电子工程师手册（英文版四）：ch061

Chen, M.S., Lai, K.C., Thallam, R.S., El-Hawary, M.E., Gross, C., Phadke, A.G., Gungor, R.B., Glover, J.D. “Transmission” The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000 61 Transmission 61.1 Alternating Current Overhead: Line Parameters, Models, Standard Voltages, Insulators Line Parameters?Models?Standard Voltages?Insulators 61.2 Alternating Current Underground: Line Parameters, Models, Standard Voltages, Cables Cable Parameters?Models?Standard Voltages?Cable Standards 61.3 High-Voltage Direct-Current Transmission Configurations of DCTransmission?Economic Comparison of AC and DC Transmission?Principles of Converter Operation?Converter Control?Developments 61.4 Compensation Series Capacitors?Synchronous Compensators?Shunt Capacitors?Shunt Reactors?Static VAR Compensators (SVC) 61.5 Fault Analysis in Power Systems Simplifications in the System Model?The Four Basic Fault Types?An Example Fault Study?Further Considerations 61.6 Protection Fundamental Principles of Protection?Overcurrent Protection?Distance Protection?Pilot Protection?Computer Relaying 61.7 Transient Operation of Power Systems Stable Operation of Power Systems 61.8 Planning Planning Tools ? Basic Planning Principles ? Equipment Ratings ? Planning Criteria ? Value-Based Transmission Planning 61.1 Alternating Current Overhead: Line Parameters, Models, Standard Voltages, Insulators Mo-Shing Chen The most common element of a three-phase power system is the overhead transmission line. The interconnec- tion of these elements forms the major part of the power system network. The basic overhead transmission lines consist of a group of phase conductors that transmit the electrical energy, the earth return, and usually one or more neutral conductors (Fig. 61.1). Line Parameters The transmission line parameters can be divided into two parts: series impedance and shunt admittance. Since these values are subject to installation and utilization, e.g., operation frequency and distance between cables, the manufacturers are often unable to provide these data. The most accurate values are obtained through measuring in the field, but it has been done only occasionally. Mo-Shing Chen University of Texas at Arlington K.C. Lai University of Texas at Arlington Rao S. Thallam Salt River Project, Phoenix Mohamed E. El-Hawary Technical University of Nova Scotia Charles Gross Auburn University Arun G. Phadke Virginia Polytechnic Institute and State University R.B. Gungor University of South Alabama J. Duncan Glover FaAAElectrical Corporation ? 2000 by CRC Press LLC Though the symmetrical component method has been used to simplify many of the problems in power system analysis, the following paragraphs, which describe the formulas in the calculation of the line parameters, are much more general and are not limited to the application of symmetrical components. The sequence impedances and admittances used in the symmetrical components method can be easily calculated by a matrix transformation [Chen and Dillon, 1974]. A detailed discussion of symmetrical components can be found in Clarke [1943]. Series Impedance The network equation of a three-phase transmission line with one neutral wire (as given in Fig. 61.1) in which only series impedances are considered is given as follows: (61.1) where Z ii–g = self-impedance of phase i conductor and Z ij–g = mutual impedance between phase i conductor and phase j conductor. The subscript g indicates a ground return. Formulas for calculating Z ii–g and Z ij–g were developed by J. R. Carson based on an earth of uniform conductivity and semi-infinite in extent [Carson, 1926]. For two con- ductors a and b with earth return, as shown in Fig. 61.2, the self- and mutual impedances in ohms per mile are (61.2) (61.3) where the “prime” is used to indicate distributed parameters in per-unit length; z a = r c + jx i = conductor a internal impedance, W/mi; h a = height of conductor a, ft; r a = radius of conductor a, ft; d ab = distance between conductors a and b, ft; S ab = distance from one conductor to image of other, ft; w = 2pf; f = frequency, cycles/s; m 0 = the magnetic permeability of free space, m 0 = 4p ′ 10 –7 ′ 1609.34 H/mi; and p, q are the correction terms for earth return effect and are given later. The conductor internal impedance consists of the effective resistance and the internal reactance. The effective resistance is affected by three factors: temperature, frequency, and current density. In coping with the temper- ature effect on the resistance, a correction can be applied. FIGURE 61.1 A three-phase transmission line with one neutral wire. FIGURE 61.2 Geometric diagram of conductors a and b. V V V V ZZZZ ZZZZ ZZZZ ZZZZ I I I I A B C N aag abg acg ang bag bbg bcg bng cag cbg c g cng nag nbg ncg nng a b c n é ? ê ê ê ê ù ? ú ú ú ú = é ? ê ê ê ê ê ù ? ú ú ú ú ú é ? ê ê ê ê ù ? ú –––– –––– –––– –––– ú ú ú + é ? ê ê ê ê ù ? ú ú ú ú V V V V a b c n ￠ =+ + +Zzj h r pjq aag a a a – ln ( )w m p w m p 00 2 2 ￠ =++Zj S d pjq abg ab ab – ln ( )w m p w m p 00 2 ? 2000 by CRC Press LLC R new = R 20° [1 + a (T new – 20)] (61.4) where R new = resistance at new temperature, T new = new temperature in °C, R 20° = resistance at 20°C (Table 61.1), and a = temperature coefficient of resistance (Table 61.1). An increase in frequency causes nonuniform current density. This phenomenon is called skin effect. Skin effect increases the effective ac resistance of a conductor and decreases its internal inductance. The internal impedance of a solid round conductor in ohms per meter considering the skin effect is calculated by (61.5) where r = resistivity of conductor, W · m; r = radius of conductor, m; I 0 = modified Bessel function of the first kind of order 0; I 1 = modified Bessel function of the first kind of order 1; and = reciprocal of complex depth of penetration. The ratios of effective ac resistance to dc resistance for commonly used conductors are given in many handbooks [such as Electrical Transmission and Distribution Reference Book and Aluminum Electrical Conductor Handbook]. A simplified formula is also given in Clarke [1943]. p and q are the correction terms for earth return effect. For perfectly conducting ground, they are zero. The determination of p and q requires the evaluation of an infinite integral. Since the series converge fast at power frequency or less, they can be calculated by the following equations: (61.6) (61.7) with TABLE 61.1 Electrical Properties of Metals Used in Transmission Lines Relative Electrical Temperature Conductivity Resistivity at Coefficient of Metal (Copper = 100) 20°C, W · m (10 –8 ) Resistance (per °C) Copper (HC, annealed) 100 1.724 0.0039 Copper (HC, hard-drawn) 97 1.777 0.0039 Aluminum (EC grade, 1/2 H-H) 61 2.826 0.0040 Mild steel 12 13.80 0.0045 Lead 8 21.4 0.0040 z m r Imr Imr = r p2 0 1 () () mj=mwr/ pk k k kk =++ ? è ? ? ? ÷ + é ? ê ù ? ú + p qqq qp q 8 1 32 16 06728 2 22 3 452 4 1536 2 34 – cos . ln cos sin cos – cos q k k kk k k =- + + - + -+ ? è ? ? ? ÷ + é ? ê ù ? ú 00386 1 2 2 1 32 2 64 3 452 384 2 10895 4 4 23 4 . cos cos cos . cos sin ln ln q pq q qqq kD f =′8565 10 4 . – r ? 2000 by CRC Press LLC where D= 2h i (ft), q = 0, for self-impedance; D = S ij (ft), for mutual impedance (see Fig. 61.2 for q); and r = earth resistivity, W/m 3 . Shunt Admittance The shunt admittance consists of the conductance and the capacitive susceptance. The conductance of a transmission line is usually very small and is neglected in steady-state studies. A capacitance matrix related to phase voltages and charges of a three-phase transmission line is (61.8) The capacitance matrix can be calculated by inverting a potential coefficient matrix. Qabc = Pabc –1 · Vabc or Vabc = Pabc · Qabc or (61.9) (61.10) (61.11) where d ij = distance between conductors i and j, h i = height of conductor i, S ij = distance from one conductor to the image of the other, r i = radius of conductor i, e = permittivity of the medium surrounding the conductor, and l = length of conductor. Though most of the overhead lines are bare conductors, aerial cables may consist of cable with shielding tape or sheath. For a single-core conductor with its sheath grounded, the capacitance C ii in per-unit length can be easily calculated by Eq. (61.12), and all C ij ’s are equal to zero. (61.12) where e 0 = absolute permittivity (dielectric constant of free space), e r = relative permittivity of cable insulation, r 1 = outside radius of conductor core, and r 2 = inside radius of conductor sheath. Models In steady-state problems, three-phase transmission lines are represented by lumped-p equivalent networks, series resistances and inductances between buses are lumped in the middle, and shunt capacitances of the Qabc Cabc Vabc Q Q Q CCC CCC CCC V V V a b c aa ab ac ba bb bc ca cb cc a b c =× é ? ê ê ê ù ? ú ú ú = é ? ê ê ê ù ? ú ú ú é ? ê ê ê ù ? ú ú ú or –– –– –– V V V PPP PPP PPP Q Q Q a b c aa ab ac ba bb bc ca cb cc a b c é ? ê ê ê ù ? ú ú ú = é ? ê ê ê ù ? ú ú ú é ? ê ê ê ù ? ú ú ú P lh r ii i i = 2 2 pe ln P l S d ij ij ij = 2pe ln C rr r = 2 0 21 pe e ln /() ? 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 power- 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 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 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 as long-rod or post types. Use of synthetic insulators on transmission lines is relatively recent, and a few questions FIGURE 61.3Generalized conductor model. TABLE 61.2Standard 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 ? 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 environ- 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 power transmission has been studied intensively by sponsors such as the U.S. Department of Energy. TABLE 61.3Typical 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 ? 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 admit- tance 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] = [Z i ] + [Z p ] (61.15) [Y] = jw[P] –1 (61.16) [P] = [P i ] + [P p ] where [P] is a potential coefficient matrix. [Z i ] = single-core cable internal impedance matrix (61.17) [Z p ] = pipe internal impedance matrix dV dx ZI () –[]()=× dI dx YV () –[]()=× = ××× ××× ××× é ? ê ê ê ê ù ? ú ú ú ú [][] [] [][] [] [] [] [] Z Z Z i i in 1 2 00 00 00 MMOM ? 2000 by CRC Press LLC (61.18) The diagonal submatrix in [Z i ] 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 (61.19) where Z ssj = sheath self-impedance = Z sheath-out + Z sheath/pipe-insulation (61.20) Z csj = mutual impedance between the core and sheath = Z ssj – Z sheath-mutual (61.21) Z ccj = core self-impedance = (Z core + Z core/sheath-insulation + Z sheath-in ) + Z csj – Z sheath-mutual (61.22) where (61.23) (61.24) FIGURE 61.4A pipe-type cable system. FIGURE 61.5A single-core cable cross section. = ××× ××× ××× é ? ê ê ê ê ê ù ? ú ú ú ú ú [][] [] [][][] [][] [] ZZ Z ZZ Z ZZ Z pp pn pp pn pn pn pnn 11 12 1 12 22 2 12 MMOM []Z ZZ ZZ ij ccj csj csj ssj = é ? ê ê ù ? ú ú Z m r Imr Imr core = r p2 1 01 11 () () Z jr r core/sheath-insulation = wm p 12 1 2 ln ? 2000 by CRC Press LLC (61.25) (61.26) (61.27) (61.28) where r = resistivity of conductor, D = I 1 (mr 3 )K 1 (mr 2 ) – I 1 (mr 2 )K 1 (mr 3 ), g = Euler’s constant = 1.7811, I i = modified Bessel function of the first kind of order i, K i = modified Bessel function of the second kind of order i, and m = = reciprocal of the complex depth of penetration. A submatrix of [Z p ] is given in the following form: (61.29) Z pjk in Eq. (61.29) is the impedance between the jth and kth inner conductors with respect to the pipe inner surface. When j = k, Z pjk = Z pipe-in ; otherwise Z pjk 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 rD ImrKmr KmrImr sheath-in =+ r p2 2 0213 0213 [( ) ( ) ( )( )] Z rrD sheath-mutual = r p2 23 Z m rD ImrKmr KmrImr sheath-out =+ r p2 3 0312 0312 [( ) ( ) ( )( )] Z jqRd qR ii i sheath/pipe-insulation = +- ? è ? ? ? ÷ - wm p 0 1 222 22 cosh jwrm/ []Z ZZ ZZ pjk pjk pjk pjk pjk = é ? ê ê ù ? ú ú Z m q Kmq Kmq jd q Kmq n K mq mqK mq i n n rn nn pipe-in =+ ? è ? ? ? ÷ ￠ é ? ê ê ù ? ú ú = ￥ ? r p wm pm2 0 1 2 1 () () () ()– () Z j q Smq Kmq Kmq dd q n Kmq n K mq mqK mq n pjk jk r jk n jk r n rn nn = + + ? è ? ? ? ÷ ￠ é ? ê ù ? ú ì í ? ? ? ? ? ü y ? ? t ? ? = ￥ ? wm p m qm m 0 0 1 2 1 2 2 1 ln () () cos( ) () ()– () – [] [ ] [] [] [] [ ] [] [] [] [ ] P P P P i i i in = ××× ××× ××× é ? ê ê ê ê ù ? ú ú ú ú 1 2 00 00 MMOM ? 2000 by CRC Press LLC (61.33) The diagonal submatrix in [P i ] 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 (61.34) where (61.35) (61.36) e 0 = absolute permittivity of free space, e sj = relative permittivity of insulation outside sheath, and e cj = relative permittivity of insulation outside core. Submatrix [P pjk ] of [P p ] is given by (61.37) P pjk 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, P pjk = P pipe-in ; otherwise P pjk is given in Eq. (61.39). (61.38) (61.39) where e p is the relative permittivity of insulation inside the pipe; R i is the outer radius of cable i; and d i , d j , and d k are the inner radii of cables i, j, and k. [] [][] [] [][] [] [][ ] [ ] P PP P PP P PP P p pp pn pp pn p n p n pnn = ××× ××× ××× é ? ê ê ê ê ê ù ? ú ú ú ú ú 11 12 1 12 22 2 12 MMOM []P PP P P P ij cj sj sj sj sj = + é ? ê ê ù ? ú ú P r r sj sj = ? è ? ? ? ÷ 1 2 0 4 3 pe e ln P r r cj cj = ? è ? ? ? ÷ 1 2 0 2 1 pe e ln []P P P P P pjk pjk pjk pjk pjk = é ? ê ê ù ? ú ú P q R d q i i p pipe-in = ? è ? ? ? ÷ é ? ê ê ù ? ú ú ì í ? ? ? ü y ? t ? ln –1 2 2 0 pe e p q S dd q n n pjk pjk jk n jk n = ? è ? ? ? ÷ × é ? ê ê ê ù ? ú ú ú = ￥ ? 1 2 0 2 1 pe e q ln – cos( ) ? 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 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 ±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. ? 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-Kashira a F 1951 30 ±100 100 Russia Gotland I a A 1954 20 ±100 96 Sweden English Channel A 1961 160 ±100 64 England-France Volgograd-Donbass b 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-B f 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 I c 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) ? 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 SACOI d H 1986 200 200 415 Corsica Island SACOI e 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 2000 g ±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 ? 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, 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 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 61.6Back-to-back dc system. FIGURE 61.7Bipolar dc system. ? 2000 by CRC Press LLC A monopolar system will have one conductor, either positive or negative polarity with current returning through either ground or another metallic return conductor. The monopolar ground return current configu- ration, shown in Fig. 61.8, has been used for undersea cable systems, where current returns through the sea. This configuration can also be used for short-term emergency operation for a two-terminal dc line system in the event of a pole outage. However, concerns for corrosion of underground metallic structures and interference with telephone and other utilities will restrict the duration of such operation. The total ampere-hour operation per year is usually the restricting criterion. In a monopolar metallic return system, shown in Fig. 61.9, return current flows through a conductor, thus avoiding problems associated with ground return current. This method is generally used as a contingency mode of operation for a normal bipolar transmission system in the event of a partial converter (one-pole equipment) outage. In the case of outage of a one-pole converter, the conductor of the affected pole will be used as the returning conductor. A metallic return transfer breaker will be opened, diverting the return current from the ground path and into the pole conductor. This conductor will be grounded at one end and will be insulated at the other end. This system can transmit half the power of the normal bipolar system capacity (and can be increased if overload capacity is available). However, the line losses will be doubled compared to the normal bipolar operation for the same power transmitted. Multiterminal DC Systems There are two basic configurations in which the dc systems can be operated as multiterminal systems: 1.Parallel configuration 2.Series configuration Parallel configuration can be either radial-connected [Fig. 61.10(a)] or mesh-connected [Fig. 61.10(b)]. In a parallel-connected multiterminal dc system, all converters operate at the same nominal dc voltage, similar to ac system interconnections. In this operation, one converter determines the operating voltage, and all other terminals operate in a current-controlling mode. FIGURE 61.8Monopolar ground return dc system. FIGURE 61.9Monopolar metallic return dc system. ? 2000 by CRC Press LLC In a series-connected multiterminal dc system (Fig. 61.11), all converters operate at the same current. One converter sets the current that will be common to all converters in the system. Except for the converter that sets the current, the remaining converters operate in voltage control mode (constant firing angle or constant extinction angle). The converters operate almost independently without requirement for high-speed commu- nication between them. The power output of a non-current-controlling converter is varied by varying its voltage. At all times, the sum of the voltages across the rectifier stations must be larger than the sum of voltages across the inverter stations. Disadvantages of a series-connected system are (1) reduced efficiency because full line insulation is not used at all times and (2) operation at higher firing angles will lead to high converter losses and higher reactive power requirements from the ac system. There are now two truly multiterminal dc systems in operation. The Sardinia–Corsica–Italy three-terminal dc system was originally commissioned as a two-terminal (Sardinia–Italy) system in 1967 with a 200-MW rating. In 1986, the Corsica tap was added and the system was upgraded to a 300-MW rating. The two-terminal Hydro Quebec–New England HVDC interconnection (commissioned in 1985) was extended to a five-terminal system and commissioned in 1990 (see Table 61.4). The largest terminal of this system at Radisson station in Quebec is rated at 2250 MW. Two more systems, the Nelson River system in Canada and the Pacific NW-SW Intertie in the United States, also operate as multiterminal systems. Each of these systems has two converters at each end of the line, but the converters at each end are constrained to operate in the same mode, either rectifier or inverter. FIGURE 61.10(a) Parallel-connected radial MTDC system; (b) parallel-connected mesh-type MTDC system. FIGURE 61.11Series-connected MTDC system. ? 2000 by CRC Press LLC Economic Comparison of AC and DC Transmission In cases where HVDC is selected on technical consider- ations, it may be the only practical option, as in the case of an asynchronous interconnection. However, for long-dis- tance power transmission, where both ac and HVDC are practical, the final decision is dependent on total costs of each alternative. Total cost of a transmission system includes the line costs (conductors, insulators, and towers) plus the right-of-way (R-o-W) costs. A dc line with two conductors can carry almost the same amount of power as the three- phase ac line with the same size of line conductors. How- ever, dc towers with only two conductors are simpler and cheaper than three-phase ac towers. Hence the per-mile costs of line and R-o-W will be lower for a dc line. Power losses in the dc line are also lower than for ac for the same power transmitted. However, the HVDC system requires converters at the two ends of the line; hence the terminal costs for dc are higher than for ac. Variation of total costs for ac and dc as a function of line length are shown in Fig. 61.12. There is a break-even distance above which the total costs of dc option will be lower than the ac transmission option. This is in the range of 500 to 800 km for overhead lines but much shorter for cables. It is between 20 and 50 km for submarine cables and twice as far for underground cables. Principles of Converter Operation Converter Circuit Since the generation and most of the transmission and utilization is alternating current, HVDC transmission requires conversion from ac to dc (called rectification) at the sending end and conversion back from dc to ac (called inversion) at the receiving end. In HVDC transmission, the basic device used for conversion from ac to dc and from dc to ac is a three-phase full-wave bridge converter, which is also known as a Graetz circuit. This is a three-phase six-pulse converter. A three-phase twelve-pulse converter will be composed of two three- phase six-pulse converters, supplied with voltages differing in phase by 30 degrees (Fig. 61.13). The phase difference of 30 degrees is obtained by supplying one six-pulse bridge with a Y/Y transformer and the other by Y/D transformer. Relationships between AC and DC Quantities Voltages and currents on ac and dc sides of the converter are related and are functions of several converter parameters including the converter transformer. The following equations are provided here for easy reference. Detailed derivations are given in Kimbark [1971]. E LL = rms line-to-line voltage of the converter ac bus I 1 = rms value of fundamental frequency component of the converter ac current h= harmonic number a= valve firing delay angle (from the instant the valve voltage is positive) u= overlap angle (also called commutation angle) f= phase angle between voltage and current cos f= displacement power factor V d0 = ideal no-load dc voltage (at a = 0 and u = 0) L c = commutating circuit inductance b= 180 – a = angle of advance for inverter g= 180 – (a + u) = margin angle for inverter FIGURE 61.12 Transmission cost as function of line length. ? 2000 by CRC Press LLC with a = 0, u = 0, (61.40) With a > 0, and u = 0 V d = V d0 cos a (61.41) Theoretically a can vary from 0 to 180 degrees (with u = 0); hence V d can vary from +V d0 to –V d0 . Since the valves conduct current in only one direction, variation of dc voltage from V d0 to –V d0 means reversal of power flow direction and the converter mode of operation changing from rectifier to inverter. (61.42) (61.43) With a > 0 and 0 < u > 60°, (61.44) (61.45) FIGURE 61.13 Basic circuit of a 12-pulse HVDC converter. VEE dLLL0 32 135== p . II I dd1 6 078== p . cos cosfa== V V d d 0 VV u dd = ++ 0 2 cos cos( )aa VE u dLL = ++32 2p aacos cos( ) ? 2000 by CRC Press LLC (61.46) The error in Eq. (61.46) is only 4.3% at u = 60 degrees (maximum overlap angle for normal steady-state operation), and it will be even lower (1.1%) for most practical cases when u is 30 degrees or less. It can be seen from Eqs. (61.45) and (61.46) that the ratio between ac and dc currents is almost fixed, but the ratio between ac and dc voltages varies as a function of a and u. Hence the HVDC converter can be viewed as a variable- ratio voltage transformer, with almost fixed current ratio. P dc = V d I d (61.47) P ac = ?–3E LL I 1 cos f (61.48) Substituting for V d and I d in (61.47) and comparing with (61.48), (61.49) From Eqs. (61.44) and (61.49), (61.50) From Eqs. (61.40), (61.44), and (61.49), V d ? 1.35E LL cos f (61.51) AC Current Harmonics The HVDC converter is a harmonic current source on the ac side. Fourier analysis of an ac current waveform, shown in Fig. 61.14, shows that it contains the fundamental and harmonics of the order 5, 7, 11, 13, 17, 19, etc. The current for zero degree overlap angle can be expressed as (61.52) and (61.53) where I 10 and I h0 are the fundamental and harmonic currents, respectively, at a = 0 and u = 0. Equation (61.53) indicates that the magnitudes of harmonics are inversely proportional to their order. Converter ac current waveform i a￠ for phase a with a Y/D transformer is also shown in Fig. 61.14. Fourier analysis of this current shows that the fundamental and harmonic components will have the same magnitude II d1 6 ? p cos cos cos( ) f aa ? ++u 2 cosf? V V d d0 it I ttt tt d () cos – cos cos – cos cos = + + +××× ? è ? ? ? ? ? ÷ ÷ ÷ 23 1 5 5 1 7 7 1 11 11 1 13 13 p www ww I I h h0 10 = ? 2000 by CRC Press LLC as in the case of the Y/Y transformer. However, harmonics of order 5, 7, 17, 19, etc. are in phase opposition, whereas harmonics of order 11, 13, 23, 25, etc. are in phase with the Y/Y transformer case. Hence harmonics of order 5, 7, 17, 19, etc. will be canceled in a 12-pulse converter and do not appear in the ac system. In practice they will not be canceled completely because of imbalances in converter and transformer parameters. Effect of Overlap. The effect of overlap due to commutation angle is to decrease the amplitude of harmonics from the case with zero overlap. Magnitudes of harmonics for a general case with finite firing angle (a) and overlap angle (u ) are given by (61.54) where Noncharacteristic Harmonics. In addition to the harmonics described above, converters also generate other harmonics due to “nonideal” conditions of converter operation. Examples of the nonideal conditions are converter ac bus voltage imbalance, perturbation of valve firing pulses, distortion of ac bus voltages, and unbalanced converter transformer impedances. Harmonics generated due to these causes are called nonchar- acteristic harmonics. These are usually smaller in magnitude compared to characteristic harmonics but can create problems if resonances exist in the ac system at these frequencies. In several instances additional filters were installed at the converter ac bus to reduce levels of these harmonics flowing into the ac system. FIGURE 61.14 AC line current waveforms, i a , i b , i c with Y/Y transformer and i a￠ with Y/D transformer. I Ix A B AB u h h 0 22 12 1 22=+ + [] – cos( )a / A h u h B h u h xu = + + = =+ sin( ) sin( – ) – cos – cos( ) 1 2 1 1 2 1 aa ? 2000 by CRC Press LLC Converter Control The static characteristic of a HVDC converter is shown in Fig. 61.15. There are three distinct features of this characteristic. Constant Firing Angle Characteristic (A–B). If the converter is operating under constant firing angle control, the converter characteristic can be described by the equation (61.55) When the ordered current is too high for the converter to deliver, it will operate at the minimum firing angle (usually 5 degrees). Then the current will be determined by the voltage V d and the load. This is also referred to as the natural voltage characteristic. The converter in this mode is equivalent to a dc voltage source with internal resistance R c , where (61.56) Constant Current Control.This is the usual mode of operation of the rectifier. When the converter is operating in constant current control mode, the firing angle is adjusted to maintain dc current at the ordered value. If the load current goes higher than the ordered current for any reason, control increases the firing angle to reduce dc voltage and the converter operation moves in the direction from B to C. At point C, the firing angle reaches 90 degrees (neglecting overlap angle), the voltage changes polarity, and the converter becomes an inverter. From C to D, the converter works as an inverter. Constant Extinction Angle Control. At point D, the inverter firing angle has increased to a point where further increase can cause commutation failure. The inverter for its safe operation must be operated with sufficient angle of advance b, such that under all operating conditions the extinction angle g is greater than the valve deionization angle. The deionization angle is defined as the time in electrical degrees from the instant current reaches zero in a particular valve to the time the valve can withstand the application of positive voltage. FIGURE 61.15HVDC converter static characteristic. VV L I dd c d = 0 3 cos –a w p R L c c = 3w p ? 2000 by CRC Press LLC Typical minimum values of g are 15 to 20 degrees for mercury arc valves and slightly less for thyristor valves. During the range D to E, the increase of load current increases the overlap angle, which reduces the dc voltage. This is the negative resistance characteristic of the inverter. The functional requirements for HVDC converter control are: 1.Minimize the generation of noncharacteristic harmonics. 2.Safe inverter operation with fewest possible commutation failures even with distorted ac voltages. 3.Lowest possible consumption of reactive power. This requires operation with smallest possible delay angle a and extinction angle g without increased risk of commutation failures. 4.Smooth transition from current control to extinction angle control. 5.Sufficient stability margins and response time when the ratio of the ac system short-circuit strength and the rated dc power (short-circuit ratio) is low. Individual Phase Control In the early HVDC systems individual phase control systems were used. The firing angle of each valve is calculated individually and operated either as constant a or constant g control. A schematic of the individual phase control system is shown in Fig. 61.16. Six timing voltages are derived from the ac bus voltage, and the six grid pulses are generated at nominally identical delay times subsequent to the respective voltage-zero crossings. The delays are produced by independent delay circuits and controlled by a common direct voltage V c , which is derived through a feedback loop to control constant dc line current or constant power. Several variations of this control were used until the late 1960s. Disadvantages of Individual Phase Control. With distorted ac bus voltages, the firing pulses will be unequally spaced, thus generating noncharacteristic harmonics in ac current. This in turn will further distort the ac bus voltage. This process could lead to harmonic instability, particularly with ac systems of low short-circuit capacity (high-impedance system). Control system filters were tried to solve this problem. However, the filters could increase the potential for commutation failures and also reduce the speed of control system response for faults or disturbances in the ac system. Equal Pulse Spacing Control A control system based on the principle of equal spacing of firing pulses at intervals of 60 degrees (electrical) independent of ac bus voltages was developed in the late 1960s. The basic components of this system, shown in Fig. 61.17, consist of a voltage-controlled oscillator and ring counter. The frequency of the oscillator is directly proportional to the dc control voltage V c . Under steady-state conditions, pulse frequency is precisely 6f, where f is the ac system frequency. The phase of each grid pulse will have some arbitrary value relative to the ac bus voltage. If the three-phase ac bus voltages are symmetrical sine waves with no distortion, then a is the same for all valves. The oscillator will be phase-locked with the ac system frequency to avoid drifting. The dc control voltage V c is derived from a feedback loop for constant current, constant power, or constant extinction angle g. The control systems used in recent projects are digital-based and much more sophisticated than the earlier versions. FIGURE 61.16Constant a control. ? 2000 by CRC Press LLC Developments During the last two or three decades, several developments in HVDC technology have taken place that improved viability of the HVDC transmission. Prior to 1970 mercury arc valves were used for converting from ac to dc and dc to ac. They had several operational problems including frequent arcbacks. Arcback is a random phe- nomenon that results in failure of a valve to block conduction in the reverse direction. This is most common in the rectifier mode of operation. In rectifier operation, the valve is exposed to inverse voltage for approximately two-thirds of each cycle. Arcbacks result in line-to-line short circuits, and sometimes in three-phase short circuits, which subject the converter transformer and valves to severe stresses. Thyristors Thyristor valves were first used for HVDC transmis- sion in the early 1970s, and since then have com- pletely replaced mercury arc valves. The term thyristor valve, carried over from mercury arc valve, is used to refer to an assembly of series and parallel connection of several thyristors to make up the required voltage and current ratings of one arm of the converter. The first test thyristor valve in a HVDC converter station was installed in 1967, replacing a mercury arc valve in the Ygne converter station on the island of Gotland (see Gotland I in Table 61.4). The Eel River back-to-back station in New Brun- swick, Canada, commissioned in 1972, was the first all-thyristor HVDC converter station. The voltage and current ratings of thyristors have increased steadily over the last two decades. Figure 61.18 shows the maximum blocking voltage of thyristors from the late 1960s to date. The current ratings have also increased in this period from 1 to 4 kA. Some of the increased current ratings were achieved with large-diameter silicon wafers (presently 100-mm diameter) and with improved cooling systems. Earlier projects used air-cooled thyristors. Water-cooled thyristors are used for all the recent projects. Other recent developments include direct light-triggered thyristors and gate turn-off (GTO) thyristors. GTO thyristors have some advantages for HVDC converters connected to weak ac systems. They are now available in ratings up to 4.5 kV and 4 kA but have not yet been applied in HVDC systems. DC Circuit Breakers Interrupting the current in ac systems is aided by the fact that ac current goes through zero every half-cycle or approximately every 8 ms in a 60-Hz system. The absence of natural current zero in dc makes it difficult to develop a dc circuit breaker. There are three principal problems in designing a dc circuit breaker: 1.Forcing current zero in the interrupting element 2.Controlling the overvoltages caused by large di/dt in a highly inductive circuit 3.Dissipating large amounts of energy (tens of megajoules) FIGURE 61.17Equal pulse spacing control. FIGURE 61.18Maximum blocking voltage development. ? 2000 by CRC Press LLC The second and third problems are solved by the application of zinc oxide varistors connected line to ground and across the breaking element. The first is the major problem, and several different solutions are adopted by different manufacturers. Basically, current zero is achieved by inserting a counter voltage into the circuit. In the circuit shown in Fig. 61.19, open- ing CB (air-blast circuit breaker) causes current to be commutated to the parallel LC circuit. The commutating circuit will be oscillatory, which creates current zero in the circuit breaker. The opening of CB increases the voltage across the commutating circuit, which will be limited by the zinc oxide varistor ZnO 1 by entering into conduction. The resistance R is the closing resistor in series with switch S. It should be noted that a two-terminal dc system does not need a dc breaker since the fast converter control response can bring the current quickly to zero. In multi- terminal systems, dc breakers can provide additional flexibility of operation. The multiterminal dc systems commissioned so far have not employed dc breakers. Defining Terms Asynchronous ac systems:AC systems with either different operating frequencies or that are not in synchro- nism. Bipole:DC system with two conductors, one positive and the other negative polarity. Rated voltage of a bipole is expressed as ±100 kV, for example. Commutation:Process of transferring current from one valve to another. Commutation angle (overlap angle):Time in electrical degrees from the start to the completion of the commutation process. Extinction angle: Time in electrical degrees from the instant the current in a valve reaches zero (end of conduction) to the time the valve voltage changes sign and becomes positive. Firing angle (delay angle):Time in electrical degrees from the instant the valve voltage is positive to the application of firing pulse to the valve (start of conduction). Pulse number of a converter: Number of ripples in dc voltage per cycle of ac voltage. A three-phase two-way bridge is a six-pulse converter. Thyristor valve:Assembly of series and parallel connection of several thyristors to make up the required current and voltage ratings of one arm of the converter. Related Topic 30.2 Power Conversion References J.D. Ainsworth, “The phase locked oscillator: A new control system for controlled static converters,” IEEE Trans. Power Appar. Syst., vol. PAS-87, pp. 859–865, March 1968. A. Ekstrom and L. Eklund, “HVDC thyristor valve development,” in Proceedings of the International Conference on DC Power Transmission, Montreal, pp. 220–227, 1984. A. Ekstrom and G. Liss, “A refined HVDC control system,” IEEE Trans. Power Appar. Syst., vol. PAS-89, no. 5, pp. 723–732, May/June 1970. E. W. Kimbark, Direct Current Transmission, vol. I, New York: Wiley-Interscience, 1971. FIGURE 61.19DC circuit breaker (one module). ? 2000 by CRC Press LLC W.F. Long et al., “Considerations for implementing multiterminal dc systems,” IEEE Trans. Power Appar. Syst., pp. 2521–2530, September 1985. K.R. Padiyar, HVDC Power Transmission Systems—Technology and System Interactions, New Delhi: Wiley Eastern Limited, 1990. J. Reeve and P.C.S. Krishnayya, “Unusual current harmonics arising from high-voltage dc transmission,” IEEE Trans. Power Appar. Syst., vol. PAS-87, no. 3, pp. 883–893, March 1968. R.S. Thallam and J. Reeve, “Dynamic analysis of harmonic interaction between AC and DC power systems,” IEEE Trans. Power Appar. Syst., vol. PAS-93, no. 2, pp. 640–646, March/April 1974. E. Uhlmann, Power Transmission by Direct Current, Berlin: Springer-Verlag, 1975. Further Information The three textbooks cited under References are excellent for further reading. The IEEE (USA) and IEE (UK) periodically hold conferences on “DC Transmission.” The last IEEE conference was held in 1984 in Montreal, and the IEE conference was held in 1991 (conf. publ. no. 345) in London. Proceedings can be ordered from these organizations. 61.4 Compensation Mohamed E. El-Hawary The term compensation is used to describe the intentional insertion of reactive power-producing devices, either capacitive or inductive, to achieve a desired effect in the electric power system. The effects include improved voltage profiles, enhanced stability performance, and improved transmission capacity. The devices are connected either in series or in shunt (parallel) at a particular point in the power circuit. For illustration purposes, we consider the circuit of Fig. 61.20, where the link has an impedance of R + jX, and it is assumed that V 1 > V 2 and V 1 leads V 2 . The corresponding phasor diagram for zero R and lagging load current I is shown in Fig. 61.21. The approximate relationship between the scalar voltage difference between two nodes in a network and the flow of reactive power Q can be shown to be [Weedy, 1972] (61.57) In most power circuits, X >> R and the voltage difference DV determines Q. The flow of power and reactive power is from A to B when V 1 > V 2 and V 1 leads V 2 . Q is determined mainly by V 1 – V 2 . The direction of reactive power can be reversed by making V 2 > V 1 . It can thus be seen that if a scalar voltage difference exists across a largely reactive link, the reactive power flows toward the node of lower voltage. Looked at from an alternative point of view, if there is a reactive power deficit at a point in an electric network, this deficit has to be supplied from the rest of the circuit and hence the voltage at that point falls. Of course, a surplus of reactive power generated will cause a voltage rise. This can be interpreted as providing voltage support by supplying reactive power at that point. FIGURE 61.20Two nodes connected by a link. FIGURE 61.21Phasor diagram for system shown in Fig. 61.20. DV RP XQ V = + 22 2 ? 2000 by CRC Press LLC Assuming that the link is reactive, i.e., with R = 0, then P 1 = P 2 = P. In this case, the active power transferred from point A to point B can be shown to be given by [El-Hawary, 1995] P = P max sin d (61.58) The maximum power transfer P max is given by (61.59) It is clear that the power transfer capacity defined by Eq. (61.59) is improved if V 2 is increased. Series Capacitors Series capacitors are employed to neutralize part of the inductive reactance of a power circuit, as shown in Fig. 61.22. From the phasor diagram of Fig. 61.23 we see that the load voltage is higher with the capacitor inserted than without the capacitor. Introducing series capacitors is associated with an increase in the circuit’s transmission capacity [from (61.59) with a net reduction in X] and enhanced stability performance as well as improved voltage conditions on the circuit. They are also valuable in other aspects such as: ?Controlling reactive power balance ?Load distribution and control of overall transmission losses Series-capacitor compensation delays investments in additional overhead lines for added transmission capacity, which is advantageous from an environmental point of view. The first worldwide series-capacitor installation was a 33-kV 1.25-MVAR bank on the New York Power & Light system, which was put in service in 1928. Since then, many higher-capacity, higher-voltage installations have been installed in the United States, Canada, Sweden, Brazil, and other countries. The reduction in a circuit’s inductive reactance increases the short-circuit current levels over those for the noncompensated circuit. Care must be taken to avoid exposing series capacitors to such large short-circuit currents, since this causes excessive voltage rise as well as heating that can damage the capacitors. Specially calibrated spark gaps and short-circuiting switches are deployed within a predetermined time interval to avoid damage to the capacitors. The interaction between a series-capacitor-compensated ac transmission system in electrical resonance and a turbine-generator mechanical system in torsional mechanical resonance results in the phenomenon of sub- synchronous resonance (SSR). Energy is exchanged between the electrical and mechanical systems at one or more natural frequencies of the combined system below the synchronous frequency of the system. The resulting mechanical oscillations can increase until mechanical failure takes place. Techniques to counteract SSR include the following: FIGURE 61.22Line with series capacitor. FIGURE 61.23Phasor diagram corresponding to Fig. 61.22. P VV X max = 12 ? 2000 by CRC Press LLC ?Supplementary excitation control: The subsynchronous current and/or voltage is detected and the exci- tation current is modulated using high-gain feedback to vary the generator output voltage, which counters the subsynchronous oscillations [see El-Serafi and Shaltout, 1979]. ?Static filters: These are connected in series with each phase of each main generator. Step-up transformers are employed. The filters are tuned to frequencies that correspond to the power system frequency and the troublesome machine natural modes of oscillations [see Tice and Bowler, 1975]. ?Dynamic filters: In a manner similar to that of excitation control, the subsynchronous oscillation is detected, and a counter emf is generated by a thyristor cycloconverter or a similar device and injected in the power line through a series transformer [see Kilgore et al., 1975]. ?Bypassing series capacitors: To limit transient torque buildup, complete or partial bypass with the aid of low set gaps. ?Amortisseur windings on the pole faces of the generator rotors can be employed to improve damping. ?A more recent damping scheme [see Hingorani, 1981] is based on measuring the half-cycle period of the series-capacitor voltage, and if this period exceeds a preset value, the capacitor’s charge is dissipated into a resistor shunting the capacitor through two antiparallel thyristors. ?A passive SSR countermeasure scheme [see Edris, 1990] involves using three different combinations of inductive and capacitive elements on the three phases. The combinations will exhibit the required equal degree of capacitive compensation in the three phases at power frequency. At any other frequency, the three combinations will appear as unequal reactances in the three phases. In this manner, asynchronous oscillations will drive unsymmetrical three-phase currents in the generator’s armature windings. This creates an mmf with a circular component of a lower magnitude, compared with the corresponding component if the currents were symmetrical. The developed interacting electromagnetic torque will be lower. Synchronous Compensators A synchronous compensator is a synchronous motor running without a mechanical load. Depending on the value of excitation, it can absorb or generate reactive power. The losses are considerable compared with static capacitors. When used with a voltage regulator, the compensator can run automatically overexcited at high- load current and underexcited at low-load current. The cost of installation of synchronous compensators is high relative to capacitors. Shunt Capacitors Shunt capacitors are used to supply capacitive kVAR to the system at the point where they are connected, with the same effect as an overexcited synchronous condenser, generator, or motor. Shunt capacitors supply reactive power to counteract the out-of-phase component of current required by an inductive load. They are either energized continuously or switched on and off during load cycles. Figure 61.24(a) displays a simple circuit with shunt capacitor compensation applied at the load side. The line current I L is the sum of the motor load current I M and the capacitor current I c . From the current phasor diagram of Fig. 61.24(b), it is clear that the line current is decreased with the insertion of the shunt capacitor. Figure 61.24(c) displays the corresponding voltage phasors. The effect of the shunt capacitor is to reduce the source voltage to V s1 from V s0 . From the above considerations, it is clear that shunt capacitors applied at a point in a circuit supplying a load of lagging power factor have the following effects: ?Increase voltage level at the load ?Improve voltage regulation if the capacitor units are properly switched ?Reduce I 2 R power loss and I 2 X kVAR loss in the system because of reduction in current ?Increase power factor of the source generators ? 2000 by CRC Press LLC ? Decrease kVA loading on the source generators and circuits to relieve an overloaded condition or release capacity for additional load growth ? By reducing kVA load on the source generators, additional active power loading may be placed on the generators if turbine capacity is available ? Reduce demand kVA where power is purchased ? Reduce investment in system facilities per kW of load supplied To reduce high inrush currents in starting large motors, a capacitor starting system is employed. This maintains acceptable voltage levels throughout the system. The high inductive component of normal reactive starting current is offset by the addition, during the starting period only, of capacitors to the motor bus. This differs from applying capacitors for motor power factor correction. When used for voltage control, the action of shunt capacitors is different from that of synchronous condens- ers, since their reactive power varies as the square of the voltage, whereas the synchronous machine maintains approximately constant kVA for sudden voltage changes. The synchronous condenser has a greater stabilizing effect upon system voltages. The losses of the synchronous condenser are much greater than those of capacitors. Note that in determining the amount of shunt capacitor kVAR required, since a voltage rise increases the lagging kVAR in the exciting currents of transformer and motors, some additional capacitor kVAR above that based on initial conditions without capacitors may be required to get the desired correction. If the load includes synchronous motors, it may be desirable, if possible, to increase the field currents to these motors. The following are the relative merits of shunt and series capacitors: ? If the total line reactance is high, series capacitors are very effective. ? If the voltage drop is the limiting factor, series capacitors are effective; also, voltage fluctuations are evened out. ? If the reactive power requirements of the load are small, the series capacitor is of little value. ? If thermal considerations limit the current, then series capacitors are of little value since the reduction in line current associated with them is small. Applying capacitors with harmonic-generating apparatus on a power system requires considering the potential of an excited harmonic resonance condition. Either a series or a shunt resonance condition may take place. In FIGURE 61.24 (a) Shunt-capacitor-compensated load; (b) current phasor diagram; (c) voltage phasor diagram. ? 2000 by CRC Press LLC actual electrical systems utilizing compensating capacitors, either type of resonance or a combination of both can occur if the resonant point happens to be close to one of the frequencies generated by harmonic sources in the system. The outcome can be the flow of excessive amounts of harmonic current or the appearance of excessive harmonic overvoltages, or both. Possible effects of this are excessive capacitor fuse operation, capacitor failure, overheating of other electrical equipment, or telephone interference. Shunt Reactors Shunt reactor compensation is usually required under conditions that are the opposite of those requiring shunt capacitor compensation (see Fig. 61.25). Shunt reactors are installed to remedy the following situations: ?Overvoltages that occur during low load periods at stations served by long lines as a result of the line’s capacitance (Ferranti effect). ?Leading power factors at generating plants resulting in lower transient and steady-state stability limits, caused by reduced field current and the machine’s internal voltage. In this case, shunt reactors are usu- ally installed at either side of the generator’s step-up transformers. ?Open-circuit line charging kVA requirements in extra-high-voltage systems that exceed the available generation capabilities. Coupling from nearby energized lines can cause severe resonant overvoltages across the shunt reactors of unenergized compensated lines. Static VAR Compensators (SVC) Advances in thyristor technology for power systems applications have lead to the development of the static VAR compensators (SVC). These devices contain standard shunt elements (reactors, capacitors) but are con- trolled by thyristors [El-Hawary, 1995]. Static VAR compensators provide solutions to two types of compensation problems normally encountered in practical power systems [Gyugyi et al., 1978]. The first is load compensation, where the requirements are usually to reduce or cancel the reactive power demand of large and fluctuating industrial loads, such as electric arc furnaces and rolling mills, and to balance the real power drawn from the ac supply lines. These types of heavy industrial loads are normally concentrated in one plant and served from one network terminal, and thus can be handled by a local compensator connected to the same terminal. The second type of compensation is related to voltage support of transmission lines at a given terminal in response to disturbances of both load and generation. The voltage support is achieved by rapid control of the SVC reactance and thus its reactive power output. The main objectives of dynamic VAR compensation are to increase the stability limit of the ac power system, to decrease terminal voltage fluctuations during load variations, and to limit overvoltages subsequent to large disturbances. SVCs are essentially thyristor-controlled reactive power devices. The two fundamental thyristor-controlled reactive power device configurations are [Olwegard et al., 1981]: ?Thyristor-switched shunt capacitors (TSC): The idea is to split a capacitor bank into sufficiently small capacitor steps and switch those steps on and off individually. Figure 61.26(a) shows the concept of the TSC. It offers stepwise control, virtually no transients, and no harmonic generation. The average delay for executing a command from the regulator is half a cycle. ?Thyristor-switched shunt reactors (TCR): In this scheme the fundamental frequency current component through the reactor is controlled by delaying the closing of the thyristor switch with respect to the natural zero crossings of the current. Figure 61.26(b) shows the concept of the TCR. Harmonic currents are generated from the phase-angle-controlled reactor. FIGURE 61.25 Shunt-reactor-compensated load. ? 2000 by CRC Press LLC The magnitude of the harmonics can be reduced using two methods. In the first, the reactor is split into smaller steps, while only one step is phase-angle controlled. The other reactor steps are either on or off. This decreases the magnitude of all harmonics. The second method involves the 12-pulse arrangement, where two identical connected thyristor-controlled reactors are used, one operated from a wye-connected secondary winding, the other from a delta-connected winding of a step-up transformer. TCR units are characterized by continuous control, and there is a maximum of one half-cycle delay for executing a command from the regulator. In many applications, the arrangement of an SVC consists of a few large steps of thyristor-switched capacitor and one or two thyristor-controlled reactors, as shown in Fig. 61.26(c). The following are some practical schemes. Fixed-Capacitor, Thyristor-Controlled Reactor (FC-TCR) Scheme This scheme was originally developed for industrial applications, such as arc furnace “flicker” control [Gyugyi and Taylor, 1980]. It is essentially a TCR (controlled by a delay angle a) in parallel with a fixed capacitor. Figure 61.27 shows a basic fixed-capacitor, thyristor-controlled reactor-type compensator and associated wave- forms. Figure 61.28 displays the steady-state reactive power versus terminal voltage characteristics of a static VAR compensator. In the figure, B C is the imaginary part of the admittance of the capacitor C, and B L is the imaginary part of the equivalent admittance of the reactor L at delay angle a. The relation between the output VARs and the applied voltage is linear over the voltage band of regulation. In practice, the fixed capacitor is usually replaced by a filter network that has the required capacitive reactance at the power system frequency but exhibits a low impedance at selected frequencies to absorb troublesome harmonics. FIGURE 61.26Basic static VAR compensator configurations. (a) Thyristor-switched shunt capacitors (TSC); (b) thyristor- switched shunt reactors (TCR); (c) combined TSC/TCR. FIGURE 61.27Basic fixed-capacitor, thyristor-controlled reactor-type compensator and associated waveforms. ? 2000 by CRC Press LLC The behavior and response of the FC-TCR type of compensator under large disturbances is uncontrollable, at least during the first few cycles following the disturbance. The resulting voltage transients are essentially determined by the fixed capacitor and the power system impedance. This can lead to overvoltage and resonance problems. At zero VAR demand, the capacitive and reactive VARs cancel out, but the capacitor bank’s current is circulated through the reactor bank via the thyristor switch. As a result, this configuration suffers from no load (standby) losses. The losses decrease with increasing the capacitive VAR output and, conversely, increase with increasing the inductive VAR output. Thyristor-Switched Capacitor, Thyristor- Controlled Reactor (TSC-TCR) Scheme This hybrid compensator was developed specifi- cally for utility applications to overcome the disad- vantages of the FC-TCR compensators (behavior under large disturbances and loss characteristic). Figure 61.29 shows a basic circuit of this compen- sator. It consists in general of a thyristor-controlled reactor bank (or banks) and a number of capacitor banks, each in series with a solid-state switch, which is composed of either a reverse-parallel-connected thyristor pair or a thyristor in reverse parallel with a diode. The reactor’s switch is composed of a reverse- parallel-connected thyristor pair that is capable of continuously controlling the current in the reactor from zero to maximum rated current. The total capacitive range is divided into n operating intervals, where n is the number of capacitor banks in the compensator. In the first interval one capacitor bank is switched in, and at the same time the current in the TCR bank is adjusted so that the resultant VAR output from capacitor and reactor matches the VAR demand. In the ith interval the output is controllable in the range [(i – 1)VAR max /n] to (i VAR max /n) by switching in the ith capacitor bank and using the TCR bank to absorb the surplus capacitive VARs. This scheme can be considered as a conventional FC-TCR, where the rating of the reactor bank is kept relatively small (1/n times the maximum VAR output) and the value of the capacitor bank is changed in discrete steps so as to keep the operation of the reactor bank within its normal control range. The losses of the TSC-TCR compensator at zero VARs output are inherently low, and they increase in proportion to the VAR output. FIGURE 61.28The steady-state reactive power versus terminal voltage characteristics of a static VAR compensator. FIGURE 61.29 Basic thyristor-switched capacitor, thyris- tor-controlled reactor-type compensator. ? 2000 by CRC Press LLC The mechanism by which SVCs introduce damping into the system can be explained as a result of the change in system voltage due to switching of a capacitor/reactor. The electrical power output of the generators is changed immediately due to the change in power transfer capability and the change in load power requirements. Among the early applications of SVC for power system damping is the application to the Scandinavian system as discussed in Olwegard et al. [1981]. More recently, SVC control for damping of system oscillations based on local measurements has been proposed. The scheme uses phase-angle estimates based on voltage and power measurements at the SVC location as the control signal [see Lerch et al., 1991]. For a general mathematical model of an SVC and an analysis of its stabilizing effects, see Hammad [1986]. Representing the SVC in transient analysis programs is an important consideration [see Gole and Sood, 1990; Lefebvre and Gerin-Lajoie, 1992]. It is important to recognize that applying static VAR compensators to series-compensated ac transmission lines results in three distinct resonant modes [Larsen et al., 1990]: ? Shunt-capacitance resonance involves energy exchange between the shunt capacitance (line charging plus any power factor correction or SVCs) and the series inductance of the lines and the generator. ? Series-line resonance involves energy exchange between the series capacitor and the series inductance of the lines, transformers, and generators. The resonant frequency will depend on the level of series compensation. ? Shunt-reactor resonance involves energy exchange between shunt reactors at the intermediate substations of the line and the series capacitors. The applications of SVCs are part of the broader area of flexible ac transmission systems (FACTS) [Hingorani, 1993] Defining Terms Capacitor bank: An assembly at one location of capacitors and all necessary accessories, such as switching equipment, protective equipment, and controls, required for a complete operating installation. Reactor: A device whose primary purpose is to introduce reactance into a circuit. Inductive reactance is frequently abbreviated inductor. Resonance: The enhancement of the response of a physical system to a periodic excitation when the excitation frequency is equal to a natural frequency of the system. Shunt: A device having appreciable impedance connected in parallel across other devices or apparatus and diverting some of the current from it. Appreciable voltage exists across the shunted device or apparatus, and an appreciable current may exist in it. Shunt reactor: A reactor intended for connection in shunt to an electric system to draw inductive current. Subsynchronous resonance: An electric power system condition where the electric network exchanges energy with a turbine generator at one or more of the natural frequencies of the combined system below the synchronous frequency of the system. Thyristor: A bistable semiconductor device comprising three or more junctions that can be switched from the off state to the on state, or vice versa, such switching occurring within at least one quadrant of the principal voltage-current characteristic. Related Topic 1.2 Capacitors and Inductors References I.S. Benko, B. Bhargava, and W.N. Rothenbuhler, “Prototype NGH subsynchronous resonance damping scheme, part II—Switching and short circuit tests,” IEEE Trans. Power Syst., vol. 2, pp. 1040–1049, 1987. L.E. Bock and G.R. Mitchell, “Higher line loadings with series capacitors,” Transmission Magazine, March 1973. E.W. Bogins and H.T. Trojan, “Application and design of EHV shunt reactors,” Transmission Magazine, March 1973. ? 2000 by CRC Press LLC C.E. Bowler, D.N. Ewart, and C. Concordia, “Self excited torsional frequency oscillations with series capacitors,” IEEE Trans. Power Appar. Syst., vol. 93, pp. 1688–1695, 1973. G.D. Brewer, H.M. Rustebakke, R.A. Gibley, and H.O. Simmons, “The use of series capacitors to obtain maximum EHV transmission capability,” IEEE Trans. Power Appar. Syst., vol. 83, pp. 1090–1102, 1964. C. Concordia, “System compensation, an overview,” Transmission Magazine, March 1973. S.E.M. de Oliveira, I. Gardos, and E.P. Fonseca, “Representation of series capacitors in electric power system stability studies,” IEEE Trans. Power Syst., vol. 6, no. 3, pp. 1119–1125, 1991. A.A. Edris, “Series compensation schemes reducing the potential of subsynchronous resonance,” IEEE Trans. Power Syst., vol. 5, no. 1, pp. 219–226, 1990. M.E. El-Hawary, Electrical Power Systems: Design and Analysis, Piscataway, N.J.: IEEE Press, 1995. A.M. El-Serafi and A. A. Shaltout, “Damping of SSR Oscillations by Excitation Control,” IEEE PES Summer Meeting, Vancouver, 1979. A.M. Gole and V.K. Sood, “A static compensator model for use with electromagnetic transients simulation programs,” IEEE Trans. Power Delivery, vol. 5, pp. 1398–1407, 1990. L. Gyugyi, R.A. Otto, and T.H. Putman, “Principles and applications of static thyristor-controlled shunt com- pensators,” IEEE Trans. Power Appar. Syst., vol. PAS-97, pp. 1935–1945, 1978. L. Gyugyi and E.R. Taylor, Jr., “Characteristics of static thyristor-controlled shunt compensators for power transmission system applications,” IEEE Trans. Power Appar. Syst., vol. PAS-99, pp. 1795–1804, 1980. A.E. Hammad, “Analysis of power system stability enhancement by static VAR compensators,” IEEE Trans. Power Syst., vol. 1, pp. 222–227, 1986. J.F. Hauer, “Robust damping controls for large power systems,” IEEE Control Systems Magazine, pp. 12–18, January 1989. R.A. Hedin, K.B. Stump, and N.G. Hingorani, “A new scheme for subsynchronous resonance damping of torsional oscillations and transient torque—Part II,” IEEE Trans. Power Appar. Syst., vol. PAS-100, pp. 1856–1863, 1981. N.G. Hingorani, “A new scheme for subsynchronous resonance damping of torsional oscillations and transient torque—Part I,” IEEE Trans. Power Appar. Syst., vol. PAS-100, pp. 1852–1855, 1981. N.G. Hingorani, B. Bhargava, G.F. Garrigue, and G.D. Rodriguez, “Prototype NGH subsynchronous resonance damping scheme, part I—Field installation and operating experience,” IEEE Trans. Power Syst., vol. 2, pp. 1034–1039, 1987. N.G. Hingorani, “Flexible AC transmission,” IEEE Spectrum. vol. 30, no. 4, pp. 40–45, 1993. IEEE Subsynchronous Resonance Working Group, “Proposed terms and definitions for subsynchronous oscil- lations,” IEEE Trans. Power Appar. Syst., vol. PAS-99, pp. 506–511, 1980. IEEE Subsynchronous Resonance Working Group, “Countermeasures to subsynchronous resonance problems,” IEEE Trans. Power Appar. Syst., vol. PAS-99, pp. 1810–1818, 1980. IEEE Subsynchronous Resonance Working Group, “Series capacitor controls and settings as countermeasures to subsynchronous resonance,” IEEE Trans. Power Appar. Syst., vol. PAS-101, pp. 1281–1287, June 1982. G. Jancke, N. Fahlen, and O. Nerf, “Series capacitors in power systems,” IEEE Transactions on Power Appar. Syst., vol. PAS-94, pp. 915–925, May/June 1975. L.A. Kilgore, D.G. Ramey, and W.H. South, “Dynamic filter and other solutions to the subsynchronous resonance problem,” Proceedings of the American Power Conference, vol. 37, p. 923, 1975. E.W. Kimbark, Power System Stability, vol. I, Elements of Stability Calculations, New York: Wiley, 1948. E.W. Kimbark, “Improvement of system stability by switched series capacitors,” IEEE Trans. Power Appar. Syst., vol. 85, pp. 180–188, February 1966. J.J. LaForest, K.W. Priest, Ramirez, and H. Nowak, “Resonant voltages on reactor compensated extra-high- voltage lines,” IEEE Trans. Power Appar. Syst., vol. PAS-91, pp. 2528–2536, November/December 1972. E.V. Larsen, D.H. Baker, A.F. Imece, L. Gerin-Lajoie, and G. Scott, “Basic aspects of applying SVC’s to series- compensated ac transmission lines,” IEEE Trans. Power Delivery, vol. 5, pp. 1466–1472, July 1990. S. Lefebvre and L. Gerin-Lajoie, “A static compensator model for the EMTP,” IEEE Trans. Power Systems, vol. 7, no. 2, pp. 477–486, May 1992. E. Lerch, D. Povh, and L. Xu, “Advanced SVC control for damping power system oscillations,” IEEE Trans. Power Syst., vol. 6, pp. 524–531, May 1991. ? 2000 by CRC Press LLC S.M. Merry and E.R. Taylor, “Overvoltages and harmonics on EHV systems,” IEEE Trans. Power Appar. Syst., vol. PAS-91, pp. 2537–2544, November/December 1972. A. Olwegard, K. Walve, G. Waglund, H. Frank, and S. Torseng, “Improvement of transmission capacity by thyristor controlled reactive power,” IEEE Trans. Power Appar. Syst., vol. PAS-100, pp. 3930–3939, 1981. J.B. Tice and C.E.J. Bowler, “Control of phenomenon of subsynchronous resonance,” Proceedings of the American Power Conference, vol. 37, pp. 916–922, 1975. B.M. Weedy, Electric Power Systems, London: Wiley, 1972. Further Information An excellent source of information on the application of capacitors on power systems is the Westinghouse Transmission and Distribution book, published in 1964. A most readable treatment of improving system stability by series capacitors is given by Kimbark’s paper [1966]. Jancke et al. [1975] give a detailed discussion of experience with the 400-kV series-capacitor compensation installations on the Swedish system and aspects of the protection system. Hauer [1989] presents a discussion of practical stability controllers that manipulate series and/or shunt reactance. An excellent summary of the state of the art in static VAR compensators is the record of the IEEE Working Group symposium conducted in 1987 on the subject (see IEEE Publication 87TH0187-5-PWR, Application of Static VAR Systems for System Dynamic Performance). For state-of-the-art coverage of subsynchronous resonance and countermeasures, two symposia are available: IEEE Publication 79TH0059-6-PWR, State-of-the-Art Symposium—Turbine Generator Shaft Torsionals, and IEEE Publication 81TH0086-9-PWR, Symposium on Countermeasures for Subsynchronous Resonance. 61.5 Fault Analysis in Power Systems Charles Gross A fault in an electrical power system is the unintentional and undesirable creation of a conducting path (a short circuit) or a blockage of current (an open circuit). The short-circuit fault is typically the most common and is usually implied when most people use the term fault. We restrict our comments to the short-circuit fault. The causes of faults include lightning, wind damage, trees falling across lines, vehicles colliding with towers or poles, birds shorting out lines, aircraft colliding with lines, vandalism, small animals entering switchgear, and line breaks due to excessive ice loading. Power system faults may be categorized as one of four types: single line-to-ground, line-to-line, double line-to-ground, and balanced three-phase. The first three types constitute severe unbalanced operating conditions. It is important to determine the values of system voltages and currents during faulted conditions so that protective devices may be set to detect and minimize their harmful effects. The time constants of the associated transients are such that sinusoidal steady-state methods may still be used. The method of symmetrical com- ponents is particularly suited to fault analysis. Our objective is to understand how symmetrical components may be applied specifically to the four general fault types mentioned and how the method can be extended to any unbalanced three-phase system problem. Note that phase values are indicated by subscripts, a, b, c; sequence (symmetrical component) values are indicated by subscripts 0, 1, 2. The transformation is defined by V V V aa aa V V V T V V V V V V aa aa V V a b c é ? ê ê ê ù ? ú ú ú = é ? ê ê ê ù ? ú ú ú é ? ê ê ê ù ? ú ú ú = é ? ê ê ê ù ? ú ú ú é ? ê ê ê ù ? ú ú ú = é ? ê ê ê ù ? ú ú ú 111 1 1 1 3 111 1 1 2 2 0 1 2 a b c 0 1 2 2 2 0 [] 1 2 1 V T V V V a b c é ? ê ê ê ù ? ú ú ú = é ? ê ê ê ù ? ú ú ú - [] ? 2000 by CRC Press LLC Simplifications in the System Model Certain simplifications are possible and usually employed in fault analysis. ?Transformer magnetizing current and core loss will be neglected. ?Line shunt capacitance is neglected. ?Sinusoidal steady-state circuit analysis techniques are used. The so-called dc offset is accounted for by using correction factors. ?Prefault voltage is assumed to be per-unit. One per-unit voltage is at its nominal value prior to the application of a fault, which is reasonable. The selection of zero phase is arbitrary and convenient. Prefault load current is neglected. For hand calculations, neglect series resistance is usually neglected (this approximation will not be necessary for a computer solution). Also, the only difference in the positive and negative sequence networks is introduced by the machine impedances. If we select the subtransient reactance X d ￠ for the positive sequence reactance, the difference is slight (in fact, the two are identical for nonsalient machines). The simplification is important, since it reduces computer storage requirements by roughly one-third. Circuit models for generators, lines, and transformers are shown in Figs. 61.30, 61.31, and 61.32, respectively. Our basic approach to the problem is to consider the general situation suggested in Fig. 61.33(a). The general terminals brought out are for purposes of external connections that will simulate faults. Note carefully the positive assignments of phase quantities. Particularly note that the currents flow out of the system. We can FIGURE 61.30Generator sequence circuit models. 10/° ? 2000 by CRC Press LLC construct general sequence equivalent circuits for the system, and such circuits are indicated in Fig. 61.33(b). The ports indicated correspond to the general three-phase entry port of Fig. 61.33(a). The positive sense of sequence values is compatible with that used for phase values. FIGURE 61.31Line sequence circuit models. FIGURE 61.32Transformer sequence circuit models. ? 2000 by CRC Press LLC The Four Basic Fault Types The Balanced Three-Phase Fault Imagine the general three-phase access port terminated in a fault impedance as shown in Fig. 61.34(a). The terminal conditions are FIGURE 61.33General fault port in an electric power system. (a) General fault port in phase (abc) coordinates; (b) corresponding fault ports in sequence (012) coordinates. FIGURE 61.34Fault types. (a) Three-phase fault; (b) single phase-to-ground fault; (c) phase-to-phase fault; (d) double phase-to-ground fault. ( )Z f V V V Z Z Z I I I a b c f f f a b c é ? ê ê ê ù ? ú ú ú = é ? ê ê ê ù ? ú ú ú é ? ê ê ê ù ? ú ú ú 00 00 00 ? 2000 by CRC Press LLC Transforming to [Z 012 ], The corresponding network connections are given in Fig. 61.35(a). Since the zero and negative sequence networks are passive, only the positive sequence network is nontrivial. (61.60) (61.61) (61.62) FIGURE 61.35 Sequence network terminations for fault types. (a) Balanced three-phase fault; (b) single phase-to-ground fault; (c) phase-to-phase fault; (d) double phase-to-ground fault. [ ][] []ZT Z Z Z T Z Z Z f f f f f f 012 1 00 00 00 00 00 00 = é ? ê ê ê ù ? ú ú ú = é ? ê ê ê ù ? ú ú ú - VV 02 0== II 02 0== VZI f11 = ? 2000 by CRC Press LLC The Single Phase-to-Ground Fault Imagine the general three-phase access port terminated as shown in Fig. 61.34(b). The terminal conditions are Therefore or Also or (61.63) Furthermore it is required that (61.64) In general then, Eqs. (61.63) and (61.64) must be simultaneously satisfied. These conditions can be met by interconnecting the sequence networks as shown in Fig. 61.35(b). The Phase-to-Phase Fault Imagine the general three-phase access port terminated as shown in Fig. 61.34(c). The terminal conditions are such that we may write It follows that (61.65) (61.66) (61.67) In general then, Eqs. (61.65), (61.66), and (61.67) must be simultaneously satisfied. The proper interconnection between sequence networks appears in Fig. 61.35(c). IIVIZ bcaaf ===00 IaIaIIaIaI 0 2 1201 2 2 0++=++= II 12 = IIaIaIIaaI b =++=++= 0 2 120 2 1 0() III 012 == VZI VVVZI afa f = ++= 012 1 3 IIIVZIV bcbfbc0 0==-=+ III 012 0++= I 0 0= II 12 =- ? 2000 by CRC Press LLC The Double Phase-to-Ground Fault Consider the general three-phase access port terminated as shown in Fig. 61.34(d). The terminal conditions indicate It follows that (61.68) (61.69) and (61.70) For the general double phase-to-ground fault, Eqs. (61.68), (61.69), and (61.70) must be simultaneously satisfied. The sequence network interconnections appear in Fig. 61.35(d). An Example Fault Study Case: EXAMPLE SYSTEM Run : System has data for 2 Line(s); 2 Transformer(s); 4 Bus(es); and 2 Generator(s) Transmission Line Data Line Bus Bus Seq R X B Srat 1 2 3 pos 0.00000 0.16000 0.00000 1.0000 zero 0.00000 0.50000 0.00000 2 2 3 pos 0.00000 0.16000 0.00000 1.0000 zero 0.00000 0.50000 0.00000 Transformer Data Trans- HV LV former Bus Bus Seq R X C Srat 1 2 1 pos 0.00000 0.05000 1.00000 1.0000 Y Y zero 0.00000 0.05000 2 3 4 pos 0.00000 0.05000 1.00000 1.0000 Y D zero 0.00000 0.05000 Generator Data No. Bus Srated Ra Xd￠￠ Xo Rn Xn Con 1 1 1.0000 0.0000 0.200 0.0500 0.0000 0.0400 Y 2 4 1.0000 0.0000 0.200 0.0500 0.0000 0.0400 Y IVVVIIZ abcbbcf ===+0 ( ) III 012 0++= VV 12 = VVZI f01 0 3-= ? 2000 by CRC Press LLC The single-line diagram and sequence networks are presented in Fig. 61.36. Suppose bus 3 in the example system represents the fault location and f = 0. The positive sequence circuit can be reduced to its Thévenin equivalent at bus 3: Similarly, the negative and zero sequence Thévenin elements are The network interconnections for the four fault types are shown in Fig. 61.37. For each of the fault types, compute the currents and voltages at the faulted bus. Balanced Three-Phase Fault The sequence networks are shown in Fig. 61.37(a). Obviously, Zero Sequence [Z] Matrix 0.0 + j(0.1144) 0.0 + j(0.0981) 0.0 + j(0.0163) 0.0 + j(0.0000) 0.0 + j(0.0981) 0.0 + j(0.1269) 0.0 + j(0.0212) 0.0 + j(0.0000) 0.0 + j(0.0163) 0.0 + j(0.0212) 0.0 + j(0.0452) 0.0 + j(0.0000) 0.0 + j(0.0000) 0.0 + j(0.0000) 0.0 + j(0.0000) 0.0 + j(0.1700) Positive Sequence [Z] Matrix 0.0 + j(0.1310) 0.0 + j(0.1138) 0.0 + j(0.0862) 0.0 + j(0.0690) 0.0 + j(0.1138) 0.0 + j(0.1422) 0.0 + j(0.1078) 0.0 + j(0.0862) 0.0 + j(0.0862) 0.0 + j(0.1078) 0.0 + j(0.1422) 0.0 + j(0.1138) 0.0 + j(0.0690) 0.0 + j(0.0862) 0.0 + j(0.1138) 0.0 + j(0.1310) FIGURE 61.36Example system. (a) Single-line diagram; (b) zero sequence network; (c) positive sequence network; (d) negative sequence network. Z EZj TT11 = ° = 100 01422 . / . EZj Z TT22 00 ==0 01422 0 00452 . . VIVI I j jV 0022 11 0 10 01422 7032 0 ==== = ° =- = / . . ; also ? 2000 by CRC Press LLC To compute the phase values, FIGURE 61.37 Example system faults at bus 3. (a) Balanced three-phase; (b) single phase-to-ground; (c) phase-to-phase; (d) double phase-to-ground. I I I T I I I aa aa j V V V a b c a b c é ? ê ê ê ù ? ú ú ú = é ? ê ê ê ù ? ú ú ú = é ? ê ê ê ù ? ú ú ú - é ? ê ê ê ù ? ú ú ú = -° ° ° é ? ê ê ê ù ? ú ú ú é ? ê ê ê [] . . . . / / / 0 1 2 2 2 111 1 1 0 7 032 0 7 032 90 7 032 150 7 032 30 ù ? ú ú ú = é ? ê ê ê ù ? ú ú ú = é ? ê ê ê ù ? ú ú ú []T 0 0 0 0 0 0 ? 2000 by CRC Press LLC Single Phase-to-Ground Fault The sequence networks are interconnected as shown in Fig. 61.37(b). The sequence voltages are The phase voltages are Phase-to-phase and double phase-to-ground fault values are calculated from the appropriate networks [Figs. 61.37(c) and (d)]. Complete results are provided. Faulted Bus Phase a Phase b Phase c 3 GGG Sequence Voltages Bus V0 V1 V2 1 0.0000/ 0.0 0.3939/ 0.0 0.0000/ 0.0 2 0.0000/ 0.0 0.2424/ 0.0 0.0000/ 0.0 3 0.0000/ 0.0 0.0000/ 0.0 0.0000/ 0.0 4 0.0000/ 0.0 0.2000/ –30.0 0.0000/ 30.0 Phase Voltages Bus Va Vb Vc 1 0.3939/ 0.0 0.3939/ –120.0 0.3939/ 120.0 2 0.2424/ 0.0 0.2424/ –120.0 0.2424/ 120.0 3 0.0000/ 6.5 0.0000/ –151.2 0.0000/ 133.8 4 0.2000/ –30.0 0.2000/ –150.0 0.2000/ 90.0 III jjj j 012 1 0 0 0452 0 1422 0 1422 3 034== = ° ++ =- / ... . I I I aa aa j j j j a b c é ? ê ê ê ù ? ú ú ú = é ? ê ê ê ù ? ú ú ú - - - é ? ê ê ê ù ? ú ú ú = -é ? ê ê ê ù ? ú ú ú 111 1 1 3 034 3 034 3 034 9 102 0 0 2 2 . . . . Vj j Vjj Vj j 0 1 2 0 0452 3 034 1371 1 0 0 1422 3 034 0 5685 0 1422 3 034 0 4314 =- - =- =- - = =- - =- .(.) ..(.). .(.) . V V V aa aa a b c é ? ê ê ê ù ? ú ú ú = é ? ê ê ê ê ù ? ú ú ú ú - - é ? ê ê ê ù ? ú ú ú =-° -° é ? ê ê ê ù ? ú ú ú 111 1 1 0 1371 0 5685 0 4314 0 0 8901 103 4 0 8901 103 4 2 2 . . . .. / / ? 2000 by CRC Press LLC Sequence Currents Bus to BusI0I1I2 1 2 0.0000/ 167.8 3.0303/ –90.0 0.0000/ 90.0 1 0 0.0000/ –12.2 3.0303/ 90.0 0.0000/ –90.0 2 3 0.0000/ 167.8 1.5152/ –90.0 0.0000/ 90.0 2 3 0.0000/ 167.8 1.5152/ –90.0 0.0000/ 90.0 2 1 0.0000/ –12.2 3.0303/ 90.0 0.0000/ –90.0 3 2 0.0000/ –12.2 1.5152/ 90.0 0.0000/ –90.0 3 2 0.0000/ –12.2 1.5152/ 90.0 0.0000/ –90.0 3 4 0.0000/ –12.2 4.0000/ 90.0 0.0000/ –90.0 4 3 0.0000/ 0.0 4.0000/ –120.0 0.0000/ 120.0 4 0 0.0000/ 0.0 4.0000/ 60.0 0.0000/ –60.0 Faulted Bus Phase a Phase b Phase c 3 GGG Phase Currents Bus to Bus Ia Ib Ic 1 2 3.0303/ –90.0 3.0303/ 150.0 3.0303/ 30.0 1 0 3.0303/ 90.0 3.0303/ –30.0 3.0303/ –150.0 2 3 1.5151/ –90.0 1.5151/ 150.0 1.5151/ 30.0 2 3 1.5151/ –90.0 1.5151/ 150.0 1.5151/ 30.0 2 1 3.0303/ 90.0 3.0303/ –30.0 3.0303/ –150.0 3 2 1.5151/ 90.0 1.5151/ –30.0 1.5151/ –150.0 3 2 1.5151/ 90.0 1.5151/ –30.0 1.5151/ –150.0 3 4 4.0000/ 90.0 4.0000/ –30.0 4.0000/ –150.0 4 3 4.0000/ –120.0 4.0000/ 120.0 4.0000/ –0.0 4 0 4.0000/ 60.0 4.0000/ –60.0 4.0000/ –180.0 Faulted Bus Phase a Phase b Phase c 3G00 Sequence Voltages BusV0V1V2 1 0.0496/ 180.0 0.7385/ 0.0 0.2615/ 180.0 2 0.0642/ 180.0 0.6731/ 0.0 0.3269/ 180.0 3 0.1371/ 180.0 0.5685/ 0.0 0.4315/ 180.0 4 0.0000/ 0.0 0.6548/ –30.0 0.3452/ 210.0 Phase Voltages Bus Va Vb Vc 1 0.4274/ 0.0 0.9127/ –108.4 0.9127/ 108.4 2 0.2821/ 0.0 0.8979/ –105.3 0.8979/ 105.3 3 0.0000/ 89.2 0.8901/ –103.4 0.8901/ 103.4 4 0.5674/ –61.8 0.5674/ –118.2 1.0000/ 90.0 ? 2000 by CRC Press LLC Sequence Currents Bus to BusI0I1I2 1 2 0.2917/ –90.0 1.3075/ –90.0 1.3075/ –90.0 1 0 0.2917/ 90.0 1.3075/ 90.0 1.3075/ 90.0 2 3 0.1458/ –90.0 0.6537/ –90.0 0.6537/ –90.0 2 3 0.1458/ –90.0 0.6537/ –90.0 0.6537/ –90.0 2 1 0.2917/ 90.0 1.3075/ 90.0 1.3075/ 90.0 3 2 0.1458/ 90.0 0.6537/ 90.0 0.6537/ 90.0 3 2 0.1458/ 90.0 0.6537/ 90.0 0.6537/ 90.0 3 4 2.7416/ 90.0 1.7258/ 90.0 1.7258/ 90.0 4 3 0.0000/ 0.0 1.7258/ –120.0 1.7258/ –60.0 4 0 0.0000/ 90.0 1.7258/ 60.0 1.7258/ 120.0 Faulted Bus Phase a Phase b Phase c 3G00 Phase Currents Bus to Bus Ia Ib Ic 1 2 2.9066/ –90.0 1.0158/ 90.0 1.0158/ 90.0 1 0 2.9066/ 90.0 1.0158/ –90.0 1.0158/ –90.0 2 3 1.4533/ –90.0 0.5079/ 90.0 0.5079/ 90.0 2 3 1.4533/ –90.0 0.5079/ 90.0 0.5079/ 90.0 2 1 2.9066/ 90.0 1.0158/ –90.0 1.0158/ –90.0 3 2 1.4533/ 90.0 0.5079/ –90.0 0.5079/ –90 0 3 2 1.4533/ 90.0 0.5079/ –90.0 0.5079/ –90 0 3 4 6.1933/ 90.0 1.0158/ 90.0 1.0158/ 90.0 4 3 2.9892/ –90.0 2.9892/ 90.0 0.0000/ –90.0 4 0 2.9892/ 90.0 2.9892/ –90.0 0.0000/ 90.0 Faulted Bus Phase a Phase b Phase c 30CB Sequence Voltages Bus V0 V1 V2 1 0.0000/ 0.0 0.6970/ 0.0 0.3030/ 0.0 2 0.0000/ 0.0 0.6212/ 0.0 0.3788/ 0.0 3 0.0000/ 0.0 0.5000/ 0.0 0.5000/ 0.0 4 0.0000/ 0.0 0.6000/ –30.0 0.4000/ 30.0 Phase Voltages Bus Va Vb Vc 1 1.0000/ 0.0 0.6053/ –145.7 0.6053/ 145.7 2 1.0000/ 0.0 0.5423/ –157.2 0.5423/ 157.2 3 1.0000/ 0.0 0.5000/ –180.0 0.5000/ –180.0 4 0.8718/ –6.6 0.8718/ –173.4 0.2000/ 90.0 ? 2000 by CRC Press LLC Sequence Currents Bus to BusI0I1I2 1 2 0.0000/ –61.0 1.5152/ –90.0 1.5152/ 90.0 1 0 0.0000/ 119.0 1.5152/ 90.0 1.5152/ –90.0 2 3 0.0000/ –61.0 0.7576/ –90.0 0.7576/ 90.0 2 3 0.0000/ –61.0 0.7576/ –90.0 0.7576/ 90.0 2 1 0.0000/ 119.0 1.5152/ 90.0 1.5152/ –90.0 3 2 0.0000/ 119.0 0.7576/ 90.0 0.7576/ –90.0 3 2 0.0000/ 119.0 0.7576/ 90.0 0.7576/ –90.0 3 4 0.0000/ 119.0 2.0000/ 90.0 2.0000/ –90.0 4 3 0.0000/ 0.0 2.0000/ –120.0 2.0000/ 120.0 4 0 0.0000/ 90.0 2.0000/ 60.0 2.0000/ –60.0 Faulted Bus Phase a Phase b Phase c 30CB Phase Currents Bus to Bus Ia Ib Ic 1 2 0.0000/ 180.0 2.6243/ 180.0 2.6243/ 0.0 1 0 0.0000/ 180.0 2.6243/ 0.0 2.6243/ 180.0 2 3 0.0000/ –180.0 1.3122/ 180.0 1.3122/ 0.0 2 3 0.0000/ –180.0 1.3122/ 180.0 1.3122/ 0.0 2 1 0.0000/ 180.0 2.6243/ 0.0 2.6243/ 180.0 3 2 0.0000/ –180.0 1.3122/ 0.0 1.3122/ 180.0 3 2 0.0000/ –180.0 1.3122/ 0.0 1.3122/ 180.0 3 4 0.0000/ –180.0 3.4641/ 0.0 3.4641/ 180.0 4 3 2.0000/ –180.0 2.0000/ 180.0 4.0000/ 0.0 4 0 2.0000/ 0.0 2.0000/ 0.0 4.0000/ – 180.0 Faulted Bus Phase a Phase b Phase c 30GG Sequence Voltages BusV0V1V2 1 0.0703/ 0.0 0.5117/ 0.0 0.1177/ 0.0 2 0.0909/ 0.0 0.3896/ 0.0 0.1472/ 0.0 3 0.1943/ –0.0 0.1943/ 0.0 0.1943/ 0.0 4 0.0000/ 0.0 0.3554/ –30.0 0.1554/ 30.0 Phase Voltages Bus Va Vb Vc 1 0.6997/ 0.0 0.4197/ –125.6 0.4197/ 125.6 2 0.6277/ 0.0 0.2749/ –130.2 0.2749/ 130.2 3 0.5828/ 0.0 0.0000/ –30.7 0.0000/ –139.6 4 0.4536/ –12.7 0.4536/ –167.3 0.2000/ 90.0 ? 2000 by CRC Press LLC Further Considerations Generators are not the only sources in the system. All rotating machines are capable of contributing to fault current, at least momentarily. Syn- chronous and induction motors will continue to rotate due to inertia and function as sources of fault current. The impedance used for such machines is usually the transient reactance X￠ d or the subtransient X￠￠ d , depending on protective equipment and speed of response. Frequently motors smaller than 50 hp are neglected. Connecting systems are mod- eled with their Thévenin equivalents. Although we have used ac circuit techniques to calculate faults, the problem is fundamentally transient since it involves sudden switching actions. Consider the so-called dc offset current. We model the system by determining its positive sequence Thévenin equivalent circuit, looking back into the positive sequence network at the fault, as shown in Fig. 61.38. The transient fault current is Sequence Currents Bus to BusI0I1I2 1 2 0.4133/ 90.0 2.4416/ – 90.0 0.5887/ 90.0 1 0 0.4133/ –90.0 2.4416/ 90.0 0.5887/ –90.0 2 3 0.2067/ 90.0 1.2208/ – 90.0 0.2943/ 90.0 2 3 0.2067/ 90.0 1.2208/ – 90.0 0.2943/ 90.0 2 1 0.4133/ –90.0 2.4416/ 90.0 0.5887/ –90.0 3 2 0.2067/ – 90.0 1.2208/ 90.0 0.2943/ – 90.0 3 2 0.2067/ – 90.0 1.2208/ 90.0 0.2943/ – 90.0 3 4 3.8854/ – 90.0 3.2229/ 90.0 0.7771/ – 90.0 4 3 0.0000/ 0.0 3.2229/ – 120.0 0.7771/ 120.0 4 0 0.0000/ –90.0 3.2229/ 60.0 0.7771/ –60.0 Faulted Bus Phase a Phase b Phase c 30GG Phase Currents Bus to Bus Ia Ib Ic 1 2 1.4396/ –90.0 2.9465/ 153.0 2.9465/ 27.0 1 0 1.4396/ 90.0 2.9465/ –27.0 2.9465/ –153.0 2 3 0.7198/ –90.0 1.4733/ 153.0 1.4733/ 27.0 2 3 0.7198/ –90.0 1.4733/ 153.0 1.4733/ 27.0 2 1 1.4396/ 90.0 2.9465/ –27.0 2.9465/ –153.0 3 2 0.7198/ 90.0 1.4733/ –27.0 1.4733/ –153.0 3 2 0.7198/ 90.0 1.4733/ –27.0 1.4733/ – 153.0 3 4 1.4396/ –90.0 6.1721/ –55.9 6.1721/ –124.1 4 3 2.9132/ –133.4 2.9132/ 133.4 4.0000/ –0.0 4 0 2.9132/ 46.6 2.9132/ –46.6 4.0000/ –180.0 FIGURE 61.38 Positive sequence circuit looking back into faulted bus. it I t Ie t () cos( )=-+ - ac dc / 2 wb t ? 2000 by CRC Press LLC This is a first-order approximation and strictly applies only to the three-phase or phase-to-phase fault. Ground faults would involve the zero sequence network also. The maximum initial dc offset possible would be Max I dc = I max = I ac The dc offset will exponentially decay with time constant t, where The maximum dc offset current would be I dc (t) The transient rms current I(t), accounting for both the ac and dc terms, would be Define a multiplying factor k i such that I ac is to be multiplied by k i to estimate the interrupting capacity of a breaker which operates in time T op . Therefore, Observe that the maximum possible value for k i is ?3. Example In the circuit of Fig. 61.38, E = 2400 V, X = 2 W, R = 0.1 W, and f = 60 Hz. Compute k i and determine the interrupting capacity for the circuit breaker if it is designed to operate in two cycles. The fault is applied at t = 0. Solution I E RX It Ie t ac dc dc / rms ac current dc offset current = + = == - 22 () t 2 t w == L R X R It Ie Ie tt dc dc / ac / ()== -- 2 It I I t I e t () ()=+ = + - ac dc ac /22 2 12 t k IT I e i T ==+ - () op ac / op 12 2 t I T ke e i T ac op / A s = X R op @= == == =+ =+ = -- 2400 2 1200 2 60 0 0333 2 37 7 0 053 12 12 1252 2 0 0067 0 053 . . . . /.. t w t ? 2000 by CRC Press LLC Therefore I = k i I ac = 1.252(1200) = 1503 A The Thévenin equivalent at the fault point is determined by normal sinusoidal steady-state methods, resulting in a first-order circuit as shown in Fig. 61.38. While this provides satisfactory results for the steady-state component I ac , the X/R value so obtained can be in serious error when compared with the rate of decay of I(t) as measured by oscillographs on an actual faulted system. The major reasons for the discrepancy are, first of all, that the system, for transient analysis purposes, is actually high-order, and second, the generators do not hold constant impedance as the transient decays. Summary Computation of fault currents in power systems is best done by computer. The major steps are summarized below: ?Collect, read in, and store machine, transformer, and line data in per-unit on common bases. ?Formulate the sequence impedance matrices. ?Define the faulted bus and Z f . Specify type of fault to be analyzed. ?Compute the sequence voltages. ?Compute the sequence currents. ?Correct for wye-delta connections. ?Transform to phase currents and voltages. For large systems, computer formulation of the sequence impedance matrices is required. Refer to Further Information for more detail. Zero sequence networks for lines in close proximity to each other (on a common right-of-way) will be mutually coupled. If we are willing to use the same values for positive and negative sequence machine impedances, [Z 1 ] = [Z 2 ] Therefore, it is unnecessary to store these values in separate arrays, simplifying the program and reducing the computer storage requirements significantly. The error introduced by this approximation is usually not impor- tant. The methods previously discussed neglect the prefault, or load, component of current; that is, the usual assumption is that currents throughout the system were zero prior to the fault. This is almost never strictly true; however, the error produced is small since the fault currents are generally much larger than the load currents. Also, the load currents and fault currents are out of phase with each other, making their sum more nearly equal to the larger components than would have been the case if the currents were in phase. In addition, selection of precise values for prefault currents is somewhat speculative, since there is no way of predicting what the loaded state of the system is when a fault occurs. When it is important to consider load currents, a power flow study is made to calculate currents throughout the system, and these values are superimposed on (added to) results from the fault study. A term which has wide industrial use and acceptance is the fault level or fault MVA at a bus. It relates to the amount of current that can be expected to flow out of a bus into a three-phase fault. As such, it is an alternate way of providing positive sequence impedance information. Define Fault level in MVA at bus pu nominal pu fault base base base iV IS Z S S Z ii ii ii = == 3 3 3 1 1 11 f f f () ? 2000 by CRC Press LLC Fault study results may be further refined by approximating the effect of dc offset. The basic reason for making fault studies is to provide data that can be used to size and set protective devices. The role of such protective devices is to detect and remove faults to prevent or minimize damage to the power system. Defining Terms DC offset:The natural response component of the transient fault current, usually approximated with a first- order exponential expression. Fault:An unintentional and undesirable conducting path in an electrical power system. Fault MVA:At a specific location in a system, the initial symmetrical fault current multiplied by the prefault nominal line-to-neutral voltage (′ 3 for a three-phase system). Sequence (012) quantities:Symmetrical components computed from phase (abc) quantities. Can be voltages, currents, and/or impedances. References P. M. Anderson, Analysis of Faulted Power Systems, Ames: Iowa State Press, 1973. M. E. El-Hawary, Electric Power Systems: Design and Analysis, Reston, Va.: Reston Publishing, 1983. M. E. El-Hawary, Electric Power Systems, New York: IEEE Press, 1995. O. I. Elgerd, Electric Energy Systems Theory: An Introduction, 2nd ed., New York: McGraw-Hill, 1982. General Electric, Short-Circuit Current Calculations for Industrial and Commercial Power Systems, Publication GET-3550. C. A. Gross, Power System Analysis, 2nd ed., New York: Wiley, 1986. S. H. Horowitz, Power System Relaying, 2nd ed, New York: Wiley, 1995. I. Lazar, Electrical Systems Analysis and Design for Industrial Plants, New York: McGraw-Hill, 1980. C. R. Mason, The Art and Science of Protective Relaying, New York: Wiley, 1956. J. R. Neuenswander, Modern Power Systems, Scranton, Pa.: International Textbook, 1971. G. Stagg and A. H. El-Abiad, Computer Methods in Power System Analysis, New York: McGraw-Hill, 1968. Westinghouse Electric Corporation, Applied Protective Relaying, Relay-Instrument Division, Newark, N.J., 1976. A. J. Wood, Power Generation, Operation, and Control, New York: Wiley, 1996. Further Information For a comprehensive coverage of general fault analysis, see Paul M. Anderson, Analysis of Faulted Power Systems, New York, IEEE Press, 1995. Also see Chapters 9 and 10 of Power System Analysis by C.A. Gross, New York: Wiley, 1986. 61.6 Protection Arun G. Phadke Fundamental Principles of Protection Protective equipment—relays—is designed to respond to system abnormalities (faults) such as short circuits. When faults occur, the relays must signal the appropriate circuit breakers to trip and isolate the faulted equipment. The protection systems not only protect the faulty equipment from more serious damage, they also protect the power system from the consequences of having faults remain on the system for too long. In modern high-voltage systems, the potential for damage to the power system—rather than to the individual equip- ment—is often far more serious, and power system security considerations dictate the design of the protective system. The protective system consists of four major subsystems as shown in Fig. 61.39. The transducers (T) ? 2000 by CRC Press LLC are current and voltage transformers, which transform high voltages and currents to a more manageable level. In the United States, the most common standard for current trans- formers is a secondary current of 5 A (or less) for steady-state conditions. In Europe, and in some other foreign countries, a 1-A standard is also common. The voltage transformer stan- dard is 69.3 V line-to-neutral or 120 V line-to-line on the transformer secondary side. Standardization of the secondary current and voltage ratings of the transducers has permitted independent development of the transducers and relays. The power handling capability of the transducers is expressed in terms of the volt-ampere burden, which they can supply with- out significant waveform distortion. In general, the transient response of the transducers is much more critical in relaying applications. The second element of the protection system is the relay (R). This is the device that, using the current, voltage, and other inputs, can determine if a fault exists on the system, for which action on the part of the relay is needed. We will discuss relays in greater detail in the following. The third element of the protection chain is the circuit breaker (B), which does the actual job of interrupting the flow of current to the fault. Modern high- voltage circuit breakers are capable of interrupting currents of up to 100,000 A, against system voltages of up to 800,000 V, in about 15 to 30 ms. Lower-voltage circuit breakers are generally slower in operating speed. The last element of the protection chain is the station battery, which powers the relays and circuit breakers. The battery voltage has also been standardized at 125 V, although some other voltage levels may prevail in generating stations and in older substations. The relays and circuit breakers must remove the faulted equipment from the system as quickly as possible. Also, if there are many alternative ways of deenergizing the faulty equipment, the protection system must choose a strategy that will remove from service the minimum amount of equipment. These ideas are embodied in the concepts of zones of protection, relay speed, and reliability of protection. Zones of Protection To make sure that a protection system removes the min- imum amount of equipment from the power system dur- ing its operation, the power system is divided into zones of protection. Each zone has its associated protection system. A fault inside the zone causes the associated pro- tection system to operate. A fault in any other zone must not cause an operation. A zone of protection usually covers one piece of equipment, such as a transmission line. The zone boundary is defined by the location of transducers (usually current transformers) and also by circuit breakers that will operate to isolate the zone. A set of zones of protection is shown in Fig. 61.40. Note that all zones are shown to overlap with their neighbors. This is to ensure that no point on the system is left unprotected. Occasionally, a circuit breaker may not exist at a zone boundary. In such cases, the tripping must be done at some other remote circuit breakers. For example, consider protection zone A in Fig. 61.40. A fault in that zone must be isolated by tripping circuit breakers X and Y. While the breaker X is near the transformer and can be tripped locally, Y is remote from the station, and some form of communication channel must be used to transfer the trip command to Y. Although most zones of protection have a precise extent, there are some zones that have a loosely defined reach. These are known as open zones and are most often encountered in transmission line protection. Speed of Protection The faster the operation of a protection function, the quicker is the prospect of removing a fault from the system. Thus, all protection systems are made as fast as possible. However, there are considerations that dictate FIGURE 61.40Zones of protection for a power system. Zones overlap; most zones are bounded by breakers. FIGURE 61.39Elements of a protection system. ? 2000 by CRC Press LLC against making the protection faster than a minimum limit. Also, occasionally, it may be necessary to slow down a protection system in order to satisfy some specific system need. In general, the fastest protection available operates in about 5 to 10 ms after the inception of a fault [Thorp et al., 1979]. If the protection is made faster than this, it is likely to become “trigger happy” and operate falsely when it should not. When a protection system is intended as a backup system for some other protection, it is necessary to deliberately slow it down so that the primary protection may operate in its own time before the backup system will operate. This calls for a deliberate slowing of the backup protection. Depending upon the type of backup system being considered, the protection may sometimes be slowed down to operate in up to several seconds. Reliability of Protection In the field of relaying, reliability implies certain very specific concepts [Mason, 1956]. A reliable protection system has two attributes: dependability and security. A dependable relay is one that always operates for conditions for which it is designed to operate. A secure relay is one that will not operate for conditions for which it is not intended to operate. In modern power systems, the failure to operate when a fault occurs—lack of dependability—has very serious consequences for the power system. Therefore, most protective systems are made secure by duplicating relaying equipment, duplicating relaying functions, and providing several levels of backup protection. Thus modern systems tend to be very dependable, i.e., every fault is cleared, perhaps by more than one relay. As a consequence, security is somewhat degraded: modern protection systems will, occasionally, act and trip equipment falsely. Such occurrences are rare, but not uncommon. As power systems become leaner, i.e., they have insufficient margins of reserve generation and transmission, lack of security can be quite damaging. This has led to recent reevaluation of the proper balance between security and dependability of the protection systems. Overcurrent Protection The simplest fault detector is a sensor that measures the increase in current caused by the fault. The fuse is the simplest overcurrent protection; in fact, it is the complete protection chain—sensor, relay, and circuit breaker—in one package. Fuses are used in lower-voltage (distribution) circuits. They are difficult to set in high-voltage circuits, where load and fault currents may be of the same order of magnitude. Furthermore, they must be replaced when blown, which implies a long duration outage. They may also lead to system unbalances. However, when applicable, they are simple and inexpensive. Inverse-Time Characteristic Overcurrent relays sense the magnitude of the current in the circuit, and when it exceeds a preset value (known as the pickup setting of the relay), the relay closes its output contact, energizing the trip coil of the appropriate circuit breakers. The pickup setting must be set above the largest load current that the circuit may carry and must be smaller than the smallest fault current for which the relay must operate. A margin factor of 2 to 3 between the maximum load on the one hand and the minimum fault current on the other and the pickup setting of the relay is considered to be desirable. The overcurrent relays usually have an inverse-time characteristic as shown in Fig. 61.41. When the current exceeds the pickup setting, the relay operating time decreases in inverse proportion to the current magnitude. Besides this built-in feature in the relay mechanism, the relay also has a time-dial setting, which shifts the inverse-time curve vertically, allowing for more flexibility in setting the relays. The time dial has 11 discrete settings, usually labeled 1/2, 1, 2, . . ., 10, the lowest setting providing the fastest operation. The inverse-time characteristic offers an ideal relay for providing primary and backup protection in one package. FIGURE 61.41Inverse-time relay characteristic. ? 2000 by CRC Press LLC Coordination Principles Consider the radial transmission system shown in Fig. 61.42. The transformer supplies power to the feeder, which has four loads at buses A, B, C, and D. For a fault at F 1 , the relay R cd must operate to open the circuit breaker B cd . The relay R bc is responsible for a zone of protection, which includes the entire zone of R cd . This constitutes a remote backup for the protection at bus C. The backup relay (R bc ) must be slower than the primary relay (R cd ), its associated circuit breaker, with a safety margin. This delay in operating of the backup relay is known as the coordination delay and is usually about 0.3 s. In a similar fashion, R ab backs up R bc . The magnitude of the fault current varies as shown in Fig. 61.42(b), as the location of the fault is moved along the length of the feeder. We may plot the inverse time characteristic of the relay with the fault location as the abscissa, recalling that a smaller current magnitude gives rise to a longer operating time for the relay. The coordinating time delay between the primary and backup relays is also shown. It can be seen that, as we move from the far end of the feeder toward the source, the fault clearing time becomes progressively longer. The coordination is achieved by selecting relays with a time dial setting that will provide the proper separation in operating times. The effect of cumulative coordination-time delays is slowest clearing of faults with the largest fault currents. This is not entirely satisfactory from the system point of view, and wherever possible, the inverse-time relays are supplemented by instantaneous overcurrent relays. These relays, as the name implies, have no intentional time delays and operate in less than one cycle. However, they cannot coordinate with the downstream relays and therefore must not operate (“see”) for faults into the protection zone of the downstream relay. This criterion is not always possible to meet. However, whenever it can be met, instantaneous relays are used and provide a preferable compromise between fast fault clearing and coordinated backup protection. Directional Overcurrent Relays When power systems become meshed, as for most subtransmission and high-voltage transmission networks, inverse time overcurrent relays do not provide adequate protection under all conditions. The problem arises because the fault current can now be supplied from either end of the transmission line, and discrimination between faults inside and outside the zone of protection is not always possible. Consider the loop system shown in Fig. 61.43. Notice that in this system there must be a circuit breaker at each end of the line, as a fault on the line cannot be interrupted by opening one end alone. Zone A is the zone of protection for the line A–D. A fault at F 1 must be detected by the relays R ad and R da . The current through the circuit breaker B da for the fault F 1 must be the determining quantity for the operation of the relay R da . However, the impedances of the lines may be such that the current through the breaker B da for the fault F 2 may be higher than the current for the fault F 1 . Thus, if current magnitude alone is the criterion, the relay R da would operate for fault F 2 , as well as for the fault F 1 . Of course, operation of R da for F 2 is inappropriate, as it is outside its zone of protection, zone A. This FIGURE 61.42Coordination of inverse-time overcurrent and instantaneous relays for a radial system. ? 2000 by CRC Press LLC problem is solved by making the overcurrent relays directional. By this is meant that the relays will respond as overcurrent relays only if the fault is in the forward direction from the relays, i.e., in the direction in which their zone of protection extends. The directionality is provided by making the relay sensitive to the phase angle between the fault current and a reference quantity, such as the line voltage at the relay location. Other reference sources are also possible, including currents in the neutral of a transformer bank at the substation. Distance Protection As the power networks become more complex, protection with directional overcurrent relays becomes even more difficult, if not impossible. Recall that the pickup setting of the relays must be set above the maximum load which the line is expected to carry. However, a network system has so many probable configurations due to various circuit breaker operations that the maximum load becomes difficult to define. For the same reason, the minimum fault current—the other defining parameter for the pickup setting—also becomes uncertain. Under these circumstances, the setting of the pickup of the overcurrent relays, and their reach, which will satisfy all the constraints, becomes impossible. Distance relays solve this problem. Distance relays respond to a ratio of the voltage and current at the relay location. The ratio has the dimensions of an impedance, and the impedance between the relay location and fault point is proportional to the distance of the fault. As the zone boundary is related to the distance between the sending end and the receiving end of the transmission line, the distance to the fault forms an ideal relaying parameter. The distance is also a unique parameter in that it is independent of the current magnitude. It is thus free from most of the difficulties associated with the directional overcurrent relays mentioned above. In a three-phase power system, 10 types of faults are possible: three single phase-to-ground faults, three phase-to-phase faults, three double phase-to-ground faults, and one three-phase fault. It turns out that relays responsive to the ratio of delta voltages and delta currents measure the correct distance to all multiphase faults. The delta quantities are defined as the difference between any two phase quantities; for example, E a – E b is the delta voltage between a and b phases. Thus for a multiphase fault between phases x and y, where x and y can be a, b, or c and Z 1 is the positive sequence impedance between the relay location and the fault. For ground distance relays, the faulted phase voltage, and a compensated faulted phase current must be used where m is a constant depending upon the line impedances and I 0 is the zero sequence current in the trans- mission line. A full complement of relays consists of three phase distance relays and three ground distance relays. As explained before, the phase relays are energized by the delta quantities, while the ground distance relays are energized by each of the phase voltages and the corresponding compensated phase currents. In many instances, ground distance protection is not preferred, and the time overcurrent relays may be used for ground fault protection. Step-Distance Protection The principle of distance measurement for faults is explained above. A relaying system utilizing that principle must take into account several features of the measurement principle and develop a complete protection scheme. Consider the system shown in Fig. 61.44. The distance relay R ab must protect line AB, with its zone of protection as indicated by the dashed line. However, the distance calculation made by the relay is not precise enough for EE II Z xy xy - - = 1 E ImI Z x x + = 0 1 FIGURE 61.43Protection of a loop (network) sys- tem with directional overcurrent relays. ? 2000 by CRC Press LLC it to be able to distinguish between a fault just inside the zone and a fault just outside the zone, near bus B. This problem is solved by providing a two-zone scheme, such that if a fault is detected to be in zone 1, the relay trips instantaneously, and if the fault is detected to be inside zone 2, the relay trips with a time delay of about 0.3 s. Thus for faults near the zone boundary, the fault is cleared with this time delay, while for near faults, the clearing is instantaneous. This arrangement is referred to as a step-distance protection scheme, consisting of an underreaching zone (zone 1), and an overreaching zone (zone 2). The relays of the neighboring line (BC) can also be backed up by a third zone of the relay, which reaches beyond the zone of protection of relay R bc . Zone 3 operation is delayed further to allow the zone 1 or zone 2 of R bc to operate and clear the fault on line BC. The distance relays may be further subdivided into categories depending upon the shape of their protection characteristics. The most commonly used relays have a directional distance, or a mho characteristic. The two characteristics are shown in Fig. 61.45. The directional impedance relay consists of two functions, a directional detection function and a distance measurement function. The mho characteristic is inherently directional, as the mho circle, by relay design, passes through the origin of the RX plane. Figure 61.45 also shows the multiple zones of the step distance protection. Loadability of Distance Relays The load carried by a transmission line translates into an apparent impedance as seen by the relay, given by FIGURE 61.44Zones of protection in a step-distance protection scheme. Zone 3 provides backup for the downstream line relays. FIGURE 61.45(a) Directional impedance characteristic. (b) Mho characteristic. Loadability limits as shown. Z E PjQ app = - ** 2 ? 2000 by CRC Press LLC where P–jQ is the load complex power and E is the voltage at the bus where a distance relay is connected. This impedance maps into the RX plane, as do all other apparent impedances, and hence the question arises whether this apparent load impedance could be mistaken for a fault by the distance relay. Clearly, this depends upon the shape of the distance relay characteristic employed. The loadability of a distance relay refers to the maximum load power (minimum apparent impedance) that the line can carry before a protective zone of a distance relay is penetrated by the apparent impedance. A typical load line is shown in Fig. 61.45. It is clear from this figure that the mho characteristic has a higher loadability than the directional impedance relay. In fact, other relay characteristics can be designed so that the loadability of a relay is increased even further. Other Uses of Distance Relays Although the primary use of distance relays is in protecting transmission lines, some other protection tasks can also be served by distance relays. For example, loss-of-field protection of generators is often based upon distance relays. Out-of-step relays and relays for protecting reactors may also be distance relays. Distance relays are also used in pilot protection schemes described next, and as backup relays for power apparatus. Pilot Protection Pilot protection of transmission lines uses communication channels (pilot channels) between the line terminals as an integral element of the protection system. In general, pilot schemes may be subdivided into categories according to the medium of communication used. For example, the pilot channels may be wire pilots, leased telephone circuits, dedicated telephone circuits, microwave channels, power line carriers, or fiber optic channels. Pilot protection schemes may also be categorized according to their function, such as a tripping pilot or a blocking pilot. In the former, the communication medium is used to send a tripping signal to a remote line terminal, while in the latter, the pilot channel is used to send a signal that prevents tripping at the remote terminal for faults outside the zone of protection of the relays. The power line carrier system is the most common system used in the United States. It uses a communication channel with a carrier signal frequency ranging between 30 and 300 kHz, the most common bands being around 100 kHz. The modulated carrier signal is coupled into one or more phases of the power line through coupling capacitors. In almost all cases, the capacitors of the capacitive-coupled voltage transformers are used for this function (see Fig. 61.46). The carrier signal is received at both the sending and the receiving ends of the transmission line by tuned receivers. The carrier signal is blocked from flowing into the rest of the power system by blocking filters, which are parallel resonant circuits, known as wave traps. Coverage of 100% of Transmission Line The step-distance scheme utilizes the zone 1 and zone 2 combination to protect 100% of the transmission line. The middle portion of the transmission line, which lies in zone 1 of relays at the two ends of the line, is protected at high speed from both ends. However, for faults in the remaining portion of the line, the near end clears the fault at high speed, i.e., in zone 1 time, while the remote end clears the fault in zone 2 time. In effect, such faults remain on the system for zone 2 time, which may be of the order 0.3 to 0.5 s. This becomes undesirable in modern power systems where the margin of stability may be quite limited. In any case, it is good protection practice to protect the entire line with high-speed clearing of all internal faults from both ends of the trans- mission line. Pilot protection accomplishes this task. FIGURE 61.46Carrier system for pilot protection of lines. Transmitter and receiver are connected to relays. ? 2000 by CRC Press LLC Directional Comparison Blocking Scheme Consider the fault at F 2 shown in Fig. 61.47. As discussed above, this fault will be cleared in zone 1 time by the step-distance relay at bus B, while the relay at bus A will clear the fault in zone 2 time. Since the relays at bus B can determine, with a high degree of certainty, that a fault such as F 2 is indeed inside the zone of protection of the relays, one could communicate this knowledge to terminal A, which can then cause the local circuit breaker to trip for the fault F 2 . If the entire relaying and communication task can be accomplished quickly, 100% of the line can be protected at high speed. One of the most commonly used methods of achieving this function is to use overreaching zones of protection at both terminals, and if a fault is detected to be inside this zone, and if the remote terminal confirms that the fault is inside the zone of protection, then the local relay may be allowed to trip. In actual practice, the complement of this information is used to block the trip at the remote end. Thus, the remote end, terminal B in this case, detects faults that are outside the zone of protection and, for those faults, sends a signal which asks the relay at terminal A to block the tripping command. Thus, for a fault such as F 3 , the relay at A will trip, unless the communication is received from terminal B that this particular fault is outside the zone of protection—as indeed fault F 3 happens to be. This mode, known as a blocking carrier, is preferred, since a loss of the carrier signal created by an internal fault, or due to causes that are unrelated to the fault, will not prevent the trip at the remote end. This is a highly dependable protection system, and precisely because of that it is somewhat less secure. Nevertheless, as discussed previously, most power systems require that a fault be removed as quickly as possible, even if in doing so for a few faults an unwarranted trip may result. Other Pilot Protection Schemes Several other types of pilot protection schemes are available. The choice of a specific scheme depends upon many factors. Some of these factors are importance of the line to the power system, the available communication medium, dependability of the communication medium, loading level of the transmission line, susceptibility of the system to transient stability oscillations, presence of series or shunt compensating devices, multiterminal lines, etc. A more complete discussion of all these issues will be found in the references [Westinghouse, 1982; Blackburn, 1987; Horowitz and Phadke, 1992]. Computer Relaying Relaying with computers began to be discussed in technical literature in the mid-1960s. Initially, this was an academic exercise, as neither the computer speeds nor the computer costs could justify the use of computers for relaying. However, with the advent of high-performance microprocessors, computer relaying has become a very practical and attractive field of research and development. All major manufacturers of electric power equipment have computer relays to meet all the needs of power system engineers. Computer relaying is also being taught in several universities and has provided a very fertile field of research for graduate students. FIGURE 61.47Pilot protection with overreaching zones of protection. This is most commonly used in a directional comparison blocking scheme. ? 2000 by CRC Press LLC Computer relaying has also uncovered new ways of measuring power system parameters and may influence future development of power system monitoring and control functions. Incentives for Computer Relaying The acceptance of computer relays has been due to economic factors which have made microcomputers relatively inexpensive and computationally powerful. In addition to this economic advantage, the computer relays are also far more versatile. Through their self-diagnostic capability, they provide an assurance of avail- ability. Thus, even if they should suffer the same (or even greater) number of failures in the field as traditional relays, their failures could be communicated to control centers and a maintenance crew called to repair the failures immediately. This type of diagnostic capability was lacking in traditional protection systems and often led to failures of relays, which went undetected for extended periods. Such hidden failures have been identified as one of the main sources of power system blackouts. The computing power available with computer relays has also given rise to newer and better protection functions in several instances. Improved protection of transformers, multiterminal lines, fault location, and reclosing are a few of the protection functions where computer relaying is likely to have a significant impact. Very significant developments in the computer relaying field are likely to occur in the coming years. Architecture for a Computer Relay There are many ways of implementing computer-based relays. Figure 61.48 is a fairly typical block diagram of a computer relay architecture. The input signals consisting of voltage and currents and contact status are filtered to remove undesired frequency components and potentially damaging surges. These signals are sampled by the CPU under the control of a sampling clock. Typical sampling frequency used in a modern digital relay varies between 4 and 32 times the nominal power system frequency. The sampled data is processed by the CPU with a digital filtering algorithm, which estimates the appropriate relaying quantity. A typical relaying quantity may be the rms value of a current, the voltage or current phasor, or the apparent impedance. The estimated parameters are then compared with prestored relay characteristics, and the appropriate control action is initiated. The decision of the relay is communicated to the substation equipment, such as the circuit breaker, through the output ports. These outputs must also be filtered to block any surges from entering the relay through the output lines. In most cases, the relay can also communicate with the outside world through a modem. The data created by a fault is usually saved by the relaying computer and can be used for fault analysis or for sequence-of-event analysis following a power system disturbance. The user may interface with the relay through a keyboard, a control panel, or a communication port. In any case, provision must be made to enter relay settings in the relay and to save these settings in case the station power supply fails. Although the block diagram in Fig. 61.48 shows different individual subsystems, the actual hardware composition of the subsystems is dependent on the computer manufacturer. Thus, we may find several microprocessors in a given implemen- tation, each controlling one or more subsystems. Also, the hardware technology is in a state of flux, and in a few years, we may see an entirely different realization of the computer relays. Experience and Future Trends Field experience with the computer relays has been excellent so far. The manufacturers of traditional relays have adopted this technology in a big way. As more experience is gained with the special requirements of computer relays, it is likely that other—nontraditional—relay manufacturers will enter the field. FIGURE 61.48Block diagram of a computer relay architecture. ? 2000 by CRC Press LLC It seems clear that in computer relaying, power system engineers have obtained a tool with exciting new possibilities. Computers, with the communication networks now being developed, can lead to improved monitoring, protection, and control of power systems. An entirely new field, adaptive relaying, has been introduced recently [Phadke and Horowitz, 1990]. The idea is that protection systems should adapt to changing conditions of the power networks. In doing so, protection systems become more sensitive and reliable. Another development, which can be traced to computer relaying, is that of synchronized phasor measurements in power systems [Phadke and Thorp, 1991]. The development of the Global Positioning System (GPS) satellites has made possible the synchronization of sampling clocks used by relays and other measuring devices across the power system. This technology is expected to have a major impact on static and dynamic state estimation and on control of the electric power networks. Defining Terms Computer relays: Relays that use digital computers as their logic elements. Distance protection: Relaying principle based upon estimating fault location (distance) and providing a response based upon the distance to the fault. Electromechanical relays: Relays that use electromechanical logic elements. Pilot: A communication medium used by relays to help reach a reliable diagnosis of certain faults. Relays: Devices that detect faults on power equipment and systems and take appropriate control actions to deenergize the faulty equipment. Reliability: For relays, reliability implies dependability, i.e., certainty of operating when it is supposed to, and security, certainty of not operating when it is not supposed to. Solid state relays: Relays that use solid state analog components in their logic elements. Transducers: Current and voltage transformers that reduce high-magnitude signals to standardized low- magnitude signals which relays can use. Related Topic 1.3 Transformers References J.L. Blackburn, “Protective relaying,” Marcel Dekker, 1987. S.H. Horowitz and A.G. Phadke, Power System Relaying, Research Studies Press, New York: Wiley & Sons, 1992. C.R. Mason, The Art and Science of Protective Relaying, New York: Wiley & Sons, 1956. A.G. Phadke and S.H. Horowitz, “Adaptive relaying,” IEEE Computer Applications in Power, vol. 3, no. 3, pp. 47–51, July 1990. A.G. Phadke and J.S. Thorp, “Improved control and protection of power systems through synchronized phasor measurements,” in Analysis and Control System Techniques for Electric Power Systems, part 3, C.T. Leondes, Ed., San Diego: Academic Press, pp. 335–376, 1991. J.S. Thorp, A.G. Phadke, S.H. Horowitz, and J.E. Beehler, “Limits to impedance relaying,” IEEE Trans. PAS, vol. 98, no. 1, pp. 246–260, January/February 1979. Westinghouse Electric Corporation, “Applied Protective Relaying,” 1982. Further Information In addition to the references provided, papers sponsored by the Power System Relaying Committee of the IEEE and published in the IEEE Transactions on Power Delivery contain a wealth of information about protective relaying practices and systems. Publications of CIGRé also contain papers on relaying, through their Study Committee 34 on protection. Relays and relaying systems usually follow standards, issued by IEEE in this country, and by such international bodies as the IEC in Europe. The field of computer relaying has been covered in Computer Relaying for Power Systems, by A.G. Phadke and J.S. Thorp (New York: Wiley, 1988). ? 2000 by CRC Press LLC 61.7 Transient Operation of Power Systems R. B. Gungor Stable operations of power transmission systems have been a great concern of utilities since the beginning of early power distribution networks. The transient operation and the stability under transient operation are studied for existing systems, as well as the systems designed for future operations. Power systems must be stable while operating normally at steady state for slow system changes under switching operations, as well as under emergency conditions, such as lightning strikes, loss of some generation, or loss of some transmission lines due to faults. The tendency of a power system (or a part of it) to develop torques to maintain its stable operation is known as stability. The determina- tion of the stability of a system then is based on the static and dynamic characteristics of its synchronous generators. Although large induc- tion machines may contribute energy to the system during the sub- transient period that lasts one or two cycles at the start of the disturbance, in general, induction machine loads are treated as static loads for transient stability calculations. This is one of the simplifi- cation considerations, among others. The per-phase model of an ideal synchronous generator with non- linearities and the stator resistance neglected is shown in Fig. 61.49, where E g is the generated (excitation) voltage and X s is the steady-state direct axis synchronous reactance. In the calculation of transient and subtransient currents, X s is replaced by transient reactance X s ￠and subtransient reactance X s ￠￠,respectively. Per-phase electrical power output of the generator for this model is given by Eq. (61.71). (61.71) where d is the power angle, the angle between the generated voltage and the terminal voltage. The simple power-angle relation of Eq. (61.71) can be used for real power flow between any two voltages separated by a reactance. For the synchronous machine, the total real power is three times the value calculated by Eq. (61.71), when voltages in volts and the reactance in ohms are used. On the other hand, Eq. (61.71) gives per-unit power when per-unit voltages and reactance are used. Figure 61.50 shows a sketch of the power-angle relation of Eq. (61.71). Here the power P 1 is carried by the machine under d 1 , and P 2 under d 2 . For gradual changes in the output power up to P max for d = 90 o , the machine will be stable. So we can define the steady-state stability limit as (61.72) A sudden change in the load of the generator, e.g., from P 1 to P 2 , will cause the rotor to slow down so that the power angle d is increased to supply the additional power to the load. However, the deceleration of the rotor cannot stop instantaneously. Hence, although at d 2 the developed power is sufficient to supply the load, the rotor will overshoot d 2 until a large enough opposite torque is built up to stop deceleration. Now the excess energy will start accelerating the rotor to decrease d. Depending on the inertia and damping, these oscillations will die out or the machine will become unstable and lose its synchronism to drop out of the system. This is the basic transient operation of a synchronous generator. Note that during this operation it may be possible for d to become larger than 90 o and the machine still stay stable. Thus d = 90 o is not the transient stability limit. Figure 61.51 shows typical power-angle versus time relations. FIGURE 61.49Per-phase model of an ideal synchronous generator. P EV X P e gt s ==sin sin max dd d ? ?d ￡° >90 0 P ? 2000 by CRC Press LLC In the discussions to follow, the damping (stabilizing) effects of (1) the excitation systems; (2) the speed governors; and (3) the damper windings (copper squirrel-cage embedded into the poles of the synchronous generators) are omitted. Stable Operation of Power Systems Figure 61.52 shows an N-bus power system with G generators. To study the stability of multimachine transmission systems, the resistances of the transmission lines and transformers are neglected and the reactive networks are reduced down to the generator internal voltages by dropping the loads and eliminating the load buses. One such reduced network is sketched in Fig. 61.53. The power flow through the reactances of a reduced network are (61.73) FIGURE 61.50Power-angle characteristics of ideal synchronous generator. FIGURE 61.51Typical power angle–time relations. P EE X ij G ij ij ij ij ==sin , ,,...,d 12 ? 2000 by CRC Press LLC The generator powers are (61.74) The system will stay stable for (61.75) Equation (61.75) is observed for two machines at a time by considering all but two (say k and n) of the powers in Eq. (61.74) as constants. Since the variations of all powers but k and n are zero, we have (61.76) FIGURE 61.52 A multimachine reactive power system. FIGURE 61.53 Multiport reduced reactive network. PP iik k G = = ? 1 ? ?d P iG i ij >=012, ,..., dP P d P d P d i i i i i i i i iG iG = + + ××× + = ? ?d d ? ?d d ? ?d d 1 1 2 2 0 ? 2000 by CRC Press LLC These G-2 equations are simultaneously solved for G-2 dd ij s, then these are substituted in dP k and dP n equations to calculate the partial derivatives of P k and P n with respect to d kn to see if Eqs. (61.75) for i =k and i =n are satisfied. Then the process is repeated for the remaining pairs. Although the procedure outlined seems complicated, it is not too difficult to produce a computer algorithm for a given system. To study the transient stability, dynamic operations of synchronous machines must be considered. An ideal generator connected to an infinite bus (an ideal source) through a reactance is sketched in Fig. 61.54. The so-called swing equation relating the accelerating (or decelerating) power (difference between shaft power and electrical power as a function of d) to the second derivative of the power angle is given in Eq. (61.77). (61.77) where M = HS/180f (MJ/electrical degree); H is the inertia constant (MJ/MVA); S is the machine rating (MVA); f is the frequency (Hz); P s is the shaft power (MW). For a system of G machines, a set of G swing equations as given in Eq. (61.78) must be solved simultaneously. (61.78) The swing equation of the single-machine system of Fig. 61.54 can be solved either graphically or analytically. For graphical integration, which is called equal-area criterion, we represent the machine by its subtransient reactance, assuming that electrical power can be calculated by Eq. (61.71), and during the transients the shaft power P s remains constant. Then, using the power-angle curve(s), we sketch the locus of operating point on the curve(s) and equate the areas for stability. Figure 61.55 shows an example for which the shaft power of the machine is suddenly increased from the initial value of P o to P s . The excess energy (area A 1 ) will start to accelerate the rotor to increase d from d o to d m for which the area (A 2 ) above P s equals the area below. These areas are (61.79) Substituting, the values of P o , P s , d o , and d s , d m can be calculated. FIGURE 61.54An ideal generator connected to an infinite bus. PPP M d dt P EE X ase s gi =- =- 2 2 d dsin M d dt PP i G i i si ii 2 2 12 d d=- = max sin ,,..., AP P d APdP ss o sm s o s s m 1 2 =-- -- ò ò ( ) sin sin ( ) max max dd d dd d d d d d d ? 2000 by CRC Press LLC Figure 61.56 illustrates another example, where a three-phase fault reduces the power transfer to infinite bus to zero. d cc is the critical clearing angle beyond which the machine will not stay stable. The third example, shown in Fig. 61.57, indicates that the power transfers before, during, and after the fault are different. Here the system is stable as long as d m ￡ d max . For the analytical solution of the swing equation a numerical integration technique is used (Euler’s method, modified Euler’s method, Runge-Kutta method, etc.). The latter is most commonly used for computer algo- rithms. The solution methods developed are based on various assumptions. As before, machines are represented by subtransient reactances, electrical powers can be calculated by Eq. (61.71), and the shaft power does not change during transients. In addition, the velocity increments are assumed to start at the beginning of time increments, and acceleration increments start at the middle of time increments; finally, an average acceleration can be used where acceleration is discontinuous (e.g., where circuit breakers open or close). FIGURE 61.55A sudden loading of a synchronous generator. FIGURE 61.56Critical clearing angle for stability. ? 2000 by CRC Press LLC Figure 61.58 shows a sketch of angle, velocity, and acceleration changes related to time as outlined above. Under these assumptions the next value of the angle d can be obtained from the previous value as (61.80) where the accelerating power is P ak = P s – P ek and P ek = P maxk sin d k For hand calculations a table, as shown in Table 61.5, can be set up for fast processing. FIGURE 61.57Power-angle relation for power transfer during fault. TABLE 61.5Numerical Calculations of Swing Equations ntP max P e P ak D k+1 dd k 00 – 00 + 00 av 1 Dt 22Dt 33Dt 44Dt 55Dt 66Dt ddddd kkkkk ak t M P ++ =+ =++ 11 2 DD D() DtP M a ( ) 2 ? 2000 by CRC Press LLC Computer algorithms are developed by using the before-fault, during-fault, and after-fault Z BUS matrix of the reactive network reduced to generator internal voltages with generators represented by their subtransient reactances. Each generator’s swing curve is obtained by numerical integration of its power angle for a specified condition, then a set of swing curves is tabulated or graphed for observation of the transient stability. An example with partial calculated data and a line plot for such a study are included on the next page. Defining Terms Critical clearing angle: Power angle corresponding to the critical clearing time. Critical clearing time:The maximum time at which a fault must be cleared for the system to stay transiently stable. Disturbance (fault):A sudden change or a sequence of changes in the components or the formation of a power system. Large disturbance: A disturbance for which the equations for dynamic operation cannot be linearized for analysis. Power angle: The electrical angle between the generated and terminal voltages of a synchronous generator. Small disturbance: A disturbance for which the equations for dynamic operation can be linearized for analysis. Stability:The tendency of a power system (or a part of it) to develop torques to maintain its stable operation for a disturbance. FIGURE 61.58 Incremental angle, velocity, and acceleration changes versus time. ? 2000 by CRC Press LLC Steady-state stability: A power system is steady-state stable if it reaches another steady-state operating point after a small disturbance. Transient operation: A power system operating under abnormal conditions because of a disturbance. Transient stability: A power system is transiently stable if it reaches a steady-state operating point after a large disturbance. Related Topic 12.1 Introduction References J. Arrillaga, C.P. Arnold, and B.J. Harker, Computer Modeling of Electrical Power Systems, New York: Wiley, 1983. A.R. Bergen, Power System Analysis, Englewood Cliffs, N.J.: Prentice-Hall, 1986. H.E. Brown, Solution of Large Networks by Matrix Methods, New York: Wiley, 1985. A.A. Fouad and V. Vittal, Power System Transient Stability Analysis, Englewood Cliffs, N.J.: Prentice-Hall, 1992. J.D. Glover and M. Sarma, Power System Analysis and Design, Boston: PWS Publishers, 1987. C.A. Gross, Power System Analysis, 2nd ed., New York: Wiley, 1986. R.B. Gungor, Power Systems, San Diego: Harcourt Brace Jovanovich, 1988. G.T. Heydt, Computer Analysis Methods for Power Systems, New York: Macmillan, 1986. W.D. Stevenson, Elements of Power System Analysis, 4th ed., New York: McGraw-Hill, 1982. Y. Wallach, Calculations & Programs for Power System Networks, Englewood Cliffs, N.J.: Prentice-Hall, 1986. Transient stability program 7-Bus system with 3 generators 3-Phase fault at bus 6, cleared at 0.5 seconds by removing the line 1-6 Time Gen Angle Power .000 1 3.46 118.38 .000 2 5.80 111.90 .000 3 15.16 95.65 .050 1 3.46 118.59 .050 2 5.31 110.95 .050 3 15.86 96.24 .100 1 3.46 119.21 .100 2 3.84 108.12 .100 3 17.97 97.99 .150 1 3.46 120.15 .150 2 1.47 103.59 .150 3 21.45 100.83 .200 1 3.46 121.31 .200 2 –1.66 97.62 .200 3 26.27 104.66 .500 1 3.46 55.48 .500 2 –26.55 –215.72 .500 3 79.92 481.86 .900 1 3.46 –198.56 .900 2 100.99 458.41 .900 3 49.43 72.78 1.950 1 3.46 125.86 1.950 2 –30.18 –216.29 1.950 3 41.40 425.31 2.000 1 3.46 125.86 2.000 2 –34.60 –216.29 2.000 3 57.78 425.31 ? 2000 by CRC Press LLC Further Information In addition to the references listed above, further and more recent information can be found in IEEE publica- tions, such as IEEE Transactions on Power Systems, IEEE Transactions on Power Delivery, IEEE Transactions on Energy Conversion, and IEEE Transactions on Automatic Control. Power Engineering Review and Computer Applications in Power of the IEEE are good sources for paper summaries. Finally, IEEE Transactions on Power Apparatus and Systems dating back to the 1950s can be consulted. 61.8 Planning J. Duncan Glover An electric utility transmission system performs three basic functions: delivers outputs from generators to the system, supplies power to the distribution system, and provides for power interchange with other utilities. The electric utility industry has developed planning principles and criteria to ensure that the transmission system reliably performs these basic functions. The North American Electric Reliability Council (NERC) has provided definitions of the terms reliability, adequacy, and security (see Defining Terms at the end of this section). System reliability may be viewed from two perspectives: short-term reliability and long-term reliability. The system operator is primarily concerned with real-time security aspects in the short term, that is, supplying steady, uninterrupted service under existing operating conditions and as they occur over the next few minutes, hours, days, or months. The transmission planning engineer, however, is concerned not only with security aspects in the short term but also adequacy and security aspects in the long term, as many as 25 or more years into the future. The actual construction of a major transmission facility requires three to five years or more, depending largely on the siting and certification process. As such, the planning process requires up to ten years prior to operation of these facilities to ensure that they are available when required. The long lead times, environmental impacts, and high costs required for new transmission facilities require careful, near-optimal planning. Future changes in system operating conditions, such as changes in spatial load and generation patterns, create uncer- tainties that challenge the transmission planning engineer to select the best technical solution among several alternatives with due consideration of nontechnical factors. Transmission planning strives to maintain an optimal balance between system reliability, environmental impacts, and cost under future uncertainties. Before transmission planning is started, long-term load forecasting and generation planning are completed. In long-term load forecasting, peak and off-peak loads in each area of the system under study are projected, year by year, from the present up to 25 years into the future. Such forecasts are based on present and past load trends, population growth patterns, and economic indicators. In generation planning, generation resources are selected with sufficient generation reserve margins to meet projected customer loads with adequate quality and reliability in an economic manner. New generating units both at new plant sites and at existing plants are selected, and construction schedules are established to ensure that new generation goes on-line in time to meet projected loads. The results of long-term load forecasting and generation planning are used by transmission planning engi- neers to design the future transmission system so that it performs its basic functions. The following are selected during the transmission planning process. ?Routes for new lines ?Number of circuits for each route or right-of-way ?EHV versus HVDC lines ?Overhead versus underground line construction ?Types of towers for overhead lines ?Voltage levels ? 2000 by CRC Press LLC ? Line ratings ? Shunt reactive and series capacitive line compensation ? Number and locations of substations ? Bus and circuit breaker configurations at substations ? Circuit breaker ratings ? Number, location, and ratings of bulk-power-system transformers ? Number, location, and ratings of voltage-regulating transformers and phase-shifting transformers ? Number, location, and ratings of static VAR systems, synchronous condensers, and shunt capacitor banks for voltage control ? Basic insulation levels (BILs) ? Surge arrester locations and ratings ? Protective relaying schemes ? Communications facilities ? Upgrades of existing circuits ? Reinforcements of system interconnections Planning Tools As electric utilities have grown in size and the number of interconnections has increased, making the above selections during the planning process has become increasingly complex. The increasing cost of additions and modifications has made it imperative that planning engineers consider a wide range of design options and perform detailed studies on the effects on the system of each option based on a number of assumptions: normal and emergency operating conditions, peak and off-peak loadings, and present and future years of operation. A large volume of network data must be collected and accurately handled. To assist the planning engineer, the following digital computer programs are used [Glover and Sarma, 1994]: 1. Power-flow programs. Power-flow (also called load-flow) programs compute voltage magnitudes, phase angles, and transmission line power flows for a power system network under steady-state operating conditions. Other output results, including transformer tap settings, equipment losses, and reactive power outputs of generators and other devices, are also computed. To do this, the locations, sizes, and operating characteristics of all loads and generation resources of the system are specified as inputs. Other inputs include the network configuration as well as ratings and other characteristics of transmission lines, transformers, and other equipment. Today’s computers have sufficient storage and speed to com- pute in less than 1 min power-flow solutions for networks with more than 2000 buses and 2500 trans- mission lines. High-speed printers then print out the complete solution in tabular form for analysis by the planning engineer. Also available are interactive power-flow programs, whereby power-flow results are displayed on computer screens in the form of single-line diagrams; the engineer uses these to modify the network from a keyboard or with a mouse and can readily visualize the results. Spreadsheet analyses are also used. The computer’s large storage and high-speed capabilities allow the engineer to run the many different cases necessary for planning. 2. Transient stability programs. Transient stability programs are used to study power systems under dis- turbance conditions to predict whether synchronous generators remain in synchronism and system stability is maintained. System disturbances can be caused by the sudden loss of a generator or a transmission line, by sudden load increases or decreases, and by short circuits and switching operations. The stability program combines power-flow equations and generator dynamic equations to compute the angular swings of machines during disturbances. The program also computes critical clearing times for network faults and allows the planning engineer to investigate the effects of various network modifica- tions, machine parameters, disturbance types, and control schemes. 3. Short-circuits programs. Short-circuits programs compute three-phase and line-to-ground fault cur- rents in power system networks in order to evaluate circuit breakers and relays that detect faults and ? 2000 by CRC Press LLC control circuit breakers. Minimum and maximum short-circuit currents are computed for each circuit breaker and relay location under various system operating conditions, such as lines or generating units out of service, in order to specify circuit breaker ratings and protective relay schemes. 4. Transients programs. Transients programs compute the magnitudes and shapes of transient overvoltages and currents that result from switching operations and lightning strikes. Planning engineers use the results of transients programs to specify BILs for transmission lines, transformers, and other equipment and to select surge arresters that protect equipment against transient overvoltages. Research efforts aimed at developing computerized, automated transmission planning tools are ongoing. Examples and references are given in Back et al. [1989] and Smolleck et al. [1989]. Other programs for trans- mission planning include production-cost, investment-cost, relay-coordination, power-system database man- agement, transformer thermal analysis, and transmission line design programs. Some of the vendors that offer software packages for transmission planning are given as follows: ? ABB Network Control Ltd., Switzerland ? CYME International, Burlington, Mass. ? EDSDA Micro Corporation, Bloomfield, Mich. ? Electric Power Consultants, Inc., Scotia, N.Y. ? Electrocon International, Inc., Ann Arbor, Mich. ? Power Technologies, Inc., Schenectady, N.Y. ? Operation Technology, Inc., Irvine, Calif. Basic Planning Principles The electric utility industry has established basic planning principles intended to provide a balance among all power system components so as not to place too much dependence on any one component or group of components. Transmission planning criteria are developed from these principles along with actual system operating history and reasonable contingencies. These planning principles are given as follows: 1. Maintain a balance among power system components based on size of load, size of generating units and power plants, the amount of power transfer on any transmission line or group of lines, and the strength of interconnections with other utilities. In particular: a. Avoid excessive generating capacity at one unit, at one plant, or in one area. b. Avoid excessive power transfer through any single transformer, through any transmission line, circuit, tower, or right-of-way, or though any substation. c. Provide interconnection capacity to neighboring utilities that is commensurate with the size of generating units, power plants, and system load. 2. Provide transmission capability with ample margin above that required for normal power transfer from generators to loads in order to maintain a high degree of flexibility in operation and to meet a wide range of contingencies. 3. Provide for power system operation such that all equipment loadings remain within design capabilities. 4. Utilize switching arrangements, associated relay schemes, and controls that permit: a. Effective operation and maintenance of equipment without excessive risk of uncontrolled power interruptions. b. Prompt removal and isolation of faulted components. c. Prompt restoration in the event of loss of any part of the system. Equipment Ratings Transmission system loading criteria used by planning engineers are based on equipment ratings. Both normal and various emergency ratings are specified. Emergency ratings are typically based on the time required for either emergency operator actions or equipment repair times. For example, up to 2 h may be required following a major event such as loss of a large generating unit or a critical transmission facility in order to bring other ? 2000 by CRC Press LLC generating resources on-line and to perform appropriate line-switching operations. The time to repair a failed transmission line typically varies from 2 to 10 days, depending on the type of line (overhead, underground cable in conduit, or pipe-type cable). The time required to replace a failed bulk-power-system transformer is typically 30 days. As such, ratings of each transmission line or transformer may include normal, 2-h emergency, 2- to 10-day emergency, and in some cases 30-day emergency ratings. The rating of an overhead transmission line is based on the maximum temperature of the conductors. Conductor temperature affects the conductor sag between towers and the loss of conductor tensile strength due to annealing. If the temperature is too high, proscribed conductor-to-ground clearances [ANSI, 1993] may not be met, or the elastic limit of the conductor may be exceeded such that it cannot shrink to its original length when cooled. Conductor temperature depends on the current magnitude and its time duration, as well as on ambient temperature, wind velocity, solar radiation, and conductor surface conditions. Standard assump- tions on ambient temperature, wind velocity, etc., are selected, often conservatively, to calculate overhead transmission line ratings [ANSI/IEEE Std. 738–85, 1985]. It is common practice to have summer and winter normal line ratings, based on seasonal ambient temperature differences. Also, in locations with higher prevailing winds, such as coastal areas, larger normal line ratings may be selected. Emergency line ratings typically vary from 110 to 120% of normal ratings. Recently, real-time monitoring of actual conductor temperatures along a transmission line has been used for on-line dynamic transmission line ratings [Henke and Sciacca, 1989]. Normal ratings of bulk-power-system transformers are determined by manufacturers’ nameplate ratings. Nameplate ratings are based on the following ANSI/IEEE standard conditions: (1) continuous loading at nameplate output; (2) 30°C average ambient temperature (never exceeding 40°C); and (3) 110°C average hot- spot conductor temperature (never exceeding 120°C) for 65°C-average-winding-rise transformers [ANSI/IEEE C57.92-1981, 1990]. For 55°C-average-winding-rise transformers, the hot-spot temperature limit is 95°C aver- age (never exceeding 105°C). The actual output that a bulk-power-system transformer can deliver at any time with normal life expectancy may be more or less than the nameplate rating, depending on the ambient temperature and actual temperature rise of the windings. Emergency transformer ratings typically vary from 130 to 150% of nameplate ratings. Planning Criteria Transmission system planning criteria have been developed from the above planning principles and equipment ratings as well as from actual system operating data, probable operating modes, and equipment failure rates. These criteria are used to plan and build the transmission network with adequate margins to ensure a reliable supply of power to customers under reasonable equipment-outage contingencies. The transmission system should perform its basic functions under a wide range of operating conditions. Transmission planning criteria include equipment loading criteria, transmission voltage criteria, stability criteria, and regional planning criteria. Equipment Loading Criteria Typical equipment loading criteria are given in Table 61.6. With no equipment outages, transmission equipment loadings should not exceed normal ratings for all realistic combinations of generation and interchange. Oper- ation of all generating units including base-loaded and peaking units during peak load periods as well as operation of various combinations of generation and interchange during off-peak periods should be considered. Also, normal ratings should not be exceeded with all transmission lines and transformers in service and with any generating unit out of service. With any single-contingency outage, emergency ratings should not be exceeded. One loading criterion is not to exceed 2-h emergency ratings when any transmission line or transformer is out of service. This gives time to perform switching operations and change generation levels, including use of peaking units, to return to normal loadings. With some of the likely double-contingency outages, the transmission system should supply all system load without exceeding emergency ratings. One criterion is not to exceed 2- to 10-day emergency ratings when any line and any transformer are out of service or when any line and any generator are out of service. This gives time to repair the line. With the outage of any transformer and any generator, 30-day emergency ratings should not be exceeded, which gives time to install a spare transformer. ? 2000 by CRC Press LLC The loading criteria in Table 61.6 do not include all types of double-contingency outages. For example, the outage of a double-circuit transmission line or two transmission lines in the same right-of-way is not included. Also, the loss of two transformers in the same load area is not included. Under these double-contingency outages, it may be necessary to shed load at some locations during heavy load periods. Although experience has shown that these outages are relatively unlikely, their consequences should be evaluated in specific situations. Factors to be evaluated include the size of load served, the degree of risk, and the cost of reinforcement. Specific loading criteria may also be required for equipment serving critical loads and critical load areas. One criterion is to maintain service to critical loads under a double-contingency outage with the prior outage of any generator. Transmission Voltage Criteria Transmission voltages should be maintained within suitable ranges for both normal and reasonable emergency conditions. Abnormal transmission voltages can cause damage or malfunction of transmission equipment such as circuit breakers or transformers and adversely affect many customers. Low transmission voltages tend to cause low distribution voltages, which in turn cause increased distribution losses as well as higher motor currents at customer loads and at power plant auxiliaries. Transmission voltage planning criteria are intended to be conservative. Maximum planned transmission voltage is typically 105% of rated nominal voltage for both normal and reasonable emergency conditions. Typical minimum planned transmission voltages are given in Table 61.7. System conditions in Table 61.7 correspond to equipment out of service in Table 61.6. Single-contingency outages correspond to the loss of any line, any transformer, or any generator. Double-contingency outages correspond to the loss of any transmission line and transformer, any transmission line and generator, any transformer and generator, or any two generators. Typical planned minimum voltage criteria shown in Table 61.7 for EHV (345 kV and higher) substations and for generator substations are selected to maintain adequate voltage levels at interconnections, at power plant auxiliary buses, and on the lower-voltage transmission systems. Typical planned minimum voltage criteria for lower HV (such as 138 kV, 230 kV) transmission substations vary from 95 to 97.5% of nominal voltage under normal system conditions to as low as 92.5% of nominal under double-contingency outages. TABLE 61.6Typical Transmission Equipment Loading Criteria Equipment Out of Service Rating Not to Be Exceeded Comment None Normal Any generator Normal Any line or any transformer 2-h emergency Before switching. Any line and any transformer* 2- to 10-day emergency After switching required for both outages. Line repair time. Any line and any generator* 2- to 10-day emergency After switching required for both outages. Line repair time. Any transformer and any 30-day emergency After switching required for both outages. generator* Install spare transformer. *Some utilities do not include double-contingency outages in transmission system loading criteria. TABLE 61.7Typical Minimum Transmission Voltage Criteria Planned Minimum Transmission Voltage at Substations, % of Nominal System Condition Generator Station EHV Station HV Station Normal 102 98 95–97.5 Single-contingency outage 100 96 92.5–95 Double-contingency outage* 98 94 92.5 *Some utilities do not include double-contingency outages in planned minimum transmission voltage criteria. ? 2000 by CRC Press LLC Equipment used to control transmission voltages includes voltage regulators at generating units (excitation control), tap-changing transformers, regulating transformers, synchronous condensers, shunt reactors, shunt capacitor banks, and static VAR devices. When upgrades are selected during the planning process to meet planned transmission voltage criteria, some of this equipment should be assumed out of service. Stability Criteria System stability is the ability of all synchronous generators in operation to stay in synchronism with each other while moving from one operating condition to another. Steady-state stability refers to small changes in operating conditions, such as normal load changes. Transient stability refers to larger, abrupt changes, such as the loss of the largest generator or a short circuit followed by circuit breakers opening, where synchronism or loss of synchronism occurs within a few seconds. Dynamic stability refers to longer time periods, from minutes up to a half hour following a large, abrupt change, where steam generators (boilers), automatic generation control, and system operator actions affect stability. In the planning process, steady-state stability is evaluated via power-flow programs by the system’s ability to meet equipment loading criteria and transmission voltage criteria under steady-state conditions. Transient stability is evaluated via stability programs by simulating system transient response for various types of distur- bances, including short circuits and other abrupt network changes. The planning engineer designs the system to remain stable for the following typical disturbances: 1.With all transmission lines in service, a permanent three-phase fault (short circuit) occurs on any transmission line, on both transmission lines on any double-circuit tower, or at any bus; the fault is successfully cleared by primary relaying. 2.With any one transmission line out of service, a permanent three-phase fault occurs on any other transmission line; the fault is successfully cleared by primary relaying. 3.With all transmission lines in service, a permanent three-phase fault occurs on any transmission line; backup relaying clears the fault after a time delay, due to a circuit breaker failure. Regional Planning Criteria The North American Electric Reliability Council (NERC) defines nine geographical regions in North America, as shown in Fig. 61.59 [NERC, 1988]. Transmission planning studies are performed at two levels: (1) individual electric utility companies separately perform planning studies of their internal systems and (2) companies jointly participate in NERC committees or working groups to perform regional and interregional planning studies. The purpose of regional planning studies is to evaluate the transfer capabilities between interconnected utilities and the impact of severe disturbances. One typical regional criterion is that the incremental power transfer capability, in addition to scheduled interchange, should provide a reasonable generation reserve margin under the following conditions: peak load, the most critical transmission line out of service, no component overloaded. Another criterion is that severe disturbances to the interconnected transmission network should not result in system instability, widespread cascading outages, voltage collapse, or system blackouts. [NERC, 1988, 1989, and 1991]. Severe disturbances include the following: 1.With any three generating units or any combination of units up to 30% of system load out of service in an area, a sudden outage of any transmission line or any transformer occurs. 2.With any two generating units or any combination of units up to 20% of system load out of service in an area, a sudden outage of any generator or any double-circuit transmission line occurs. 3.With any transmission line or transformer out of service in an area, a sudden outage of any other transmission line or transformer occurs. 4.With any transmission line or transformer out of service in an area as well as any two generating units or any combination of units up to 20% of system load, a sudden outage of a transmission line occurs. 5.A sudden outage of all generating units at a power plant occurs. 6.A sudden outage of either a transmission substation or all transmission lines on a common right-of- way occurs. 7.A sudden outage of a large load or a major load center occurs. ? 2000 by CRC Press LLC When evaluating the impacts of the above severe disturbances, regional planning studies should consider steady-state stability, transient stability, and dynamic stability. These studies should also consider the effects of three-phase faults and slow fault clearing due to improper relaying or failure of a circuit breaker to open, as well as the anticipated load range and various operating conditions. Value-Based Transmission Planning Recently some utilities have begun to use a value-of-service concept in transmission planning [EPRI, 1986]. This concept establishes a method of assigning a dollar value to various levels of reliability in order to balance reliability and cost. For each particular outage, the amount and dollar value of unserved energy are determined. Dollar value of unserved energy is based on rate surveys of various types of customers. If the cost of the transmission project required to eliminate the outage exceeds the value of service, then that project is given a lower priority. As such, reliability is quantified, and benefit-to-cost ratios are used to compare and prioritize planning options. FIGURE 61.59 Nine regional reliability councils established by NERC. (Source: 1996 Annual Report, Princeton, N.J.: North American Electric Reliability Council, 1997. With permission.) ? 2000 by CRC Press LLC NIKOLA TESLA (1856–1943) ikola Tesla was born of Serbian parents in the village of Smiljan, in what is now Yugo- slavia. He showed his technical brilliance early, but felt that his native country offered him only limited opportunities. In 1884 he emigrated to the United States and began working for Thomas Edison. He soon struck out on his own, however, for Edison had little use for Tesla’s bold new ideas — in partic- ular, his brilliant solution to the problems of applying alternating current in light and power systems. Tesla’s polyphase ac system was brought to market by George Westinghouse, and after an acrimonious struggle with the Edison interests, which were wed- ded to the use of direct current (dc), the Tesla system became the standard in the twentieth century. Tesla’s other inventions included the synchronous ac motor, devices for generating high voltage and high frequency N ? 2000 by CRC Press LLC Defining Terms The North American Electric Reliability Council (NERC) defines reliability and the related terms adequacy and security as follows [NERC, 1988]: Adequacy: The ability of the bulk-power electric system to supply the aggregate electric power and energy requirements of the consumers at all times, taking into account scheduled and unscheduled outages of system components. Reliability: In a bulk-power electric system, reliability is the degree to which the performance of the elements of that system results in power being delivered to consumers within accepted standards and in the amount desired. The degree of reliability may be measured by the frequency, duration, and magnitude of adverse effects on consumer service. Security: The ability of the bulk-power electric system to withstand sudden disturbances such as electric short circuits or unanticipated loss of system components. References ANSI C2-1993, National Electrical Safety Code, 1993 Edition, Piscataway, N.J.: IEEE, 1993. ANSI/IEEE C57.92-1981, IEEE Guide for Loading Mineral-Oil Immersed Power Transformers Up to and Including 100 MVA with 55°C or 65°C Average Winding Rise, Piscataway, N.J.: IEEE, 1990. ANSI/IEEE Std. 738-1985, Calculation of Bare Overhead Conductor Temperature and Ampacity under Steady- State Conditions, Piscataway, N.J.: IEEE, 1985. H. Back et al., “PLATINE—A new computerized system to help in planning the power transmission networks,” IEEE Trans. Power Systems, vol. 4, no. 1, pp.242–247, 1989. currents, and contributions to radio technology. Tesla received the Edison Medal of the American Institute of Electrical Engineers in 1916. (Courtesy of the IEEE Center for the History of Electrical Engineering.) Electric Power Research Institute (EPRI), Value of Service Reliability to Consumers, Report EA-4494, Palo Alto, Calif.: EPRI, March 1986. J.D. Glover and M.S. Sarma, Power System Analysis and Design with Personal Computer Applications, 2nd ed., Boston: PWS Publishing Co., 1994. R.K. Henke and S.C. Sciacca, “Dynamic thermal rating of critical lines—A study of real-time interface require- ments,” IEEE Computer Applications in Power, pp. 46–51, July 1989. NERC, Reliability Concepts, Princeton, N.J.: North American Electric Reliability Council, February 1985. NERC, Overview of Planning Reliability Criteria, Princeton, N.J.: North American Electric Reliability Council, April 1988. NERC, Electricity Transfers and Reliability, Princeton, N.J.: North American Electric Reliability Council, October 1989. NERC, A Survey of the Voltage Collapse Phenomenon, Princeton, N.J.: North American Electric Reliability Council, 1991. H.A. Smolleck et al., “Translation of large data-bases for microcomputer-based application software: Method- ology and a case study,” IEEE Comput. Appl. Power, pp. 40–45, July 1989. Further Information The North American Electric Reliability Council (NERC) was formed in 1968, in the aftermath of the November 9, 1965, northeast blackout, to promote the reliability of bulk-electric-power systems of North America. Transmission planning criteria presented here are partially based on NERC criteria as well as on specific criteria used by transmission planning departments from three electric utility companies: American Electric Power Service Corporation, Commonwealth Edison Company, and Pacific Gas & Electric Company. NERC’s publi- cations, developed by utility experts, have become standards for the industry. In most cases, these publications are available at no charge from NERC, Princeton, N.J. ? 2000 by CRC Press LLC