[James_H._Harlow]_Electric_Power_Transformer_Engin(BookSee.org)

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E1 = 1000 N1 = 100 E/N = 10 N2 = 50 E2 = 50 10 = 500 N3 = 20 E3 = 20 10 = 200 FIGURE 1.6 Steel core with windings. FIGURE 1.4 Loss characteristics for electrical core-steel materials over a range of magnetic induction (core flux density). FIGURE 1.7 Hysteresis loop. FIGURE 1.5 Equivalent circuit. drop across the resistance of the winding and a small inductive drop across the inductance of the winding. We can represent these impedances as R1 and X1 in the equivalent circuit. However, these voltage drops are very small and can be neglected in the practical case. Since the flux flowing in all parts of the core is essentially equal, the voltage induced in any turn placed around the core will be the same. This results in the unique characteristics of transformers with steel cores. Multiple secondary windings can be placed on the core to obtain different output voltages. Each turn in each winding will have the same voltage induced in it, as seen in Figure 1.6. The ratio of the voltages at the output to the input at no-load will be equal to the ratio of the turns. The voltage drops in the resistance and reactance at no-load are very small, with only magnetizing current flowing in the windings, so that the voltage appearing across the primary winding of the equivalent circuit in Figure 1.5 can be considered to be the input voltage. The relationship E1/N1 = E2/N2 is important in transformer design and application. The term E/N is called “volts per turn.” A steel core has a nonlinear magnetizing characteristic, as shown in Figure 1.7. As shown, greater ampere-turns are required as the flux density B is increased from zero. Above the knee of the curve, as the flux approaches saturation, a small increase in the flux density requires a large increase in the ampere-turns. When the core saturates, the circuit behaves much the same as an air core. As the flux density decreases to zero, becomes negative, and increases in a negative direction, the same phenomenon of saturation occurs. As the flux reduces to zero and increases in a positive direction, it describes a loop known as the “hysteresis loop.” The area of this loop represents power loss due to the hysteresis effect in the steel. Improvements in the grade of steel result in a smaller area of the hysteresis loop and a sharper knee point where the B-H characteristic becomes nonlinear and approaches the saturated state. 1.4 The Practical <strong>Transformer</strong> 1.4.1 Magnetic Circuit In actual transformer design, the constants for the ideal circuit are determined from tests on materials and on transformers. For example, the resistance component of the core loss, usually called no-load loss, is determined from curves derived from tests on samples of electrical steel and measured transformer no-load losses. The designer will have curves similar to Figure 1.4 for the different electrical steel grades as a function of induction. Similarly, curves have been made available for the exciting current as a function of induction. A very important relationship is derived from Equation 1.11. It can be written in the following form: B = 0.225 (E/N)/(f A) (1.13) The term E/N is called “volts per turn”: It determines the number of turns in the windings; the flux density in the core; and is a variable in the leakage reactance, which is discussed below. In fact, when the © 2004 by CRC Press LLC © 2004 by CRC Press LLC
designer starts to make a design for an operating transformer, one of the first things selected is the volts per turn. The no-load loss in the magnetic circuit is a guaranteed value in most designs. The designer must select an induction level that will allow him to meet the guarantee. The design curves or tables usually show the loss per unit weight as a function of the material and the magnetic induction. The induction must also be selected so that the core will be below saturation under specified overvoltage conditions. Magnetic saturation occurs at about 2.0 T in magnetic steels but at about 1.4 T in amorphous ribbon. 1.4.2 Leakage Reactance Additional concepts must be introduced when the practical transformer is considered,. For example, the flow of load current in the windings results in high magnetic fields around the windings. These fields are termed leakage flux fields. The term is believed to have started in the early days of transformer theory, when it was thought that this flux “leaked” out of the core. This flux exists in the spaces between windings and in the spaces occupied by the windings, as seen in Figure 1.8. These flux lines effectively result in an impedance between the windings, which is termed “leakage reactance” in the industry. The magnitude of this reactance is a function of the number of turns in the windings, the current in the windings, the leakage field, and the geometry of the core and windings. The magnitude of the leakage reactance is usually in the range of 4 to 20% at the base rating of power transformers. The load current through this reactance results in a considerable voltage drop. Leakage reactance is termed “percent leakage reactance” or “percent reactance,” i.e., the ratio of the reactance voltage drop to the winding voltage 100. It is calculated by designers using the number of turns, the magnitudes of the current and the leakage field, and the geometry of the transformer. It is measured by short-circuiting one winding of the transformer and increasing the voltage on the other winding until rated current flows in the windings. This voltage divided by the rated winding voltage 100 is the percent reactance voltage or percent reactance. The voltage drop across this reactance results in the voltage at the load being less than the value determined by the turns ratio. The percentage decrease in the voltage is termed “regulation,” which is a function of the power factor of the load. The percent regulation can be determined using the following equation for inductive loads. where %Reg = percentage voltage drop across the resistance and the leakage reactance %R = percentage resistance = (kW of load loss/kVA of transformer) 100 %X = percentage leakage reactance = angle corresponding to the power factor of the load cos –1 pf For capacitance loads, change the sign of the sine terms. In order to compensate for these voltage drops, taps are usually added in the windings. The unique volts/turn feature of steel-core transformers makes it possible to add or subtract turns to change the voltage outputs of windings. A simple illustration of this concept is shown in Figure 1.9. The table in the figure shows that when tap 4 is connected to tap 5, there are 48 turns in the winding (maximum tap) and, at 10 volts/turn, the voltage E2 is 480 volts. When tap 2 is connected to tap 7, there are 40 turns in the winding (minimum tap), and the voltage E2 is 400 volts. 1.4.3 Load Losses The term load losses represents the losses in the transformer that result from the flow of load current in the windings. Load losses are composed of the following elements. • Resistance losses as the current flows through the resistance of the conductors and leads • Eddy losses caused by the leakage field. These are a function of the second power of the leakage field density and the second power of the conductor dimensions normal to the field. • Stray losses: The leakage field exists in parts of the core, steel structural members, and tank walls. Losses and heating result in these steel parts. Again, the leakage field caused by flow of the load current in the windings is involved, and the eddy and stray losses can be appreciable in large transformers. In order to reduce load loss, it is not sufficient to reduce the winding resistance by increasing the cross-section of the conductor, as eddy losses in the conductor will increase faster than joule heating losses decrease. When the current is too great for a single conductor to be used for the winding without excessive eddy loss, a number of strands must be used in parallel. Because the parallel components are joined at the ends of the coil, steps must be taken to %Reg = %R(cos ) + %X(sin ) + {[%X(cos ) – %R(sin )] 2 /200} (1.14) E2 8 7 6 5 4 3 2 20 2 2 2 2 20 1 Steel Core Winding 1 FIGURE 1.8 Leakage flux fields. Leakage Flux Lines Winding 2 E1 E1 = 100 N1 = 10 E/N = 10 E2 = E/N X N2 N2 E2 4 to 5 = 48 E2 = 10 48 = 480 Volts 4 to 6 = 46 E2 = 10 46 = 460 Volts 3 to 6 = 44 E2 = 10 44 = 440 Volts 3 to 7 = 42 E2 = 10 42 = 420 Volts 2 to 7 = 40 E2 = 10 40 = 400 Volts FIGURE 1.9 Illustration of how taps added in the windings can compensate for voltage drops. © 2004 by CRC Press LLC © 2004 by CRC Press LLC
Page 1 and 2: ELECTRIC POWER TRANSFORMER ENGINEER
Page 3 and 4: I wish to recognize the interest of
Page 5 and 6: Contents 1 Theory and Principles Ch
Page 7: 1.3 Equivalent Circuit of an Iron-C
Page 11 and 12: • Transient voltages generated du
Page 13 and 14: the transformer’s bushings and, m
Page 15 and 16: % regulation = [(V NL - V FL )/V FL
Page 17 and 18: In core-form transformers, the wind
Page 19 and 20: FIGURE 2.1.14 Layer windings (singl
Page 21 and 22: the transformer design, which may b
Page 23 and 24: consumer’s service circuit is a d
Page 25 and 26: FIGURE 2.2.3 Single-phase transform
Page 27 and 28: is installed so that the tank never
Page 29 and 30: above which persons might be burned
Page 31 and 32: FIGURE 2.2.16 Two-bushing subway. (
Page 33 and 34: carbon steel or the very expensive
Page 35 and 36: FIGURE 2.2.31 Radial-style dead fro
Page 37 and 38: FIGURE 2.2.36 Complete transformer
Page 39 and 40: 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
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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
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a) H1 b) Ip X2 FLUX H2 LEAKAGE FLUX
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and for CTs is TCF = RCF - (PA/2600
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RCF x Bx Bt RCF t - RCF 0 co
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2000 1000 5% Vex BANDWITH FROM NOMI
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This may be more useful when operat
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also some uncertainty in repeatabil
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FIGURE 2.6.25 Standard two-element
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2.7 Step-Voltage Regulators Craig A
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Source Bypass Switch Source Bypass
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2.7.4 Theory A step-voltage regulat
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FIGURE 2.7.22 Equalizer winding inc
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TABLE 2.7.4 Increase in Ampere Load
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References IEEE, Standard Requireme
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300% FIGURE 2.8.4 Schematic of a co
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TABLE 2.8.1 Typical Sizing Workshee
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Input with Interruption Ferro Outpu
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FIGURE 2.8.20A Performance of a rid
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• Input frequency or frequency ra
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References 1. Sola/Hevi-Duty Corp.,
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FIGURE 2.9.5 Typical phase-reactor
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FIGURE 2.9.10 Two generator arrange
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• Overloading of lines • Increa
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FIGURE 2.9.23 34-kV, 25-MVAR (per p
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V 90 ( X X ) s T (2.9.10a) where,
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Therefore, Line reactive losses = (
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ate of rise of transient-recovery v
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the LLCR is provided in IEEE Std. C
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aluminum shielding, i.e., an oil-im
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Leo J. Savio ADAPT Corporation Ted
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3.1.2.2.2 Heat Dissipation A second
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FIGURE 3.2.1 Solid-type bushing. ma
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1.6 cm. This means that most of the
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where HS = steady-state bushing ho
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the conductivity of the water-solub
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of 178 ohm-m, and a test duration o
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2. Easley, J.K. and Stockum, F.R.,
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FIGURE 3.3.5 Reactance-type LTC, in
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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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Page 239 and 240:
Page 241:
TABLE 3.14.13 Relevant Documents fo
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[James_H._Harlow]_Electric_Power_Transformer_Engin(BookSee.org)

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