electrical engg notes

8/6/2019 Electrical Engg Notes

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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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electrical engg notes

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