[James_H._Harlow]_Electric_Power_Transformer_Engin(BookSee.org)

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Like sound pressure, sound intensity level L I is also quantified using a dB scale, where the measured intensity I in W/m 2 is expressed as a ratio to a reference intensity level I 0 as follows: where L I = sound intensity level, dB I 0 = reference level = 10 –12 W/m 2 L I = 10 log (I/I 0 ) (3.9.2) 3.9.1.5 Relationship between Sound Intensity and Sound Pressure Level For any free progressive wave, there is a unique relation between the mean-square sound pressure and the intensity. This relation at a particular point and in the direction of the wave propagation is described as follows: I = P 2 rms/c (3.9.3) where I = sound intensity, W/m 2 P 2 rms = mean-square sound pressure, (N/m 2 ) 2 , measured at that particular point where I is desired in the free progressive wave c = characteristic resistance, mks rayls Note that for air, at T = 20C and atmospheric pressure = 0.751 m of Hg, c = 406 mks rayls. This value does not change significantly over generally encountered ambient temperature and atmospheric pressure conditions. As described in Equation 3.9.2, sound intensity level, in decibels is: L I = 10 log (I/I 0 ) where I = sound intensity (power passing in a specified direction through a unit area), W/m 2 Combining the above equations, the sound intensity level can be expressed as: L I = 10 log [(P 2 rms/c)/I 0 ] = 10 log (P rms /P 0 ) 2 + 10 log [(P 2 0/c)/I 0 ] (3.9.4) From this expression, L I can be defined as follows: L I = L p – 10 log K (3.9.5) where K = constant = I 0 c/P 2 0, which is dependent upon ambient pressure and temperature By definition, P 2 0/I 0 = (20 10 –6 ) 2 /10 –12 = 400 mks rayls Note that the quantity 10 log K will equal zero when K = 1 or when c equals 400. As described earlier, under commonly encountered temperature and atmospheric conditions, c 400. Therefore, in free field measurements, L p L I . That is, noise pressure and noise intensity measurement, in free space, yield the same numerical value. 3.9.2 Sound-Energy Measurement Techniques Sound level of a source can be measured by directly measuring sound pressure or sound intensity at a known distance. Both of these measurement techniques are quite equivalent and acceptable. In most of the industry worldwide, sound-pressure measurements have been used for quantifying sound levels in transformers. As a result of the recent work completed by CIGRE, sound-intensity measurements are now being incorporated as an alternative in IEC Std. 60076-10. 3.9.2.1 Sound-Pressure-Level Measurement A sound-level meter is an instrument designed to respond to sound in approximately the same way as the human ear and to give objective, reproducible measurements of sound pressure level. There are many different sound measuring systems available. Although different in detail, each system consists of a microphone, a processing section and a readout unit. The microphone converts the sound signal to an equivalent electrical signal. The most suitable type of microphone for sound-level meters is the condenser microphone, which combines precision with stability and reliability. The electrical signal produced by the microphone is quite small. It is therefore amplified by a preamplifier before being processed. Several different types of processing may be performed on the signal. The signal may pass through a weighting network of filters. It is relatively simple to build an electronic circuit whose sensitivity varies with frequency in the same way as the human ear, thus simulating the equal-loudness contours. This has resulted in three different internationally standardized characteristics termed the A, B, and C weightings. The A-weighting network is the most widely used, since the B and C weightings do not correlate well with subjective tests. 3.9.2.2 Sound-Intensity Measurements Until recently, only sound pressure that was dependent on the sound field could be measured. Sound power can be related to sound pressure only under carefully controlled conditions where special assumptions are made about the sound field. Therefore, a noise source had to be placed in specially constructed rooms, such as anechoic or reverberant chambers, to measure sound power levels with the desired accuracy. Sound intensity, however, can be measured in any sound field. This property allows all the measurements to be done directly in situations where a plurality of sound sources are present. Measurements on any sound source can be made even when all the others are radiating noise simultaneously. Sound intensity measurements are directional in nature and only measure sound energy radiated form a sound source. Therefore, steady background noise makes no contribution to the sound power of the source determined with sound-intensity measurements. Sound intensity is the time-averaged product of the pressure and particle velocity. A single microphone can measure pressure. However, measuring particle velocity is not as simple. With Euler’s linearized equation, the particle velocity can be related to the pressure gradient (i.e., the rate at which the instantaneous pressure changes with distance). Euler’s equation is essentially Newton’s second law applied to a fluid. Newton’s second law relates the acceleration given to a mass to the force acting on it. If the force and the mass are known, the acceleration can be found. This can then be integrated with respect to time to find the velocity. With Euler’s equation, it is the pressure gradient that accelerates a fluid of density . With the knowledge of pressure gradient and density of the fluid, the particle acceleration (or deceleration) can be calculated as follows. a = –1/ P/r (3.9.6) where a = particle deceleration due to a pressure change P in a fluid of density across a distance r Integrating Equation 3.9.6 gives the particle velocity, u, as follows: u = º 1/ P/r dt (3.9.7) It is possible to measure the pressure gradient with two closely spaced microphones facing each other and relate it to the particle velocity using the above equation. With two closely spaced microphones A © 2004 by CRC Press LLC © 2004 by CRC Press LLC
FIGURE 3.9.1 Measurement of pressure gradient using two closely spaced microphones. and B separated by a distance r (Figure 3.9.1), it is possible to obtain a linear approximation of the pressure gradient by taking the difference in their measured pressures, P A and P B , and dividing it by the distance r between them. This is called a finite-difference approximation. The pressure-gradient signal must now be integrated to give the particle velocity u as follows: u = –1/ [(P A – P B )/r]dt (3.9.8) Since intensity I is the time-averaged product of pressure P and particle velocity u, I = –P/ [(P A – P B )/r]dt (3.9.9) where P = (P A + P B )/2. This is the basic principle of signal processing in sound-intensity-measuring equipment. 3.9.3 Sources of Sound in Transformers Unlike cooling-fan or pump noise, the sound radiated from a transformer is tonal in nature, consisting of even harmonics of the power frequency. It is generally recognized that the predominant source of transformer noise is the core. The low frequency, tonal nature of this noise makes it harder to mitigate than the broadband higher frequency noise that comes from the other sources. This is because low frequencies propagate farther with less attenuation. Also, tonal noise can be perceived more acutely than broadband levels, even with high background noise levels. This combination of low attenuation and high perception makes tonal noise the dominant problem in the neighboring communities around transformers. To address this problem, most noise ordinances impose penalties or stricter requirements for tonal noise. Even though the core is the principal noise source in transformers, the load noise, which is primarily caused by the electromagnetic forces in the windings, can also be a significant influence in low-soundlevel transformers. The cooling equipment (fans and pumps) noise typically dominates the very lowand very high-frequency ends of the sound spectrum, whereas the core noise dominates in the intermediate range of frequencies between 100 and 600 Hz. These sound-producing mechanisms can be further characterized as follows. 3.9.3.1 Core Noise When a strip of iron is magnetized, it undergoes a very small change in its dimensions (usually only a few parts in a million). This phenomenon is called magnetostriction. The change in dimension is independent of the direction of magnetic flux; therefore, it occurs at twice the line frequency. Because the magnetostriction curve is nonlinear, higher harmonics of even order also appear in the resulting core vibration at higher induction levels (above 1.4 T). Flux density, core material, core geometry, and the wave form of the excitation voltage are the factors that influence the magnitude and frequency components of the transformer core sound levels. The mechanical resonance in transformer mounting structure as well as in core and tank walls can also have a significant influence on the magnitude of transformer vibrations and, consequently, on the acoustic noise generated. 3.9.3.2 Load Noise Load noise is caused by vibrations in tank walls, magnetic shields, and transformer windings due to the electromagnetic forces resulting from leakage fields produced by load currents. These electromagnetic forces are proportional to the square of the load currents. The load noise is predominantly produced by axial and radial vibration of transformer windings. However, marginally designed magnetic shielding can also be a significant source of sound in transformers. A rigid design for laminated magnetic shields with firm anchoring to the tank walls can greatly reduce their influence on the overall load sound levels. The frequency of load noise is usually twice the power frequency. An appropriate mechanical design for laminated magnetic shields can be helpful in avoiding resonance in the tank walls. The design of the magnetic shields should take into account the effects of overloads to avoid saturation, which would cause higher sound levels during such operating conditions. Studies have shown that except in very large coils, radial vibrations do not make any significant contribution to the winding noise. The compressive electromagnetic forces produce axial vibrations and thus can be a major source of sound in poorly supported windings. In some cases, the natural mechanical frequency of winding clamping systems may tend to resonate with electromagnetic forces, thereby severely intensifying the load noise. In such cases, damping of the winding system may be required to minimize this effect. The presence of harmonics in load current and voltage, most especially in rectifier transformers, can produce vibrations at twice the harmonic frequencies and thus a sizeable increase in the overall sound level of a transformer. Through several decades, the contribution of the load noise to the total transformer noise has remained moderate. However, in transformers designed with low induction levels and improved core designs for complying with low sound-level specifications, the load-dependent winding noise of electromagnetic origin can become a significant contributor to the overall sound level of the transformer. In many such cases, the sound power of the winding noise is only a few dB below that of the core noise. 3.9.3.3 Fan and Pump Sound Power transformers generate considerable heat because of the losses in the core, coils, and other metallic structural components of the transformer. This heat is removed by fans that blow air over radiators or coolers. Noise produced by the cooling fans is usually broadband in nature. Cooling fans usually contribute more to the total noise for transformers of smaller ratings and for transformers that are operated at lower levels of core induction. Factors that affect the total fan noise output include tip speed, blade design, number of fans, and the arrangement of the radiators. 3.9.4 Sound Level and Measurement Standards for Transformers In NEMA Publication TR-1, Tables 02 thorough 04 list standard sound levels for liquid-filled power, liquid-filled distribution, and dry-type transformers. These sound-level requirements must be met unless special lower sound levels are specified by the customer. The present sound-level measurement procedures as described in IEEE standards C57.12.90 and C57.12.91 specify that the sound-level measurements on a transformer shall be made under no-load conditions. Sound-pressure measurements shall be made to quantify the total sound energy radiated by a transformer. Sound-intensity measurements have already been incorporated into IEC Sound Level Measurement Standard 60076-10 as an acceptable alternative. It is anticipated that this method will be adopted in the IEEE standards also in the near future. The following is a brief description of the procedures used for this determination. 3.9.4.1 Transformer Connections during Test This test is performed by exciting one of the transformer windings at rated voltage of sinusoidal wave shape at rated frequency while all the other windings are open circuited. The tap changer (if any) is at © 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
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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
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
Page 169 and 170: TABLE 3.6.3 Transformer Short-Circu
Page 171 and 172: FIGURE 3.7.3 Control for voltage re
Page 173 and 174: FIGURE 3.7.6A Feeder with power-fac
Page 175 and 176: 3. Circulating current (current bal
Page 177 and 178: FIGURE 3.7.10 Control block diagram
Page 179 and 180: Primary Current (Amps) 60 40 20 0 -
Page 181 and 182: current transformer having two prim
Page 183 and 184: 87R1 87BL1 (A) Independent Harmonic
Page 185 and 186: Winding 1 Secondary Currents Data A
Page 187 and 188: Y Y 20 18 3 rd Harmonic CTR1=40 CTR
Page 189 and 190: 230 kV 3 180 MVA 138 kV 5 CTR1 = 2
Page 191: 29. Concordia, C. and Rothe, F.S.,
Page 195 and 196: H 2m 1. Vertical Forced Air 2. Prin
Page 197 and 198: Gade, S., Sound Intensity Instrumen
Page 199 and 200: nected. This steady-state voltage d
Page 201 and 202: where [A] = state matrix [B] = inpu
Page 203 and 204: where C = capacitance between the t
Page 205 and 206: L ijo = N i N j ijo (3.10.31) 1.4
Page 207 and 208: % VOLTAGE % VOLTAGE 100 BIL 90 50 3
Page 209 and 210: 29. Degeneff, R.C., Reducing Storag
Page 211 and 212: 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
Page 217 and 218: • Has heating occurred as the res
Page 219 and 220: a reference value) of the currents
Page 221 and 222: The next data-processing step is to
Page 223 and 224: temperature. As the transformer coo
Page 225 and 226: 3.13.3.2 Instrument Transformers Th
Page 227 and 228: FIGURE 3.13.5 Analysis of bushing s
Page 229 and 230: temperature. Under abnormal conditi
Page 231 and 232: 3.14.1.2 Accredited Standards Commi
Page 233 and 234: FIGURE 3.14.4 IEC technical-committ
Page 235 and 236: TABLE 3.14.2 Relevant Documents for
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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