[James_H._Harlow]_Electric_Power_Transformer_Engin(BookSee.org)

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FIGURE 2.8.2 Components of a typical constant-voltage transformer. 2.8.1.3.1 Saturation of Ferromagnetic Core A flux-current curve is shown in Figure 2.8.3 [4]. In the linear portion of the curve, as the current increases, the magnetic-flux density increases. However, a point is reached where further increases in current yield smaller and smaller increases in flux density. This point is called the saturation point (see Figure 2.8.3) and is characterized by a dramatic reduction in the slope of the curve. In fact, the curve is no longer linear. Because the slope of the flux-current curve is proportional to the inductance of the coil, the reduction in the slope causes reduction in the inductance. The new inductance may be 100 times less than the inductance in the linear portion of the curve. As shown on the hysteresis curve in Figure 2.8.3, the magnitude of current that causes the iron to go into saturation is not the same as the magnitude at which the iron comes out of saturation. The boundary between linear operation and saturated operation is not fixed but, instead, depends on the previous values of that current. The hysteresis phenomenon is a fundamental property of ferromagnetic materials. Hysteresis occurs because of residual flux density stored in the iron that must be overcome when the current changes direction. It should be noted that, for a particular value of flux, there are two values of current for which the core would be in saturation. 2.8.1.3.2 Ferroresonance Most engineers are well versed with linear resonance (referred to simply as resonance). In a circuit, capacitive and inductive reactances (Z C and Z L , respectively) are calculated as shown in Equation 2.8.1 and Equation 2.8.2. Resonance occurs when the inductive and capacitive reactances of a circuit exactly balance. The resonating frequency is calculated as shown in Equation 2.8.3. 1 Z C jC Z L j L 1 f 2 LC (2.8.1) (2.8.2) (2.8.3) FIGURE 2.8.3 Flux-current curve with hysteresis curve. There is ferroresonance between the resonating winding on the saturated core and the capacitor. This arrangement acts as a tank circuit, drawing power from the primary. This results in sustained, regulated oscillations at the secondary with the applied line frequency. 2.8.1.3 The Working of a Constant-Voltage <strong>Transformer</strong> The working of a CVT can be explained with two physical phenomena: • Saturation of the ferromagnetic core • Ferroresonance The inductance value used in Equation 2.8.2 and Equation 2.8.3 refers to the unsaturated or linear value of the inductor. However, the case when the core is saturated needs special consideration. If the inductor core is saturated, the relationship between flux () and current (I) is no longer linear, and the inductance value is no longer a single value (L). The inductance in the nonlinear portion of the fluxcurrent curve is not fixed and cannot be represented by a single value. Once the ferromagnetic inductance “enters” into saturation, it remains saturated until the current magnitude reduces. If the inductance when saturated causes a resonance (i.e., results in an inductive reactance that matches the capacitive reactance in the circuit), this phenomenon is called “ferroresonance.” At the ferroresonance point, the current magnitude can increase dramatically, further driving the iron into saturation. If the current is constantly fed (as happens in a CVT), a stable resonant point is obtained [5]. If, at ferroresonance, the inductor value is L S , the resonant frequency (f S ) is given by Equation 2.8.4. f S 1 2 LC (2.8.4) It should be noted that L S
300% FIGURE 2.8.4 Schematic of a constant-voltage transformer. Percent Voltage 200% Voltage Breakdown Concern 115% 106% 100% Computer Voltage Tolerance Envelope 87% Lack of Stored Energy in Some Manufacturers Equipment 30% 0% 0.001 0.01 0.4 0.51.0 6 10 30 100 1000 Time in Cycles (60 Hz) Output Voltage Jump Resonance Down V o3 V o2 V o1 Regulating Mode Jump Resonance Up Non-Regulating Mode V 1 V 2 Input Voltage V 3 FIGURE 2.8.5 Output voltage vs. input voltage for constant-voltage transformer with jump resonance . The salient features of ferroresonance are: • Resonance occurs when the inductance is in saturation. • As the value of inductance in saturation is not known precisely, a wide range of capacitances can potentially lead to ferroresonance at a given frequency. • More than one stable, steady-state response is possible for a given configuration and parameter values [6]. A schematic of a constant-voltage transformer is shown in Figure 2.8.4. In the ferroresonant circuit of a constant-voltage transformer, more than one steady-state response is possible for a given configuration and parameter values. This phenomenon (referred as “jump resonance”) is described next. The y-axis in Figure 2.8.5 is the CVT’s output voltage at the secondary terminals, while the x-axis is the CVT’s input primary voltage. There are three possible modes of behavior, depending on the level of FIGURE 2.8.6 Voltage-tolerance envelope specified by the Computer and Business Equipment Manufacturers Association. Note: This is reproduced from IEEE Std. 446 (Orange Book). the input voltage. At input voltage V 1 , the CVT operates in nonsaturation mode. The secondary responds linearly to the primary supply. Note that this mode is used in a conventional transformer but is undesirable in a CVT. At input voltage V 2 , there are three outputs denoted by V o1 , V o2 , and V o3 . Outputs V o1 and V o3 are both stable states. Output V o1 corresponds to the normal state, whereas V o3 corresponds to ferroresonant state. Output V o2 is an unstable state that cannot be obtained in practice. Whether CVT output is V o1 or V o3 depends on the initial value of residual flux and voltage at the capacitor terminals. The phenomenon where the output voltage either suddenly changes to the regulating mode of operation at some value of the ascending input voltage, or suddenly drops out of the regulating mode of operation with descending input voltage, is called jump resonance [7]. The jump resonance is a factor during dynamic supplyvoltage conditions. This is discussed in detail when the applications of a CVT are considered (Section 2.8.2). At input voltage V 3 , the CVT operates in ferroresonant mode. The CVT must operate in this mode for proper operation. 2.8.1.4 Voltage Regulation on the Customer Side The purpose of a voltage regulator is to maintain constant output voltage to the load in the face of variations in the input line voltage. In the past, however, voltage regulation was usually not a primary requirement for sensitive loads within end-user facilities. For instance, the Computer and Business Equipment Manufacturers Association (CBEMA) curve (see Figure 2.8.6) indicates that computer equipment should be able to handle steady-state voltage variations in the range of 87 to 106% of nominal. (Note that the CBEMA <strong>org</strong>anization has been assumed by Information Technology Industry Council [ITIC] group.) However, with increased user-equipment sensitivity and the industry’s dependency on sophisticated process-control devices in manufacturing, some types of equipment may have more stringent voltage-regulation requirements than the regulation tolerances specified. Also, the particular electricservice supply point may not be compatible with the connected electric load. In these cases, it is usually prudent to implement voltage regulation at the end-user’s equipment level. © 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
Page 41 and 42: mounted transformers can have arres
Page 43 and 44: V S + V S I V L Z=R+jX a) V L V S V
Page 45 and 46: Z = jX (2.3.19) 0.7 Then the curren
Page 47 and 48: X1 L* X1 S =X1 L X2 L* X3 L* a) S L
Page 49 and 50: 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: References IEEE, Standard Requireme
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 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
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3.3.5 Selection of Load Tap Changer
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FIGURE 3.3.19 Effect of the leakage
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References Goosen, P.V. , Transform
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If i 1 is the full-load current rat
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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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