[James_H._Harlow]_Electric_Power_Transformer_Engin(BookSee.org)

for a period of 10 to 15 min as the windings cool down toward the surrounding average oil temperature.
The average oil temperature is itself falling, but at a much slower rate (with a longer time constant). Data
for the changing resistance vs. time is then plotted and extrapolated back to the instant of shutdown.
With computers, the extrapolation can be done using a regression-based curve-fitting approach. The
extrapolated value of winding resistance at the instant of shutdown is used to calculate winding temperature,
using the method discussed below, with some correction for the drop in top-oil rise during the 1-
h loading at rated current. The winding temperature, thus determined, minus ambient temperature is
equal to the winding temperature rise at a given loading.
Similar tests are repeated for all ratings for which temperature rise tests are required.
3.6.6.4.5 Determining the Average Temperature by Resistance
The average winding temperature, as determined by the following method, is sometimes called the
“average winding temperature by resistance.” The word measurement is implied at the end of this phrase.
The conversion of measured winding resistance to average winding temperature is accomplished as
follows. Initial resistance measurements are made at some time before commencement of the heat run
when the transformer is in thermal equilibrium. When in equilibrium, the assumption can be made that
the temperature of the conductors is uniform and is equal to that of the transformer oil surrounding the
coils. Initial resistance measurements are made and recorded, along with the oil temperature. This
measurement is sometimes called the cold-resistance test, so the winding resistance measured during the
test will be called the cold resistance R c , and the temperature will be called the cold temperature T c . At
the end of the heat run, R h , the hot resistance is determined from the time series of measured resistance
values by extrapolation to the moment of shutdown. The formula given below is used to determine T h ,
the hot temperature, knowing the hot resistance, cold resistance, and the cold temperature. This calculated
temperature is the average winding temperature by resistance.
Rh
T
R T T T
h
[
c
k]
k
c
(3.6.5)
where
T h is the “hot” temperature
T c is the “cold” temperature
R h is the “hot” resistance
R c is the “cold” resistance
T k is a material constant: 234.5C for copper, 225C for aluminum
Accurate measurements of R c and T c during the cold-resistance test, as well as accurate measurements
of hot winding resistance, R h , at the end of the heat run are extremely critical for accurate determination
of average winding temperature rises by resistance. The reason for this will be evident by analyzing the
above formula. The following discussion illustrates how measurement errors in the three measured
quantities, R h , R c , and T c , affect the computed quantity, T h , via the functional relationship by which T h
is computed.
Shown in Table 3.6.2 are computed values for T h and the resulting error, e Th , in the computation of
T h for sample sets of the measured quantities R h , R c , and T c , measured in error by the amounts e Rh , e Rc ,
and e Tc , respectively. Let us examine this table row by row. The way that measurement error propagates
in the calculation is shown in the formula below for copper conductors.
( T e ( Rh
eRh)
)
( ) [( T e
R e
) . ] .
h
Th
c
Tc
234 5 234 5
c
Rc
(3.6.6)
TABLE 3.6.2 Effect of Measurement Error in Average Winding Temperature by Resistance
Row T h + e Th (C) R h + e Rh () R c + e Rc () T c + e Th (C)
1 87.375 + 0 0.030 + 0 0.024 + 0 23.0 + 0
2 87.375 – 3.187 =
0.030 + 0 0.024 + 0.00024 = 23.0 + 0
84.188 (–3.6%)
0.02424 (+1.0%)
3 87.375 + 3.218 =
0.030 + 0.0003 =
0.024 + 0 23.0 + 0
90.594 (+3.7%)
0.0303 (+1.0%)
4 87.375 + 1.25 =
88.625 (+1.43%)
0.030 + 0 0.024 + 0 23.0 + 1.0 =
24.0 (4.35 %)
In row 1 of Table 3.6.2, there is no measurement error. The sample shows a set of typical measured
values. The value for T h in this row can be considered the “correct answer.” In row 2 the cold-resistance
measurement was 1% too high, causing the calculated value of T h to be 3.6% too low. This amplification
of the relative measurement error is due to the functional relationship employed to perform the
calculated result. This example illustrates the importance of measuring the resistance very carefully
and accurately. Similarly, in row 3 a hot-resistance reading 1% too high results in a calculated hot
temperature that is 3.7% too high. Row 4 shows the result if the cold-resistance reading is 1C too
high. The result is that the determined hot resistance is 1.25C too high. In this case, while there is a
reduction in the error expressed as percent, the absolute error in C is in fact greater than the original
temperature error in the cold-temperature reading. These examples show that all three measured
quantities — R h , R c , and T c — must be measured accurately to obtain an accurate determination of
the average winding temperature.
Other methods for correction to the instant of shutdown based on W/kg, or W/kg and time, are given
in the IEEE test code [2]. The cooling-curve method, however, is preferred.
3.6.7 Other Tests
3.6.7.1 Short-Circuit-Withstand Tests
3.6.7.1.1 Purpose of Short-Circuit Tests
Short-circuit currents during through-fault events expose the transformer to mechanical stresses caused
by magnetic forces, with typical magnitudes expressed in thousands of kilograms. Heating of the conductors
and adjacent insulation due to I 2 R losses also occurs during a short-circuit fault. The maximum
mechanical stress is primarily determined by the square of the peak instantaneous value of current.
Hence, the short-circuit magnitude and degree of transient offset are specified in the test requirements.
Fault duration and frequency of occurrence also affect mechanical performance. Therefore, the number
of faults, sometimes called “shots,” during a test and the duration of each fault are specified. Conductor
and insulation heating is for the most part determined by the rms value of the fault current and the fault
duration.
Short-circuit-withstand tests are intended primarily to demonstrate the mechanical-withstand capability
of the transformer. Thermal capability is demonstrated by calculation using formulas provided by
IEEE C57.12.00 [1].
3.6.7.1.2 Transformer Short-Circuit Categories
The test requirements and the pass-fail evaluation criteria for short-circuit tests depend upon transformer
size and construction. For this purpose, transformers are separated into four categories as shown in
Table 3.6.3. The IEEE standards [1] and [2] refer to these categories while discussing the test requirements
and test results evaluation.
3.6.7.1.3 Configurations
A short circuit is applied using low-impedance connections across either the primary or the secondary
terminals. A secondary fault is preferred, since it more directly represents the system conditions. The
fault can be initiated in one of two ways:
© 2004 by CRC Press LLC
© 2004 by CRC Press LLC