Electromechanical Energy Conversion

ELECTROMECHANICAL

ENERGY CONVERSION

THE DYNAMO-PRINCIPLES

AND CONSTRUCTION

Dynamo

– is a rotating electrical machine in which the energy transformation takes place. There are two general types of dynamo, namely:

a. generator- mechanical energy is converted to electric a. generator- mechanical energy is converted to electric

energy

b. motor – electric energy is converted to mechanical energy

Note: Generators and motors are fundamentally similar in construction - and this is particularly true of dc machines - they differ only in the way they are used.

DC Generator and Motor Principles

The fundamental principles governing generator action and

motor action were originally discovered by Michael Faraday

in 1831. Briefly summarized, these basic principles may be

stated as follows:

Generator action – involving the development of voltage, may result (a) by moving a conductor in such a manner that it cuts across magnetic lines of force (dc generator), (b) by moving magnetic lines of force in such a manner that they cut across a conductor (ac generator/alternator), and (c) by changing the number of lines of force that link with a wire or coil of wire (transformer).

General Voltage Equation for

Direct-Current Generator

*Remembering that the generated voltage depends

upon the rate at which flux is cut and that 1 volt

results from cutting 10

8

_{lines of force per second.}

The ff. analysis will lead to a very useful fundamental

equation:

1) Each one of Z conductors cuts Φ x P line of force

per revolution, where Φ is the flux supplied by each

of the poles P.

2) Assuming

a

parallel armature paths, the number of

conductors per path will therefore be Z/

a

.

3) If the speed of the armature is represented by

General Voltage Equation for

Direct-Current Generator

3) If the speed of the armature is represented by

rpm, the speed in revolutions per second is

rpm/60.

4) If (Φ x P) is multiplied by rpm/60, the product

would represent the flux cut by each conductor per

second.

5) Since 1 volt is generated for every 10

8

_{lines cut}

per second, multiplying the product in (4), i.e., (Φ

x P x rpm/60) by 10

-8

_{would give the voltage}

General Voltage Equation for

Direct-Current Generator

x P x rpm/60) by 10 would give the voltage

generated in each conductor.

6) Finally, multiplying (Φ x P x rpm/60 x 10

-8

_{) by}

(Z/

a)

would yield the total generated voltage, E

_g

.

8 g

x

10

a

60

P

Z

E

====

Φ

Φ

Φ

Φ

−−−−

Where E

g

= total generated voltage

General Voltage Equation for

Direct-Current Generator

Where E

g

= total generated voltage Φ = flux per pole, Maxwell

P = number of poles, an even number N = speed of the armature, rpm

Z = total number of conductors effectively used to add to resulting voltage

a

= number of armature paths connected in parallel (determined by type of armature winding)

Direction of a Generated Voltage

The direction of the generated voltage in a

conductor, or more correctly in a coil of wire, as

it is rotated to cut the lines of force produced by

the electromagnets in a generator, will depend

upon two factors only:

upon two factors only:

1) the direction of the flux determined by

the magnet polarity

Right-Hand Rule

– used to determine the direction of the generated voltage

Thumb

– represents the direction of the motion of the conductor

Direction of a Generated Voltage

conductor

Forefinger

– represents the direction of the flux (from north pole to south pole)

Middle finger

– represents the direction of the generated voltage

Dot

–

generated voltage in the conductor will be toward the observer

Cross

– generated voltage in the conductor will be away from the observer

magnetic lines of force

Direction of a Generated Voltage

S N

Fig.1 two-pole generator

The Elementary Alternating-current

Generator

The dc generator is fundamentally an ac

generator because, internally, in the armature

conductors, the current reverses periodically as the

wires move to cut lines of force successively under

wires move to cut lines of force successively under

the north and south poles.

The frequency, f in cycles per second (cps), of

the alternating current is proportional to both the

speed in revolutions per second, rpm/60, and the

number of pairs of poles, P/2.

(((( ))))((((

))))

120

rpm

P

60

rpm

x

2

P

f

====

====

The Elementary Alternating-current

Generator

120

60

2

Where:

f

= frequency, cps (Hz)

P = no. of poles

rpm = speed of revolution

The ff. diagrams illustrate graphically how the number of cycles per revolution is affected by the number of poles:

The Elementary Alternating-current

Generator

N

S

1 cycle

N

N

The Elementary Alternating-current

Generator

Fig.3 Four poles - two cycles per revolution

N

S

N

S

Commutation in DC Generator

From the foregoing discussion, it should be clear

that the generated voltage, as well as the

current, in dc armature winding is alternating. It

is true, of course, that nothing can be done in the

modern generator to develop an internal dc emf;

is true, of course, that nothing can be done in the

modern generator to develop an internal dc emf;

what can be done, however, is to rectify the

internal alternating current so that the brush

voltage – the external voltage – is direct current.

The mechanism for doing this consists of the

commutator

(in its simplest form it may be

represented by a split ring) and its

brushes

.

(See

Commutation in DC Generator

Brushes are located so that they touch two

segments exactly on top and bottom.

Each conductor is permanently connected to

Commutation in DC Generator

Each conductor is permanently connected to

a segment (or a semi ring).

The split ring rotates with the rotating coil.

Generation of Unidirectional Current

+ -a a b a

S

N

S

y x

N

y x (a) Load I (b) b Load b Load

When the plane of the coil is vertical, it will be short-circuited by the brushes, thus, the generated voltage is zero. When conductor a is moving downward (clockwise rotation) and cutting the flux under a north pole, semi ring x will be negative; at the same time, conductor b will be moving upward and cutting flux under a south pole, thus making semi ring y positive. The brush touching semi ring y will therefore be positive, while the other brush will be negative; the current through the load will be from left to right.

b a + a b

S

N

S

y

N

y x x

Generation of Unidirectional Current

LoadLoad a (c) Load I (d)

During the next half revolution, conductor a will change places with conductor b under the poles, and this exchange will cause the generated voltages in the two conductors to reverse their direction. However, when this happens, the semi rings, to which they are connected, automatically change places under the stationary brushes.

aa

S

N

y

x It follows therefore that the polarity of the

brushes does not change. Hence, the current through the load will always be from left to right.

Generation of Unidirectional Current

b Load b Load (e) Fig. 5 (a) (b) (c) (d) (e)

It is true that the magnitude of the

current will change as the conductors a and b occupy different positions under the poles, but there will be no reversal of current through the load (see

resultant

When several coils are joined together properly so that their

combined effect acts are additively, the result is not only increased

voltage, but also voltage pulsations

Generation of Unidirectional Current

Fig. 6 Two coils in series

coil A

coil B

voltage, but also voltage pulsations that are not so violent; in other words, the voltage wave becomes smoother as the number of coils are increased (see figure).

Strictly speaking, a dc generator does not deliver a pure direct current, as does a storage battery, for example, but approaches such a current very closely as the number of coils and commutator segments are increased.

Motor action

– involving the development

of force, results when a current-bearing

of force, results when a current-bearing

conductor is placed in a magnetic field so

that it is not parallel to the direction of the

lines of force.

Force and Torque Developed by

Direct-current Motors

N

S

S

N

Force

Fig. 7 Fields produced by main poles and by

current-carrying conductors Fig. 8 Resultant field and force produced by magnet poles and

current-carrying conductors

Force

The first important point to be made in connection with the study of motor is this: if a current-bearing wire is in nonuniform magnetic field so that the flux density on one side of the conductor is greater than that of the other side, the conductor will experience a force action in a direction away from the higher density to the lower density.

In the actual dc motor the nonuniform flux distribution results from the interaction of two magnetic fields, one being the field produced by the stationary main poles and the other field created by a large number of current-carrying

Force and Torque Developed by

Direct-current Motors

the other field created by a large number of current-carrying conductors on the armature core. Secondly, the force action exerted by a current-carrying conductor placed in a

magnetic field depends upon:

1) the strength of the main field

Force and Torque Developed by

Direct-current Motors

Experiment has shown that a force of 1 dyne will

be exerted upon a conductor 1 cm long carrying a

current of 10 amp when placed under a pole area

current of 10 amp when placed under a pole area

of which is 1 cm

2

_{and producing one line of force.}

This leads to the equation:

dynes

,

10

Il

F

====

ββββ

Force and Torque Developed by

Direct-current Motors

If the units of

F,

β, and

ℓ

are specified in more practical terms, that is, pounds, lines per in2 _{and inches}

respectively, the equation becomes:

lb

,

000

,

300

,

11

Il

F

====

ββββ

Where: β = flux density

I

= current in the conductor

Commutation in DC Motors

It should be clear here that the function of

the commutator and the brushes in a dc

motor is to act as an

inverter

, that is, to

motor is to act as an

inverter

, that is, to

change the direct current to alternating

current, because the current in the armature

conductors must be alternating if rotation in

the same direction is to continue.

Arrangement of Generator and Motor

Parts

For the purposes of description, the electric generators and motors may be divided into two sections, namely:

the stationary part (

stator)

-

The most important

the stationary part (

stator)

-

The most important function of the stator is to serve as the seat of the

magnetic flux that must be made to enter the armature core. The field generally consists of a cylindrical yoke or frame to which is bolted a set of electromagnets.

Arrangement of Generator and Motor

Parts

Field-Pole cores _{– built up of a}

stack of steel laminations, about 0.025 in. thick per lamination, having good magnetic qualities; rivets are driven through the rivets are driven through the holes in the sheets to fasten together a stack of such

laminations equal to the axial length of the armature core. The shape of the assembled core is such that the smaller cross

section is provided for the field winding or windings, while the spread-out portion called the pole shoe permits the flux to spread out over a wider area where the flux enters the armature core.

Arrangement of Generator and Motor

Parts

Field windings _{- Each of the main pole}

cores may have one of three types of the field-winding construction

depending upon whether the machine is to be operated as shunt, series, or is to be operated as shunt, series, or compound dynamo:

(1) shunt winding – has a

comparatively large number of turns of fine wires; its resistance is therefore high enough so that it may be

connected directly across the armature

voltage or to a separate source of emf of about the same order of magnitude. (2) series winding – has relatively few turns of heavy wire and is connected in such a way that high values of current usually pass through it; its resistance is extremely low so that even when carrying normal load current, its voltage drop will be small.

Arrangement of Generator and Motor

Parts

(3) compound winding – a combination of the shunt and series field. The series coil is wound over the shunt coil; this is good general practice because the series field, carrying high values of current, is kept cool more readily

when placed on the outside.

the rotating part (rotor) - which is the

the rotating part (rotor) - which is the

real source of the electric (generator) power or the mechanical (motor) power, is built up of laminated steel core,

slotted to receive the insulated copper armature winding. The number of slots is carefully selected in conjunction with the number of commutator segments, on the basis of good design.

Arrangement of Generator and Motor

Parts

Arrangement of Generator and Motor

Parts

commutator – built-up group of hard-drawn copper bars, wedge-shaped in section when viewed on end, and having V-shaped grooves at each end. Together grooves at each end. Together with the stationary brushes that ride over its rotating surface, it is assigned the duty of changing an internally generated

alternating current to an

external direct current in the generator and of changing an externally applied direct current to an internal alternating current in the motor.

Arrangement of Generator and Motor

Parts

armature winding – virtually the heart of the dynamo; it is where the voltage is generated in the generator or where torque is developed in the motor. The armature-coil ends are soldered to the commutator.

Armature Windings

Function: It is where the electric power originates in the generator and where the torque is developed in the

motor.

Types of Armature winding: Types of Armature winding:

The two types of armature winding used on modern dc machines are designated lap and wave. They may be distinguished from each other in two general ways:

1) from the standpoint of construction they differ only by the manner in which the coil ends are connected to the commutator bars.

Armature Windings

Lap coil Wave Coil

Coil end Adjacent Commutator Segments (a) Simplex-Lap Connections Coil end

nearly 360 Electrical degrees

(b) Simplex-Wave Connections

Fig. 9 Sketches showing how the coil ends are connected to the commutator in lap- and wave-wound armature windings

Armature Windings

Recognizing this simple construction difference, it should, therefore, be clear that:

(a) a lap winding is one in which the coil ends are

(a) a lap winding is one in which the coil ends are

connected to the commutator segments that are near one another and;

(b) a wave winding is one in which the coil ends are connected to commutator segments that are some distance from one another- nearly 360 electrical degrees apart.

Armature Windings

2)

from the standpoint of an electrical circuit they

differ in the number of parallel paths between

the positive and the negative brushes. Like for

the positive and the negative brushes. Like for

example, simplex-lap windings have as many

parallel paths as main poles, while simplex-wave

windings have two parallel paths regardless of

the number of poles.

Armature Winding Parameters

Coil Pitch (or Span) - refers to the distance between

the two sides of the individual coils, measured in terms of the number of slots. It is determined in

exactly the same way for all windings, whether lap or exactly the same way for all windings, whether lap or wave.

The fundamental rule that fixes the coil pitch in any given machine is: the distance between the two sides of the coil must be equal (or very nearly so) to the distance between two adjacent poles.

Armature Winding Parameters

k

P

S

Y

_S

====

−−−−

k

P

Y

_S

====

−−−−

Where Y_S = coil pitch, slots

S = total number of armature slots P = number of main poles

k = any part of S/P that is subtracted to make Y_S an integer

Armature Winding Parameters

Example:

Calculate the coil pitches and indicate the slots which the first coils should be placed for the following armature

windings: (a) 28 slots, 4 poles; (b) 39 slots, 4 poles. windings: (a) 28 slots, 4 poles; (b) 39 slots, 4 poles.

7

0

4

28

====

−−−−

====

S

Y

a) Slots 1 and 10 b)

₉

4

3

4

39

====

−−−−

====

S

Y

Slots 1 and 8

Armature Winding Parameters

Commutator Pitch- refers to the distance on the commutator between the two ends of a coil element,

measured in terms of commutator segments. Its value is determined in a different way for lap and wave windings. determined in a different way for lap and wave windings.

For Lap: Y_C is equal merely to the degree of

multiplicity – the plex – of the lap winding. Thus, Y_C equals 1,2,3,4 etc., for simplex-, duplex-, triple-, quadruplex-,

Armature Winding Parameters

For Wave:

2

P

m

C

Y

_c

====

±±±±

Where: Y_C = commutator pitch

C = total number of commutator segments P = number of poles

m= multiplicity

Note: Use +m if winding is progressive. Use –m if winding is retrogressive.

Armature Winding Parameters

Example:

Calculate the commutator pitches for the following pole and commutator segment combinations: (a) 6 poles, 34 segments; (b) 8 poles, 63 segments.

segments; (b) 8 poles, 63 segments.

a)

11

3

1

34

====

−−−−

====

C

Y

Tracing, 1-12-23-34 b)

₁₆

4

1

63

====

++++

====

C

Y

Tracing, 1-17-33-49-2

Armature Winding Parameters

number of parallel paths,

a

-

number of groups of coils in series connection and connected in parallel between the “+” and “-“ brushes.

When the current passes through any armature winding, it always divides into an even number of parallel paths.

For Lap: For Wave: For Frog-leg:

mP

Armature Winding Parameters

reentrancy – All dc armatures have closed-circuit windings; this implies that they may be traced

completely from any point through all or part of the winding, and such tracing will always lead back to the winding, and such tracing will always lead back to the starting point.

For Lap: The degree of reentrancy is that number which is the highest common factor between the

number of commutator segments and the commutator pitch.

Armature Winding Parameters

For Wave: Reentrancy = m, if

m

Y

_C

is integer.

Reentrancy = 1, if

Y

C is NOT an integer. Reentrancy = 1, if

m

Y

_C

is NOT an integer.

multiplicity, m (

simplex, duplex, triplex, etc.)

– is the number of segments progressed or retrogressed by

the end terminal of a set of successive coils in series from its starting point in tracing around the armature.

Armature Winding Parameters

Example:

Determine the commutator pitch for a four-pole simplex-wave-wound armature having 21 segments. Also list the commutator segments in the proper order as the coils are commutator segments in the proper order as the coils are traced through the entire winding from segment 1 until it closes.

Solution:

11

or

10

2

1

21

====

±±±±

====

C

Y

Armature Winding Parameters

Using

Y

_C

====

10

, the succession of commutator segments is as follows:

1-11-21-10-20-9-19-8-18-7-17-6-16-5-15-4-14-3-13-2-12 then reentering segment 1

Using

Y

_C

====

11

, the succession of commutator segments is as follows:

1-12-2-13-3-14-4-15-5-16-6-17-7-18-8-19-9-20-10-21-11 then reentering segment 1

Armature Winding Parameters

number of brushes, b

For Lap

:

b = P

For Wave: b = 2 or P

width of each brush = m segments

Note: Brushes are positioned to short circuit conductors in neutral position.

Armature Winding Parameters

Pole pitch (or span)- is the number of slots spanned by two successive, opposite polarity poles (i.e., pair of N & S poles).

S

For Lap and Wave:

P

S

Y

_P

====

Where: S = number of slots P = number of poles

Note: If Y_P= integer, then armature winding is a full-pitch winding.

If Y_P is not an integer, then the armature winding is a fractional-pitch winding.

Armature Winding Parameters

Example:

Given: Duplex, progressive lap winding, S = 8, C= 8, P =2 Required: Draw a complete winding diagram (assume

dynamo to be a generator rotating clockwise) dynamo to be a generator rotating clockwise)

Solution:

a) Y_S = (8/2) – 0 = 4 slots b) Y_C = 2 segments

c) a = (2)(2) = 4 parallel paths

d) Reentrancy = HCF of 8 & 2 = 2 (doubly reentrant)

e) m = 2 f) b = 2

g) width of each brush = 2 segments

h) total no. of coils = 8 coils (single-element coil)

Armature Winding Parameters

a g h 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 b c d e f

Armature with More Segments than

Slots

Modern armatures are generally constructed with more

commutator segments than slots for the following reasons: 1) As the number of segments is increased, the

1) As the number of segments is increased, the voltage between those that are adjacent to each other decreases. For a given terminal voltage,

therefore, this also decreases the number of turns of wire in the coil or coils connected to adjacent

segments. The result is that, from the performance standpoint, commutation is improved.

Armature with More Segments than

Slots

(2) As the number of core slots is reduced, the teeth become mechanically stronger, and this results in

less damage to laminations and coils when these are handled in manufacture.

handled in manufacture.

(3) Assuming that a comparatively large number of segments has been selected for good commutation, the choice of an armature with one-half, one-third, one-fourth, etc., as many slots means that fewer coils will be constructed; this reduces the

Multi-Element Winding

When there are n times as many segments as slots, each complete coil must have n coil elements. Thus, if the ratio of segments to slots is 2, 3, 4, etc., the individual coils will have 2, 3, 4, etc., elements.

have 2, 3, 4, etc., elements.

a) Number of active elements = number of

commutator segments, C Number of coils = C; if C=S (single-element coil)

Number of active elements = C; if C is not equal to S (multi-element

Multi-Element Winding

b) Number of elements per coil =

K

S

C ++++

Where: K = a decimal number to be added to C / S to round it off to the nearest integer

to round it off to the nearest integer Note: If C / S is an integer, then no dummy

element is present If C / S is not an integer, then a dummy

element is present c) Total number of elements = number of coils X

number of elements per coil = C + dummy

Multi-Element Winding

d) Number of element-sides (conductors) per

slot = 2 X number of elements

slot = 2 X number of elements

Multi-Element Winding

Example:

Given: Simplex- lap, S = 12 slots, C = 24 segments, P = 4 poles

Required: Draw a complete winding diagram. Required: Draw a complete winding diagram.

Solution:

a) Y_S = (12/4) – 0= 3 slots b) Y_C = 1

c) a = (1)(4)= 4 parallel paths

d) Reentrancy = HCF of 24 & 1 = 1 (singly-reentrant) e) m=1

Multi-Element Winding

g) width of each brush = 1 segment

h) Number of elements per coil = 24/12= 2

elements per coil

elements per coil

i) Number of active elements = 24 elements

j) Number of conductors per slot = (2)(2)= 4

Multi-Element Winding

2-element coil 12 1 2 3 4 5 6 7 8 9 10 11 1 2 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 2324 ₊ 3 +

Dead, or Dummy, Elements in

Armature Winding

When the ratio of segments to slots (C/S) is

not a whole number, it will always be found that

there is one complete element of a multi-element

there is one complete element of a multi-element

coil that cannot be used electrically; there are not

sufficient segments for exactly two ends of one

element. The unconnected element is called a

dead or dummy element

. It serves only to keep

the revolving structure balance mechanically.

Dead, or Dummy, Elements in

Armature Winding

Equalizer Connections for Lap

Windings

The voltages generated in the various paths of lap-wound armature are rarely the same. This situation arises in the practical machine because the air gaps under all the poles are not always alike, due to some degree of

poles are not always alike, due to some degree of

misalignment, and because the reluctances of the several iron magnetic circuits are unequal. As a result of such

voltage inequalities, circulating currents flow in the armature winding and tends to heat the armature to

temperatures well above those caused by the normal load current.

Equalizer Connections for Lap

Windings

Moreover, these undesirable currents pass across the

brush contacts as they circulate from one path to another, and this produces an unusual amount of arcing and

burning at the commutator; in fact, if the situation burning at the commutator; in fact, if the situation becomes serious, a flashover between positive and negative brushes is likely to occur, a situation that

represents a direct short circuit across the supply lines. To overcome the detrimental effects resulting from the circulating currents, it is customary to use

equalizer

connections

in all lap-wound armatures.

Equalizer Connections for Lap

Windings

Equalizer connections

– these are low-resistance

copper wires that connect between points on the

armature winding that are 360 electrical degrees

armature winding that are 360 electrical degrees

apart; they are placed on the armature outside

the influence of the magnetic field. They are

non-potential-generating wires and carry equalizing

currents only.

Equalizer Connections for Lap

Windings

They relieve the brushes of the circulating

current load by causing the latter to be

Functions:

They create a magnetic effect that actually

reduces the flux under those poles where there

is too much magnetism and increases the flux

under those poles where there is too little

magnetism.

current load by causing the latter to be

bypassed.

Equalizer Connections for Lap

Windings

N S A a a' c' Equalizer N N S S B C b' b c

Fig. 11 Sketch illustrating one equalizer connection in a 6-pole machine

Equalizer Connections for Lap

Windings

Since equalizers must connect points that are exactly 360 electrical degrees apart, it follows that the total number of coils in an armature winding must be

divisible by half the number of poles. Thus for 100% divisible by half the number of poles. Thus for 100% equalization,

2

equalizers

of

no.

P

C

====

Where: C = number of commutator segments P = number of poles

Frog-leg Winding

Another construction of the armature winding, which combines the advantages of both lap and wave types and which is used on machines manufactured by the

Allis-Chalmers Manufacturing company, is called a frog-leg Chalmers Manufacturing company, is called a frog-leg winding. The term frog-leg is used to indicate the

similarity between this type of coil and the legs of a frog. In this discussion, it must be noted that the real purpose of this type of winding is to eliminate the equalizer

connections and yet to retain their advantages. The wave portion of the frog-leg winding, acting together with the lap portion, serves to replace the equalizers, but acts, in addition, as a current-carrying winding.

Frog-leg Winding

It is thus possible to obtain 100% equalization of the winding and also to make the maximum use of all copper placed on the armature.

Going back to figure 11, it discloses the fact Going back to figure 11, it discloses the fact that, theoretically, points A, B, and C are at the same potential. Since this is so, it is at once evident that points a and a’, b and b’, and c and c’ are also at the same potential because these points are connected to the equalizer and are themselves outside the

Frog-leg Winding

N S A a a' c' Equalizer

D It is quite possible, without

affecting the winding in any way, to connect points a’ and b by

N N S S B C b' b c

Fig. 12 Sketch illustrating a sort of lap-wave winding

E

F

to connect points a’ and b by connection E; points b’ and c by connection F; and points c’ and a by connection D. Figure 12 indicates the change suggested here.

By carefully looking at figure 12, you will observe that it really represents a sort of combination lap-wave winding. The wave winding was introduced when the second set of connections was made, i.e., E, F and D.

Suppose that the wire representing each of the single-turn

Frog-leg Winding

Suppose that the wire representing each of the single-turn coil of Fig.12 is slit in half lengthwise from each of the

commutator segments up to the points a, a’, b, b’, c and c’. Electrically, no change has taken place from such an

imaginary slitting process. Furthermore, the equalizer can now be omitted for the reason that any wave elements, such as E, and the succeeding lap element, such as B, connect two points on the commutator exactly two pole pitches apart.

Frog-leg Winding

N S A a a' c' D Lap Coil Wave Coil

In addition, the net voltage theoretically generated in elements E and B is zero. Elements E and B

together therefore have the two important characteristic properties that must be possessed by an

N N S S B C b' b c

Fig. 13 Frog-Leg winding

E

F

Wave Coil

that must be possessed by an

equalizer connection and may serve in replace of the removed

connections. This combination lap-wave coil has been appropriately named frog-leg coil by the engineers of the Allis-Chalmers Manufacturing Company to be known as the frog-leg winding. The connections are as given in Figure 13.

Frog-leg Winding

In practice, the lap portion of the frog-leg winding is always simplex, so that it is necessary to give the wave portion a multiplicity equal to P/2. Thus for frog-leg winding, the number of parallel paths is for frog-leg winding, the number of parallel paths is given by

(((( ))))

P

P

P

a

m

mP

a

a

a

a

FL

FL

W

L

FL

2

2

2

1

2

====













++++

====

++++

====

++++

====

Example:

Determine the coil and commutator pitches for a 24-slot, 48-segment, 6-pole frog-leg armature winding.

Frog-leg Winding

Solution:

For both lap and wave sections:

0

4

6

24

====

−−−−

====

S

Y

Wave portion must be triplex:

1

====

c

Y

Lap portion will be simplex:

15

3

3

48

====

−−−−

====

c

Y

DIRECT CURRENT GENERATOR

CHARACTERISTICS

Types of DC Generators

According to the type of the main field winding used

a) Series Generator - it uses only the series field winding

Types of DC Generators

b) Shunt Generator - it uses only the shunt field winding

c) Compound Generator - it uses both the series and the field windings

Types of DC Generators

R

_SH

R

_SE

R

_SH

According to the Source of Excitation for its field windings

a) Self-Excited DC Generator – the field windings are excited by current supplied by its own armature.

Types of DC Generators

b) Separately- Excited DC Generator – the field windings are excited by current supplied by a separate source.

Types of DC Generators

c) Dual Excited DC Generator – the source of excitation for the field windings is both the

armature and a separate source. This applies to compound generators.

Types of DC Generators

Types of Self-Excited Compound Generators

According to the connection of the field windings with respect to the armature

respect to the armature

a) Short-shunt Compound Generator - the shunt field is directly connected across the armature. b) Long-shunt Compound Generator – the shunt field is connected in parallel across the armature through the series field.

Types of DC Generators

According to the direction of the magnetic

field produced by the series field and the shunt

field windings

a)

Cumulative compound

– the direction of

magnetic fields for series and shunt are the

same.

b)

Differential compound

– the direction of

the magnetic fields for series and shunt

Types of DC Generators

According to the relative magnitude of the output

terminal voltage at no-load and full-load (for cumulative compound)

a) Flat Compounded – the no-load voltage is equal to the full-load voltage

b) Under Compounded – the no-load voltage is greater than the full-load voltage

c) Over compounded – the no-load voltage is less than the full-load voltage

No-Load Characteristics of DC

Generators

When a shunt or compound generator operates without load- that is, when it is driven by a prime mover, is properly excited, and has none of the load switches closed – a

voltage will appear at the terminals that are normally voltage will appear at the terminals that are normally

connected to the electrical devices. This generated voltage will depend, for a given machine, upon two factors:

(1) the speed of rotation

No-Load Characteristics of DC

Generators

No-Load Characteristics of DC

Generators

If the flux is kept constant while the speed is increased or decreased, the voltage will rise or fall, respectively, in direct proportion to the change in speed.

0 50 100 150 200 250 300 0 500 1000 1500 2000 2500 Speed (rpm) E g

No-Load Characteristics of DC

Generators

Similarly, if the speed is held constant while the flux (not the field current) is varied, the voltage will change in direct proportion to the change in magnetism. However, to show that the generated voltage is directly proportional to the that the generated voltage is directly proportional to the flux is much more difficult because magnetism

measurements are not made as readily as are those of amperes and volts. This determination is not particularly important from a practical point of view, because it is more desirable to know how the no-load generated voltage is

No-Load Characteristics of DC

Generators

This relationship is not a direct one for all changes in excitation, because magnetic saturation sets in after the field current is increased beyond a certain value.

To show the relationship between the generated To show the relationship between the generated voltage and the field current, a so-called saturation

curve (sometimes called

magnetization curve

) can be plotted. Note particularly that the curve is virtually a straight line up to the so-called “knee”; this is true because, in this region, the iron portions of the

magnetic circuit are unsaturated and require a comparatively low percent of the total mmf.

No-Load Characteristics of DC

Generators

200 250 300 350 400 E g knee accelerating voltage build-up voltage 0 50 100 150 200 0 0.5 1 1.5 2 2.5 3 3.5 Field Current E g excitation line

Saturation Curve for dc generator operating at constant speed

No-Load Characteristics of DC

Generators

With increasing values of flux density the iron

saturates, the magnetic permeability drops, and

a greater percent, of the field ampere-turns are

a greater percent, of the field ampere-turns are

required for the iron. It should also be observed

that the initial voltage is not zero at zero field

current; its value Er, usually low, is due to

No-Load Characteristics of DC

Generators

Significance of the Saturation (Magnetization) Curve
Such a curve emphasizes the extremely important fact that the generated voltage is directly proportional fact that the generated voltage is directly proportional to the flux and not the field current.

Curve such as this is extremely important for the purpose of analyzing, predicting, and comparing the operating performance of the various types of

Building Up the Voltage of a

Self-Excited Shunt Generator

To build up means to rise from its residual voltage, E_r, to its normal operating value.

Requirements for Build-Up: Requirements for Build-Up:

 The machine must develop a small voltage resulting from residual magnetism.

The voltage of a self-excited shunt generator will not rise much above an extremely low residual value if the

residual flux is insufficient; generators that are expected to operate at voltages up to 250 V should have residual values of flux so that 4 to 10 residual volts are developed.

Building Up the Voltage of a

Self-Excited Shunt Generator

600 700

180 ohms

A generator will fail to build up if the slope of excitation line is about equal to or greater than

 The total field resistance must be lower than the so-called critical resistance.

0 100 200 300 400 500 600 0 0.5 1 1.5 2 2.5 3 3.5 4 Field Current E g _{100 ohms} 150 ohms 125 ohms 110 ohms

about equal to or greater than the straight-line portion of the magnetization; in fact, a

generator will not build up if the total field resistance is greater than the so-called critical value, the latter being defined as the resistance below which machine will build up and above which it will not.

Building Up the Voltage of a

Self-Excited Shunt Generator

 The speed of the armature must be above the so-called critical speed.

350 400

2000 rpm 1800 rpm

A generator will, in fact, fail to build up if, for a given field

resistance, the speed is below the

0 50 100 150 200 250 300 350 0 0.5 1 1.5 2 2.5 3 3.5 Field Current E g 1000 rpm 1800 rpm 1600 rpm 1400 rpm 1200 rpm

resistance, the speed is below the so-called critical speed, the latter being defined as the speed above which build-up will occur and

below which it will not. The critical speed may be determined

experimentally if, starting from rest, the armature speed is gradually increased; the critical speed will be indicated by a sudden rapid rise in voltage.

Building Up the Voltage of a

Self-Excited Shunt Generator

 There must be a proper relation between the

direction of rotation and the connections of the field to the armature terminals.

A generator will not build up if the initial field current, at the instant the field switch is closed is in such a

direction that the residual flux is opposed; under this condition the machine will build down, not up. This means that there must be a definite relation between the direction of rotation and the connections of the field terminals with respect to the armature terminals.

Building Up the Voltage of a

Self-Excited Shunt Generator

Thus, if a generator fails to build up, and other

conditions have been fulfilled, the difficulty may be corrected:

(a) by reversing the direction of rotation or (a) by reversing the direction of rotation or (b) by interchanging the field terminals with respect to the armature terminals.

However, if rotation is reversed, the electrical polarity of the brushes will change.

Behavior of a Shunt Generator under

Load

After a self-excited shunt generator builds up to a required voltage, a no-load voltage, it is ready to supply power to a number of electrical loads up to, and a little above, its rated capacity.

above, its rated capacity.

One of the most important characteristics of any generator is its behavior with regard to the terminal voltage when the load current is increased. In the shunt type of generator, the voltage always falls down as more current is delivered to the load. There are three reasons for this:

Behavior of a Shunt Generator under

Load

As more current is delivered by the armature,

the voltage drop in the armature I

_A

R

_A

increases,

thus making a lower emf available at the load

thus making a lower emf available at the load

terminals.

When the armature terminal voltage falls, the

field winding suffers a corresponding reduction

in current, which, in turn, reduces the flux; the

latter further reduces the generated emf

.

Behavior of a Shunt Generator under

Load

When

the

armature

winding

carries

increasing values of load current, the armature

core becomes an electromagnet, apart from

core becomes an electromagnet, apart from

the

effect

of

the

main

poles;

this

electromagnetic action of the armature reacts

with the main field flux further to reduce the

flux, the result being that the generated emf

suffers an additional drop.

Behavior of a Shunt Generator under

Load

IARA

VNL

V

In this analysis, it should be clearly understood that the generated voltage, which depends upon the flux is always greater than the terminal voltage by exactly the

VFL

Rated output

Characteristic load vs. output curve of self-excited shunt

generator

terminal voltage by exactly the amount of voltage drop in the armature circuit. This leads to the equation

V

_t

= E

_g

– I

_A

R

_A

V

_t

= kΦ - I

_A

R

_A

Compound Generator Behavior under

Load – Cumulative

The addition of the series field connected to aid the shunt field has the important fundamental purpose of creating additional values of flux with increasing load currents so that the armature will generate greater currents so that the armature will generate greater voltages and thus compensate for the normal tendency of the shunt machine to lose terminal voltage. The behavior of a cumulative compound generator will depend upon the degree of compounding of the said machine, i.e., whether a given generator is flat-, over-, or undercompounded.

Compound Generator Behavior under

Load – Cumulative

This degree of compounding is determined primarily by the number of series-field ampere-turns with respect to the shunt-field ampere turns. If the series field will produce a sufficient amount of ampere-turns to permit produce a sufficient amount of ampere-turns to permit the generated voltage to increase by an amount that is exactly equal to the armature voltage drop when the armature current changes from zero to I_AFL, then V_FL can be made equal to V_NL; under such condition the machine is said to be flat-compounded.

Compound Generator Behavior under

Load – Cumulative

If, on the other hand, the series field has an

overcompensating effect so that E_G increases to a greater extent between no load to full load than the armature

resistance voltage drop, then V will exceed V ; under this resistance voltage drop, then V_FL will exceed V_NL; under this condition the machine is said to be overcompounded.

Finally, if the full-load generated voltage is more than the no-load value by an amount that is somewhat less than the armature-resistance drop, the external characteristic may droop; under this condition the generator is said to be

Compound Generator Behavior under

Load – Cumulative

under flat Rated output flat over VFL

Characteristic Curves for Cumulative Compound Generator

Compound Generator Behavior under

Load – Cumulative

Degree of Compounding Adjustment

It is customary in manufacturing practice to equip compound

generators with sufficient series-field generators with sufficient series-field turns so that they will operate

considerably overcompounded. Then, by connecting a very low-resistance shunt across the series field, the no load voltage may be brought up to almost any desired value to meet individual demands. It is therefore possible to modify an overcompound generator so that it will be flat- or under- compounded.

Compound Generator Behavior under

Load – Cumulative

The effect of the series shunt is to by-pass or diverts a portion of the normal load current from the

flux-producing series-field winding, under which the

condition the degree of compounding is lessened. The condition the degree of compounding is lessened. The so-called diverter is located where it will have no

magnetic influence; moreover, its ohmic value,

compared with that of the series field, will determine how much current is diverted. When the diverter

resistance is extremely large, the diverted current will be small and the external characteristic will be that of an overcompounded generator.

Compound Generator Behavior under

Load – Cumulative

On the other hand, if the resistance of the diverter approaches that of a short circuit, practically the load current will be diverted around the series field and the external characteristic will resemble that of a shunt

external characteristic will resemble that of a shunt generator.

Since the series-field resistance R_SE and the diverter resistance R_D are in parallel, the total line current I_L will divide so that I_SE and I_D are related to each other by an inverse ratio of the respective resistances.

Compound Generator Behavior under

Load – Cumulative

Thus

SE

D

D

SE

R

R

I

I

====

SE

D

D

SE

L

I

I

I

====

++++

SE

D

D

L

SE

R

R

R

x

I

I

++++

====

Since It follows that

Series-Generator Behavior under

Load

Since the armature, series field, and load are all

connected in series, any current that is delivered to the load must, among all other things, simultaneously

serve to perform the following functions: serve to perform the following functions:

 It must develop useful energy to the load.

 It must provide the necessary excitation for the series field so that a voltage is generated in the armature.

 It must create demagnetizing armature-reaction effect.

Series-Generator Behavior under

Load

When the load is zero (on open circuit), the current is

zero; under this condition the series field ampere-turns will be zero and the generated voltage will be the residual

value E . If the circuit is closed through a load resistance, a value E_r. If the circuit is closed through a load resistance, a current I will flow, in which event the series field will

create additional flux and thereby cause a higher voltage to be generated; at the same time the armature will

develop a demagnetizing action, and a voltage drop will occur in the armature and series field resistances.

Series-Generator Behavior under

Load

Therefore, the voltage that will appear at the series

generator terminals will be stabilized at some value that is a function of the net generated voltage (due to the net

flux) and the I(R_A + R_SE) voltage drop. The terminal emf V_t flux) and the I(R_A + R_SE) voltage drop. The terminal emf V_t will, obviously, rise with the load current so long as the

overall voltage increases more rapidly that those factors which tend to reduce it. However, for considerable loads, the iron portions of the magnetic circuit becomes highly saturated under which condition the subtractive effects exceed the slowly rising generated emf; the terminal voltage begins to drop.

Series-Generator Behavior under

Load

Thus, as the load current increases, the external

characteristic of a series generator rises rapidly from its initial Er value during the initial stages, then tapers off to a maximum, and finally drops to zero.

Because of the varying nature of the terminal voltage with respect to load, the series generator has few

practical applications, and then only when V_t vs. I curve is advantageous to the installation. The series

generator is sometimes used in a dc system for voltage-boosting purposes or to minimize leakage currents in grounded dc systems so that electrolytic action in underground structures may be reduced.

Series-Generator Behavior under

Load

110 120 130 140 150 160 170 180 190 200 Generated Voltage 400 800 1200 1600 10 20 30 40 50 60 70 80 90 10 20 30 40 50 60 70 80 90 100 110 120 0

Field Ampere Turns Load Amperes

Magnetization Curve _{Characteristic}External

Graphical method to determine the external characteristic of a series generator

VOLTAGE REGULATION

Voltage Regulation

– is a measure of the extent to which the voltage of a generator changes as the load is gradually lowered from its rated value to zero load. The foregoing may be expressed in percent load. The foregoing may be expressed in percent form as follows:

%

100

x

V

V

V

Regulation

Voltage

%

FL FL L

−−−−

====

Example:

The following data were obtained for the magnetization curve of a 4-pole interpole shunt generator, each field coil of which has 1000 turns.

of which has 1000 turns.

I_f E I_f E I_f E

0 6 0.8 160 1.56 260

0.1 20 1.0 200 1.92 280

0.4 80 1.14 220 2.40 300

0.6 120 1.32 240 3.04 320

b) If the total shunt field resistance

(including the field rheostat) is 125 Ω,

determine the voltage to which the machine

determine the voltage to which the machine

will build up as a self-excited generator.

c) Determine the full-load voltage and the

percent regulation of the generator if the

full-load armature resistance voltage drop is

30 V.

300 350 400

Solution:

0 50 100 150 200 250 300 0 0.5 1 1.5 2 2.5 3 3.5 Build-up voltage = 300 volts

300 350 400 I_AFLR_A= 30 V 0 50 100 150 200 250 300 0 0.5 1 1.5 2 2.5 3 3.5 I_AFLR_A= 30 V V_FL = 252 V

%

100

x

V

V

V

.

R

.

V

%

FL FL L

−−−−

====

%

05

.

19

%

100

x

252

252

300

V

_FL

====

−−−−

====

Example:

A 20-kW 250-volt short shunt compound generator has a series field whose resistance is 0.022 Ω and each of whose four coils has 6 ½ turns. If a diverter having a resistance of four coils has 6 ½ turns. If a diverter having a resistance of 0.058 Ω is connected across the series field, calculate the series-field ampere-turns per pole at full load.

Solution:

A

80

V

250

kW

20

I

_FL

====

====

V

250

((((

))))

58

A

022

.

0

058

.

0

058

.

0

A

80

I

_SE

====

++++

====

(((( ))))

((((

))))

pole

per

turns

Ampere

377

turns

2

1

6

A

58

I

_SE

−−−−

====













====

Magnetic Action of Armature

(Armature Reaction)

Armature Reaction –

is produced by the load

current in the armature conductors that results

in a magnetic field whose direction is displaced

in a magnetic field whose direction is displaced

90 electrical degrees with respect to the main

field. It depends upon and directly proportional

to the load current.