.~
.::
K-Factor Transformers and Non-linear Loads
Kiran Deshpande*,
Prof.Rajesh
Holmukhe*,
Prof.Yogesh
Angal**
Abstract-Harmonic
currents generated by non-linear loads can cause problems in the power systems and particularly the
distribution transformers as they are vulnerable to overheating and premature failure. Normally designers recommend an oversized
transformer to protect transformer from overheating. K-factor transformers are specifically designed to accommodate harmonic
currents. K-transformers are preferred because they have additional thermal capacity of known limits, design features that minimize
harmonic current losses, and neutral and terminal connections sized at 200% of normal. K-factor transformers allow operation up to
nameplate capacity without derating.
Index Terms- Additional thermal capacity, Derating, Distribution transformers, Harmonic currents, K- Factor, Nameplate capacity,
Neutral and Terminal connections, Non-linear loads, Overheating.
I. INTRODUCTION
Today's modem offices and plants are dominated by nonlinear
loads, desktop computers, solid state ballasts, PID lighting,
programmable controllers, and variable speed drives to name a
few. Due to these electronic loads, significant harmonic loads
have been added to the building's distribution systems. The
result is premature failure ofthe transformer due to
overheating. Till recent times, the only solution to this problem
was to derate the transformer. This solution is no longer
acceptable.
II.
A review of Nonlinear Loads
The effect of nonlinear loads on the electrical power systems
has become matter of concern since past few years. Nonlinear
loads draw currents which are not sinusoidal. They include
equipments such as solid state motor drives, arc furnaces,
battery chargers, UPS systems, and the increasing electronic
power supplies. The increased use of these nonlinear loads is
the cause of concern as larger percentage of power systems
tend to become nonlinear. The nonlinear loads were thought to
be matter of concern for industrial power systems where large
static power converters were being used. But now larger
application of electronics to practically every electrical load,
nonlinear loads are present in commercial and even residential
power system. Nonlinear loads produce harmonic currents
which flow from the load towards the power source following
the path of least impedances. Harmonic currents are the
currents which have frequencies that are whole number
multiples of fundamental frequency. The harmonic currents
superimposed on the fundamental currents result in the nonsinusoidal waveform associated with the nonlinear loads.Fig.l
show the voltages and current waveforms for nonlinear loads.
It can be seen that voltage waveform is sinusoidal but current
waveform is not.
• Dept.of Electrical Engineering, College of Engineering, Bharati Vidyapeeth
University, Pune,
E-mail: irkin85@hotmail.com
•• Dept.of Instrumentation Engineering, Dr.D. Y.Patil Institute of Engineering
and Technology, Pimpri, Pune: 411 018.
Fig. 1. Voltage and current waveform
III.
for nonlinear load.
Effects of Harmonic Currents on Power System
Harmonic currents adversely affect every component of the
power system. These currents create additional dielectric,
thermally, and/or mechanical
stresses. Harmonic currents
flowing through the power system impedances result in
harmonic voltage drops which are observed as harmonic
voltage distortion. The voltage distortions could become very
severe when the power systems inductive and capacitive
impedances become equal, a condition of parallel resonance.
This condition could appear at one of the nonlinear load's
significant harmonic current frequencies (typically the 5th,
II th or 13th harmonic). Harmonic currents can cause losses in
normal power components even when resonance conditions do
not prevail. Due to skin and proximity effects, wiring
experience additional heating. If normal wiring sizing methods
are employed, then the derating for wiring for harmonics is
minimal and can be ignored.
r.
IV. Methods to Derate Transformer
as suggested by ANSI!
IEEE Standards .
Harmonic
currents
cause additional
heating
in the form of
Typical tr.m fo mer dtrall
additional winding eddy current losses in transformers.ANSI /
IEEE C 57.110 provides methods to derate a transformer for
any given load profile. This standard considers the winding
eddy current losses to be proportional to the harmonic number
required. This relationship has been found to be accurate for
lower power frequency harmonics, but result in an
overestimation of losses for higher harmonics (generally
greater than II th). A typical derating curve is shown in fig.2.
Transformers directly supplying single phase power supplies
may require derating of 30% to 40% to avoid overheating.
'Underwriters Laboratories' (UL) recognize the potential
safety hazards associated with nonlinear loads and developed
a rating system to indicate the capability of transformer to
handle harmonic loads. The ratings are described in UL-I56I
and are known as K-Factors. K-Factors are a weighing of the
harmonic load currents according to their effects on
transformer heating, as derived from ANSIIIEEE C57.II O. A
K-Factor of 1.0 indicates a linear load (no harmonics).The
higher the K-Factor, the greater the effect of harmonic
heating (I].
U)
(1)
Load
Where Ih is the load current at the harmonic h, expressed in a
per-unit basis such that the total RMS current equals one
ampere, i.e.
(2)
The problem associated with calculating K- Factor is selecting
the range of harmonic frequencies that should be included.
Some use up to 15th harmonic, others up to 25 th harmonic, and
still others include up to 50th harmonic. For the same load,
each of these calculations can yield significantly different
K-Factors, because even very small current levels associated
with higher harmonics, when multiplied by the harmonic
number squared, can yield significantly to the K-Factor. Based
on the underlying assumptions of C57.II0, it seems
reasonable to limit the K-Factor calculation to harmonic
currents less than 25 th harmonic. Sample calculations are
given in Table No.l.ln establishing standard transformer KFactor rating; UL chose ratings of 1, 4, 9, 13, 20, 30, 40 and
50. From a practical viewpoint individual loads with KFactors greater than 20 are infrequent. At best office areas
with some nonlinear loads and large computer rooms normally
have observed K-Factors of 4 to 9. Areas with high
concentrations of single phase computers and terminals have
observed K- Factors of 13 to 17. When multiple nonlinear
loads are powered from the same source, lower harmonic
current levels may be expected due to phase shifts and
cancellations. In one study of commercial buildings, single
phase loads with current distortion of 104%, THD (Total
Harmonic Distortion) resulted in only a 7% THD at the
service entrance, when added with other loads in the building.
Additional studies of typical loads are beginning to provide
information which could aid in the development of
additional rules of thumb to use when direct load
1!
~
K~acto'
Fig. 2.Typical Transformer derating for
Nonlinear loads
measurements are not available. K-Factor transformers are
designed to be operated fully loaded with any harmonic load
having K-Factor equal to or less than its K-rating. For
example, a K-13 transformer can be fully loaded with any
harmonic load having a K-Factor up to K-13. If the load has a
K-Factor greater than 13, then the transformer cannot be
safely operated at full load and would require derating.
v.
How do K-Factor Transformers
Standard Transformers?
differ from
K-Factor transformers have additional thermal capacity to
tolerate the heating effects of the harmonic currents. A well
designed K-Transformer will also minimize the winding eddycurrent losses through the use of parallel conductors and other
winding techniques. The K-factor indicates the multiples of
the 60 Hz winding eddy current losses that the transformer can
safely dissipate. Transformer load losses consist of winding
12R losses plus stray losses. Using UL best methods, stray
losses are assumed to be primarily winding eddy current
losses for transformers 300 KVA and smaller.
For example, a transformer having winding 12Rlosses of2000
watts and 60 Hz stray losses of 1000 watts would, with a K-20
rating, is required to dissipate the 2000 watts ofeR losses plus
20 times the 60Hz stray losses of 1000 watts for a total load
loss of 4000 watts without exceeding the maximum winding
temperature rise. The result is a larger, more expensive
transformer.
For K-Factor transformers, UL also requires that the neutral
terminal and connections to be sized to accommodate twice
the rated phase conductor size (double the minimum neutral
capacity) of standard transformers.
Development of
Triplen Harmonic Current
Instantaneous 3.phase 60 Hz currents = 0 at any instant
There are several areas where designs are changed to
accommodate the effects of harmonics.
1.
2.
3.
4.
Secondary Windings: The secondary windings,
instead of working with a pure sine wave and
producing normal values and stray losses have to
cope up with non-sinusoidal waveforms containing
multiple harmonics, which raise the stray losses
significantly. To compensate for these increased
losses, a multiple of small, individually insulated
conductors are used. Transposition is used wherever
necessary.
Neutral: Since harmonic currents are additive in
neutral, neutral currents in excess of two times phase
currents can be measured. To compensate for this,
double sized neutral lugs and lug pads is furnished.
Primary winding: The primary winding has some
lower order harmonics circulating within the delta,
producing losses and additional heating. This is
compensated for by using a heavier conductor.
Core: The core is affected by voltage harmonic
distortion. This voltage distortion increases the core
flux density, creating higher core loss, higher
magnetizing currents, higher audible noise and
heating problems. To reduce flux density, alloy
induction designed core is used.
VI. About Standard Transformers not marked with
K-Factor ratings:
Standard transformers, i.e. transformers not marked with a KFactor rating, may have some tolerance to nonlinear loading,
but their capability is unknown to the user and is not certified
by a third party such as UL. Currently marking transformer
with a K-Factor rating is not required by UL. Due to
conservative design application, some unmarked transformer
may therefore have enough extra thermal capacity to tolerate
additional harmonic load heating. This is particularly true for
80° C or 115°C rise transformers built with 220°C insulation
material which can safely withstand a 150°C winding
temperature rise.
VII. Consideration of additional Over Current
Protection for Transformers supplying
Nonlinear Loads.
Additional over current protection should be considered for all
transformers supplying nonlinear loads. The National Electric
Code allows primary-only over current protection at 125°C of
the transformer's primary full load amperes. With three-phase
transformers, the triplen harmonics are cancelled in the delta
winding and do not appear in the input current. The output
currents and transformer loading greater than is apparent from
AmPS
C
Instantaneous triplen 3rd harmonic currents (180
Hz )where neutral current = 3 x phase currents
Fig.3. Development of Triplen Harmonic current.
the input current. Therefore a transformer can be overloaded
without the primary over-current protection ever tripping.
Adding secondary over-current protection helps, but it
still does not protect the transformer from the heating effects
of harmonic currents. The use of supplemental protection in
the form of winding temperature sensors can be used to
provide alarm and/or system shutdown in the event of
overload, excessive harmonic current, high ambient
temperature, or inadequate cooling
VIII. More on Triplen Harmonic currents.
Triplen harmonic currents are phase currents which flow from
each of the phases into the fourth wire neutral and have
frequencies in integer multiples of three times the 60 Hz base
frequency (180 Hz, 360Hz, 540Hz etc). At each of these third
multiple triplen frequencies, these triplen phase currents are in
phase with each other and when flowing in the neutral as zero
sequence currents are equal to three times their RMS phase
values. The development of triplen harmonic current is shown
in fig.3.
In a 3 phase, 4 wire system, single phase line to neutral
currents flow in each phase conductor and return in common
neutral. Since the three 60 Hz currents are separated by 120°,
when balanced they cancel each other. The measured resultant
current is equal to zero.
Theory also states that for even harmonics, starting with the
second order, when balanced, the even harmonic will cancel in
the common neutral. Other odd harmonics add in the common
neutral, but their magnitude is considerably less than triplens.
The RMS value of the total current is the square root of the
RMS value of the individual currents squared.
I Total --
IJoHz
+ liaoHz + liooHz + IJzoHz + ...
(3)
Where I = RMS value of current.
At any given instant, the 60 Hz currents on the three phase
legs have a vector resultant of zero and cancel in the neutral.
But, the third (and other odd triplen harmonics) on the phase
legs are in phase and become additive in the neutral.
IX. The UL Approach to Transformers
A. A transformer intended for use with loads drawing
non-sinusoidal currents shall be marked "Suitable for
non-sinusoidal current load with K-Factor not to
exceed x. (x= 4, 9, 13, 20, 30, 40 or 50).
B. Formulas to determine eddy losses and total losses
where the transformer load losses (PLL) are to be
determined as follows:
PLL
= PDC(l + K(PEC))
(4)
Where, PDC = Total 12Rlosses
K = the K-Factor rating at the transformer (4, 9, 13, 20, 30,
40 or 50).
Shielde~Transformer
sn~l~
&
~I
UnshieldedTransformer
~1t~~
t~l1t~
J
T ~I'"
~l ~
~
I
II ~i!
',.r.
~.
~
:..
·.1.
\ '-----''j
Fig. 4. Shielded and unshielded Transformers.
Relatively small DC components (up to the RMS magnitude
of the transformer excitation current at rated voltage) are
expected to have no significant effects on the load carrying
of the transformer excitation current at rated voltage) are
expected to have no significant effect on the load carrying
capability of a transformer determined by this recommended
practice. Higher DC load components may adversely affect
transformer capability and must be corrected by the user.
Harmonic currents flowing through transformer leakage
Impedance and through system impedance may also produce
some small harmonic distortion in the voltage waveform at the
transformer terminals. Such voltage harmonics may cause
extra harmonic losses in the transformer core. However,
operating experience has indicated that core temperature rise
usually will not be the limiting parameter for determination of
safe magnitudes of non-sinusoidal load currents.
PEC = assumed eddy current losses calculated as follows:
For Transformers rated 300 KVA or less, and for transformers
Rated 300 KVA and above, in which;
PAC = Impedance loss
C= 0.7 for transformers having a turn ratio greater than 4:1
and having one or more winding with a current rating greater
than 1000 amperes., or C= 0.6 for all other transformers.
PDC-I = the fR losses for the inner winding.
The impedance losses and the fR losses shall be determined
in accordance with the test code for Dry Type Distribution and
Power Transformers, ANSI/IEEE C57.12.91-1979. [4]
As stated in ANSI/IEEE C57.1 10-1986, harmonic load
currents may be accompanied by DC components in the load
current which are frequently caused by the loss of a diode in a
rectifier circuit. A DC component of load current will increase
the transformer core loss slightly, and may increase the
magnetizing current and audible sound level. [3].
The Noise Isolation Transformer suppresses common mode
noise by introducing a ground shield between its primary and
secondary windings. The ground shield provides a low
impedance path to ground by capacitive coupling which
prevents unwanted high frequency signals contained in the
source voltage from reaching the transformer secondary.
The grounded shield between primary and secondary windings
is called an electrostatic shield. This shield does not perform
any function with regard to harmonic current or voltage
distortion wave forms. However this shield is extremely
valuable in protecting sensitive equipments from common
mode electrical noise and transients generated on the line side
of the transformer. The shielded and unshielded transformers
are shown in fig, 4.
The ratio of common mode noise attenuation (CMA) on the
input to that of the output of the transformer is expressed in
decibels as shown in equation shown here below:
CMA
= 20 10glo [Vin]
Vout
dB
(5)
Table No.1.Calculations for a typical nonlinear load
h
(harmonic
number)
In
(In)2
InlL (In)2)
(nonlinear
Load
Current)
(In)2
h2
I
100.0%
1.000
0.792
0.626
0.626
3
65.7
0.432
0.520
0.270
2.434
5
37.7
0.142
0.296
0.089
2.226
7
12.7
0.016
0.101
0.010
0.495
9
4.4
0.002
0.035
0.001
0.098
II
5.3
0.003
0.042
0.002
0.213
13
2.5
0.001
0.020
0.000
0.066
15
1.9
0.000
0.015
0.000
0.051
17
1.8
0.000
0.014
0.000
0.059
19
1.1
0.000
0.009
0.000
0.027
21
0.6
0.000
0.005
0.000
0.010
23
0.8
0.000
0.006
0.000
0.021
25
0.4
0.000
0.003
0.000
0.006
1.00
6.33
Total
1.596
An isolation transformer with an electrostatic shield can have
a ratio of input noise voltage (VIN) to output noise voltage
(VOUT) within the range of 10:1 to 1000:1 or even higher.
The calculations for K-Factor loads can be carried out with the
help of information available in the Table No.2 and 3.
X. Disadvantage of using Derated Transformers
instead ofK-Factor Transformer
The use of derated standard transformers instead of K-Factor
Transformers carries some disadvantage as under:
I.
2.
First is the issue of managing the derating when the
transformer nameplate indicates greater capacity.
Initially, the transformer may be operated at reduced
loading. But in the future, the loading may be
increased without considering the intended derating.
If smaller overcurrent protection is used intentionally
to limit the overloading, nuisance tripping may occur
due to the transformer inrush current. Larger overcurrent protection may be required for the oversized
(derated) standard transformer resulting in larger
conductor requirements with the associated higher
Table No.2. K- Factors for various types of Loads
Load
Incandescent
Lighting
Electric Resistance
Heating
Motors (without
solid state drives)
Control
Transformers
Motor-Generators
Distribution
Transformers
Electric Discharge
Lighting
UPS
Welders
Induction Heating
Equipment
PLCs and solid
state controls
Telecommunication
Equipment (e.g.
PBX)
UPS without input
filtering
Multiwire
receptable circuits
in general care
areas of health care
facilities
Main frame
computer loads
Solid State Motor
Drives
Multiwire
receptable circuits
in Industrial,
Medical and
Educational
Laboratories
Small Main Frames
(Mini and Micro)
Other loads
identified as
producing very high
amounts of
harmonics
K- Factor
ILK
K-I
0.00
K-I
0.00
K-I
0.00
K-I
0.00
K-I
0.00
K-I
0.00
K-4
25.82
K-4
K-4
25.82
25.82
K-4
25.82
K-4
25.82
K-13
57.74
K-13
57.74
K-13
57.74
K-20
80.94
K-20
80.94
K-30
123.54
K-30
123.54
K-40
208.17
Table No.3. Index of K-rating
KFactor
ILK
K-40
K-I
K-4
K-9
K-13
K-20
K-30
0.0
25.82
44.72
57.74
80.94
123.54 208.17
.:
3.
feeder costs.
The transformers designed specifically for nonlinear
loads minimize losses due to harmonic currents. They
operate with the nonlinear loads more efficiently and
generate less heat that need to be dissipated.
power systems increasing as more electronic loads are added.
Whether this will provide sufficient impetus for new rating
system for other power system components is problematical.
One thing is sure, though, until the day that harmonic currents
actually diminish, K-Factor Transformers will play an
important role in coping with the problems harmonics create.
Xl. Using a K-Factor Transformer
References
Once the harmonic current of the total load is known, and a KFactor is specified (K4, K13 etc.), the appropriate type KFactor transformer can be fully loaded up to 100% or
nameplate KVA. All other optional feature that the industry is
accustomed to can be specified.
I.
2.
3.
[2] Gruzs, T.M. "A survey of Neutral Currents in Threephase Computer Power Systems", IEEE Transactions on
Industry Application, Vo1.26, No.4, July/August 1990.
Copper or Aluminum.
80° C, 115°C, 150°C.
Electro-static shield.
XII. What should be remembered when using a
K-Factor Transformer?
I). Harmonic loads do cause premature
standard transformers are used.
2)
3)
[I] The Institute of Electrical & Electronic Engineers,
"Recommended Practice for establishing Transformer
capabilities when supplying Non-sinusoidal Load
Currents", ANSIIIEEE C57.110-1986, New York, 1986.
failure when
Average reading RMS meters do not measure
harmonic currents. True reading RMS meters should
be used.
3rd
Insist on a K-Factor transformer that has been
party tested. Accept no verbal claims. The proof must
be on the label.
Conclusions:
Because transformers are the power system components most
affected by nonlinear loads, they are the first to receive a
harmonic rating system. K-Factor ratings are based on heating
effects of harmonics and are not necessarily applicable to
other power system components. If harmonic rating systems
for other components are needed, they will have to be
developed by other methods, e.g., THD, crest factor, or some
new and component-specific weighing of harmonic currents.
What is the likelihood that additional rating systems will
actually be developed? That's hard to predict. The best
solution to the problem caused by harmonic currents would be
preventive, i.e. the use of components does not generate
harmonics. Impending standards such as lEC 555 and IEEE
519 encourage the development of such devices.
Indeed, low harmonic current power supplies and electronic
ballasts are already available. As such new designs are
implemented, they should gradually displace existing
electronic loads (and their greater harmonics), serving to
reduce the prevalence of harmonic currents over the long term.
Short term, however, projection show harmonic levels in
[3] IEEE P-l100 Working Group. Recommended Practice
for Powering and Grounding Sensitive Electronic
Equipments. Draft 1992.
[4] Underwriters Laboratory. Proposed Requirements and
Proposed Effective Dates for the First Edition of the
Standard for Dry Type General Purpose and Power
Transformers, UL 156. Santa Clara CA, 1991.
[5] Computer Business Equipment Association (CBEMA).
Three Phase Power Source Overloading Caused by Small
Computers and Electronic Office Equipment. ESC-3
Information Letter, 1987.
[6] McGranaghan et al. "Analysis of Harmonic Distortion
Levels in Commercial Buildings." PQA 91,Paris, France,
October 1991.
[7] ANSI/IEEE Standard 519-1981. IEEE Guide to Harmonic
Control and Reactive Compensation of Static Power
Converters.
[8] McPartland Brian J.: "Use K-Factor Transformers?
Definitely! But Which K-Factor?" EDI, June 1991, Vo\.2
No.6.