[James_H._Harlow]_Electric_Power_Transformer_Engin(BookSee.org)

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etc.). If a reactor is off-load, then the losses are zero, and if the reactor is energized, then it exhibits power-loss consumption. Thus reactor losses can be treated in the same way as transformer load losses. The main aspects that need to be considered when assessing reactor losses are: • Anticipated load profile (load factor) • Rated (operating) bus-bar voltage (for shunt and filter reactors) • Ambient temperature • Harmonics FIGURE 2.9.37 Results of a TRV study for a subtransmission substation: (a) circuit breaker TRV capability, (b) system TRV with no reactor installed, (c) system TRV with a current-limiting reactor installed, (d) system TRV with capacitor across reactor terminals. 2.9.6 Reactor Loss Evaluation Loss evaluation is often given a high profile by utilities in their tender analysis when purchasing reactors. The consideration of the cost of losses can be a significant factor in the design of reactors, so that the purchaser needs to ensure that loss evaluation, if applied, is made under clearly defined conditions according to clearly defined procedures. Reactor designs can readily be modified to provide the lowest-loss evaluated equipment total cost (the sum of capital cost and cost of losses as calculated from the loss evaluation). 2.9.6.1 Reactor Losses The losses in a reactor loaded with fundamental current and, if present, with harmonic current can be determined by Equation 2.9.41, P n N 2 n 1 In . X Q (2.9.41) where P = reactor loss, kW n = harmonic number (n = 1 … fundamental current) N = maximum harmonic order I n = current in the reactor at harmonic order n, A X n = reactor reactance at harmonic order n, Q n = reactor q-factor at harmonic order n Unlike transformers, reactors do not have no-load losses, and in most cases they have nil or negligible auxiliary losses (oil-immersed reactors only have auxiliary losses associated with cooling fans, oil pumps, n n Series reactors (current-limiting and load-balancing reactors) are load-cycled, and thus the loss will vary with current. Shunt reactors are constantly at full load when they are connected to the bus. Their losses depend only on the operating voltage of the bus bar, and the cost of losses is a function of connection time. As the reactor losses vary with temperature it is important to specify an appropriate reference temperature at which the losses shall be declared by the reactor manufacturer. A standard reference temperature is 75˚C. In case of highly loss-evaluated reactors, the temperature rise of the winding is usually low. For this condition, it is reasonable to specify a lower reference temperature. For example, if the average winding-temperature rise of a reactor is 35˚C and the average ambient is 20˚C, then 55˚C instead of 75˚C will better represent a reference temperature for loss evaluation. It should be noted that harmonic currents can be decisive in declaring the losses for filter reactors, but the losses at harmonic frequencies of reactors other than filter reactors are usually almost negligible in comparison with those at fundamental frequency. Also, harmonic losses (Q factor) are not usually included in loss evaluations, since filter-quality factors at the tuning frequency are often dictated by other filter design considerations, such as filter bandwidth, damping requirements, and required level of harmonic filtering. 2.9.6.2 Basic Concepts for Loss Evaluation Each supply authority determines the cost of losses for its own particular operating conditions. Because these differ from authority to authority, the cost of capitalized losses will also vary. The cost of losses is generally the sum of two components: 1. The cost reflecting the generating capacity (installation cost) The cost of installing the generating capacity to supply the peak losses in the supply system so that it, in turn, can supply the power losses in the reactors. The cost of capacity is generally assumed to be the lowest-cost means of providing the peaking capacity, e.g., gasturbine peaking units, or alternatively it can be based on the average cost of new generating capacity. 2. The energy cost (kilowatt-hour cost) of reactor losses The energy cost to reflect the actual cost of supplying the energy consumed by the reactor. Because energy is consumed throughout the entire life of the reactor, further factors need to be considered to determine a present-value worth of the future losses. These include: Load factor or connection time (shunt reactors) Efficiency of supplying the energy consumed by the reactor Cost escalation rate for energy Discount rate for present-valuing future costs Anticipated operating life of the reactor Typical loss-evaluation figures (load-power-loss cost rates, LLCR), range from a few hundred dollars per kilowatt to a few thousands of dollars per kilowatt. Loss penalties for reactors with measured losses exceeding guaranteed values are often applied at the same rate as the evaluation. A method of calculating © 2004 by CRC Press LLC © 2004 by CRC Press LLC
the LLCR is provided in IEEE Std. C57.120-1991, IEEE Loss Evaluation Guide for <strong>Power</strong> <strong>Transformer</strong>s and Reactors.[18] 2.9.6.3 Operational Benefits of Loss Evaluation Where loss evaluations are significant and result in lower-loss reactor designs, further operational advantages may ensue, including: • Lower reactor operating temperature and hence increased service life • Increased reactor-overload capability • Less cooling required for indoor units 2.9.7 De-Q’ing Various levels of electrical damping are required in a number of reactor applications, including harmonic filters, shunt-capacitor banks, and series-capacitor banks. All are inductive/capacitive circuits, and damping is usually governed by the resistive component of the reactor impedance. If this is insufficient, then other means of providing damping must be employed. The required level of damping in a harmonic filter depends on system parameters. In the case of harmonic-filter, shunt-capacitor-bank, and seriescapacitor-bank applications, the required level of damping is driven by system design. Damping is usually required at a specific frequency. The Q factor is a measure of the damping, with a lower Q indicating higher damping. The Q factor is the ratio of reactive power to active power in the reactor at a specific frequency. In cases requiring high damping, the natural Q factor of the reactor is usually too high. However, there are methods available to reduce the Q of a reactor by increasing the stray losses through special design approaches, including increasing conductor eddy loss and mechanical clamping-structure eddy loss. In the case of reactors for shunt-capacitor-bank and series-capacitor-bank applications, this method is usually sufficient. In the case of reactors for harmonic-filter applications, other more-stringent approaches may be necessary. One traditional method involves the use of resistors, which, depending on their rating, can be mounted in the interior or on top of the reactor or separately mounted. Resistors are usually connected in parallel with the reactor. Figure 2.9.38 shows a tapped-filter reactor with a separately mounted resistor for an ac filter on an HVDC project. Another more-innovative and patented approach involves the use of de-Q’ing rings, which can reduce the Q factor of the reactor by a factor of as much as 10. A filter reactor with de-Q’ing rings is illustrated in Figure 2.9.39. The de-Q’ing system comprises a single or several coaxially arranged closed rings that couple with the main field of the reactor. The induced currents in the closed rings dissipate energy in the rings, which lowers the Q-factor of the reactor. Because of the large energy dissipated in the rings, they must be constructed to have a very large surface-to-volume ratio in order to dissipate the heat. Therefore, they are usually constructed of thin, tall sheets of stainless steel. Cooling is provided by thermal radiation and by natural convection of the surrounding air, which enters between the sheets at the bottom end of the de-Q’ing system and exits at its top end. The stainless-steel material used for the rings can be operated up to about 300C without altering the physical characteristics/parameters. Especially important is that the variation of resistance with temperature be negligible. The physical dimensions of the rings, their number, and their location with respect to the winding are chosen to give the desired Q-factor at the appropriate frequency. The Q characteristic of a reactor with de-Q’ing rings is very similar to that of a reactor shunted by a resistor. The basic theory for both approaches is described in the following paragraphs. 2.9.7.1 Paralleled Reactor and Resistor Figure 2.9.40a shows a circuit diagram corresponding to a resistor in parallel with a fully modeled reactor, i.e., one having series resistance. For simplicity, it is assumed that the series resistance is not frequency dependent. For this nonideal case, the expression for Q is given by Equation 2.9.42. FIGURE 2.9.38 AC filter for an HVDC project; capacitors, tapped filter reactors, and separately mounted resistors. LR 1 p Q 2 2 2 RR R L s p s (2.9.42) where L 1 = self inductance of reactor, H R p = resistance of parallel resistor, R s = series resistance of reactor, The Q-vs.-frequency characteristic is shown in Figure 2.9.40b. For very low frequencies, the system behaves like a series R-L circuit, i.e., Q is approximately equal to L 1 /R s , and Q equals zero when equals zero. For very high frequencies, the system behaves like a paralleled R-L circuit, with Q approximately equal to R p / L 1 and approaching zero as approaches infinity. It can be shown that Q reaches a maximum at a frequency given by Equation 2.9.43. 1 2 RR s p Rs L1 The maximum value of the Q is given by Equation 2.9.44. Qmax 2 R R R (2.9.43) (2.9.44) 2.9.7.2 Reactor with a De-Q’ing Ring The circuit diagram for a reactor with a de-Q’ing ring is shown in Figure 2.9.41a. For simplicity, it is assumed that the series resistance is not a function of frequency. The expression for Q as a function of frequency is given by Equation 2.9.45, 1 p 2 s p RS © 2004 by CRC Press LLC © 2004 by CRC Press LLC
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ELECTRIC POWER TRANSFORMER ENGINEER
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I wish to recognize the interest of
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Contents 1 Theory and Principles Ch
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1.3 Equivalent Circuit of an Iron-C
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designer starts to make a design fo
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• Transient voltages generated du
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the transformer’s bushings and, m
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% regulation = [(V NL - V FL )/V FL
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In core-form transformers, the wind
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FIGURE 2.1.14 Layer windings (singl
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the transformer design, which may b
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consumer’s service circuit is a d
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FIGURE 2.2.3 Single-phase transform
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is installed so that the tank never
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above which persons might be burned
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FIGURE 2.2.16 Two-bushing subway. (
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carbon steel or the very expensive
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FIGURE 2.2.31 Radial-style dead fro
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FIGURE 2.2.36 Complete transformer
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voltage in each winding simultaneou
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mounted transformers can have arres
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V S + V S I V L Z=R+jX a) V L V S V
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Z = jX (2.3.19) 0.7 Then the curren
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X1 L* X1 S =X1 L X2 L* X3 L* a) S L
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150 V(%) 100 50 0 -50 40 80 T(s) 12
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2.3.8.1.2 Series Connection • The
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A six-pulse single-way transformer
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The degree of coupling also influen
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where I h = current for the hth har
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In the case of liquid-filled transf
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FIGURE 2.4.21 A 36-pulse system mad
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Vacuum-pressure encaps ulated — T
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FIGURE 2.6.1 Typical wiring and sin
Page 67 and 68: a) H1 b) Ip X2 FLUX H2 LEAKAGE FLUX
Page 69 and 70: and for CTs is TCF = RCF - (PA/2600
Page 71 and 72: RCF x Bx Bt RCF t - RCF 0 co
Page 73 and 74: 2000 1000 5% Vex BANDWITH FROM NOMI
Page 75 and 76: This may be more useful when operat
Page 77 and 78: also some uncertainty in repeatabil
Page 79 and 80: FIGURE 2.6.25 Standard two-element
Page 81 and 82: 2.7 Step-Voltage Regulators Craig A
Page 83 and 84: Source Bypass Switch Source Bypass
Page 85 and 86: 2.7.4 Theory A step-voltage regulat
Page 87 and 88: FIGURE 2.7.22 Equalizer winding inc
Page 89 and 90: TABLE 2.7.4 Increase in Ampere Load
Page 91 and 92: References IEEE, Standard Requireme
Page 93 and 94: 300% FIGURE 2.8.4 Schematic of a co
Page 95 and 96: TABLE 2.8.1 Typical Sizing Workshee
Page 97 and 98: Input with Interruption Ferro Outpu
Page 99 and 100: FIGURE 2.8.20A Performance of a rid
Page 101 and 102: • Input frequency or frequency ra
Page 103 and 104: References 1. Sola/Hevi-Duty Corp.,
Page 105 and 106: FIGURE 2.9.5 Typical phase-reactor
Page 107 and 108: FIGURE 2.9.10 Two generator arrange
Page 109 and 110: • Overloading of lines • Increa
Page 111 and 112: FIGURE 2.9.23 34-kV, 25-MVAR (per p
Page 113 and 114: V 90 ( X X ) s T (2.9.10a) where,
Page 115 and 116: Therefore, Line reactive losses = (
Page 117: ate of rise of transient-recovery v
Page 121 and 122: aluminum shielding, i.e., an oil-im
Page 123 and 124: Leo J. Savio ADAPT Corporation Ted
Page 125 and 126: 3.1.2.2.2 Heat Dissipation A second
Page 127 and 128: FIGURE 3.2.1 Solid-type bushing. ma
Page 129 and 130: 1.6 cm. This means that most of the
Page 131 and 132: where HS = steady-state bushing ho
Page 133 and 134: the conductivity of the water-solub
Page 135 and 136: of 178 ohm-m, and a test duration o
Page 137 and 138: 2. Easley, J.K. and Stockum, F.R.,
Page 139 and 140: FIGURE 3.3.5 Reactance-type LTC, in
Page 141 and 142: FIGURE 3.3.10 LTC with delta connec
Page 143 and 144: 3.3.5 Selection of Load Tap Changer
Page 145 and 146: FIGURE 3.3.19 Effect of the leakage
Page 147 and 148: References Goosen, P.V. , Transform
Page 149 and 150: If i 1 is the full-load current rat
Page 151 and 152: TABLE 3.4.1 Loading Recommendations
Page 153 and 154: 3.5.4 Three-Phase Transformer Conne
Page 155 and 156: FIGURE 3.5.4 Interconnected star-gr
Page 157 and 158: 3.6.1.1 Standards ANSI standards fo
Page 159 and 160: ANSI standards. LTC control setting
Page 161 and 162: FIGURE 3.6.7 Discharging the capaci
Page 163 and 164: FIGURE 3.6.10 Standard switching-im
Page 165 and 166: voltage of the excited winding, rea
Page 167 and 168: FIGURE 3.6.18 Current, voltage, and
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TABLE 3.6.3 Transformer Short-Circu
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FIGURE 3.7.3 Control for voltage re
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FIGURE 3.7.6A Feeder with power-fac
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3. Circulating current (current bal
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FIGURE 3.7.10 Control block diagram
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Primary Current (Amps) 60 40 20 0 -
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current transformer having two prim
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87R1 87BL1 (A) Independent Harmonic
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Winding 1 Secondary Currents Data A
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Y Y 20 18 3 rd Harmonic CTR1=40 CTR
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230 kV 3 180 MVA 138 kV 5 CTR1 = 2
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29. Concordia, C. and Rothe, F.S.,
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FIGURE 3.9.1 Measurement of pressur
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H 2m 1. Vertical Forced Air 2. Prin
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Gade, S., Sound Intensity Instrumen
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nected. This steady-state voltage d
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where [A] = state matrix [B] = inpu
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where C = capacitance between the t
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L ijo = N i N j ijo (3.10.31) 1.4
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% VOLTAGE % VOLTAGE 100 BIL 90 50 3
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29. Degeneff, R.C., Reducing Storag
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All connections should be cleaned a
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6. Costs to set up and use a mobile
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Records of relay operation must be
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• Has heating occurred as the res
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a reference value) of the currents
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The next data-processing step is to
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temperature. As the transformer coo
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3.13.3.2 Instrument Transformers Th
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FIGURE 3.13.5 Analysis of bushing s
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temperature. Under abnormal conditi
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3.14.1.2 Accredited Standards Commi
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FIGURE 3.14.4 IEC technical-committ
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TABLE 3.14.2 Relevant Documents for
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TABLE 3.14.13 Relevant Documents fo
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[James_H._Harlow]_Electric_Power_Transformer_Engin(BookSee.org)

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