UNIT I D.C. MACHINES - vidyarthiplus.com

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 rotating
part called rotor.
The stator consists of main poles used to produce magnetic flux ,commutating poles or
interpoles in between the main poles to avoid sparking at the commutator but in the case of small
machines sometimes the interpoles are avoided and finally the frame or yoke which forms the
supporting structure of the machine.
The rotor consist of an armature a cylindrical metallic body or core with slots in it to place
armature 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 magnetic
structure of generator or motor.
The major parts can be identified as,
1. Frame
2. Yoke
4. Armature
6. Commutating poles
7. Compensating winding
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Frame
Frame is the stationary part of a machine on which the main poles and commutator poles are bolted
and it forms the supporting structure by connecting the frame to the bed plate. The ring shaped
body 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 because
cast iron is saturated by a flux density of 0.8 Wb/sq.m where as saturation with cast iron steel is
about 1.5 Wb/sq.m.So for the same magnetic flux density the cross section area needed for cast
steel is less than cast iron hence the weight of the machine too.If we use cast iron there may be
chances of blow holes in it while casting.so now rolled steels are developed and these have
consistent 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 frame
head with bearing are attached to the frame.If the armature diameter is greater than 1m pedestral
type bearings are mounted on the machine bed plate outside the frame.These bearings could be
ball or roller type but generally plain pedestral bearings are employed.If the diameter of the
armature 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 fastened
to the frame by means of bolts. Pole shoes are generally laminated. Sometimes pole
body and pole shoe are formed from the same laminations. The pole shoes are shaped so as to have
a slightly increased air gap at the tips. Inter-poles are small additional poles located in between the
main poles. These can be solid, or laminated just as the main poles. These are also fastened to the
yoke by bolts. Sometimes the yoke may be slotted to receive these poles. The inter poles could be
of tapered section or of uniform cross section. These are also called as commutating poles or com
poles. The width of the tip of the com pole can be about a rotor slot pitch.
Armature
The armature is where the moving conductors are located. The armature is
constructed by stacking laminated sheets of silicon steel. Thickness of these lamination
is kept low to reduce eddy current losses. As the laminations carry alternating flux
the choice of suitable material, insulation coating on the laminations, stacking it etc
are 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 forces
coming on the same. Open parallel sided equally spaced slots are normally punched in
the rotor laminations. These slots house the armature winding. Large sized machines
employ a spider on which the laminations are stacked in segments. End plates are
suitably shaped so as to serve as ’Winding supporters’. Armature construction process
must ensure provision of sufficient axial and radial ducts to facilitate easy removal of
heat from the armature winding.
Field windings:
In the case of wound field machines (as against permanent magnet excited
machines) the field winding takes the form of a concentric coil wound around the main
poles. These carry the excitation current and produce the main field in the machine.
Thus the poles are created electromagnetically. Two types of windings are generally
employed. In shunt winding large number of turns of small section copper conductor isof
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used. The resistance of such winding would be an order of magnitude larger than the
armature winding resistance. In the case of series winding a few turns of heavy cross
section conductor is used. The resistance of such windings is low and is comparable
to 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 is
calculated from the magnetic circuit calculations. The total mmf required is divided
equally between north and south poles as the poles are produced in pairs. The mmf
required to be shared between shunt and series windings are apportioned as per the
design requirements. As these work on the same magnetic system they are in the form
of 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
the armature, such construction becomes mechanically weak. The conductors may fly
away when the armature starts rotating. Hence the armature windings are in general
pre-formed, taped and lowered into the open slots on the armature. In the case of
small machines, they can be hand wound. The coils are prevented from flying out due
to 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 used
to restrain the coils from flying away. The end portion of the windings are taped at
the free end and bound to the winding carrier ring of the armature at the commutator
end. The armature must be dynamically balanced to reduce the centrifugal forces at
the operating speeds.
Compensating winding One may find a bar winding housed in the slots on the pole
shoes. This is mostly found in d.c. machines of very large rating. Such winding is
called compensating winding. In smaller machines, they may be absent.
Commutator:
Commutator is the key element which made the d.c. machine of the present
day possible. It consists of copper segments tightly fastened together with mica/micanite
insulating separators on an insulated base. The whole commutator forms a rigid and
solid 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 get
connected. The surface of the commutator is machined and surface is made concentric
with the shaft and the current collecting brushes rest on the same. Under-cutting the
mica 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 commutator
gets 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 commutator
and the working voltage. The hardness of the graphite brush is selected to be lower than that of the
commutator. When the brush wears out the graphite works as a solid lubricant reducing frictional
coefficient. More number of relatively smaller width brushes are preferred in place of large broad
brushes. The brush holders provide slots for the brushes to be placed. The connection Brush holder
with a Brush and Positioning of the brush on the commutator from the brush is taken out by means
of flexible pigtail. The brushes are kept pressed on the commutator with the help of springs. This is
to ensure proper contact between the brushes and the commutator even under high speeds of
operation. Jumping of brushes must be avoided to ensure arc free current collection and to keep the
brushcontact 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. They
support the bearings which are on the shaft. Proper machining is to be ensured for
easy assembly. Fans can be external or internal. In most machines the fan is on the
non-commutator end sucking the air from the commutator end and throwing the same
out. Adequate quantity of hot air removal has to be ensured.
Bearings Small machines employ ball bearings at both ends. For larger machines roller
bearings are used especially at the driving end. The bearings are mounted press-fit
on the shaft. They are housed inside the end shield in such a manner that it is not
necessary to remove the bearings from the shaft for dismantling.
Generator E.M.F Equation
= No.of slots x No.of conductors/slot
P = No.of generator poles
N = 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 = dΦ/dt volt (n=1)
Now, flux cut/conductor in one revolution dΦ = ΦP Wb
No.of revolutions/second = N/60
Hence, according to Faraday's Laws of Electroagnetic Induction,
E.M.F generated/conductor is
No.of parallel paths = 2
E.M.F. generated/path is
E.M.F.generated/path
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.
Self-excited generators: series generators, shunt generators, compound generators.
o With self-excited generators, residual magnetism must be present in the machine
iron 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=Ea−IaRa (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 it
is assumed that the motor terminals are supplied from a constant-voltage source.
In a motor the relation between the emf Ea generated in the armature and and the armature
terminal voltage Va is
Va=Ea+IaRa (7.11)
The application advantages of dc machines lie in the variety of performance characteristics
offered by the possibilities of shunt, series, and compound excitation.
Figure
Torque and power:
ωm
=KaΦdIa
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
armature I 2 R losse
Ka= poles.Ca
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=Ea±IaRa
IL=Ia±If
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 because armature reaction effect 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 terminal
voltage V will be less than E due to voltage drop in the armature circuit. Therefore, this curve will
lie below the internal characteristic. This characteristic is very important in determining the
suitability of a generator for a given purpose. It can be obtained by making simultaneous
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 If at 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 If is 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 If is 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.
The O.C.C curve 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 μ 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 is
determined 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
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 the
curve. 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.
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.C provided the
armature and field resistances are known and also if the demagnetising effect or the armature
reaction is known.
Figure above shows the external characteristic
curves for generators with 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 with
increased 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 the short circuit condition, 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
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 the
generator is practically constant. Under such condition, the generator performance deals primarily
with the relation between excitation, terminal voltage and load. These relations can be best
exhibited graphically by means of curves known as generator characteristics. These characteristics
show 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 (that
which 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 obtained
experimentally by disconnecting the field winding from the machine and exciting it from a
separate 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 between
the generated e.m.f. E. on load and armature current. Due to armature reaction, the flux in the
machine will be less than the flux at no load. Hence, e.m.f. E generated under load conditions will
be 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 below
the O.C.C. curve; the difference between them representing the effect of armature reaction [See
Fig. 3.7 (ii)].
terminal voltage and load current IL.
Therefore, external characteristic curve will lie below internal characteristic
curve by an amount equal to ohmic drop[i.e., Ia(Ra+Rse)] in the machine as
shown in Fig. (3.7) (ii).
The internal and external characteristics of a d.c. series generator can be plotted from one another
as shown in Fig. (3.8). Suppose we are given the internal characteristic of the generator. Let the
line OC represent the resistance of the whole machine i.e. Ra+Rse.If the load current is OB, drop in
the 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, other
points of external characteristic can be located. It is easy to see that we can also plot internal
characteristic from the external characteristic.
Characteristics Shunt DC generator:
Fig (3.9) (i) shows the connections of a shunt wound generator. The armature current Ia splits up
into two parts; a small fraction Ish flowing through shunt field winding while the major part IL goes
to the external load.
(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 at
normal speed, it will build up a voltage OM. At no-load, the terminal voltage of the generator will
be constant (= OM) represented by the horizontal dotted line MC.
(ii)Internal characteristic When 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 internal
characteristic (E/Ia) drops down slightly as shown in Fig.(3.9) (ii).
(iii)External characteristic
Curve 2 shows the external characteristic of a shunt generator. It gives the
relation between terminal voltage V and load current IL.
V = E – IaRa = E -(IL +Ish)Ra
Therefore, external characteristic curve will lie below the internal characteristic curve by an
amount equal to drop in the armature circuit [i.e., (IL +Ish)Ra ] as shown in Fig. (3.9) (ii).
Note. It may be seen from the external characteristic that change in terminal
voltage from no-load to full load is small. The terminal voltage can always be
maintained 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 load
resistance. Any decrease of load resistance beyond this point, instead of increasing the current,
ultimately results in reduced current. Consequently, the external characteristic turns back (dotted
curve) as shown in Fig. (3.10). The tangent OA to the curve represents the minimum external
resistance required to excite the shunt generator on load and is called critical external resistance. If
the resistance of the external circuit is less than the critical external resistance (represented by
tangent OA in Fig. 3.10), the machine will refuse to excite or will de-excite if already running This
means that external resistance is so low as virtually to short circuit the machine and so doing away
with its excitation.
generator viz., (i) critical field resistance (ii) critical external resistance. For the shunt generator to
build 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-shunt
connection S) or across armature plus series field (long-shunt connection G). The compound
generator can be cumulatively compounded or differentially compounded generator. The latter is
rarely used in practice. Therefore, we shall discuss the characteristics of cumulatively compounded
generator. It may be noted that external characteristics of long and short shunt compound
generators are almost identical.
External characteristic Fig. (3.14) shows the external characteristics of a cumulatively compounded
generator. The series excitation aids the shunt excitation. The degree of compounding depends
upon 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 voltage
increases, it is called over-compounded generator. In such a case, as the load current increases, the
series field m.m.f. increases and tends to increase the flux and hence the generated voltage. The
increase in generated voltage is greater than the IaRa drop so that instead of decreasing, the
terminal voltage increases as shown by curve A in Fig. (3.14).
(ii) If series winding turns are so adjusted that with the increase in load
current, 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-compounded
machine 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, the
terminal voltage falls with increase in load
current as indicated by curve C m Fig. (3.14). Such a machine is called under-compounded
generator.
Voltage Regulation
The change in terminal voltage of a generator between full and no load (at constant speed) is called
the voltage regulation, usually expressed as a percentage of the voltage at full-load.
% Voltage regulation= [ (VNL-VFL)/VFL ] × 100
VFL = Terminal voltage of generator at full load
Note 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 the
load 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 their
characteristic curves. For every motor, there is a specific Torque/Speed curve and
Power curve.
The graph above shows a torque/speed curve of a typical D.C. motor. Note that torque
is inversely proportioal to the speed of the output shaft. In other words, there is a
tradeoff between how much torque a motor delivers, and how fast the output shaft
spins. 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 a
maximum, but the shaft is not rotating.
The no load speed, , is the maximum output speed of the motor (when no
torque is applied to the output shaft).
The curve is then approximated by connecting these two points with a line, whose
equation can be written in terms of torque or angular velocity as equations 3) and 4):
The linear model of a D.C. motor torque/speed curve is a very
good approximation. The torque/speed curves shown below are
actual curves for the green maxon motor (pictured at right) used
by students in 2.007. One is a plot of empirical data, and the other
was plotted mechanically using a device developed at MIT. Note
that the characteristic torque/speed curve for this motor is quite
linear.
This is generally true as long as the curve represents the direct
output of the motor, or a simple gear reduced output. If the
specifications are given as two points, it is safe to assume a linear
curve.
Recall that earlier we defined power as the product of torque and angular velocity. This
corresponds to the area of a rectangle under the torque/speed curve with one cornerat
the origin and another corner at a point on the curve (see figures below). Due to the
linear inverse relationship between torque and speed, the maximum power occurs at the
point where = ½ , and = ½ .
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 both
speed and torque are quadratics, as shown in equations 5. and 6.
From these equations, we again find that maximum output power occurs at = ½ ,
and = ½ repectively.
Direct on line starter
In electrical engineering, a direct on line (DOL) or across the line starter starts electric
motors by applying the full line voltage to the motor terminals. This is the simplest type of motor
starter. A DOL motor starter also contain protection devices, and in some cases, condition
monitoring. Smaller sizes of direct on-line starters are manually operated; larger sizes use an
electromechanical 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 excessive
voltage drop in the supply circuit. The maximum size of a motor allowed on a direct on line starter
may be limited by the supply utility for this reason. For example, a utility may require rural
customers 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 draw
a high starting current until it has run up to full speed. This starting current is commonly around
six times the full load current, but may as high as 12 times the full load current. To reduce
Transformer introduction:
A transformer is a device that transfers electrical energy from one circuit to another
through inductively coupled conductors—the transformer's coils. A varying current in the first or
primary winding creates a varying magnetic flux in the transformer's core, and thus a varying
magnetic field through the secondary winding. This varying magnetic field induces a varying
electromotive force (EMF) or "voltage" in the secondary winding. This effect is called mutual
induction.
If a load is connected to the secondary, an electric current will flow in the secondary
winding and electrical energy will be transferred from the primary circuit through the transformer
to the load. In an ideal transformer, the induced voltage in the secondary winding (VS) is in
proportion to the primary voltage (VP), and is given by the ratio of the number of turns in the
secondary (NS) to the number of turns in the primary (NP) as follows:
By appropriate selection of the ratio of turns, a transformer thus allows an alternating
current (AC) voltage to be "stepped up" by making NS greater than NP, or "stepped down" by
making NS less than NP.
In the vast majority of transformers, the windings are coils wound around a ferromagnetic
core, air-core transformers being a notable exception.
Basic principles
The transformer is based on two principles: firstly, that an electric current can produce a
magnetic field (electromagnetism) and secondly that a changing magnetic field within a coil of
wire induces a voltage across the ends of the coil (electromagnetic induction). Changing the
current in the primary coil changes the magnetic flux that is developed. The changing magnetic
flux induces a voltage in the secondary coil.
An ideal transformer
An ideal transformer is shown in the adjacent figure. Current passing through the primary
coil creates a magnetic field. The primary and secondary coils are wrapped around a core of very
high magnetic permeability, such as iron, so that most of the magnetic flux passes through both the
primary and secondary coils.
Induction law
The voltage induced across the secondary coil may be calculated from Faraday's law of
induction, which states that: where VS is the instantaneous voltage, NS is the number of turns in the
secondary coil and Φ 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 flux
density 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 the
excitation of the primary. Since the same magnetic flux passes through both the primary and
secondary coils in an ideal transformer, the instantaneous voltage across the primary winding
equals
Taking the ratio of the two equations for VS and VP gives the basic equation for stepping up
or stepping down the voltage
Ideal power equation
The ideal transformer as a circuit element If the secondary coil is attached to a load that allows
current 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 the
primary circuit to the magnetic field and into the secondary circuit. If this condition is met, the
incoming 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 impedance
in one circuit is transformed by the square of the turns ratio. [26]
For example, if an impedance ZS is
attached across the terminals of the secondary coil, it appears to the primary circuit to have an
impedance of. This relationship is reciprocal, so that the impedance ZP of the primary circuit
appears 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 the
load circuit is called the secondary. Although in the actual construction the two windings are
usually wound one over the other, for the sake of simplicity, the figures for analyzing transformer
theory show the windings on opposite sides of the core, as shown below
When the primary winding is connected to an ac supply mains, current flows through
it. 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 winding
is the same as that of the flux or that of the s supply voltage. The induced emf in the secondary
winding enables it to deliver current to an external load connected across it. Thus the energy is
transformed from primary winding to the secondary winding by means of electro-magnetic
induction without any change in frequency. The flux Ø of the iron core links not only with the
secondary winding but also with the primary winding, so produces self-induced emf in the primary
winding: This induced in the primary winding opposes the applied voltage and therefore
sometimes it is known as back emf of the primary. In fact the induced emf in the primary winding
limits the primary current in much the same way that the back emf in a dc motor limits the
armature current.
Construction
Cores
Laminated core transformer showing edge of laminations at top of photo
Laminated steel cores
Transformers for use at power or audio frequencies typically have cores made of high
permeability silicon steel. [53]
The steel has a permeability many times that of free space, and the
core thus serves to greatly reduce the magnetizing current, and confine the flux to a path which
closely couples the windings. [54]
Early transformer developers soon realized that cores constructed
from 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 by
stacking layers of thin steel laminations, a principle that has remained in use. Each lamination is
insulated from its neighbors by a thin non-conducting layer of insulation. [46]
The universal
transformer 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 enclose
little flux, and so reduce their magnitude. Thinner laminations reduce losses, [53]
but are more
Thin laminations are generally used on high frequency
transformers, 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 of E-shaped steel
sheets capped with I-shaped pieces, leading to its name of "E-I transformer". [55]
Such a design
tends to exhibit more losses, but is very economical to manufacture. The cut-core or C-core type is
made by winding a steel strip around a rectangular form and then bonding the layers together. It is
then cut in two, forming two C shapes, and the core assembled by binding the two C halves
together with a steel strap. [55]
They have the advantage that the flux is always oriented parallel to
the metal grains, reducing reluctance.
A steel core's remanence means that it retains a static magnetic field when power is
removed. 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 alternating
current. [56]
Overcurrent protection devices such as fuses must be selected to allow this harmless
inrush to pass. On transformers connected to long, overhead power transmission lines, induced
currents due to geomagnetic disturbances during solar storms can cause saturation of the core and
operation 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 initial
cost 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 above
main frequencies and up to a few tens of kilohertz. These materials combine high magnetic
permeability 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]
Some
adjustment of the coupling coefficient (and bandwidth) of tuned radio-frequency circuits.
Small toroidal core transformer
Toroidal transformers are built around a ring-shaped core, which, depending on operating
frequency, is made from a long strip of silicon steel or permalloy wound into a coil, powdered
iron, 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 shape
eliminates air gaps inherent in the construction of an E-I core. [32]
The cross-section of the ring is
usually square or rectangular, but more expensive cores with circular cross-sections are also
available. The primary and secondary coils are often wound concentrically to cover the entire
surface of the core. This minimizes the length of wire needed, and also provides screening to
minimize the core's magnetic field from generating electromagnetic interference.
Toroidal transformers are more efficient than the cheaper laminated E-I types for a similar
power 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), lower
exterior magnetic field (about one tenth), low off-load losses (making them more efficient in
standby circuits), single-bolt mounting, and greater choice of shapes. The main disadvantages are
higher cost and limited power capacity (see "Classification" above). Because of the lack of a
residual 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 of
kilohertz to hundreds of megahertz, to reduce losses, physical size, and weight of switch-mode
power supplies. A drawback of toroidal transformer construction is the higher labor cost of
winding. 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 are
uncommon above ratings of a few kVA. Small distribution transformers may achieve some of the
benefits of a toroidal core by splitting it and forcing it open, then inserting a bobbin containing
primary and secondary windings.
core" transformer. The air which comprises the magnetic circuit is essentially lossless, and so an
air-core transformer eliminates loss due to hysteresis in the core material. [30]
The leakage
inductance 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 frequently
employed in radio-frequency applications, [60]
for which a satisfactory coupling coefficient is
maintained by carefully overlapping the primary and secondary windings. They're also used for
resonant transformers such as Tesla coils where they can achieve reasonably low loss in spite of
the high leakage inductance.
Cut view through transformer windings. White: insulator. Green spiral: Grain oriented
silicon steel. Black: Primary winding made of oxygen-free copper. Red: Secondary winding. Top
left: Toroidal transformer. Right: C-core, but E-core would be similar. The black windings are
made of film. Top: Equally low capacitance between all ends of both windings. Since most cores
are at least moderately conductive they also need insulation. Bottom: Lowest capacitance for one
end of the secondary winding needed for low-power high-voltage transformers. Bottom left:
Reduction of leakage 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 current
travels throughout every turn. [33]
For small power and signal transformers, in which currents are
low and the potential difference between adjacent turns is small, the coils are often wound from
enamelled magnet wire, such as Formvar wire. Larger power transformers operating at high
voltages may be wound with copper rectangular strip conductors insulated by oil-impregnated
paper and blocks of pressboard. [61]
High-frequency transformers operating in the tens to hundreds of kilohertz often have
windings 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 power
frequencies 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 the
complete conductor. The transposition equalizes the current flowing in each strand of the
conductor, and reduces eddy current losses in the winding itself. The stranded conductor is also
more flexible than a solid conductor of similar size, aiding manufacture. [61]
For signal transformers, the windings may be arranged in a way to minimize leakage
inductance and stray capacitance to improve high-frequency response. This can be done by
splitting up each coil into sections, and those sections placed in layers between the sections of the
other 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 voltage
ratio. The taps may be connected to an automatic on-load tap changer for voltage regulation of
distribution circuits. Audio-frequency transformers, used for the distribution of audio to public
address 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-pull
circuit. Modulation transformers in AM transmitters are very similar.
Certain transformers have the windings protected by epoxy resin. By impregnating the
transformer with epoxy under a vacuum, one can replace air spaces within the windings with
epoxy, thus sealing the windings and helping to prevent the possible formation of corona and
absorption 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.
Small transformers do not
generate significant heat and are cooled by air circulation and radiation of heat. Power
transformers 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 is
removal 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 transformer
operating temperature. Indoor liquid-filled transformers must use a non-flammable liquid, or must
be located in fire resistant rooms. [66]
Air-cooled dry transformers are preferred for indoor
applications 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 natural
convection; some large transformers employ forced circulation of the oil by electric pumps, aided
by external fans or water-cooled heat exchangers. [65]
Oil-filled transformers undergo prolonged
drying processes to ensure that the transformer is completely free of water vapor before the cooling
oil 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 includes
fire protection measures such as walls, oil containment, and fire-suppression sprinkler systems.
Polychlorinated biphenyls have properties that once favored their use as a coolant, though
concerns 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 a
fire-resistant liquid offsets additional building cost for a transformer vault. [63][66]
Before 1977, even
transformers that were nominally filled only with mineral oils may also have been contaminated
with 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" transforers (containing no liquid) are enclosed in sealed, pressurized tanks
and cooled by nitrogen or sulfur hexafluoride gas. [63]
Experimental power transformers in the 2 MVA range have been built with superconducting
windings which eliminates the copper losses, but not the core steel loss. These are cooled by liquid
nitrogen or helium.
Terminals
Very small transformers will have wire leads connected directly to the ends of the coils, and
brought out to the base of the unit for circuit connections. Larger transformers may have heavy
bolted terminals, bus bars or high-voltage insulated bushings made of polymers or porcelain. A
large bushing can be a complex structure since it must provide careful control of the electric field
gradient without letting the transformer leak oil.
Applications
transformers, each with a capacity of 185MVA
A major application of transformers is to increase voltage before transmitting electrical
energy 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 electrical
power to a high-voltage (and therefore low-current) form for transmission and back again
afterward, transformers enable economic transmission of power over long distances. Consequently,
transformers have shaped the electricity supply industry, permitting generation to be located
remotely from points of demand. [71]
All but a tiny fraction of the world's electrical power has
passed through a series of transformers by the time it reaches the consumer.
Transformers are also used extensively in electronic products to step down the supply
voltage to a level suitable for the low voltage circuits they contain. The transformer also
electrically isolates the end user from contact with the supply voltage.
Signal and audio transformers are used to couple stages of amplifiers and to match devices
such as microphones and record players to the input of amplifiers. Audio transformers allowed
telephone circuits to carry on a two-way conversation over a single pair of wires. A balun
transformer converts a signal that is referenced to ground to a signal that has balanced voltages to
ground, such as between external cables and internal circuits.
Practical considerations
Leakage flux
Main article: Leakage inductance
The ideal transformer model assumes that all flux generated by the primary winding links
all the turns of every winding, including itself. In practice, some flux traverses paths that take it
outside the windings. [31]
Such flux is termed leakage flux, and results in leakage inductance in
series with the mutually coupled transformer windings. [30]
Leakage results in energy being
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 under
heavy 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 magnetic
paths, air gaps, or magnetic bypass shunts may be deliberately introduced to a transformer's design
to limit the short-circuit current it will supply. [30]
Leaky transformers may be used to supply loads
that exhibit negative resistance, such as electric arcs, mercury vapor lamps, and neon signs; or for
safely 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-frequency
transformers in circuits that have a direct current flowing through the windings. Leakage
inductance 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 will
automatically 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 rms
voltage Erms of the winding , and the supply frequency f, number of turns N, core cross-sectional
area a and peak magnetic 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-cycle
average voltage Eavg of any waveshape:
The time-derivative term in Faraday's Law shows that the flux in the core is the integral
with respect to time of the applied voltage. [33]
Hypothetically an ideal transformer would work
with direct-current excitation, with the core flux increasing linearly with time. [34]
In practice, the
flux would rise to the point where magnetic saturation of the core occurs, causing a huge increase
in the magnetizing current and overheating the transformer. All practical transformers must
therefore operate with alternating (or pulsed) current. [34]
The EMF of a transformer at a given flux density increases with frequency. [28]
By operating
at higher frequencies, transformers can be physically more compact because a given core is able to
transfer more power without reaching saturation and fewer turns are needed to achieve the same
impedance. However, properties such as core loss and conductor skin effect also increase with
frequency. Aircraft and military equipment employ 400 Hz power supplies which reduce core and
winding weight. [35]
Conversely, frequencies used for some railway electrification systems were
much lower (e.g. 16.7 Hz and 25 Hz) than normal utility frequencies (50 - 60 Hz) for historical
reasons concerned mainly with the limitations of early electric traction motors. As such, the
transformers used to step down the high over-head line voltages (e.g. 15 kV) are much heavier for
the 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 intended
will 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 of
voltages, losses, and cooling to establish if safe operation is practical. For example, transformers
may need to be equipped with "volts per hertz" over-excitation relays to protect the transformer
from overvoltage at higher than rated frequency.
One example of state-of-the-art design is those transformers used for electric multiple unit high
speed trains, particularly those required to operate across the borders of countries using different
standards of electrification. The position of such transformers is restricted to being hung below the
passenger compartment. They have to function at different frequencies (down to 16.7 Hz) and
voltages (up to 25 kV) whilst handling the enhanced power requirements needed for operating the
trains at high speed.
Knowledge of natural frequencies of transformer windings is of importance for the determination
of 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. In
practical transformers energy is dissipated in the windings, core, and surrounding structures.
Larger transformers are generally more efficient, and those rated for electricity distribution usually
perform better than 98%. [36]
Experimental transformers using superconducting windings achieve efficiencies of
99.85%. [37]
While the increase in efficiency is small, when applied to large heavily loaded
transformers 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 energy
loss even when not supplying any power to the device. Though individual losses may be only a
few watts, it has been estimated that the cumulative loss from such transformers in the United
States 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 contribute
to over 99% of the no-load loss. The no-load loss can be significant, meaning that even an idle
transformer constitutes a drain on an electrical supply, which encourages development of low-loss
transformers (also see energy efficient transformer). [39]
Transformer losses are divided into losses in the windings, termed copper loss, and those in
the magnetic circuit, termed iron loss. Losses in the transformer arise from:
Current flowing through the windings causes resistive heating of the conductors. At
higher frequencies, skin effect and proximity effect create additional winding resistance
and losses.
Hysteresis losses
Each time the magnetic field is reversed, a small amount of energy is lost due to
hysteresis within the core. For a given core material, the loss is proportional to the
frequency, and is a function of the peak flux density to which it is subjected.
Eddy currents
Ferromagnetic materials are also good conductors, and a solid core made from such
a material also constitutes a single short-circuited turn throughout its entire length. Eddy
currents therefore circulate within the core in a plane normal to the flux, and are
responsible for resistive heating of the core material. The eddy current loss is a complex
function of the square of supply frequency and inverse square of the material thickness.
Magnetostriction
Magnetic flux in a ferromagnetic material, such as the core, causes it to physically expand
and contract slightly with each cycle of the magnetic field, an effect known as
magnetostriction. This produces the buzzing sound commonly associated with
transformers, [27]
and in turn causes losses due to frictional heating in susceptible cores.
Mechanical losses
electromagnetic forces between the primary and secondary windings. These incite
vibrations within nearby metalwork, adding to the buzzing noise, and consuming a small
amount of power. [40]
Stray losses
Leakage inductance is by itself largely lossless, since energy supplied to its magnetic fields
is returned to the supply with the next half-cycle. However, any leakage flux that intercepts
nearby conductive materials such as the transformer's support structure will give rise to
eddy currents and be converted to heat. [41]
There are also radiative losses due to the
oscillating magnetic field, but these are usually small.
Dot convention
It is common in transformer schematic symbols for there to be a dot at the end of each coil
within a transformer, particularly for transformers with multiple windings on either or both of the
primary and secondary sides. The purpose of the dots is to indicate the direction of each winding
relative to the other windings in the transformer. Voltages at the dot end of each winding are in
phase, while current flowing into the dot end of a primary coil will result in current flowing out of
the dot end of a secondary coil.
EMF Equation of Transformer:
Let the applied voltage V1 applied to the primary of a transformer, with secondary open-circuited,
be sinusoidal (or sine wave). Then the current I1, due to applied voltage V1, will also be a sine
time phase with the current I1 and varies sinusoidally.
Let the sinusoidal variation of flux Ø be expressed as
Ø = Ømax sin wt
Where Ømax is the maximum value of the magnetic flux in webers and w is the angular
frequency in rad/sec
The emf e1 induced in the primary N1 turns by the alternating flux is given by
The emfs induced in primary and secondary windings of a transformer are given as
follows
E1 = 4.44 f N1 Ømax volts
E2 = 4.44 f N2 Ømax volts
Where Ømax is the maximum value of flux is webers, f is the supply frequency in Hz, N1 is the
number of turns on primary winding and N2 is the number of turns on secondary winding.
In an ideal transformer, the voltage drops in primary and secondary windings are negligible
and, therefore E1 will be approximately equal and opposite to voltage impressed across primary,
V1 and terminal voltage V2 will be approximately equal to E2.
So voltage ratio, v2/v1 = E2/E1 = 4.44fN2 max / 4.44fN1 max = N2/N1
Voltage Transformation Ratio.
The ratio of secondary voltage to primary voltage is known as the voltage transformation
ratio and is designated by letter K. i.e. Voltage transformation ratio, K = V2/V1 = E2/E1 = N2/N1
Current Ratio.
The ratio of secondary current to primary current is known as current ratio and is reciprocal
of voltage transformation ratio in an ideal transformer.
Transformer on No Load.
When the primary of a transformer is connected to the source of an ac supply and the
secondary is open circuited, the transformer is said to be on no load. The
Transformer on No Load
alternating applied voltage will cause flow of an alternating current I0 in the primary
winding, which will create alternating flux Ø. No-load current I0, also known as excitation or
exciting current, has two components the magnetizing component Im and the energy component
Ie. Im is used to create the flux in the core and Ie is used to overcome the hysteresis and eddy
current losses occurring in the core in addition to small amount of copper losses occurring in the
primary only (no copper loss occurs in the secondary, because it carries no current, being open
circuited.)
From vector diagram shown in above it is obvious that
1. Induced emfs in primary and secondary windings, E1 and E2 lag the main flux Ø by and are in
phase with each other.
2. Applied voltage to primary V1 and leads the main flux Ø by and is in phase opposition to E1.
3. Secondary voltage V2 is in phase and equal to E2 since there is no voltage drop in secondary.
4. Im is in phase with Ø and so lags V1 by
5. Ie is in phase with the applied voltage V1.
6. Input power on no load = V1Ie = V1I0 cos Ø0 where Ø0 = tan -1
Transformer on Load:
The transformer is said to be loaded, when its secondary circuit is completed through an
impedance or load. The magnitude and phase of secondary current (i.e. current flowing through
secondary) I2 with respect to secondary terminals depends upon the characteristic of the load i.e.
current I2 will be in phase, lag behind and lead the terminal voltage V+2+ respectively when the
load is non-inductive, inductive and capacitive. The net flux passing through the core remains
almost constant from no-load to full load irrespective of load conditions and so core losses remain
almost constant from no-load to full load. Vector diagram for an ideal transformer supplying
inductive load is shown
Resistance and Leakage Reactance
In actual practice, both of the primary and secondary windings have got some ohmic resistance
causing voltage drops and copper losses in the windings.
In actual practice, the total flux created does not link both of the primary and secondary windings
but is divided into three components namely the main or mutual flux Ø linking both of the primary
and secondary windings, primary leakage flux ØL1 linking with primary winding only and
secondary leakage flux ØL2 linking with secondary winding only. The primary leakage flux ØL1 is
produced by primary ampere-turns and is proportional to primary current, number of primary turns
being fixed. The primary leakage flux ØL1 is in phase with I1 and produces self induced emf ØL1 is
in phase with I1 and produces self induced emf EL1 given as 2f L1 I1 in the primary winding. The
self induced emf divided by the primary current gives the reactance of primary and is denoted by
X1.
Similarly leakage reactance of secondary X2 = EL2/E2 = 2fπL2I2/I2 = 2πfL2
Equivalent Resistance and Reactance. The equivalentresistances and reactances of transformer
windings referred to primary and secondary sides are given as below
Referred to primary side
Equivalent circuit
The physical limitations of the practical transformer may be brought together as an
equivalent circuit model (shown below) built around an ideal lossless transformer. [42]
Power loss in
the windings is current-dependent and is represented as in-series resistances RP and RS. Flux
leakage results in a fraction of the applied voltage dropped without contributing to the mutual
coupling, and thus can be modeled as reactances of each leakage inductance XP and XS in series
with the perfectly coupled region.
Iron losses are caused mostly by hysteresis and eddy current effects in the core, and are
proportional to the square of the core flux for operation at a given frequency. [43]
Since the core flux
is proportional to the applied voltage, the iron loss can be represented by a resistance RC in parallel
with the ideal transformer.
A core with finite permeability requires a magnetizing current IM to maintain the mutual
flux in the core. The magnetizing current is in phase with the flux; saturation effects cause the
relationship between the two to be non-linear, but for simplicity this effect tends to be ignored in
most circuit equivalents. [43]
With a sinusoidal supply, the core flux lags the induced EMF by 90°
and this effect can be modeled as a magnetizing reactance (reactance of an effective inductance)
XM in parallel with the core loss component. RC and XM are sometimes together termed the
magnetizing branch of the model. If the secondary winding is made open-circuit, the current I0
taken by the magnetizing branch represents the transformer's no-load current. [42]
The secondary impedance RS and XS is frequently moved (or "referred") to the primary
side after multiplying the components by the impedance scaling factor (NP/NS) 2 .
Transformer equivalent circuit, with secondary impedances referred to the primary side the
resulting model is sometimes termed the "exact equivalent circuit", though it retains a number of
approximations, such as an assumption of linearity. analysis may be simplified by moving the
magnetizing branch to the left of the primary impedance, an implicit assumption that the
magnetizing current is low, and then summing primary and referred secondary impedances,
resulting in so-called equivalent impedance.
The parameters of equivalent circuit of a transformer can be calculated from the results of two
transformer tests: open-circuit test and short-circuit test
is shown
Regulation. The change in secondary terminal voltage from no-load to full load is known as
regulation of the transformer is expressed as a percentage of the secondary no-load terminal
voltage.
Regulation will be zero when power factor angle Ø = tan -1
- R'2/X'2
Regulation will be maximum when pf angle Ø = tan -1
X'2/R2
Transformer Losses. Since the transformer is a static mechine, so there are no friction and windage
losses. Hence the losses occurring in a transformer are (i) iron loss and (ii) copper loss. Iron loss is
caused by the alternating flux in the core and consists of hysteresis and eddy currents. The copper
loss occurs due to ohmic resistance of the transformer windings. The iron or core loss remains
almost constant, as already explained where as copper loss varies as the square of the load current.
For example if copper loss at full load is Pc’ then at one-half of the full load the copper loss will be
(1/2) 2
TRANSFORMER TESTS
1. Open-circuit or No-load Test. This test is performed to determine core or iron loss, Pi and no-
load current I0. This test is helpful in determination of magnetizing component Im’ energy
component Ie and so no-load resistance R0 being given as V1/Ie and no-load reactance given as
V1/Im.
In this test secondary (usually high voltage) winding is left open, all metering instruments
(ammeter, voltmeter and wattmeter) are connected on primary side and normal rated voltage is
applied to the primary (low voltage) winding, as illustrated below
Iron loss P1 = Input power on no-load – W0 watts (wattmeter reading)
No-load current = 0 amperes (ammeter reading)
Angle of lag, Ø0 = cos -1
Wo/V1Io
o - I 2
e
Caution: Since no load current I0 is very small, therefore, pressure coils of watt meter and the volt
meter should be connected such that the current taken by them should not flow through the current
taken by them should not flow through the current coil of the watt meter.
2. Short-circuit or Impedance Test. This test is performed to determine the full-load copper loss
and equivalent resistance and reactance referred to secondary side.
In this test, the terminals of the secondary (usually the low voltage) winding are short – circuited,
all meters (ammeter, voltmeter and wattmeter) are connected on primary side and a low voltage,
usually 5 to 10 % of normal rated primary voltage at normal frequency is applied to the primary, as
shown in fig below. The applied voltage to the primary, say Vs’ is gradually increased till the
ammeter A indicates the full load current of the side in which it is connected. The reading Ws of
the wattmeter gives total copper loss (iron losses being negligible due to very low applied voltage
resulting in very small flux linking with the core) at full load. Le the ammeter reading be Is.
Full load copper loss, Pc= I 2
s R1 = Ws
s
- (R'1) 2 '
Commercial Efficiency and All-day Efficiency
(a) Commercial Efficiency. Commercial efficiency is defined as the ratio of power output to
power input in kilowatts.
(b) All-day Efficiency. The all day efficiency is defined as the ratio of output in kwh to the input
in kwh during the whole day.
Transformers used for distribution are connected for the whole day to the line but loaded
intermittently. Thus the core losses occur for the whole day but copper losses occur only when the
transformer is delivering the load current. Hence if the transformer is not used to supply the load
current for the whole day all day efficiency will be less than commercial efficiency.
The efficiency (commercial efficiency) will be maximum when variable losses (copper losses) are
equal to constant losses (iron or core losses).
Determination of Voltage Regulation and Efficiency.
The percentage voltage regulation is given as
% age regulation = I2R'2 cos∅ + I2 X'2 sin∅/ E2 X100 ….(4.11)
Note : + sign is for inductive load and –sign is for capacitive load
Transformer efficiency, η = V2I2 cos∅ / V2 I2 cos∅ + P1 + x 2 P2 ….(4.12)
Where x is the ratio of secondary current I2 and rated full load secondary current.
Unit III
Induction motor
An induction motor or asynchronous motor is a type of alternating current motor where power is
supplied to the rotor by means of electromagnetic induction.
An electric motor converts electrical power to mechanical power in its rotor (rotating part).
There are several ways to supply power to the rotor. In a DC motor this power is supplied to the
armature directly from a DC source, while in an induction motor this power is induced in the
rotating device. An induction motor is sometimes called a rotating transformer because the stator
(stationary part) is essentially the primary side of the transformer and the rotor (rotating part) is the
secondary side. Unlike the normal transformer which changes the current by using time varying
flux, induction motors use rotating magnetic fields to transform the voltage. The primary side's
current creates an electromagnetic field which interacts with the secondary side's electromagnetic
field to produce a resultant torque, thereby transforming the electrical energy into mechanical
energy. Induction motors are widely used, especially polyphase induction motors, which are
frequently used in industrial drives.
Induction motors are now the preferred choice for industrial motors due to their rugged
construction, absence of brushes (which are required in most DC motors) and—thanks to modern
power electronics—the ability to control the speed of the motor.
Principle of operation and comparison to synchronous motors
3-phase power supply provides a rotating magnetic field in an induction motor. The basic
difference between an induction motor and a synchronous AC motor is that in the latter a current is
supplied into the rotor (usually DC) which in turn creates a (circular uniform) magnetic field
around the rotor. The rotating magnetic field of the stator will impose an electromagnetic torque on
the still magnetic field of the rotor causing it to move (about a shaft) and rotation of the rotor is
speed of the rotating magnetic field in the stator.
By way of contrast, the induction motor does not have any direct supply onto the rotor; instead, a
secondary current is induced in the rotor. To achieve this, stator windings are arranged around the
rotor so that when energised with a polyphase supply they create a rotating magnetic field pattern
which sweeps past the rotor. This changing magnetic field pattern induces current in the rotor
conductors. These currents interact with the rotating magnetic field created by the stator and in
effect causes a rotational motion on the rotor.
However, for these currents to be induced, the speed of the physical rotor must be less than the
speed of the rotating magnetic field in the stator, or else the magnetic field will not be moving
relative to the rotor conductors and no currents will be induced. If by some chance this happens,
the rotor typically slows slightly until a current is re-induced and then the rotor continues as
before. This difference between the speed of the rotor and speed of the rotating magnetic field in
the stator is called slip. It is unitless and is the ratio between the relative speed of the magnetic
field as seen by the rotor (the slip speed) to the speed of the rotating stator field. Due to this an
induction motor is sometimes referred to as an asynchronous machine.
Construction
The stator consists of wound 'poles' that carry the supply current to induce a magnetic field that
penetrates the rotor. In a very simple motor, there would be a single projecting piece of the stator
(a salient pole) for each pole, with windings around it; in fact, to optimize the distribution of the
magnetic field, the windings are distributed in many slots located around the stator, but the
magnetic field still has the same number of north-south alternations. The number of 'poles' can
vary between motor types but the poles are always in pairs (i.e. 2, 4, 6, etc.).
Induction motors are most commonly built to run on single-phase or three-phase power, but two-
phase motors also exist. In theory, two-phase and more than three phase induction motors are
possible; many single-phase motors having two windings and requiring a capacitor can actually be
viewed as two-phase motors, since the capacitor generates a second power phase 90 degrees from
the single-phase supply and feeds it to a separate motor winding. Single-phase power is more
widely available in residential buildings, but cannot produce a rotating field in the motor (the field
merely oscillates back and forth), so single-phase induction motors must incorporate some kind of
starting mechanism to produce a rotating field. They would, using the simplified analogy of salient
poles, have one salient pole per pole number; a four-pole motor would have four salient poles.
Three-phase motors have three salient poles per pole number, so a four-pole motor would have
twelve salient poles. This allows the motor to produce a rotating field, allowing the motor to start
with no extra equipment and run more efficiently than a similar single-phase motor.
There are three types of rotor:
Squirrel-cage rotor
The most common rotor is a squirrel-cage rotor. It is made up of bars of either solid copper (most
common) or aluminum that span the length of the rotor, and those solid copper or aluminium strips
can be shorted or connected by a ring or some times not, i.e. the rotor can be closed or semiclosed
type. The rotor bars in squirrel-cage induction motors are not straight, but have some skew to
reduce noise and harmonics.
Slip ring rotor
A slip ring rotor replaces the bars of the squirrel-cage rotor with windings that are connected to
slip rings. When these slip rings are shorted, the rotor behaves similarly to a squirrel-cage rotor;
they can also be connected to resistors to produce a high-resistance rotor circuit, which can be
beneficial in starting
Solid core rotor
A rotor can be made from a solid mild steel. The induced current causes the rotation.
Speed control
The synchronous rotational speed of the rotor (i.e. the theoretical unloaded speed with no slip) is
controlled by the number of pole pairs (number of windings in the stator) and by the frequency of
the supply voltage. Under load, the induction motor's speed varies according to size of the load. As
the load is increased the speed of the motor decreases, increasing the slip, which increases the
rotor's field strength to bear the extra load. Before the development of economical semiconductor
power electronics, it was difficult to vary the frequency to the motor and induction motors were
mainly used in fixed speed applications. As an induction motor has no brushes and is easy to
control, many older DC motors are now being replaced with induction motors and accompanying
inverters in industrial applications.
Starting of induction motors
Direct-on-line starting
The simplest way to start a three-phase induction motor is to connect its terminals to the line. This
method is often called "direct on line" and abbreviated DOL.
In an induction motor, the magnitude of the induced emf in the rotor circuit is proportional to the
stator field and the slip speed (the difference between synchronous and rotor speeds) of the motor,
and the rotor current depends on this emf. When the motor is started, the rotor speed is zero. The
synchronous speed is constant, based on the frequency of the supplied AC voltage. So the slip
speed is equal to the synchronous speed, the slip ratio is 1, and the induced emf in the rotor is
large. As a result, a very high current flows through the rotor. This is similar to a transformer with
the secondary coil short circuited, which causes the primary coil to draw a high current from the
addition, because it causes heavy line voltage drop, other appliances connected to the same line
may be affected by the voltage fluctuation. To avoid such effects, several other strategies are
employed for starting motors.
Wye-Delta starters
An induction motor's windings can be connected to a 3-phase AC line in two different ways:
wye in U.S, star in Europe, where the windings are connected from phases of the supply to
the neutral;
delta (sometimes mesh in Europe), where the windings are connected between phases of
the supply.
A delta connection of the machine winding results in a higher voltage at each winding compared to
a wye connection (the factor is ). A wye-delta starter initially connects the motor in wye, which
produces a lower starting current than delta, then switches to delta when the motor has reached a
set speed. Disadvantages of this method over DOL starting are:
Lower starting torque, which may be a serious issue with pumps or any devices with
significant breakaway torque
Increased complexity, as more contactors and some sort of speed switch or timers are
needed
Two shocks to the motor (one for the initial start and another when the motor switches
from wye to delta)
Variable-frequency drives
Variable-frequency drives (VFD) can be of considerable use in starting as well as running motors.
A VFD can easily start a motor at a lower frequency than the AC line, as well as a lower voltage,
so that the motor starts with full rated torque and with no inrush of current. The rotor circuit's
impedance increases with slip frequency, which is equal to

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