Application Note

Power Quality Troubleshooting Fluke Corporation 15
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Transformer Capacity (%)
After Derating for
Electronic Load
Switched-Mode Power Supply Load (% of Overall Load)
value, %HD (harmonic distor-
tion) of the harmonic currents,
and the square of the harmonic
order (number). It is not neces-
sary to actually perform the cal-
culation because a harmonic
analyzer will do that for you.
The important thing to under-
stand is that the harmonic order
is squared in the equation and
that is precisely where the
high- frequency heating effects,
like eddy current losses, are
taken into account.
K-rated transformers are de-
signed to minimize and accom-
modate the heating effects of
harmonics. K-rated transformers
do not eliminate harmonics
(unless additional elements like
filters are added). They accom-
modate harmonics with tech-
niques such as the use of
a number of smaller, parallel
windings instead of a single
large winding: this gives more
skin for the electrons to travel
on. The primary delta winding
is up-sized to tolerate the circu-
lating third harmonic currents
without overheating. The neu-
tral on the secondary is also
up-sized for third harmonics
(typically sized at twice the
phase ampacity).
Application issues with
K-factor transformers
K-rated transformers have been
widely applied, but there are
certain issues with them. Many
consultants do not see the need
for using transformers with a
rating higher than K-13 al-
though K-20 and higher might
be supplied as part of an inte-
grated Power Distribution Unit
(PDU). Also, early applications
sometimes overlooked the fact
that K-rated transformers nec-
essarily have a lower internal
impedance. Whereas a standard
transformer has an impedance
typically in the 5-6% range,
K-rated transformers can go
as low as 2-3% (lower as the
K-rating increases). In retrofit
situations, where a standard
transformer is being replaced by
a K-rated transformer of equiva-
lent kVA, this may require new
short circuit calculations and
re-sizing of the secondary
overcurrent protective devices.
3. Derating standard
transformers
Some facilities managers use
a 50% derating as a rule-of-
thumb for their transformers
serving single-phase, predomi-
nantly nonlinear loads. This
means that a 150 kVA trans-
former would only supply 75
kVA of load. The derating curve,
taken from IEEE 1100-1992
(Emerald Book), shows that a
transformer with 60% of its
loads consisting of SMPS
(switched-mode power sup-
plies), which is certainly pos-
sible in a commercial office
building, should in fact be
derated by 50%.
The following is an accepted
method for calculating trans-
former derating for single-phase
loads only. It is based on the
very reasonable assumption
that in single-phase circuits, the
third harmonic will predominate
and cause the distorted current
waveform to look predictably
peaked.
Use a true-rms meter to make
these current measurements:
1. Measure rms and peak cur-
rent of each secondary
phase. (Peak refers to the in-
stantaneous peak, not to the
inrush or “peak load” rms
current).
2. Find the arithmetic average
of the three rms readings and
the three peak currents and
use this average in step 3
(if the load is essentially
balanced, this step is not
necessary).
3. Calculate Xformer Harmonic
Derating Factor:
xHDF
= (1.414 * I
RMS
) / I
PEAK
4. Or, since the ratio of Peak/
RMS is defined as Crest
Factor, this equation can
be rewritten as:
xHDF = 1.414 / CF
If your test instrument has
the capability, measure the
CF of each phase directly. If
the load is unbalanced, find
the average of the three
phases and use the average
in the above formula.
Since a sine wave current
waveform has a CF=1.414, it
will have an xHDF=1; there will
be no derating. The more the
3rd harmonic, the higher the
peak, the higher the CF. If the
CF were 2.0, then the
xHDF=1.414 / 2 =.71. A CF=3
gives us an xHDF =.47. A wave
with CF=3 is about as badly
distorted a current waveform
as you can expect to see on
a single-phase distribution
transformer.
(Caution: This method does not apply to
transformers feeding three-phase loads,
where harmonics other than the third tend to
predominate and CF is not useful as a simple
predictor of the amount of distortion. A
calculation for three-phase loads is available
in ANSI/IEEE C57.110. However, there is some
controversy about this calculation since it may
underestimate the mechanical resonant
vibrations that harmonics can cause, and that
accelerate transformer wear above and
beyond the effects of heat alone.)
4. Forced air cooling
If heat is the problem, cooling is
the solution. Break out the fan,
turn it on the transformer and
use forced air cooling. Some
experienced hands figure that’s
worth 20-30% on the up side.
In any case, it can only help.
Figure 3-6 Transformer derating curve (IEEE 1100-1992).