[James_H._Harlow]_Electric_Power_Transformer_Engin(BookSee.org)

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R1 Es 4 1 R2 R3 FIGURE 2.4.14 Three-phase bridge rectifier. N DC Winding 6 R2 3 R1 2 Es 2 R3 5 R2 LQ Figure 2.4.14 shows a three-phase bridge rectifier. A periodic switching converts electrical power from one form to another. A dc voltage with superimposed high-frequency ripple is produced. The ripple voltage consists of the supply voltage with a frequency of multiples of six times the fundamental frequency. This can be done using either diode rectifiers or thyristors. Energy balance and Fourier analysis of the square waves confirms that each 6n harmonic in the dc voltage requires harmonic currents of frequencies of 6n + 1 and 6n – 1 in the ac line. The magnitude of the harmonic current is essentially inversely proportional to the harmonic number, or a value of 1/h. This is true of all converters. Once the number of pulses is determined from a converter, the harmonics generated will begin to be generated on either side of the pulse number. So a six-pulse converter begins to generate harmonics on the 5th and 7th harmonic, then again on the 11th and 13th harmonic, and so on. A 12-pulse converter will begin to generate harmonics on the 11th and 13th harmonic, and again on the 23rd and 25th harmonic, and so on. In order to reduce harmonics, topologies are developed to increase the number of pulses. This can be done using more-sophisticated converters or by using multiple converters with phase shifts. From this, we can express the above in a general formula for all pulse converters as: h = kq 1 (2.4.6) where k = any integer q = converter pulse number Table 2.4.1 shows a variety of theoretical harmonics that are produced based on the pulse number of the rectifier system. It should be emphasized that these are theoretical maximum magnitudes. In reality, harmonics are generally reduced due to the impedances in the transformer and system, which block the flow of harmonics. In fact, harmonics may need to be expressed at different values, depending on the load. On the other hand, due to system interaction and circuit topology, sometimes the harmonic current values are greater than the ideal values for certain harmonic values. The interaction of devices such as filters and power-factor correction capacitors can have a great affect on the harmonic values. These interactions are not always predictable. This is also one of the problems faced by filter designers. This has increasingly led toward multisecondary transformers that cancel the harmonics at their primary terminals, although the transformer generally still has to deal with the harmonics. Id Es − + Ed R3 H2 I2 H1 H3 EL AC Winding Instantaneous DC Volts + to − TABLE 2.4.1 Theoretical Harmonic Currents Present in Input Current to a Typical Static Power Rectifier, Per Unit of the Fundamental Current Harmonic Order Rectifier Pulse Number 6 12 18 24 30 36 48 5 0.2000 — — — — — — 7 0.1429 — — — — — — 11 0.0909 0.0909 — — — — — 13 0.0769 0.0769 — — — — — 17 0.0588 — 0.0588 — — — — 19 0.0526 — 0.0526 — — — — 23 0.0435 0.0435 — 0.0435 — — — 25 0.0400 0.0400 — 0.0400 — — — 29 0.0345 — — — 0.0345 — — 31 0.0323 — — — 0.0323 — — 35 0.0286 0.0286 0.0286 — — 0.0286 — 37 0.0270 0.0270 0.0270 — — 0.0270 — 41 0.0244 — — — — — — 43 0.0233 — — — — — — 47 0.0213 0.0213 — 0.0213 — — 0.0213 49 0.0204 0.0204 — 0.0204 — — 0.0204 A quick study of Table 2.4.1 shows that the harmonic currents are greatly reduced as the pulse number increases. Of course, the cost of the rectifiers and transformers increases as the complexity of the design increases. One must determine what level of power quality one can afford or what level is necessary to meet the limits given by IEEE 519. 2.4.7 Harmonic Spectrum One requirement of ANSI/IEEE C57.18.10 is that the specifying engineer supply the harmonic load spectrum to the transformer manufacturer. There are too many details of circuit operation, system parameters, and other equipment, such as power-factor correction capacitors, for the transformer manufacturer to be able to safely assume a harmonic spectrum with complete confidence. The requirement to specify the harmonic spectrum is of utmost importance. Indeed, the problem of harmonic heating was the primary reason for the creation of ANSI/IEEE C57.18.10, which shows the theoretical harmonic spectrum similar to that presented in Table 2.4.1, also in theoretical values. The 25th harmonic was used as the cutoff point, since the theoretical values were given in the table. Table 1 of ANSI/IEEE C57.18.10 provides very conservative values. Consider what would happen if we used the theoretical values of harmonic current and allowed the spectrum to go on and on. The harmonic-loss factor from such an exercise would be infinity for any pulse system. A reasonable cutoff point and accurate harmonic spectrum are necessary to properly design transformers for harmonic loads. While it may be prudent to be somewhat conservative, the specifying engineer must recognize the cost of being overly conservative. If the transformer spectrum is underestimated, the transformer may overheat. If the harmonic spectrum is estimated at too high a value, the transformer will be overdesigned, and the user will invest more capital in the transformer than is warranted. It is also not possible to simply specify the total harmonic distortion (THD) of the current in order to specify the harmonics. Many different harmonic-current spectra can give the same THD, but the harmonic-loss factor may be different for each of them. Total percent harmonic distortion, as it relates to current, can be expressed as: H h2 I THD = I h2 /I 12 100% (2.4.7) © 2004 by CRC Press LLC © 2004 by CRC Press LLC
where I h = current for the hth harmonic, expressed in per-unit terms I 1 = fundamental frequency current, expressed in per-unit terms Limits of allowable total harmonic distortion are given in IEEE 519, Recommended Practices and Requirements for Harmonic Control in Electric Power Systems. Likewise, total harmonic distortion as it relates to voltage can be expressed as: H h2 V THD = V h2 /V 12 100% (2.4.8) where V h = voltage for the hth harmonic, expressed in per-unit terms V 1 = fundamental frequency current, expressed in per-unit, terms Again, IEEE 519 also addresses total harmonic distortion and its limits. Typically, voltage harmonics do not affect a rectifier transformer. Voltage and current harmonics usually do not create a core-heating problem. However, if there is dc current in the secondary waveform, the core can go into saturation. This results in high vibration, core heating, and circulating currents, since the core can no longer hold the flux. Nevertheless, the normal effect of harmonics is a noisier core as it reacts to different load frequencies. Assume a harmonic spectrum as shown in Table 2.4.2. TABLE 2.4.2 Theoretical Harmonic Spectrum Harmonic Harmonic, Per Unit Current 1 1.0000 5 0.1750 7 0.1000 11 0.0450 13 0.0290 17 0.0150 19 0.0100 23 0.0090 25 0.0080 TABLE 2.4.3 Comparison of Harmonic-Loss Factor for the Theoretical Spectrum and an Example Spectrum Harmonic h I h Theoretical I h Example h 2 I 2 h Theoretical I 2 h Example I h2 h 2 Theoretical I h2 h 2 Example 1 1.0000 1.0000 1 1.0000 1.0000 1.0000 1.0000 5 0.2000 0.1750 25 0.0400 0.3063 1.0000 0.7656 7 0.1429 0.1000 49 0.0204 0.0100 1.0000 0.4900 11 0.0909 0.0450 121 0.0083 0.0020 1.0000 0.2450 13 0.0769 0.0290 169 0.0059 0.0008 1.0000 0.1421 17 0.0588 0.0150 289 0.0035 0.0002 1.0000 0.0650 19 0.0526 0.0100 361 0.0028 0.0001 1.0000 0.0361 23 0.0435 0.0090 529 0.0019 0.0001 1.0000 0.0428 25 0.0400 0.0080 625 0.0016 0.0001 1.0000 0.0400 F HL = 9.0000 2.8266 2.4.8 Effects of Harmonic Currents on Transformers To better understand how harmonic currents affect transformers one must first understand the basic construction. For power transformers up to about 50 MVA, the typical construction is core form. The low-voltage winding is generally placed next to the core leg, with the high-voltage winding wound concentrically over the low-voltage winding. For some high-current transformers, these windings may be reversed, with the low-voltage winding wound on the outside over the high-voltage coil. The core and coils are held together with core clamps, and the core and coil is generally enclosed by a tank or enclosure. See Figure 2.4.15 for this construction and a view of leakage field around the transformer. Losses in the transformer can be broken down into core loss, no-load loss, and load loss. Load losses can be further broken down into I 2 R loss and stray loss. Stray loss can be further broken down into eddycurrent losses and other stray losses. Electromagnetic fields from the ac currents produce voltages across conductors, causing eddy currents to flow in them. This increases the conductor loss and operating temperature. Other stray losses are due to losses in structures other than the windings, such as core clamps and tank or enclosure walls. If we look at the theoretical spectrum shown in Table 2.4.2 and compare it with an example spectrum in Table 2.4.3, we can see that the effects of the harmonic currents are quite different. The harmonic-loss factor, F HL , is calculated for both the theoretical spectrum and the example spectrum in Table 2.4.3. The results in Table 2.4.3 dramatically show the reality of many harmonic spectra. The winding eddyand stray-loss multiplier from the example harmonic spectrum is much less than the theoretical value would indicate. This was one of the failings of rating transformers using the UL K-factor and then assigning an arbitrary value based on service. While this approach may be conservative and acceptable in a safety standard, it is not an engineering solution to the problem. The values of F HL above demonstrate the need to have a reasonable harmonic spectrum for applications. Many site-specific installations measure and determine their harmonic spectra. For ease of specification, many specifying engineers use a standard spectrum that may not be applicable in all installations. This practice runs the risk of underspecifying or overspecifying the transformer. Underspecifying the harmonic spectrum results in overheated transformers and possible failures. Overspecifying the harmonic spectrum results in overbuilt and more costly capital equipment. Core Steel LV Winding C/L Core Clamp HV Winding Tank Wall Electromagnetic Field Produced by Load Current in a Transformer FIGURE 2.4.15 Transformer construction and electromagnetic leakage field. © 2004 by CRC Press LLC © 2004 by CRC Press LLC
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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 and 8: 1.3 Equivalent Circuit of an Iron-C
Page 9 and 10: designer starts to make a design fo
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: The degree of coupling also influen
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 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
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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
Page 169 and 170:
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.,
Page 193 and 194:
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
Page 213 and 214:
6. Costs to set up and use a mobile
Page 215 and 216:
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
Page 237 and 238:
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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