[James_H._Harlow]_Electric_Power_Transformer_Engin(BookSee.org)
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
where<br />
I h = current for the hth harmonic, expressed in per-unit terms<br />
I 1 = fundamental frequency current, expressed in per-unit terms<br />
Limits of allowable total harmonic distortion are given in IEEE 519, Recommended Practices and Requirements<br />
for Harmonic Control in <strong>Electric</strong> <strong>Power</strong> Systems.<br />
Likewise, total harmonic distortion as it relates to voltage can be expressed as:<br />
H<br />
<br />
h2<br />
V THD = V h2 /V 12 100% (2.4.8)<br />
where<br />
V h = voltage for the hth harmonic, expressed in per-unit terms<br />
V 1 = fundamental frequency current, expressed in per-unit, terms<br />
Again, IEEE 519 also addresses total harmonic distortion and its limits.<br />
Typically, voltage harmonics do not affect a rectifier transformer. Voltage and current harmonics<br />
usually do not create a core-heating problem. However, if there is dc current in the secondary waveform,<br />
the core can go into saturation. This results in high vibration, core heating, and circulating currents,<br />
since the core can no longer hold the flux. Nevertheless, the normal effect of harmonics is a noisier core<br />
as it reacts to different load frequencies.<br />
Assume a harmonic spectrum as shown in Table 2.4.2.<br />
TABLE 2.4.2 Theoretical Harmonic Spectrum<br />
Harmonic Harmonic, Per Unit Current<br />
1 1.0000<br />
5 0.1750<br />
7 0.1000<br />
11 0.0450<br />
13 0.0290<br />
17 0.0150<br />
19 0.0100<br />
23 0.0090<br />
25 0.0080<br />
TABLE 2.4.3 Comparison of Harmonic-Loss Factor for the Theoretical Spectrum and an Example Spectrum<br />
Harmonic<br />
h<br />
I h<br />
Theoretical<br />
I h<br />
Example<br />
h 2 I<br />
2<br />
h<br />
Theoretical<br />
I<br />
2<br />
h<br />
Example<br />
I h2 h 2<br />
Theoretical<br />
I h2 h 2<br />
Example<br />
1 1.0000 1.0000 1 1.0000 1.0000 1.0000 1.0000<br />
5 0.2000 0.1750 25 0.0400 0.3063 1.0000 0.7656<br />
7 0.1429 0.1000 49 0.0204 0.0100 1.0000 0.4900<br />
11 0.0909 0.0450 121 0.0083 0.0020 1.0000 0.2450<br />
13 0.0769 0.0290 169 0.0059 0.0008 1.0000 0.1421<br />
17 0.0588 0.0150 289 0.0035 0.0002 1.0000 0.0650<br />
19 0.0526 0.0100 361 0.0028 0.0001 1.0000 0.0361<br />
23 0.0435 0.0090 529 0.0019 0.0001 1.0000 0.0428<br />
25 0.0400 0.0080 625 0.0016 0.0001 1.0000 0.0400<br />
F HL = 9.0000 2.8266<br />
2.4.8 Effects of Harmonic Currents on <strong>Transformer</strong>s<br />
To better understand how harmonic currents affect transformers one must first understand the basic<br />
construction. For power transformers up to about 50 MVA, the typical construction is core form. The<br />
low-voltage winding is generally placed next to the core leg, with the high-voltage winding wound<br />
concentrically over the low-voltage winding. For some high-current transformers, these windings may<br />
be reversed, with the low-voltage winding wound on the outside over the high-voltage coil. The core and<br />
coils are held together with core clamps, and the core and coil is generally enclosed by a tank or enclosure.<br />
See Figure 2.4.15 for this construction and a view of leakage field around the transformer.<br />
Losses in the transformer can be broken down into core loss, no-load loss, and load loss. Load losses<br />
can be further broken down into I 2 R loss and stray loss. Stray loss can be further broken down into eddycurrent<br />
losses and other stray losses. Electromagnetic fields from the ac currents produce voltages across<br />
conductors, causing eddy currents to flow in them. This increases the conductor loss and operating<br />
temperature. Other stray losses are due to losses in structures other than the windings, such as core<br />
clamps and tank or enclosure walls.<br />
If we look at the theoretical spectrum shown in Table 2.4.2 and compare it with an example spectrum in<br />
Table 2.4.3, we can see that the effects of the harmonic currents are quite different. The harmonic-loss<br />
factor, F HL , is calculated for both the theoretical spectrum and the example spectrum in Table 2.4.3.<br />
The results in Table 2.4.3 dramatically show the reality of many harmonic spectra. The winding eddyand<br />
stray-loss multiplier from the example harmonic spectrum is much less than the theoretical value<br />
would indicate. This was one of the failings of rating transformers using the UL K-factor and then<br />
assigning an arbitrary value based on service. While this approach may be conservative and acceptable<br />
in a safety standard, it is not an engineering solution to the problem. The values of F HL above demonstrate<br />
the need to have a reasonable harmonic spectrum for applications. Many site-specific installations<br />
measure and determine their harmonic spectra. For ease of specification, many specifying engineers use<br />
a standard spectrum that may not be applicable in all installations. This practice runs the risk of<br />
underspecifying or overspecifying the transformer. Underspecifying the harmonic spectrum results in<br />
overheated transformers and possible failures. Overspecifying the harmonic spectrum results in overbuilt<br />
and more costly capital equipment.<br />
Core<br />
Steel<br />
LV<br />
Winding<br />
C/L<br />
Core<br />
Clamp<br />
HV<br />
Winding<br />
Tank<br />
Wall<br />
Electromagnetic<br />
Field Produced by<br />
Load Current in a<br />
<strong>Transformer</strong><br />
FIGURE 2.4.15 <strong>Transformer</strong> construction and electromagnetic leakage field.<br />
© 2004 by CRC Press LLC<br />
© 2004 by CRC Press LLC