[James_H._Harlow]_Electric_Power_Transformer_Engin(BookSee.org)

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If (V 0 / 1 > sat at the end of time t 1 , the flux reaches the saturation flux sat , voltage V is equal to V 1 , and the inductance of the saturated coil becomes L S . As L S is very small compared with L, the capacitor suddenly “discharges” across the coil in the form of an oscillation of pulsation a − Fundamental Mode v(t) |V(f)| v 2 (2.8.8) The current and flux peak when the electromagnetic energy stored in the coil is equivalent to the electrostatic energy 1 /2CV 2 restored by the capacitor. At instant t 2 , the flux returns to sat , the inductance reassumes the value L, and since the losses have been ignored, voltage V, which has been reversed, is equal to –V 1 . At instant t 3 , the flux reaches – sat and voltage V is equal to –V 2 . As 1 is in practice very small, we can consider V 2 V 1 V 0 . Consequently, period T of the oscillation is included between 2 LC in the 2 nonsaturated case and 22 LC S S 22( t( 3 t 3 t 2 t) 2 ) in the saturated case, where sat ( t3 t2) . The corre- V 0 sponding frequency f (f = 1/T) is thus such that: 1 LC S t T f 0 3f 0 nf 0 f b − Subharmonic Mode v(t) |V(f)| v t Ferroresonant Mode (1 Point) Normal Mode (n Points) i 1 1 f 2 LC 2 L C S nT f 0 /n f 0 /3 f 0 f i This initial frequency depends on sat , i.e., on the nonlinearity and the initial condition V 0 . In practice, due to the losses Ri 2 in the resistance R, the amplitude of voltage V decreases (V 2 < V 1 < V 0 ). Because the flux varies as follows, v(t) c − Quasi-Periodic Mode |V(f)| v t 3 2 stat t 2 vdt t (Closed Curve) a decrease of V results in a reduction in frequency. If the energy losses are supplied by the voltage source in the system, the frequency of the oscillations, as it decreases, can lock at the frequency of the source (if the initial frequency is greater than the power frequency) or even submultiple frequency of the source frequency (if the initial frequency is smaller than the power frequency). Note that there can be four resonance types, namely fundamental mode, subharmonic mode, quasiperiodic mode, or chaotic mode (see Figure 2.8.22). v(t) d − Chaotic Mode |V(f)| f 2 −f 1 f 1 f 2 3f 1 −f 2 nf 1 +mf 2 f v i t Strange Attractor f i FIGURE 2.8.22 Waveforms typical of a periodic ferroresonance. © 2004 by CRC Press LLC © 2004 by CRC Press LLC
References 1. Sola/Hevi-Duty Corp., About Sola/Hevi-Duty, www.sola-hevi-duty.com/about/solahist.html, October 18, 2002. 2. Advance Galatrek, CVT Background Data, http://www.aelgroup.co.uk/hb/hb003.htm, October 18, 2002. 3. EPRI, System Compatibility Projects to Characterize Electronic Equipment Performance under Varying Electric Service Supply Conditions, EPRI PEAC, Knoxville, TN, May 1993. 4. Godfrey, S., Ferroresonance, http://www.physics.carleton.ca/courses/75.364/mp-1html/node7.html, October 18, 2002. 5. Cadicorp, Ferro-Resonance, Technical Bulletin 004a, www.cadicorp.com, October 18, 2002. 6. Groupe Schneider, Ferroresonance, No. 190, www.schneiderelectric.com, October 19, 2002. 7. IEEE, Standard for Ferroresonant Voltage Regulators, IEEE Std. 449-1998, Institute of Electrical and Electronics Engineers, Piscataway, NJ, 1998. 8. EPRI, Sizing Constant-Voltage Transformers to Maximize Voltage Regulation for Process Control Devices, PQTN Application No. 10, EPRI PEAC, Knoxville, TN, October 1997. 9. EPRI, Ferro-Resonant Transformer Output Performance under Varying Supply Conditions, PQTN Brief No. 13, EPRI PEAC, Knoxville, TN, May 1993. 10. EPRI, Ferro-Resonant Transformer Output Performance under Dynamic Supply Conditions, PQTN Brief No. 14, EPRI PEAC, Knoxville, TN, January 1994. 11. EPRI, Ferro-Resonant Transformer Input Electrical Characteristics during Linear and Nonlinear Loading, PQTN Brief No. 16, EPRI PEAC, Knoxville, TN, February 1994. 12. EPRI, Testing a Prototype Ferro-Resonant Transformer, EPRI PEAC, Knoxville, TN, unpublished. 2.9 Reactors Richard F. Dudley, Michael Sharp, Antonio Castanheira, and Behdad Biglar Reactors, like capacitors, are basic to and an integral part of both distribution and transmission power systems. Depending on their function, reactors are connected either in shunt or in series with the network. Reactors are connected either singularly (current-limiting reactors, shunt reactors) or in conjunction with other basic components such as power capacitors (shunt-capacitor-switching reactors, capacitordischarge reactors, filter reactors). Reactors are utilized to provide inductive reactance in power circuits for a wide variety of purposes, including fault-current limiting, inrush-current limiting (for capacitors and motors), harmonic filtering, VAR compensation, reduction of ripple currents, blocking of power-line carrier signals, neutral grounding, damping of switching transients, flicker reduction for arc-furnace applications, circuit detuning, load balancing, and power conditioning. Reactors can be installed at any industrial, distribution, or transmission voltage level and can be rated for any current duty from a few amperes to tens of thousands of amperes and fault-current levels of up to hundreds of thousands of amperes. 2.9.1 Background and Historical Perspective Reactors can be either dry type or oil immersed. Dry-type reactors can be of air-core or iron-core construction. In the past, dry-type air-core reactors were only available in open-style construction (Figure 2.9.1), their windings held in place by a mechanical clamping system and the basic insulation provided by the air space between turns. Modern dry-type air-core reactors (Figure 2.9.2) feature fully encapsulated windings with the turns insulation provided by film, fiber, or enamel dielectric. Oil-immersed reactors can be of gapped iron-core (Figure 2.9.3) or magnetically shielded construction. The application range FIGURE 2.9.1 Open-style reactor. for the different reactor technologies has undergone a major realignment from historical usage. In the past, dry-type air-core reactors (open-style winding technology) were limited to applications at distribution-voltage class. Modern dry-type air-core reactors (fully encapsulated with solid-dielectric-insulated windings) are employed over the full range of distribution and transmission voltages, including high voltage (HV) and extra high voltage (EHV) ac transmission voltage classes (high-voltage series reactors) and high-voltage direct-current (HVDC) systems (ac and dc filter reactors, smoothing reactors). Oil-immersed reactors are primarily used for EHV-shunt-reactor and for some HVDCsmoothing-reactor applications. Dry-type iron-core reactors (Figure 2.9.4) are usually used at low voltage and indoors for applications such as harmonic filtering and power conditioning (di /dt, smoothing, etc.). Applicable IEEE standards, such as IEEE C57.21-1990 (R 1995), IEEE C57.16-1996 (R 2001), and IEEE 1277-2000, reflect these practices. [6,8,9] These standards provide considerable information not only concerning critical reactor ratings, operational characteristics, tolerances, and test code, but also guidance for installation and important application-specific considerations. 2.9.2 Applications of Reactors 2.9.2.1 General Overview Reactors have always been an integral part of power systems. The type of technology employed for the various applications has changed over the years based on design evolution and breakthroughs in construction and materials. Dry-type air-core reactors have traditionally been used for current-limiting applications due to their inherent linearity of inductance vs. current. For this application, fully © 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
Page 51 and 52: 2.3.8.1.2 Series Connection • The
Page 53 and 54: A six-pulse single-way transformer
Page 55 and 56: The degree of coupling also influen
Page 57 and 58: where I h = current for the hth har
Page 59 and 60: In the case of liquid-filled transf
Page 61 and 62: FIGURE 2.4.21 A 36-pulse system mad
Page 63 and 64: Vacuum-pressure encaps ulated — T
Page 65 and 66: 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: • Input frequency or frequency ra
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 and 118: ate of rise of transient-recovery v
Page 119 and 120: the LLCR is provided in IEEE Std. C
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
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3.5.4 Three-Phase Transformer Conne
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FIGURE 3.5.4 Interconnected star-gr
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3.6.1.1 Standards ANSI standards fo
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ANSI standards. LTC control setting
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FIGURE 3.6.7 Discharging the capaci
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FIGURE 3.6.10 Standard switching-im
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voltage of the excited winding, rea
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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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