year Power DC Volts, Line/Cable, Supplier† Commissioned Rating, MW kV km Location
000 SYSTEM 丰圈丰 SYSTEM FIGURE 61.6 Back-to-back dc system. SYSTEM SYSTEM FIGURE 61.7 Bipolar dc system Configurations of DC Transmission HVDC transmission systems can be classified into three categories Back-to-back systems 2. Two-terminal, or point-to-point, systems 3. Multiterminal systems These will be briefly described here Back-to-Back DC System a back-to-back dc system(Fig. 61.6), both rectifier and inverter are located in the same station, usually in the same building. The rectifier and inverter are usually tied with a reactor, which is generally of outdoor, air- core design. A back-to-back dc system is used to tie two asynchronous ac systems(systems that are not in synchronism). The two ac systems can be of different operating frequencies, for example, one 50 Hz and the other 60 Hz. Examples are the Sakuma and Shin-Shinano converter stations in Japan. Both are used to link the 0-and 60-Hz ac systems. The Acaray station in Paraguay links the Paraguay system(50 Hz)with the Brazilian system, which is 60 Hz. Back-to-back dc links are also used to interconnect two ac systems that are of the same frequency but are not operating in synchronism. In North America, eastern and western systems are not synchronized, and Quebec and Texas are not synchronized with their neighboring systems. a dc link offers a practical solution as a tie between nonsynchronous systems. Thus to date, there are 10 back-to-back dc links in operation interconnecting such systems in North America. Similarly, in Europe, eastern and western systems are not synchronized, and dc offers the practical choice for interconnection between ther TwO- Terminal or Point-to- Point, DC Transmission Two-terminal dc systems can be either bipolar or monopolar Bipolar configuration, shown in Fig. 61.7, is the ommonly used arrangement for systems with overhead lines. In this system, there will be two conductors, one for each polarity (positive and negative)carrying nearly equal currents. Only the difference of these currents, which is usually small, flows through ground return. c 2000 by CRC Press LLC
© 2000 by CRC Press LLC Configurations of DC Transmission HVDC transmission systems can be classified into three categories: 1. Back-to-back systems 2. Two-terminal, or point-to-point, systems 3. Multiterminal systems These will be briefly described here. Back-to-Back DC System In a back-to-back dc system (Fig. 61.6), both rectifier and inverter are located in the same station, usually in the same building. The rectifier and inverter are usually tied with a reactor, which is generally of outdoor, aircore design. A back-to-back dc system is used to tie two asynchronous ac systems (systems that are not in synchronism). The two ac systems can be of different operating frequencies, for example, one 50 Hz and the other 60 Hz. Examples are the Sakuma and Shin-Shinano converter stations in Japan. Both are used to link the 50- and 60-Hz ac systems. The Acaray station in Paraguay links the Paraguay system (50 Hz) with the Brazilian system, which is 60 Hz. Back-to-back dc links are also used to interconnect two ac systems that are of the same frequency but are not operating in synchronism. In North America, eastern and western systems are not synchronized, and Quebec and Texas are not synchronized with their neighboring systems. A dc link offers a practical solution as a tie between nonsynchronous systems. Thus to date, there are 10 back-to-back dc links in operation interconnecting such systems in North America. Similarly, in Europe, eastern and western systems are not synchronized, and dc offers the practical choice for interconnection between them. Two-Terminal, or Point-to-Point, DC Transmission Two-terminal dc systems can be either bipolar or monopolar. Bipolar configuration, shown in Fig. 61.7, is the commonly used arrangement for systems with overhead lines. In this system, there will be two conductors, one for each polarity (positive and negative) carrying nearly equal currents. Only the difference of these currents, which is usually small, flows through ground return. FIGURE 61.6 Back-to-back dc system. FIGURE 61.7 Bipolar dc system