Transformer Book
Transformer Book
Transformer Book
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Introduction
In current transformer design, the core characteristics must be carefully selected
because excitation current I e essentially subtracts from the metered current and
affects the ratio and phase angle of the output current.
The higher the exciting current or core loss the larger the error
When choosing a core material a reasonable value for B m (0,2 ... 0,3 T) typically
results in L c and R fe values large enough to reduce the current flowing in these
elements so as to satisfy the ratio and phase requirements.
Effect of Gapping
[McLyman.]
The time constant of the circuit depends on the inductance of the coil and on the
resistance in the circuit in accordance to the following simple formula:
General
Measuring current transformer = A current transformer intended to
supply indicating instruments, integrating meters and similar
apparatus.
Definitions
Composite error = Under steady-state conditions, the r.m.s value of
the difference between:
a) the instantaneous values of the primary current
b) the instantaneous values of the actual secondary current multiplied
by the rated transformation ratio.
Accuracy requirements
For measuring current transformers the accuracy class is designated
by the highest permissible percentage current error at rated current
prescribed for the accuracy class concerned.
The standard accuracy classes for measuring current transformers
are: 0,1 - 0,2 - 0,5 - 1 - 3 - 5
Accuracy +/- Percentage +/- Phase displacement at
class current error at percentage of rated current shown
percentage of rated below
current shown below
Minutes Centiradians
5 20 100 120 5 20 100 120 5 20 100 120
0,1 0,4 0,2 0,1 0,1 15 8 5 5 0,45 0,24 0,15 0,15
0,2 0,75 0,35 0,2 0,2 30 15 10 10 0,9 0,45 0,3 0,3
0,5 1,5 1,5 0,5 0,5 90 45 30 30 2,7 1,35 0,9 0,9
1 3,0 3,0 1,0 1,0 180 90 60 60 5,4 2,7 1,8 1,8
5 5 5
[SFS 2874:E]
Marking
The rating plate shall carry the appropriate information in accordance
general marking.
The accuracy class and instrument security factor shall be indicated
following the indication of corresponding rated output (e.g. 15 VA
Class 0,5 F s 10). F s = instrument security factor
General
Protective current transformer = A current transformer intended to
supply protective relays.
Definitions
Composite error = Under steady-state conditions, the r.m.s value of
the difference between:
a) the instantaneous values of the primary current
b) the instantaneous values of the actual secondary current multiplied
by the rated transformation ratio.
Accuracy requirements
For protective current transformers the accuracy class is designated
by the highest permissible percentage composite error at the rated
accuracy limit primary current prescribed for the accuracy class
concerned, followed by the letter "P" (meaning protection) at
ratecurrent prescribed for the accuracy class concerned.
The standard accuracy classes for protective current transformers are:
5 P and 10 P
Accuracy Percentage Phase Composite error at
class current error at displacement at rated accuracy limit
primary current rated primary primary current in %
in % current
Minutes Centiradians
5P +/- 1 +/- 60 +/- 1,8 6
10 P +/- 3 10
Marking
The rating plate shall carry the appropriate information in accordance
general marking.
The rated accuracy limit factor shall be indicated following the
corresponding output and accuracy class (e.g. 30 VA Class 5 P 10). 10
= Accuracy limit factor
[SFS 2874:E]
current transformer:
one output at the
two coils with the same double core current
secondary
core transformer
two alternative
symbols
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[ABB Catalogue. KOLMA and IHDA Indoor Type Cable Current Transformers.]
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Current transformers
● Definitions
● Measuring current transformer
● Protective current transformer
● Rating and performance requirements
● Types of current transformers
● A current transformer design
Introduction
Current transformer is an instrument transformer in which the
secondary current, in normal conditions of use, is substantially
proportional to the primary current and differs in phase from it by an
angle which is approximately zero for an appropriate direction of the
connections.
Current error
The error which a transformer introduces into the measurement of a
current arises from the fact that the actual transformation ratio is not
equal to the rated transformation ratio. The higher the exciting
current or core loss the larger the error.
The current error expressed in percent is given by the formula:
Burden
Burden = The impedance of the secondary circuit in ohms and power
factor. The burden is usually expressed as the apparent power (S) in
volt-amperes absorbed at a specified power-factor at the rated
secondary current.
Secondary
winding
impedance
(internal
burden) Z s
Secondary
load
impedance
Z0
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Core types
The configuration of a three-phase transformer depends on the core
type of the transformer. There are three choices:
3x single-phase
Core configuration
k=a
coefficient that
depends on the
number of steps
Core sheet
Coil material
The coil material can be copper or aluminum. The term copper loss is
still used to indicate resistance losses of winding materials whether
copper or aluminum is used.
Copper ρ k = 8.93 kg/dm3
Aluminum ρ k = 2.69 kg/dm3
ρ k = The weight by volume
Coil configuration
Foil coil
Tank
The tank and the cover are manufactured of hot-rolled, unalloyed
steel sheet and profile balks. Fine granular steel is used in
transformers for low ambient temperatures.
Areas where strong eddy currents can be generated due to high
currents, and where ordinary hot-rolled steel can become too warm,
are made of non-magnetic (austenite) steel. Such areas are for
example the surroundings if high current bushings and bushbars. The
tanks are welded and manufactured in accordance with modern
welding methods.
The tank has lifting lugs for lifting the transformer (fully-equipped
transformer including oil) and at least four jacking points an the
lower part if the tank for lifting by hydraulic jacks. For transport
wheels there are fixing points at the bottom of the tank. The tank is
provided with at least two earthing lugs made of stainless steel.
The connecting flanges of the coolers and the flanges for filling,
draining, filtering and sampling valves are welded to the tank. Also
the fixing brackets of cooler fans are welded to the tank. Usually the
support of the oil conservator is fastened to the tank too. The
transformer cover is fixed to the tank usually by means of a bolt joint
using oil resistant rubber cork as the gasket. A gasket made of special
rubber can also be used. The cover can also be fixed to the tank by
welding. The welded seams are tighter and more reliable than bolted
ones. They can be quite easily opened and rewelded.
The transformer cover is constructed so that no water pockets or
other water collector points are formed. An air pipe is connected to
the gas relay from all the turrets, flanges etc. where it is possible for
gas pockets to develop.
[ABB Catalogue. Power Transformers Construction.]
Coolers
Transformers are usually provided with radiators for cooling (cooling
method ONAN or ONAN/ONAF). The radiators are manufactured of
welded elements and they are vacuum-proof.
The radiators are connected to the transformer tank by means of
shut-valves. This method allows individual radiators to be removed
without draining oil from the transformer. The shut-off valve is
provided with a position indicating handle and with a locking spring.
The lower part of the radiators has a plug for oil outlet and the upper
part a plug for air release.
In the transformers which have ONAN/ONAF cooling, the fans
forcing the air circulation are under or at a low noise level and they
are equipped with steel sheet guard and the necessary protective
mesh. The fan motors can normally be connected to the 380/220 V
supply, but if required, motors with other voltage ratings can also be
used.
The transformer can also be provided with water cooling, cooling
method OFWF or oil-air cooler, cooling method OFAF. In each case,
the oil circulation through coolers is handled by means of an oil
pump. The coolers can be installed so as to rest upon the transformer
tank or on a frame separated from the transformer. The pipe work is
provided with the necessary valves for removing the cooler and the
pump for inspection and maintenance.
[ABB Catalogue. Power Transformers Construction.]
The hysteresis curve of soft alloys is thin and therefore the coercive force is
small. These alloys are mostly used in electromechanical machines and
transformers.
The hysteresis curve of hard alloys is wide and therefore the coercive force is
high. These alloys are mostly used in permanent magnets.
Back
[McLyman.]
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Coil configuration
Cylinder coil
Show the primary!
Coil configuration
Layer coil
Collar coil
Losses of a transformer
No-load loss
No-load losses are mainly iron losses. The iron loss become important in
cases where a lighting load is being supplied and in which the
transformer itself remains excited, even though not actually supplying
any load. It is also important in cases where a transformer is working on
a low load factor.
Apparent loss
The loss that is due to the magnetizing current in the primary winding is
called the apparent loss.
The flow of the magnetizing current through the resistance of the
winding does create a real I 2 R loss and voltage drop, although both are
generally quite small.
Hysteresis losses
The hysteresis loss per cycle in a core of volume V that has a uniform
flux density B throughout its volume is
Eddy-current losses
The AC flux induces emfs in the core that produce eddy currents that
circulate in the iron. Eddy-current losses are proportional to the
frequency, the maximum flux density, the thickness of the core sheet and
the resistivity of the iron (inversely).
Excited = ?
= running idle
= running without load
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Load loss
The sum of copper losses and the stray losses is called the load
losses, being I 2 R eg , as determined from the short-circuit test. While
the equivalent circuits, including the approximate equivalent circuit,
may be used to calculate the losses for a given output, it is usually
more convenient to use data of the short-circuit test directly.
● The term copper loss is still used to indicate resistance losses of
winding materials whether copper of aluminum is used.
● The term copper losses is still sometimes used instead of load
losses and when so used is meant to include the stray losses.
[Matsch L. W. , Morgan J. D.]
Copper loss
The load currents through the resistance's of the primary and
secondary windings create I 2 R losses that heat up the copper wires
and cause voltage drops. There load losses are called copper losses
(winding material can be copper or aluminum).
Stray loss
Two factors that contribute to losses (and other undesirable
phenomena) are stray capacitance and leakage inductance. Stray
capacitance inevitably exists between turns, between one winding
and another, and between windings and the core.
[Lowdon E.]
What is a transformer?
A transformer is a device that transfers energy from one AC system to another.
A transformer can accept energy at one voltage and deliver it at another
voltage. This permits electrical energy to be generated at relatively low
voltages and transmitted at high voltages and low currents, thus reducing line
losses, and to be used at safe voltages.
Three-phase transformer
Three-phase power may be transformed by using either two or three
single-phase transformers, or by a single three-phase transformer. When a set
of single-phase transformers is employed to transform three phases, it is called
a three-phase bank of transformers.
Symmetrical three-phase transformer
[Sähkötekniikan käsikirja]
[Sähkötekniikan käsikirja]
A two-winding transformer
The transformer may be defined as a device in which two or more stationary
electric circuits are coupled magnetically, the windings linked by a common
timevarying magnetic flux. One of these windings, known as the primary,
receives power at a given voltage and frequency from the source; and the other
[Sähkötekniikan käsikirja]
[Sähkötekniikan käsikirja]
Exciting current
The exciting current I e, is considered as having two components, the core-loss
current I fe and the magnetizing current I m. The core-loss current is a
real-power component and is due to the core losses. The magnetizing current
is, in effect, the component of current that furnishes the mmf to overcome the
magnetic reluctance of the core.
Voltage Regulation
The voltage regulation is an important measure of transformer performance
and is expressed by the formula:
The percent regulation is of 100 times the per-unit regulation. In the above
expression, V 2 Io is the secondary voltage under load, and V 2 nI is the
secondary no-load voltage (I 2 = 0), with primary voltage held constant at the
value it had under load. The quantities used in the formula are magnitudes, not
phasors.
[McPherson G. , Laramore R. D.]
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Power transformer
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Power transformer
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Basics of a transformer
● What is a transformer?
● Three-phase transformer
● A two-winding transformer
● Connections
● Exciting current
● Current inrush
● Voltage Regulation
● Losses and efficiency
Magnetic materials
Each magnetic material belongs to one of the three groups.
1. Diamagnetic materials have a very low value of relative
permeability µ. These materials can even decrease the magnetic
field.
Permeability
Permeability is the ability to conduct flux. Mathematically, it is the
ratio of the flux density (B) to the magnetizing force (H) that causes
B. In Symbols
Saturation
The B-H curve shows the meaning of saturation. It can be seen that
beyond a certain value of H (point C). There is a little increase in B;
the iron is approaching the saturation.
Different materials saturate at different values of flux density. At the
saturation point the permeability is very small or zero. These means
that the inductance is very small.
L = The inductance
R m = The reluctance of circuit
A = The core area
I = The length of the magnetic circuit
Hysteresis
The nonlinear properties of magnetic materials are characterized by
the hysteresis loop.
Fringing
The phenomenon of flux spreading to a larger cross section when it
leaves a high-permeability material entering a relatively
low-permeability material such as air in an air gap.
Electromagnetics
● Magnetic materials
● Permeability
● Magnetic permeance and reluctance
● Saturation
● Hysteresis
● Magnetic Leakage and Fringing
● Faraday's induction law
● Kirchoff´s laws
Distribution transformers
● Basics of a transformer
● Configuration of a distribution transformer
● Losses of a transformer
DIRECTORY
in alphabetic order
Air-gapped current transformers Hysteresis curve of a soft and hard alloy
REFERENCES
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Working group
Ilpo Havunen
Leena Korpinen
Kimmo Kähärä
Erja Toivonen
Thomas Hager
Feedback: leena@cc.tut.fi