[James_H._Harlow]_Electric_Power_Transformer_Engin(BookSee.org)
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FIGURE 2.2.36 Complete transformer equivalent circuit. (By permission of ABB Inc., Jefferson City, MO.)<br />
2.2.10.2 Complete Equivalent Circuit<br />
Figure 2.2.36 shows a complete equivalent circuit of the transformer. An ideal transformer is inserted to<br />
represent the current- and voltage-transformation ratios. A parallel resistance and inductance representing<br />
the magnetizing impedance are placed across the primary of the ideal transformer. Resistance and<br />
inductance of the two windings are placed in the H 1 and X 1 legs, respectively.<br />
2.2.10.3 Simplified Model<br />
To create a simplified model, the magnetizing impedance has been removed, acknowledging that noload<br />
loss is still generated and magnetizing current still flows, but it is so small that it can be ignored<br />
when compared with the rated currents. The R and X values in either winding can be translated to the<br />
other side by using percent values or by converting ohmic values with a factor equal to the turns ratio<br />
squared (N P /N S ) 2 . To convert losses or ohmic values of R and X to percent, use Equation 2.2.1 or Equation<br />
2.2.2:<br />
Load Loss ( R)<br />
kVA<br />
% R <br />
<br />
2<br />
10 kVA kV<br />
(2.2.1)<br />
AW ( L)<br />
kVA<br />
% X <br />
(2.2.2)<br />
2<br />
10 kVA kV<br />
where AW is apparent watts, or the scalar product of applied voltage and exciting current in units of<br />
amperes. Once the resistances and inductances are translated to the same side of the transformer, the<br />
ideal transformer can be eliminated and the percent values of R and X combined. The result is the simple<br />
model shown in Figure 2.2.37. A load, having power factor cos may be present at the secondary.<br />
2.2.10.4 Impedance<br />
The values of %R and %X form the legs of what is known as the “impedance triangle.” The hypotenuse<br />
of the triangle is called the transformer’s impedance and can be calculated using Equation 2.2.3.<br />
% Z % R %<br />
X<br />
2 2<br />
(2.2.3)<br />
A transformer’s impedance is sometimes called “impedance volts” because it can be measured by<br />
shorting the secondary terminals and applying sufficient voltage to the primary so that rated current<br />
flows in each winding. The ratio of applied voltage to rated voltage, times 100, is equal to the percent<br />
impedance.<br />
FIGURE 2.2.37 Simplified transformer model. (By permission of ABB Inc., Jefferson City, MO.)<br />
2.2.10.5 Short-Circuit Current<br />
If the load (right) side of the model of Figure 2.2.37 is shorted and rated voltage from an infinite source<br />
is applied to the left side, the current I SC will be limited only by the transformer impedance:<br />
I 100 I % Z<br />
SC<br />
(2.2.4)<br />
For example, if the rated current, I R , is 100 A and the impedance is 2.0%, the short-circuit current<br />
will be 100 100/2 = 5000 A.<br />
2.2.10.6 Percent Regulation<br />
When a transformer is energized with no load, the secondary voltage will be exactly the primary voltage<br />
divided by the turns ratio (N P /N S ). When the transformer is loaded, the secondary voltage will be<br />
diminished by an amount determined by the transformer impedance and the power factor of the load.<br />
This change in voltage is called regulation and is actually defined as the rise in voltage when the load is<br />
removed. One result of the definition of regulation is that it is always a positive number. The primary<br />
voltage is assumed to be held constant at the rated value during this process. The exact calculation of<br />
percent regulation is given in Equation 2.2.5:<br />
<br />
05 .<br />
2 2 2<br />
% reg L % R % X 200 L % X sin% R cos10000 – 100<br />
(2.2.5)<br />
where cos is the power factor of the load and L is per unit load on the transformer. The most significant<br />
portion of this equation is the cross products, and since %X predominates over %R in the transformer<br />
impedance and cos predominates over sin for most loads, the percent regulation is usually less than<br />
the impedance (at L = 1). When the power factor of the load is unity, then sin is zero and regulation<br />
is much less than the transformer impedance. A much simpler form of the regulation calculation is given<br />
in Equation 2.2.6. For typical values, the result is the same as the exact calculation out to the fourth<br />
significant digit or so.<br />
<br />
% X* cos – % R*sin<br />
% reg L % R * cos % X *sin <br />
2 <br />
<br />
<br />
<br />
200 <br />
(2.2.6)<br />
2.2.10.7 Percent Efficiency<br />
As with any other energy conversion device, the efficiency of a transformer is the ratio of energy delivered<br />
to the load divided by the total energy drawn from the source. Percent efficiency is expressed as:<br />
5<br />
L kVAcos<br />
10<br />
% Efficiency <br />
3 2<br />
L kVAcos<br />
10<br />
NL L LL<br />
R<br />
<br />
(2.2.7)<br />
© 2004 by CRC Press LLC<br />
© 2004 by CRC Press LLC