[James_H._Harlow]_Electric_Power_Transformer_Engin(BookSee.org)

voltage of the excited winding, readings are taken of the rms current, the rms voltage, and the no-load
power. The ratio of the measured rms current to the rated load current of the excited winding, expressed
in percent, is commonly referred to as the percent excitation current. The measured no-load loss is
corrected to a sine-wave basis by a formula given in the IEEE test code [2], using the readings of the two
voltmeters. The correction is shown below. The corrected value is reported as the no-load loss of the
transformer.
Pm
Pc
Vr
P 2
1 P
V
2
(3.6.1)
where
P c is the corrected (reported) value of no-load loss
P m is the measured value of no-load loss
V a is the reading of the average-responding, rms-calibrated voltmeter
V r is the reading of the true-rms-responding voltmeter
P1 and P2 are the per-unit hysteresis and per-unit eddy-current losses, respectively
According to the IEEE test code [2], if the actual values of P1 and P2 are not available, it is suggested
that the two loss components be assumed equal in value, assigning each a value of 0.5 p.u.
3.6.6.2 Load Loss and Impedance Measurements
3.6.6.2.1 Purpose of Load Loss Measurements
A transformer dissipates a load loss that depends upon the transformer load current. Load loss is a cost
to the user during the lifetime of the transformer. Maximum values of the load loss of transformers at
rated current are specified and often guaranteed by the manufacturer. Load-loss measurements are made
to verify that the load loss does not exceed the specified or guaranteed value.
3.6.6.2.2 Nature of the Quantity Being Measured
The magnitude of the load loss is a function of the transformer load current. Its magnitude is zero when
there is no load on the transformer. Load loss is always given for a specified transformer load, usually at
rated load. Transformer load loss, often called copper loss or winding loss, includes I 2 R losses due to
load current in the winding conductors and stray losses in various metallic transformer parts due to eddy
currents induced by leakage fields. Stray losses are produced in the winding conductors, in core clamps,
in metallic structural parts, in magnetic shields, and in tank walls due to the presence of leakage fields.
Stray losses also include power loss due to circulating currents in parallel windings and in parallel
conductors within windings.
Because winding resistance varies with conductor temperature, and because the resistivities of the
structural parts producing stray losses vary with temperature, the transformer load losses are a function
of temperature. For this reason, a standard reference temperature (usually 85C) for reporting the load
loss is established in ANSI and IEEE standards [1]. To correct the load-loss measurements from the
temperature at which they are measured to the standard reference temperature, a correction formula is
provided in the IEEE test code [2]. This correction involves the calculation of winding I 2 R losses, where
I is the rated current of the winding in amperes, and R is the measured dc resistance of the winding. The
I 2 R losses and the stray losses are separately corrected and combined in the formula given in the standard.
The measurement of the dc winding resistance, R, is covered in Section 3.6.6.3. Stray losses are determined
by subtracting the I 2 R losses from the measured total load losses. All of this is covered in detail in the
IEEE test code [2]. The formula for this conversion is stated in general in Equation 3.6.2:
W
LL
2 2 2 2
( I
pRp IsRs)( Tk Tr)
( WmI pRp IsRs)( Tk Tm)
( T T )
( T T )
k
m
a
k
r
(3.6.2)
where
T r is the reference temperature (C)
T m is the temperature at which the load loss is measured (C)
W m is the load loss (W) as measured at temperature T m (C)
W LL is the load loss (W) corrected to a reference temperature T r (C)
T k is a winding material constant: 234.5 for copper, 225 for aluminum
R p and R s are, respectively, the primary and secondary resistances ()
I p and I s are the primary and secondary rated currents (A)
It can be seen from Equation 3.6.2 that the measurement of load losses and correction to the reference
temperature involves the measurement of five separate quantities:
1. Electric power (the load loss as measured)
2. Temperature (the temperature at time of test)
3. Resistance of the primary winding (at a known temperature)
4. Resistance of the secondary winding (at a known temperature)
5. Electric current (needed to adjust the current to the required values)
Another characteristic of transformer load loss is its low power factor. Most often, when considering
electric-power measurement applications, the power factor of the load being measured is relatively high,
usually exceeding 80%. For large modern power transformers, the power factor can be very low, in the
range from 1 to 5%. The measurement of electric power at very low power factor requires special
consideration, as discussed in the next section.
3.6.6.2.3 How Load Loss Is Measured
Load losses are normally measured by connecting one winding, usually the low-voltage winding, to a
short circuit with adequately sized shorting bars and connecting the other winding, usually the highvoltage
winding, to a power-frequency voltage source. The source voltage is adjusted until the impressed
voltage causes rated current to flow in both windings. Input rms voltage, rms current, and electric power
are then measured. Figure 3.6.15 shows a circuit commonly used for measurement of load losses of a
single-phase transformer. Three-phase measurement is carried out in the same way but with three sets
of instruments and instrument transformers. Precision scaling devices are usually required because of
the high magnitudes of current, voltage, and power involved.
The applied test voltage when the transformer is connected as in Figure 3.6.15, with rated currents in
the windings, is equal to the impedance voltage of the transformer. Hence impedance, or impedance
voltage, is also measured during the load-loss test. The ratio of the measured voltage to the rated voltage
of the winding, multiplied by 100, is the percent impedance voltage of the transformer. This quantity is
commonly called “percent impedance” or, simply, “impedance.”
3.6.6.2.4 Discussion of the Measurement Process
The equivalent circuit of the transformer being tested in the load-loss test and the phasor diagram of
test voltage and current during the test are shown in Figure 3.6.16. The load-loss power factor for the
load-loss test is cos = E R /E Z . Because the transformer leakage impedance, consisting of R and X in
Figure 3.6.16, is mainly reactive, and more so the larger the transformer, the power factor during the
load-loss test is very low. In addition, there is a trend in modern transformers to create designs with
lower losses due to increased demands for improved efficiency and transformer load-loss evaluations for
optimal life-cycle costs. Transformer designs for low values of load loss lead to reductions in the equivalent
resistance shown in Figure 3.6.16, and hence to low values for the quantity, E R , which translates to lower
values for the load-loss power factor in modern transformers. In fact the load-loss power factors for large
modern transformers are often very low, in the range from 0.01 to 0.05 per unit. Under circuit conditions
with very low power factor, the accurate measurement of electric power requires special scaling devices
having very low phase-angle error and power measuring instruments having high accuracy at low power
factor. In addition to the IEEE test code [2], a Transformer Loss Measurement Guide, C57.123, has
© 2004 by CRC Press LLC
© 2004 by CRC Press LLC