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UNITI
D.C. MACHINES
Principles of d.c. machines
D.C. machines are the electro mechanical energy converters which
work from a
d.c. source and generate mechanical power or convert mechanical
power into a d.c. power.
Construction of d.c. machines
A D.C. machine consists mainly of two part the stationary part
called stator and the rotatingpart called rotor.
The stator consists of main poles used to produce magnetic flux
,commutating poles orinterpoles in between the main poles to avoid
sparking at the commutator but in the case of smallmachines
sometimes the interpoles are avoided and finally the frame or yoke
which forms thesupporting structure of the machine.
The rotor consist of an armature a cylindrical metallic body or
core with slots in it to placearmature windings or bars,a
commutator and brush gears
The magnetic flux path in a motor or generator is show below and
it is called the magneticstructure of generator or motor.
The major parts can be identified as,1. Frame2. Yoke3. Poles
Institute of Technology Madras4. Armature5. Commutator and brush
gear6. Commutating poles7. Compensating winding8. Other mechanical
parts
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Frame
Frame is the stationary part of a machine on which the main
poles and commutator poles are boltedand it forms the supporting
structure by connecting the frame to the bed plate. The ring
shapedbody portion of the frame which makes the magnetic path for
the magnetic fluxes from the main
poles and interpoles is called Yoke.
Why we use cast steel instead of cast iron for the construction
of Yoke?
In early days Yoke was made up of cast iron but now it is
replaced by cast steel.This is becausecast iron is saturated by a
flux density of 0.8 Wb/sq.m where as saturation with cast iron
steel isabout 1.5 Wb/sq.m.So for the same magnetic flux density the
cross section area needed for caststeel is less than cast iron
hence the weight of the machine too.If we use cast iron there may
bechances of blow holes in it while casting.so now rolled steels
are developed and these haveconsistent magnetic and mechanical
properties.
End Shields or Bearings
If the armature diameter does not exceed 35 to 45 cm then in
addition to poles end shields or framehead with bearing are
attached to the frame.If the armature diameter is greater than 1m
pedestral
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type bearings are mounted on the machine bed plate outside the
frame.These bearings could beball or roller type but generally
plain pedestral bearings are employed.If the diameter of
thearmature is large a brush holder yoke is generally fixed to the
frame.
Main poles:
Solid poles of fabricated steel with separate/integral pole
shoes are fastenedto the frame by means of bolts. Pole shoes are
generally laminated. Sometimes polebody and pole shoe are formed
from the same laminations. The pole shoes are shaped so as to havea
slightly increased air gap at the tips. Inter-poles are small
additional poles located in between themain poles. These can be
solid, or laminated just as the main poles. These are also fastened
to theyoke by bolts. Sometimes the yoke may be slotted to receive
these poles. The inter poles could beof tapered section or of
uniform cross section. These are also called as commutating poles
or compoles. The width of the tip of the com pole can be about a
rotor slot pitch.
ArmatureThe armature is where the moving conductors are located.
The armature is
constructed by stacking laminated sheets of silicon steel.
Thickness of these laminationis kept low to reduce eddy current
losses. As the laminations carry alternating fluxthe choice of
suitable material, insulation coating on the laminations, stacking
it etcare to be done more carefully. The core is divided into
packets to facilitate ventilation.The winding cannot be placed on
the surface of the rotor due to the mechanical forcescoming on the
same. Open parallel sided equally spaced slots are normally punched
inthe rotor laminations. These slots house the armature winding.
Large sized machinesemploy a spider on which the laminations are
stacked in segments. End plates aresuitably shaped so as to serve
as Winding supporters. Armature construction processmust ensure
provision of sufficient axial and radial ducts to facilitate easy
removal ofheat from the armature winding.
Field windings:In the case of wound field machines (as against
permanent magnet excitedmachines) the field winding takes the form
of a concentric coil wound around the mainpoles. These carry the
excitation current and produce the main field in the machine.Thus
the poles are created electromagnetically. Two types of windings
are generallyemployed. In shunt winding large number of turns of
small section copper conductor is ofTechnology Madrasused. The
resistance of such winding would be an order of magnitude larger
than thearmature winding resistance. In the case of series winding
a few turns of heavy crosssection conductor is used. The resistance
of such windings is low and is comparableto armature resistance.
Some machines may have both the windings on the poles.The total
ampere turns required to establish the necessary flux under the
poles iscalculated from the magnetic circuit calculations. The
total mmf required is dividedequally between north and south poles
as the poles are produced in pairs. The mmfrequired to be shared
between shunt and series windings are apportioned as per thedesign
requirements. As these work on the same magnetic system they are in
the formof concentric coils. Mmf per pole is normally used in these
calculations.Armature winding As mentioned earlier, if the armature
coils are wound on the surface of
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the armature, such construction becomes mechanically weak. The
conductors may flyaway when the armature starts rotating. Hence the
armature windings are in generalpre-formed, taped and lowered into
the open slots on the armature. In the case ofsmall machines, they
can be hand wound. The coils are prevented from flying out dueto
the centrifugal forces by means of bands of steel wire on the
surface of the rotor in
small groves cut into it. In the case of large machines slot
wedges are additionally usedto restrain the coils from flying away.
The end portion of the windings are taped atthe free end and bound
to the winding carrier ring of the armature at the commutatorend.
The armature must be dynamically balanced to reduce the centrifugal
forces atthe operating speeds.Compensating winding One may find a
bar winding housed in the slots on the poleshoes. This is mostly
found in d.c. machines of very large rating. Such winding iscalled
compensating winding. In smaller machines, they may be absent.
Commutator:
Commutator is the key element which made the d.c. machine of the
presentday possible. It consists of copper segments tightly
fastened together with mica/micaniteinsulating separators on an
insulated base. The whole commutator forms a rigid andsolid
assembly of insulated copper strips and can rotate at high speeds.
Each com-mutator segment is provided with a riser where the ends of
the armature coils getconnected. The surface of the commutator is
machined and surface is made concentricwith the shaft and the
current collecting brushes rest on the same. Under-cutting themica
insulators that are between these commutator segments has to be
done periodi-cally to avoid fouling of the surface of the
commutator by mica when the commutatorgets worn out. Some details
of the construction of the commutator are seen in Fig. 8.
Brush and brush holders:Brushes rest on the surface of the
commutator. Normally electro-graphite is used as brush
material. The actual composition of the brush depends on the
peripheral speed of the commutatorand the working voltage. The
hardness of the graphite brush is selected to be lower than that of
thecommutator. When the brush wears out the graphite works as a
solid lubricant reducing frictionalcoefficient. More number of
relatively smaller width brushes are preferred in place of large
broadbrushes. The brush holders provide slots for the brushes to be
placed. The connection Brush holderwith a Brush and Positioning of
the brush on the commutator from the brush is taken out by meansof
flexible pigtail. The brushes are kept pressed on the commutator
with the help of springs. This isto ensure proper contact between
the brushes and the commutator even under high speeds ofoperation.
Jumping of brushes must be avoided to ensure arc free current
collection and to keep thebrushcontact drop low.
Other mechanical parts End covers, fan and shaft bearings form
other important me-chanical parts. End covers are completely solid
or have opening for ventilation. Theysupport the bearings which are
on the shaft. Proper machining is to be ensured foreasy assembly.
Fans can be external or internal. In most machines the fan is on
thenon-commutator end sucking the air from the commutator end and
throwing the sameout. Adequate quantity of hot air removal has to
be ensured.
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Bearings Small machines employ ball bearings at both ends. For
larger machines rollerbearings are used especially at the driving
end. The bearings are mounted press-fiton the shaft. They are
housed inside the end shield in such a manner that it is
notnecessary to remove the bearings from the shaft for
dismantling.
Generator E.M.F Equation
Let
= flux/pole in weber
Z = total number of armture conductors
= No.of slots x No.of conductors/slot
P = No.ofgenerator poles
A = No.of parallel paths in armatureN = armature rotation in
revolutions per minute (r.p.m)
E = e.m.f induced in any parallel path in armature
Generated e.m.f Eg = e.m.f generated in any one of the parallel
paths i.e E.
Average e.m.f geneated /conductor = d/dt volt (n=1)
Now, flux cut/conductor in one revolution d = P Wb
No.of revolutions/second = N/60
Time for one revolution, dt = 60/N second
Hence, according to Faraday's Laws of Electroagnetic
Induction,
E.M.F generated/conductor is
For a simplex wave-wound generator
No.of parallel paths = 2
No.of conductors (in series) in one path = Z/2
E.M.F. generated/path is
For a simplex lap-wound generator
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No.of parallel paths = P
No.of conductors (in series) in one path = Z/P
E.M.F.generated/path
In general generated e.m.f
where A = 2 - for simplex wave-winding
A = P - for simplex lap-winding
METHODS OF EXCITATION:
Various methods of excitation of the field windings are shown in
Fig.
Figure shows Field-circuit connections of dc machines:(a)
separate excitation, (b) series, (c) shunt, (d) compound.
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Consider first dc generators.
Separately-excited generators. Self-excited generators: series
generators, shunt generators, compound generators.
o With self-excited generators, residual magnetism must be
present in the machineiron to get the self-excitation process
started.
o N.B.: long- and short-shunt, cumulatively and differentially
compound. Typical steady-state volt-ampere characteristics are
shown in Fig.7.5, constant-speed
operation being assumed. The relation between the steady-state
generated emf Ea and the armature terminal voltage
Va is Va=EaIaRa (7.10)
Figure Volt-ampere characteristics of dc generators.Any of the
methods of excitation used for generators can also be used for
motors.
Typical steady-state dc-motor speed-torque characteristics are
shown in Fig.7.6, in which itis assumed that the motor terminals
are supplied from a constant-voltage source.
In a motor the relation between the emfEa generated in the
armature and and the armatureterminal voltage Va is
Va=Ea+IaRa (7.11)
The application advantages of dc machines lie in the variety of
performance characteristicsoffered by the possibilities of shunt,
series, and compound excitation.
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Figure
Figure Speed-torque characteristics of dc motors.
Torque and power:
The electromagnetic torque Tmech
Tmech=KadIa
The generated voltageEa
Ea=Kadm
EaIa : electromagnetic power
Tmech=EaIa
m
=KadIa
Note that the electromagnetic power differs from the mechanical
power at the machine shaft by the
rotational losses and differs from the electric power at the
machine terminals by the shunt-field and
armatureI2R losse
Ka= poles.Ca
2m
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Voltage and current:
Va: the terminal voltage of the armature winding
Vt: the terminal voltage of the dc machine, including the
voltage drop across the series connected
field winding
Va=Vt if there is no series field winding
Ra: the resistance of armature, Rs: the resistance of the series
field
Va=EaIaRa
Vt=EaIa( Ra+Rs )
IL=IaIf
Generator Characteristics:
The three most important characteristics or curves of a d.c
generator are
1.OpenCircuitCharacteristic(O.C.C.)
This curve shows the relation between the generated e.m.f. at
no-load (E0) and the field current (If)
at constant speed. It is also known as magnetic characteristic
or no-load saturation curve. Its shape
is practically the same for all generators whether separately or
self-excited. The data for O.C.C.
curve are obtained experimentally by operating the generator at
no load and constant speed and
recording the change in terminal voltage as the field current is
varied.
2. Internal or Total characteristic (E/Ia)
This curve shows the relation between the generated e.m.f. on
load (E) and the armature current
(Ia). The e.m.f. E is less than E0 due to the demagnetizing
effect of armature reaction. Therefore,
this curve will lie below the open circuit characteristic
(O.C.C.). The internal characteristic is of
interest chiefly to the designer. It cannot be obtained directly
by experiment. It is because a
voltmeter cannot read the e.m.f. generated on load due to the
voltage drop in armature resistance.
The internal characteristic can be obtained from external
characteristic if winding resistances are
known becausearmature reactioneffect is included in both
characteristics
3. External characteristic (V/IL)This curve shows the relation
between the terminal voltage (V) and load current (IL). The
terminalvoltage V will be less than E due to voltage drop in the
armature circuit. Therefore, this curve willlie below the internal
characteristic. This characteristic is very important in
determining thesuitability of a generator for a given purpose. It
can be obtained by making simultaneous
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1. No-load saturation characteristic (E0/If)
It is also know as Magnetic characteristic or Open circuit
Characteristic ( O.C.C). It shows the
reation between the no-load generated e.m.f in armature, E0 and
the field or exciting current Ifat a
given fixed speed. It is just te magnetisation curve for the
material of the electromagnets.Its shape
is practically the same for all generators whether
separately-excited or self-excited.
A typical no load saturation curve is shown in Figure.It has
generator output voltage plotted
against field current.The lower straight line portion of the
curve represents the air gap because the
magnetic parts are not saturated. When the magnetic parts start
to saturate, the curve bends over
until complete saturation is reached. Then the curve becomes a
straight line again.
2.Separately-excited Generator
The No-load saturation curve of a separately excited generator
will be as shown in the above
figure.It is obvous that when Ifis increased from its initial
small value, the flux and hence
generated e.m.f Eg increase irectly as curent so long as the
poles are unsaturated.This is
represented by straight portion in figure.But as the flux denity
increases,the poles become
saturated, so a greater increase Ifis required to produce a
given increase in voltage than on the
lower part of the curve.That is why the upper portion of the
curve bends.
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The O.C.Ccurve for self-excited generators whether shunt or
series wound is shown in above
figure.Due to the residal magnetism in the poles, some e.m.f
(=OA) is gnerated even when If
=0.Hence, the curve starts a little way up.The slight curvature
at the lower end is due to magnetic
inertia.It is seen that the first part of the curve is
practically straight.This is due to fact that at low
flux densities reluctance of iron path being negligible,total
reluctance is given by the air gap
reluctance which is constant.Hence,the flux and consequently,the
generated e.m.f is directly
proportional to the exciting current.However, at high flux
densities, where is small,iron path
reluctance becomes appreciable and straight relation between E
and If no longer holds good.In
other words,after point B, saturation of pole starts.However,
the initial slope of the curve isdetermined by air-gap width.O.C.C
for higher speed would lie above this curve and for lower
speed,would lie below it.
Separately-excited Generator
Let us consider a separately-excited generator giving its rated
no-load voltage of E0 for a certain
constant field current.If there were no armature reaction and
armature voltage drop,then this
voltage would have remained constant as shown in figure by the
horizontal line 1. But when the
generator is loaded, the voltage falls due to these two causes,
thereby gving slightly dropping
characteristics.If we subtract from E0 the values of voltage
drops due to armature reaction for
different loads, then we get the value of E-the e.m.f actually
induced in the armature under load
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conditions.Curve 2 is plotted in this way and is known as the
internal characteristic.
Series Generator
In this genarator, because field windings are in series with the
armature, they carry full armature
current Ia. As Ia is increased, flux and hence generated e.m.f.
is also increased as shown by thecurve. Curve Oa is the O.C.C. The
extra exciting current necessary to neutralize the weakening
effect of armature reaction at full load is given by the
horizontal distance ab. Hence, point b is on
the internal characteristic.
3. External characteristic (V/I)
It is also referred to as performance characteristic or
sometimes voltage-regulating curve.
It gives relation between the terminal voltage V and the load
current I .This curve lies below the
internal characteristic because it takes in to account the
voltage drop over the armature circuit
resistance.The values of V are obtained by subtracting IaRa from
corresponding values of E.This
characteristic is of great importnce in judging the suitability
of a generator for a particular
purpose.It may be obtained in two ways (i) by making
simultaneous measurements with a suitable
voltmeter and an ammeter on a loaded generator or (ii)
graphically from the O.C.Cprovided the
armature and field resistances are known and also if the
demagnetising effect or the armature
reaction is known.
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Figure above shows the external characteristic
curves forgeneratorswith various types of excitation. If a
generator, which is separately excited, is
driven at constant speed and has a fixed field current, the
output voltage will decrease withincreased load current as shown.
This decrease is due to the armature resistance and armature
reaction effects. If the field flux remained constant, the
generated voltage would tend to remain
constant and the output voltage would be equal to the generated
voltage minus the IR drop of the
armature circuit. However, the demagnetizing component of
armature reactions tends to decrease
the flux, thus adding an additional factor, which decreases the
output voltage.
In a shunt excited generator, it can be seen that the output
voltage decreases faster than with
separate excitation. This is due to the fact that, since the
output voltage is reduced because of the
armature reaction effect and armature IR drop, the field voltage
is also reduced which further
reduces the flux. It can also be seen that beyond a certain
critical value, the shunt generator shows
a reversal in trend of current values with decreasing voltages.
This point of maximum current
output is known as the breakdown point. At theshort
circuitcondition, the only flux available to
produce current is the residual magnetism of the armature.
To build up the voltage on a series generator, the external
circuit must be connected and its
resistance reduced to a comparatively low value. Since the
armature is in series with the field, load
current must be flowing to obtain flux in the field. As the
voltage and current rise the load
resistance may be increased to its normal value. As the external
characteristic curve shows, the
voltage output starts at zero, reaches a peak, and then falls
back to zero.
The combination of a shunt field and a series field gives the
best external characteristic as
illustrated in Figure. The voltage drop, which occurs in the
shunt machine, is compensated for by
the voltage rise, which occurs in the series machine. The
addition of a sufficient number of series
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turns offsets the armature IR drop and armature reaction effect,
resulting in a flat-compound
generator, which has a nearly constant voltage. If more series
turns are added, the voltage may rise
with load and the machine is known as an over-compound
generator.
The speed of a d.c. machine operated as a generator is fixed by
the prime mover. For general-purpose operation, the prime mover is
equipped with a speed governor so that the speed of thegenerator is
practically constant. Under such condition, the generator
performance deals primarilywith the relation between excitation,
terminal voltage and load. These relations can be bestexhibited
graphically by means of curves known as generator characteristics.
These characteristicsshow at a glance the behaviour of the
generator under different load conditions.
characteristics Series of DC generator:
Fig. shows the connections of a series wound generator. Since
there is only one current (thatwhich flows through the whole
machine), the load currentis the same as the exciting current.
(i)O.C.C.Curve 1 shows the open circuit characteristic (O.C.C.)
of a series generator. It can be obtainedexperimentally by
disconnecting the field winding from the machine and exciting it
from aseparate d.c. source as discussed in Sec. (3.2).(ii) Internal
characteristic
Curve 2 shows the total or internal characteristic of a series
generator. It gives the relation betweenthe generated e.m.f. E. on
load and armature current. Due to armature reaction, the flux in
themachine will be less than the flux at no load. Hence, e.m.f. E
generated under load conditions willbe less than the e.m.f. EO
generated under no load conditions. Consequently, internal
characteristic
curve generated under no load conditions. Consequently, internal
characteristic curve lies belowthe O.C.C. curve; the difference
between them representing the effect of armature reaction [SeeFig.
3.7 (ii)].
(iii)ExternalcharacteristicCurve 3 shows the external
characteristic of a series generator. It gives the relation
betweenterminal voltage and load current IL.
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V= E-Ia(Ra+Rse)
Therefore, external characteristic curve will lie below internal
characteristiccurve by an amount equal to ohmic drop[i.e., I
a(Ra+Rse)] in the machine asshown in Fig. (3.7) (ii).
The internal and external characteristics of a d.c. series
generator can be plotted from one anotheras shown in Fig. (3.8).
Suppose we are given the internal characteristic of the generator.
Let theline OC represent the resistance of the whole machine i.e. R
a+Rse.If the load current is OB, drop inthe machine is AB i.e.AB =
Ohmic drop in the machine = OB(Ra+Rse)
Now raise a perpendicular from point B and mark a point b on
this line such that ab = AB. Then
point b will lie on the external characteristic of the
generator. Following similar procedure, otherpoints of external
characteristic can be located. It is easy to see that we can also
plot internalcharacteristic from the external characteristic.
Characteristics Shunt DC generator:
Fig (3.9) (i) shows the connections of a shunt wound generator.
The armature current I a splits upinto two parts; a small fraction
Ish flowing through shunt field winding while the major part IL
goesto the external load.
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(i) O.C.C.The O.C.C. of a shunt generator is similar in shape to
that of a series generator as shown in Fig.(3.9) (ii). The line OA
represents the shunt field circuit resistance. When the generator
is run atnormal speed, it will build up a voltage OM. At no-load,
the terminal voltage of the generator willbe constant (= OM)
represented by the horizontal dotted line MC.
(ii)Internal characteristicWhen the generator is loaded, flux
per pole is reduced due to armature reaction. Therefore, e.m.f.E
generated on load is less than the e.m.f. generated at no load.As a
result, the internalcharacteristic (E/Ia) drops down slightly as
shown in Fig.(3.9) (ii).
(iii)External characteristicCurve 2 shows the external
characteristic of a shunt generator. It gives therelation between
terminal voltage V and load current I L.
V = EIaRa = E -(IL +Ish)Ra
Therefore, external characteristic curve will lie below the
internal characteristic curve by anamount equal to drop in the
armature circuit [i.e., (I L +Ish)Ra ] as shown in Fig. (3.9)
(ii).
Note. It may be seen from the external characteristic that
change in terminalvoltage from no-load to full load is small. The
terminal voltage can always bemaintained constant by adjusting the
field rheostat R automatically
Critical External Resistance for Shunt Generator
If the load resistance across the terminals of a shunt generator
is decreased, then load
current increase? However, there is a limit to the increase in
load current with the decrease of loadresistance. Any decrease of
load resistance beyond this point, instead of increasing the
current,ultimately results in reduced current. Consequently, the
external characteristic turns back (dottedcurve) as shown in Fig.
(3.10). The tangent OA to the curve represents the minimum
externalresistance required to excite the shunt generator on load
and is called critical external resistance. Ifthe resistance of the
external circuit is less than the critical external resistance
(represented bytangent OA in Fig. 3.10), the machine will refuse to
excite or will de-excite if already running Thismeans that external
resistance is so low as virtually to short circuit the machine and
so doing awaywith its excitation.
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Note. There are two critical resistances for a shuntgenerator
viz., (i) critical field resistance (ii) critical external
resistance. For the shunt generator tobuild up voltage, the former
should not be exceeded and the latter must not be gone below
Characteristics compound generator:
In a compound generator, both series and shunt excitation are
combined as shown in Fig.(3.13). The shunt winding can be connected
either across the armature only (short-shuntconnection S) or across
armature plus series field (long-shunt connection G). The
compoundgenerator can be cumulatively compounded or differentially
compounded generator. The latter israrely used in practice.
Therefore, we shall discuss the characteristics of cumulatively
compoundedgenerator. It may be noted that external characteristics
of long and short shunt compoundgenerators are almost
identical.
External characteristicFig. (3.14) shows the external
characteristics of a cumulatively compoundedgenerator. The series
excitation aids the shunt excitation. The degree of compounding
dependsupon the increase in series excitation with the increase in
load current.
(i) If series winding turns are so adjusted that with the
increase in load current the terminal voltageincreases, it is
called over-compounded generator. In such a case, as the load
current increases, theseries field m.m.f. increases and tends to
increase the flux and hence the generated voltage. Theincrease in
generated voltage is greater than the IaRa drop so that instead of
decreasing, theterminal voltage increases as shown by curve A in
Fig. (3.14).
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(ii) If series winding turns are so adjusted that with the
increase in loadcurrent, the terminal voltage substantially remains
constant, it is called flat-compounded generator.The series winding
of such a machine has lesser number of turns than the one in
over-compoundedmachine and, therefore, does not increase the flux
as much for a given load current. Consequently,the full-load
voltage is nearly equal to the no-load voltage
as indicated by curve B in Fig (3.14).(iii) If series field
winding has lesser number of turns than for a flat compounded
machine, theterminal voltage falls with increase in loadcurrent as
indicated by curve C m Fig. (3.14). Such a machine is called
under-compoundedgenerator.
Voltage Regulation
The change in terminal voltage of a generator between full and
no load (at constant speed) is calledthe voltage regulation,
usually expressed as a percentage of the voltage at full-load.
% Voltage regulation= [(VNL-VFL)/VFL ] 100
where VNL = Terminal voltage of generator at no load
VFL = Terminal voltage of generator at full loadNote that
voltage regulation of a generator is determined with field circuit
and speed held constant.If the voltage regulation of a generator is
10%, it means that terminal voltage increases 10% as theload is
changed from full load to no load
2. Motor Characteristics
Section 3.1: TORQUE/SPEED CURVES
In order to effectively design with D.C. motors, it is necessary
to understand theircharacteristic curves. For every motor, there is
a specific Torque/Speed curve andPower curve.
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The graph above shows a torque/speed curve of a typical D.C.
motor. Note that torqueis inversely proportioal to the speed of the
output shaft. In other words, there is atradeoffbetween how much
torque a motor delivers, and how fast the output shaftspins. Motor
characteristics are frequently given as two points on this
graph:
The stall torque, , represents the point on the graph at which
the torque is amaximum, but the shaft is not rotating.
The no load speed, , is the maximum output speed of the motor
(when notorque is applied to the output shaft).
The curve is then approximated by connecting these two points
with a line, whoseequation can be written in terms of torque or
angular velocity as equations 3) and 4):
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The linear model of a D.C. motor torque/speed curve is a
verygood approximation. The torque/speed curves shown below
areactual curves for the green maxon motor (pictured at right)
usedby students in 2.007. One is a plot of empirical data, and the
otherwas plotted mechanically using a device developed at MIT.
Notethat the characteristic torque/speed curve for this motor is
quitelinear.
This is generally true as long as the curve represents the
directoutput of the motor, or a simple gear reduced output. If
thespecifications are given as two points, it is safe to assume a
linearcurve.
Recall that earlier we defined power as the product of torque
and angular velocity. Thiscorresponds to the area of a rectangle
under the torque/speed curve with one corneratthe origin and
another corner at a point on the curve (see figures below). Due to
thelinear inverse relationship between torque and speed, the
maximum power occurs at thepoint where = , and = .
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Up to Contents
Section 3.2: POWER/TORQUE and POWER/SPEED CURVES
By substituting equations 3. and 4. (torque and speed,section
2.1) into equation 2.(power,section 1.3), we see that the power
curves for a D.C. motor with respect to bothspeed and torque are
quadratics, as shown in equations 5. and 6.
From these equations, we again find that maximum output power
occurs at = ,and = repectively.
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Direct on line starter
In electrical engineering, a direct on line (DOL) or across the
line starter starts electricmotors by applying the full line
voltage to the motor terminals. This is the simplest type of
motorstarter. A DOL motor starter also contain protection devices,
and in some cases, conditionmonitoring. Smaller sizes of direct
on-line starters are manually operated; larger sizes use
anelectromechanical contactor (relay) to switch the motor circuit.
Solid-state direct on line starters
also exist.
A direct on line starter can be used if the high inrush current
of the motor does not cause excessivevoltage drop in the supply
circuit. The maximum size of a motor allowed on a direct on line
startermay be limited by the supply utility for this reason. For
example, a utility may require ruralcustomers to use
reduced-voltage starters for motors larger than 10 kW.[1]
DOL starting is sometimes used to start small water pumps,
compressors, fans and conveyor belts.In the case of an asynchronous
motor, such as the 3-phase squirrel-cage motor, the motor will
drawa high starting current until it has run up to full speed. This
starting current is commonly aroundsix times the full load current,
but may as high as 12 times the full load current. To reduce
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Induction law
The voltage induced across the secondary coil may be calculated
from Faraday's law ofinduction, which states that: where VS is the
instantaneous voltage, NS is the number of turns in thesecondary
coil and equals the magnetic flux through one turn of the coil. If
the turns of the coil
are oriented perpendicular to the magnetic field lines, the flux
is the product of the magnetic fluxdensity B and the area A through
which it cuts. The area is constant, being equal to the
cross-sectional area of the transformer core, whereas the magnetic
field varies with time according to theexcitation of the primary.
Since the same magnetic flux passes through both the primary
andsecondary coils in an ideal transformer, the instantaneous
voltage across the primary windingequals
Taking the ratio of the two equations for VS and VP gives the
basic equation for stepping upor stepping down the voltage
Ideal power equation
The ideal transformer as a circuit element If the secondary coil
is attached to a load that allowscurrent to flow, electrical power
is transmitted from the primary circuit to the secondary
circuit.Ideally, the transformer is perfectly efficient; all the
incoming energy is transformed from theprimary circuit to the
magnetic field and into the secondary circuit. If this condition is
met, theincoming electric power must equal the outgoing power.
Pincoming = IPVP = Poutgoing = ISVS
giving the ideal transformer equation
Transformers normally have high efficiency, so this formula is a
reasonable approximation.
If the voltage is increased, then the current is decreased by
the same factor. The impedancein one circuit is transformed by the
square of the turns ratio.[26]For example, if an impedance ZS
isattached across the terminals of the secondary coil, it appears
to the primary circuit to have animpedance of. This relationship is
reciprocal, so that the impedance ZP of the primary circuitappears
to the secondary to be.
Basic Construction and Working Principle of Transformer
An elementary transformer consists of a soft iron or silicon
steel core and two windings,placed on it. The windings are
insulated from both the core and each other. The core is built up
of
thin soft iron or low reluctance to the magnetic flux. The
winding connected to the magnetic flux.The winding connected to the
supply main is called the primary and the winding connected to
theload circuit is called the secondary. Although in the actual
construction the two windings areusually wound one over the other,
for the sake of simplicity, the figures for analyzing
transformertheory show the windings on opposite sides of the core,
as shown below
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Simple Transformer
When the primary winding is connected to an ac supply mains,
current flows throughit. Since this winding links with an iron
core, so current flowing through this winding produces an
alternating flux in the core. Since this flux is alternating and
links with the secondary winding also,so induces an emf in the
secondary winding. The frequency of induced emf in secondary
windingis the same as that of the flux or that of the s supply
voltage. The induced emf in the secondarywinding enables it to
deliver current to an external load connected across it. Thus the
energy istransformed from primary winding to the secondary winding
by means of electro-magneticinduction without any change in
frequency. The flux of the iron core links not only with
thesecondary winding but also with the primary winding, so produces
self-induced emf in the primarywinding: This induced in the primary
winding opposes the applied voltage and thereforesometimes it is
known as back emf of the primary. In fact the induced emf in the
primary windinglimits the primary current in much the same way that
the back emf in a dc motor limits thearmature current.
Construction
Cores
Laminated core transformer showing edge of laminations at top of
photo
Laminated steel cores
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Transformers for use at power or audio frequencies typically
have cores made of highpermeability silicon steel.[53] The steel
has a permeability many times that of free space, and thecore thus
serves to greatly reduce the magnetizing current, and confine the
flux to a path whichclosely couples the windings.[54] Early
transformer developers soon realized that cores constructedfrom
solid iron resulted in prohibitive eddy-current losses, and their
designs mitigated this effect
with cores consisting of bundles of insulated iron wires.
[9]
Later designs constructed the core bystacking layers of thin
steel laminations, a principle that has remained in use. Each
lamination isinsulated from its neighbors by a thin non-conducting
layer of insulation. [46] The universaltransformer equation
indicates a minimum cross-sectional area for the core to avoid
saturation.
The effect of laminations is to confine eddy currents to highly
elliptical paths that encloselittle flux, and so reduce their
magnitude. Thinner laminations reduce losses,[53]but are
morelaborious and expensive to construct.[55]Thin laminations are
generally used on high frequencytransformers, with some types of
very thin steel laminations able to operate up to 10 kHz.
Laminating the core greatly reduces eddy-current losses
One common design of laminated core is made from interleaved
stacks ofE-shaped steelsheets capped with I-shaped pieces, leading
to its name of "E-I transformer".[55]Such a designtends to exhibit
more losses, but is very economical to manufacture. The cut-core or
C-core type ismade by winding a steel strip around a rectangular
form and then bonding the layers together. It isthen cut in two,
forming two C shapes, and the core assembled by binding the two C
halvestogether with a steel strap.[55]They have the advantage that
the flux is always oriented parallel tothe metal grains, reducing
reluctance.
A steel core's remanence means that it retains a static magnetic
field when power isremoved. When power is then reapplied, the
residual field will cause a high inrush current until the
effect of the remaining magnetism is reduced, usually after a
few cycles of the applied alternatingcurrent.[56] Overcurrent
protection devices such as fuses must be selected to allow this
harmlessinrush to pass. On transformers connected to long, overhead
power transmission lines, inducedcurrents due to geomagnetic
disturbances during solar storms can cause saturation of the core
andoperation of transformer protection devices.[57]
Distribution transformers can achieve low no-load losses by
using cores made with low-loss high-permeability silicon steel or
amorphous (non-crystalline) metal alloy. The higher initialcost of
the core material is offset over the life of the transformer by its
lower losses at light load .[58]
Solid cores
Powdered iron cores are used in circuits (such as switch-mode
power supplies) that operate abovemain frequencies and up to a few
tens of kilohertz. These materials combine high
magneticpermeability with high bulk electrical resistivity. For
frequencies extending beyond the VHF band,cores made from
non-conductive magnetic ceramic materials called ferrites are
common.[55]Someradio-frequency transformers also have movable cores
(sometimes called 'slugs') which allowadjustment of the coupling
coefficient (and bandwidth) of tuned radio-frequency circuits.
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Toroidal cores
Small toroidal core transformer
Toroidal transformers are built around a ring-shaped core,
which, depending on operating
frequency, is made from a long strip ofsilicon steel or
permalloy wound into a coil, powderediron, or ferrite.[59]A strip
construction ensures that the grain boundaries are optimally
aligned,improving the transformer's efficiency by reducing the
core's reluctance. The closed ring shapeeliminates air gaps
inherent in the construction of an E-I core.[32]The cross-section
of the ring isusually square or rectangular, but more expensive
cores with circular cross-sections are alsoavailable. The primary
and secondary coils are often wound concentrically to cover the
entiresurface of the core. This minimizes the length of wire
needed, and also provides screening tominimize the core's magnetic
field from generating electromagnetic interference.
Toroidal transformers are more efficient than the cheaper
laminated E-I types for a similarpower level. Other advantages
compared to E-I types, include smaller size (about half), lower
weight (about half), less mechanical hum (making them superior
in audio amplifiers), lowerexterior magnetic field (about one
tenth), low off-load losses (making them more efficient instandby
circuits), single-bolt mounting, and greater choice of shapes. The
main disadvantages arehigher cost and limited power capacity (see
"Classification" above). Because of the lack of aresidual gap in
the magnetic path, toroidal transformers also tend to exhibit
higher inrush current,compared to laminated E-I types.
Ferrite toroidal cores are used at higher frequencies, typically
between a few tens ofkilohertz to hundreds of megahertz, to reduce
losses, physical size, and weight ofswitch-modepower supplies. A
drawback of toroidal transformer construction is the higher labor
cost ofwinding. This is because it is necessary to pass the entire
length of a coil winding through the core
aperture each time a single turn is added to the coil. As a
consequence, toroidal transformers areuncommon above ratings of a
few kVA. Small distribution transformers may achieve some of
thebenefits of a toroidal core by splitting it and forcing it open,
then inserting a bobbin containingprimary and secondary
windings.
Air cores
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A physical core is not an absolute requisite and a functioning
transformer can be producedsimply by placing the windings in close
proximity to each other, an arrangement termed an "air-core"
transformer. The air which comprises the magnetic circuit is
essentially lossless, and so anair-core transformer eliminates loss
due to hysteresis in the core material.[30]The leakageinductance is
inevitably high, resulting in very poor regulation, and so such
designs are unsuitable
for use in power distribution.
[30]
They have however very high bandwidth, and are
frequentlyemployed in radio-frequency applications,[60]for which a
satisfactory coupling coefficient ismaintained by carefully
overlapping the primary and secondary windings. They're also used
forresonant transformers such as Tesla coils where they can achieve
reasonably low loss in spite ofthe high leakage inductance.
Windings
Windings are usually arranged concentrically to minimize flux
leakage.
Cut view through transformer windings. White: insulator. Green
spiral: Grain orientedsilicon steel. Black: Primary winding made
ofoxygen-free copper. Red: Secondary winding. Topleft: Toroidal
transformer. Right: C-core, but E-core would be similar. The black
windings aremade of film. Top: Equally low capacitance between all
ends of both windings. Since most coresare at least moderately
conductive they also need insulation. Bottom: Lowest capacitance
for oneend of the secondary winding needed for low-power
high-voltage transformers. Bottom left:Reduction ofleakage
inductance would lead to increase of capacitance.
The conducting material used for the windings depends upon the
application, but in all
cases the individual turns must be electrically insulated from
each other to ensure that the currenttravels throughout every
turn.[33]For small power and signal transformers, in which currents
arelow and the potential difference between adjacent turns is
small, the coils are often wound fromenamelled magnet wire, such as
Formvar wire. Larger power transformers operating at highvoltages
may be wound with copper rectangular strip conductors insulated by
oil-impregnatedpaper and blocks ofpressboard.[61]
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High-frequency transformers operating in the tens to hundreds of
kilohertz often havewindings made of braided Litz wire to minimize
the skin-effect and proximity effect losses.[33]Large power
transformers use multiple-stranded conductors as well, since even
at low powerfrequencies non-uniform distribution of current would
otherwise exist in high-current windings.[61]Each strand is
individually insulated, and the strands are arranged so that at
certain points in the
winding, or throughout the whole winding, each portion occupies
different relative positions in thecomplete conductor. The
transposition equalizes the current flowing in each strand of
theconductor, and reduces eddy current losses in the winding
itself. The stranded conductor is alsomore flexible than a solid
conductor of similar size, aiding manufacture.[61]
For signal transformers, the windings may be arranged in a way
to minimize leakageinductance and stray capacitance to improve
high-frequency response. This can be done bysplitting up each coil
into sections, and those sections placed in layers between the
sections of theother winding. This is known as a stacked type or
interleaved winding.
Both the primary and secondary windings on power transformers
may have external
connections, called taps, to intermediate points on the winding
to allow selection of the voltageratio. The taps may be connected
to an automatic on-load tap changer for voltage regulation
ofdistribution circuits. Audio-frequency transformers, used for the
distribution of audio to publicaddress loudspeakers, have taps to
allow adjustment of impedance to each speaker. A center-tapped
transformer is often used in the output stage of an audio power
amplifier in a push-pullcircuit. Modulation transformers in AM
transmitters are very similar.
Certain transformers have the windings protected by epoxy resin.
By impregnating thetransformer with epoxy under a vacuum, one can
replace air spaces within the windings withepoxy, thus sealing the
windings and helping to prevent the possible formation of corona
andabsorption of dirt or water. This produces transformers more
suited to damp or dirty environments,
but at increased manufacturing cost.
[62]
Coolant
Cut-away view of three-phase oil-cooled transformer. The oil
reservoir is visible at the top.Radiative fins aid the dissipation
of heat.
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High temperatures will damage the winding insulation. [63] Small
transformers do notgenerate significant heat and are cooled by air
circulation and radiation of heat. Powertransformers rated up to
several hundred kVA can be adequately cooled by natural convective
air-cooling, sometimes assisted by fans.[64] In larger
transformers, part of the design problem isremoval of heat. Some
power transformers are immersed in transformer oil that both cools
and
insulates the windings.
[65]
The oil is a highly refined mineral oil that remains stable at
transformeroperating temperature. Indoor liquid-filled transformers
must use a non-flammable liquid, or mustbe located in fire
resistant rooms.[66] Air-cooled dry transformers are preferred for
indoorapplications even at capacity ratings where oil-cooled
construction would be more economical,because their cost is offset
by the reduced building construction cost.
The oil-filled tank often has radiators through which the oil
circulates by naturalconvection; some large transformers employ
forced circulation of the oil by electric pumps, aidedby external
fans or water-cooled heat exchangers.[65]Oil-filled transformers
undergo prolongeddrying processes to ensure that the transformer is
completely free ofwater vapor before the coolingoil is introduced.
This helps prevent electrical breakdown under load. Oil-filled
transformers may
be equipped with Buchholz relays, which detect gas evolved
during internal arcing and rapidly de-energize the transformer to
avert catastrophic failure.[56]Oil-filed transformers may fail,
rupture,and burn, causing power outages and losses. Installations
of oil-filled transformers usually includesfire protection measures
such as walls, oil containment, and fire-suppression sprinkler
systems.
Polychlorinated biphenyls have properties that once favored
their use as a coolant, thoughconcerns over their environmental
persistence led to a widespread ban on their use.[67]Today,
non-toxic, stable silicone-based oils, or fluorinated hydrocarbons
may be used where the expense of afire-resistant liquid offsets
additional building cost for a transformer vault.[63][66]Before
1977, eventransformers that were nominally filled only with mineral
oils may also have been contaminatedwith polychlorinated biphenyls
at 10-20 ppm. Since mineral oil and PCB fluid mix, maintenance
equipment used for both PCB and oil-filled transformers could
carry over small amounts of PCB,contaminating oil-filled
transformers.[68]
Some "dry" transformers (containing no liquid) are enclosed in
sealed, pressurized tanksand cooled by nitrogen or sulfur
hexafluoride gas.[63]
Experimental power transformers in the 2 MVA range have been
built with superconductingwindings which eliminates the copper
losses, but not the core steel loss. These are cooled by
liquidnitrogen or helium.
Terminals
Very small transformers will have wire leads connected directly
to the ends of the coils, andbrought out to the base of the unit
for circuit connections. Larger transformers may have heavybolted
terminals, bus bars or high-voltage insulated bushings made of
polymers or porcelain. Alarge bushing can be a complex structure
since it must provide careful control of the electric fieldgradient
without letting the transformer leak oil.
Applications
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Image of an electrical substation in Melbourne, Australia
showing 3 of 5 220kV/66kVtransformers, each with a capacity of
185MVA
A major application of transformers is to increase voltage
before transmitting electricalenergy over long distances through
wires. Wires have resistance and so dissipate electrical energy
at a rate proportional to the square of the current through the
wire. By transforming electricalpower to a high-voltage (and
therefore low-current) form for transmission and back
againafterward, transformers enable economic transmission of power
over long distances. Consequently,transformers have shaped the
electricity supply industry, permitting generation to be
locatedremotely from points ofdemand.[71]All but a tiny fraction of
the world's electrical power haspassed through a series of
transformers by the time it reaches the consumer.
Transformers are also used extensively in electronic products to
step down the supplyvoltage to a level suitable for the low voltage
circuits they contain. The transformer alsoelectrically isolates
the end user from contact with the supply voltage.
Signal and audio transformers are used to couple stages
ofamplifiers and to match devicessuch as microphones and record
players to the input of amplifiers. Audio transformers
allowedtelephone circuits to carry on a two-way conversation over a
single pair of wires. A baluntransformer converts a signal that is
referenced to ground to a signal that has balanced voltages
toground, such as between external cables and internal
circuits.
Practical considerations
Leakage flux
Leakage flux of a transformerMain article: Leakage
inductance
The ideal transformer model assumes that all flux generated by
the primary winding linksall the turns of every winding, including
itself. In practice, some flux traverses paths that take itoutside
the windings.[31]Such flux is termed leakage flux, and results in
leakage inductance inseries with the mutually coupled transformer
windings.[30]Leakage results in energy being
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alternately stored in and discharged from the magnetic fields
with each cycle of the power supply.It is not directly a power loss
(see "Stray losses" below), but results in inferior voltage
regulation,causing the secondary voltage to fail to be directly
proportional to the primary, particularly underheavy
load.[31]Transformers are therefore normally designed to have very
low leakage inductance.
However, in some applications, leakage can be a desirable
property, and long magneticpaths, air gaps, or magnetic bypass
shunts may be deliberately introduced to a transformer's designto
limit the short-circuit current it will supply.[30]Leaky
transformers may be used to supply loadsthat exhibit negative
resistance, such as electric arcs, mercury vapor lamps, and neon
signs; or forsafely handling loads that become periodically
short-circuited such as electric arc welders.[32]
Air gaps are also used to keep a transformer from saturating,
especially audio-frequencytransformers in circuits that have a
direct current flowing through the windings. Leakageinductance is
also helpful when transformers are operated in parallel. It can be
shown that if the"per-unit" inductance of two transformers is the
same (a typical value is 5%), they willautomatically split power
"correctly" (e.g. 500 kVA unit in parallel with 1,000 kVA unit, the
larger
one will carry twice the current).
[citation needed]
Effect of frequency
Transformer universal EMF equation
If the flux in the core is purely sinusoidal, the relationship
for either winding between its rmsvoltage Erms of the winding , and
the supply frequency f, number of turns N, core cross-sectionalarea
a and peakmagnetic flux density B is given by the universal EMF
equation:
If the flux does not contain even harmonics the following
equation can be used for half-cycleaverage voltage Eavg of any
waveshape:
The time-derivative term in Faraday's Law shows that the flux in
the core is the integralwith respect to time of the applied
voltage.[33]Hypothetically an ideal transformer would workwith
direct-current excitation, with the core flux increasing linearly
with time.[34]In practice, theflux would rise to the point where
magnetic saturation of the core occurs, causing a huge increasein
the magnetizing current and overheating the transformer. All
practical transformers musttherefore operate with alternating (or
pulsed) current.[34]
The EMF of a transformer at a given flux density increases with
frequency.
[28]
By operatingat higher frequencies, transformers can be
physically more compact because a given core is able totransfer
more power without reaching saturation and fewer turns are needed
to achieve the sameimpedance. However, properties such as core loss
and conductor skin effect also increase withfrequency. Aircraft and
military equipment employ 400 Hz power supplies which reduce core
andwinding weight.[35]Conversely, frequencies used for some railway
electrification systems weremuch lower (e.g. 16.7 Hz and 25 Hz)
than normal utility frequencies (50 - 60 Hz) for historicalreasons
concerned mainly with the limitations of early electric traction
motors. As such, the
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transformers used to step down the high over-head line voltages
(e.g. 15 kV) are much heavier forthe same power rating than those
designed only for the higher frequencies.
Operation of a transformer at its designed voltage but at a
higher frequency than intendedwill lead to reduced magnetizing
current; at lower frequency, the magnetizing current will
increase. Operation of a transformer at other than its design
frequency may require assessment ofvoltages, losses, and cooling to
establish if safe operation is practical. For example,
transformersmay need to be equipped with "volts per hertz"
over-excitation relays to protect the transformerfrom overvoltage
at higher than rated frequency.
One example of state-of-the-art design is those transformers
used for electric multiple unit highspeed trains, particularly
those required to operate across the borders of countries using
differentstandards of electrification. The position of such
transformers is restricted to being hung below thepassenger
compartment. They have to function at different frequencies (down
to 16.7 Hz) andvoltages (up to 25 kV) whilst handling the enhanced
power requirements needed for operating thetrains at high
speed.
Knowledge of natural frequencies of transformer windings is of
importance for the determinationof the transient response of the
windings to impulse and switching surge voltages.
Energy losses
An ideal transformer would have no energy losses, and would be
100% efficient. Inpractical transformers energy is dissipated in
the windings, core, and surrounding structures.Larger transformers
are generally more efficient, and those rated for electricity
distribution usuallyperform better than 98%.[36]
Experimental transformers using superconducting windings achieve
efficiencies of99.85%.[37]While the increase in efficiency is
small, when applied to large heavily loadedtransformers the annual
savings in energy losses are significant.
A small transformer, such as a plug-in "wall wart" power adapter
commonly used for low-power consumer electronics devices, may be as
low as 20% efficient, with considerable energyloss even when not
supplying any power to the device. Though individual losses may be
only afew watts, it has been estimated that the cumulative loss
from such transformers in the UnitedStates alone exceeded 32
billion kilowatt-hours (kWh) in 2002.[38]
The losses vary with load current, and may be expressed as
"no-load" or "full-load" loss.
Winding resistance dominates load losses, whereas hysteresis and
eddy currents losses contributeto over 99% of the no-load loss. The
no-load loss can be significant, meaning that even an
idletransformer constitutes a drain on an electrical supply, which
encourages development of low-losstransformers (also see energy
efficient transformer).[39]
Transformer losses are divided into losses in the windings,
termed copper loss, and those inthe magnetic circuit, termed iron
loss. Losses in the transformer arise from:
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