YASAR UNIVERSITY

Electrical and Electronics Eng. Dept.

Inrush Current & Derating Factor in Transformers

Dr. Hacer Şekerci

• Inrush current may cause fuses, reclosers, or relays to falsely operate.

• It may also falsely operate faulted-circuit indicators or cause

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 reference: https://electrical-engineering-
portal.com/the-worst-transformer-inrush-current-
occurs-when
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The worst inrush occurs with residual flux left on the transformer core

This quickly saturates the core. The effective magnetizing branch drops to the air-core impedance of the transformer.

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 The inrush current phenomenon occurs due to temporary over fluxing of the
transformer core. This may depend upon:
• Switching instant on the voltage waveform at which the transformer is energised.
• The magnitude and polarity of the residual flux present in the transformer during
re – energisation.
• Rating of the transformer.
• Total resistance of the primary winding (with source impedance).

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 Inrush Current Calculation

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 Transformer Inrush Current Protection
• A transformer draws inrush current that can exceed saturation current at power up.
• The Inrush Current affects the magnetic property of the core.
• This happens even if the transformer has no load with its secondary open.
• The magnitude of the inrush current depends on the point on the AC wave the
transformer is switched on.
• If turn-on occurs when the AC voltage wave is at its peak value, there will be no
inrush current drawn by the transformer. The magnitude of the current in this case will
be at normal no load value.
• If at turn-on, the AC wave is going through its zero value, then the current drawn will
be very high and exceed the saturation current.

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 Solving Inrush Problems
The most significant problem associated with inrush currents is the resulting voltage sag.
ANSI C50.41-2000, “American National Standard for Polyphase Induction Motors for
Power Generation Stations,” states that motors must be able to start as long as the voltage
is not less than 85% of the rated voltage.
In addition, most utilities limit the allowable voltage variation at the point of common
coupling (PCC) caused by a single motor start to about 4%.
The voltage variation on the distribution system is determined by the impedance of the
distribution system supply in relation to the impedance of the step-down transformer and
secondary cabling to the motor.

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Inrush current (pulse) is a factor of: Influence of high inrush current & resulting
distortion
• Remaining capacitor voltage due to
fast switching in automatic capacitor • High stress on the capacitor reduces lifetime,
banks, • Welding or fast wear-off of the main contacts
• Short circuit power of supply of contactors,
transformer, • Negative effects on power quality (e.g. voltage
• Output of capacitor switched in transients),
parallel to output of others already • Overvoltage,
energized, • Insulation problems
• Fault level of supply network. • Defects of electronic equipment
• Production stop
• Undervoltage/voltage zero crossing,
• Measurement failure
• Problems with numeric controlled equipment
• Production stops due to computer failure
• High cost of maintenance and production
standstill.

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 Motor Inrush Characteristics
Motors have the undesirable characteristic of drawing several times their full load
current while starting.
By flowing through system impedances, this large current will cause voltage sags
that dim lights, cause contactors to drop out, and disrupt sensitive equipment.
Theses sags also affect the starting itself, as large enough sags will prevent a
successful start.
Even small and medium horsepower motors can have inrush currents that are six to
10 times the normal steady-state current levels.
High-efficiency motors can have even higher inrush currents.
If the motor starting operation results in a voltage sag that causes tripping of
equipment within the facility or at other customer facilities, you can use one of the
following methods to reduce the voltage sag.
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 Inrush Current in the Motor
• Keep large motors on a separate supply from the sensitive loads. Following this advice usually
prevents problems with other equipment. The PCC will be at the distribution voltage level, where the
voltage sag is less severe than at the motor terminals.

• Use resistance and reactance starters. These initially insert an impedance in series with the motor.
After a time delay, the starter bypasses this impedance. Starting resistors may be bypassed in several
steps while starting reactors are bypassed in a single step. This approach requires the motor be able
to develop sufficient torque with the added impedance.

• Use delta-wye starters. These connect the stator in wye for starting, then after a time delay,
reconnect the windings in delta. The wye connection reduces the starting voltage to 57% of the
system line-line voltage, which causes the starting torque to fall to 33% of its full start value. The
reduced voltage during the initial stage of the starting reduces the inrush current — and the resulting
voltage sag.

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• Use shunt capacitor starters. These devices work by switching in, along with the motor, a large
shunt capacitor bank that supplies a large portion of the motor VAR requirements during the start
process. The capacitor bank then automatically disconnects once the motor is up to speed
(usually based on overvoltage relay).

• Use series capacitors on distribution circuits supplying large motors. This will reduce the
effective impedance seen by the motor during starting as well as the resulting voltage sag on the
motor side of the series capacitor. However, the source side of the series capacitor may still
experience a more severe voltage sag.

• Change frequency response characteristics. This will counter the potential for system resonance
caused by harmonics in transformer inrush currents. You may be able to do this by switching out
one or more shunt capacitors prior to energizing the transformer.

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 Derating Transformers Serving Non-linear Loads
Transformers are normally designed and built for use at rated frequency and prefect
sinusoidal load current.
Due to the widespread use of non-linear loads such as computers, variable speed drives in
heating, ventilation and air conditioning (HVAC) systems and electronic ballasts of
fluorescent lamps, harmonic distortion is increasing in the commercial user and services.
Non-linear loads on a transformer lead to higher losses, early fatigue of insulation,
premature failure and reduction of the useful life of the transformer.
To prevent these problems, the rated capacity of a transformer, which supply non-linear
loads must be reduced.

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Effect of Non-linear Loads on the Transformer Losses
Transformer losses consist of no-load losses (or core losses) and load losses:
The no-load losses are due to the core excitation.
The harmonic currents passing through the transformer leakage impedance and system impedance
may distort the transformer output voltage slightly.
Experience shows that the temperature rise of the core is not the limiting factor in determining the
permissible current for non-linear loads. IEEE-C57-110 standard also ignores the increase in core
losses due to the non-linear loads. The load losses are;

With the rated eddy current losses known, the eddy current losses due to any non-sinusoidal load
current can be calculated;

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 Stray losses or total eddy current losses plus other stray losses can be determined for any non-
sinusoidal load using a similar procedure.
In the standard 1561, 1562 of UL laboratory, factor K is defined as follows;

K_Factor shows the influence of amplitude and frequency of the harmonic current upon the
increase of the eddy current losses of the transformer under non-sinusoidal loads. In the revised
version of the standard IEEE C57-110, the factor of harmonic losses (FHL) has been defined as
follows:

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If the rms current of the load is equal to the rated current of the transformer, the numerical value
of factor K will be equal to the harmonic loss factor.

There are two effects that cause increase in winding eddy current losses, namely the skin effect and proximity
effect. The winding eddy current loss in power frequency spectrum tends to proportional to the square of the
load current and square of the frequency due to both skin effect and proximity effect.

Skin effect Skin effect is the trend of current to Proximity effect These losses will increase with square
flow on the circumference of the wire so that the of load current. A dc component of the load current will
current density is greater at the surface than at the increase the transformer core loss slightly.
core. High frequency noise in the range of 1kHz-
1.5MHz increases the inductive reactance of the
wire. This forces the electrical charge towards the
outer surface of the wire. This means that the total
available space of the wire is not used to carry the
electrical power.
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Derating is used to reduce the transformer KVA loading such that total transformer losses are
limited to rated losses.
The main methods for estimating transformer derating are: K-Factor, Harmonic Loss Factor, online
harmonic loss measurement and computed harmonic losses.
The IEEE standard. C57.110-1998 introduced a term called the K-factor for rating a transformer as
per their capability to handle load currents with significant harmonic contents.
It is an alternate technique for transformer de-rating which considers load characteristics.
It is a rating applied to a transformer indicating its suitability for use with loads that draw non-
sinusoidal currents.
It is an index that determines the changes in conventional transformers must undergo so that they
can dissipate heat due to additional iron and copper losses because of harmonic currents at rated
power.
There are two methods of determining the equivalent power of a transformer for non-linear load.
The first method is used where complete data concerning the density of the transformer losses are
available.
The second method is less accurate and is employed where only the test data of the transformer
exists. Designers, therefore, generally use the first method, whilst users use the second method. The
following assumptions are made in the second method:
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• All stray losses are equal to the eddy current losses of winding.
• Ohmic losses of any winding are distributed uniformly.
• For all transformers having rated currents lower than 1000 A, the distribution of the eddy current
losses is 60% for the internal winding and 40% for the external winding. This distribution will be
70% and 30% for transformers having rated currents larger than 1000 A.
• Maximum density of eddy current losses in any winding is equal to 400% of the average density of
eddy current losses.

For a three -phase 20 kV/0.4 kV distribution transformer, under nominal conditions, is obtained as
follows;

The I2R losses at the rated load are 1 pu, and it is assumed that all stray losses are equal to the eddy
current losses of the windings. Equation can be simplified as follows:

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Hence the K-factor can be given as

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Harmonic current leads to additional load on transformers which are associated with additional
losses.
This means that, because of these harmonic currents the transformer can be overloaded even
while the load current is below the nominal current. In order to prevent these overload
conditions transformers need to be derated.
The derating is generally based on the harmonic load factor or the K-factor which are both
parameters that are not always available.
In this paper the relation between these factors and a common available parameter (THD(I)) is
evaluated and derating factors are determined.
Next to this derating the relation with the US K-factor is made which allows to determine this
factor based on THD(I).
This evaluation is made based on real life measurements on multiple transformers with different
load levels so representing a real industrial relevance.

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 References
Inrush Current
• Gopika R, Deepa Sankar, “Study on Power Transformer Inrush Current”, IOSR Journal of Electrical and Electronics
Engineering (IOSR-JEEE) e-ISSN: 2278-1676,p-ISSN: 2320-3331, PP 59-63
• Li-Cheng Wu,, Chih-Wen Liu, Shih-En Chien, Ching-Shan Chen, “The Effect of Inrush Current on Transformer
Protection”, October 2006, https://www.researchgate.net/publication/224703830
• “Damping of Inrush Currents Power Quality Solutions”, https://www.tdk-
electronics.tdk.com/download/530812/2527ef892bc3b986bf1df898ffc0fea4/pdf-pqs-dampinginrushcurrentsan113.pdf
• https://www.ecmweb.com/content/article/20892020/evaluating-motor-and-transformer-inrush-currents
Deratnig Factor
• Vishakha L. Meshram, Mrs. S. V. Umredkar, “Distribution Transformer Due to Non-linear Loads”, International Journal of
Engineering Research and Applications (IJERA) ISSN: 2248-9622 April 2014
• J. Faiz, M. B. B. Sharifian, S. A. Fakheri & E. Sabet-marzooghi, “Derating Of Distribution Transformers For Non-sinusoidal
Load Currents Using Finite Element Method”, Iranian Journal of Science & Technology, Transaction B, Vol. 28, No. B3
Printed in Islamic Republic of Iran, 2004
• Bart VERHELST, Johan RENS, & Jan DESMET, “Derating method for dry type power transformers based on current
distortion Parameters”, 25th International Conference on Electricity Distribution, Madrid, 3-6 June 2019
• Jan Desmet & Gregory Delaere, “Power Quality Application Guide Selection and Rating of Transformers”, Copper
Development Association IEE Endorsed Provider
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