UNIT-Ieeeaitsrajampet.com/files/a924mUNIT - 1.pdf · 2019. 12. 17. · Non-Salient / Cylindrical / Wound type. (i). Salient (or) ... Operation of an Alternator:- The rotor winding

Electrical Machines-III Principle & Operation of Synchronous Generator

Prepared by Dr. P. B. Chennaiah, Associate Professor, EEE Department, AITS, Rajampet 1

UNIT-I

1. CONSTRUCTION & PRINCIPLE of OPERATION OF

SYNCHRONOUS GENERATOR or ALTERNATOR or

AC GENERATOR

Electrical Machine:- It is a device, which converts one form of energy into another form of energy by utilizing the force as motion of electric charge is called known as ‘electrical machine’.

Synchronism:- Achieved a coincidence within a point of time is known as synchronism.

Synopsis:- AC system has a number of advantages over dc system. Now-a-days the three phase AC system is being used for generation, transmission and distribution of power. The machine which converts mechanical power into 3- electrical power is called an

“alternator / synchronous generator / AC generator”. Alternators are the primary source of till the electrical energy which we consumed. These

machines are the largest energy converters in the world. The prime mover which is used for generation purpose is turbines. For commercial and

industrial purpose the four-stroke engines are used as prime movers to give mechanical power to the alternators.

Principle of an Alternator:- An alternator operates on the same fundamental principle of electro-magnetic induction as a dc generator. i.e., when the flux cuts the conductor (or) conductor cuts the flux an emf

induced in the conductor. Like a dc generator, an alternator also has an armature winding and a field winding. But the one important difference between the two is, For an alternator, armature winding is placed or housed in a stator instead of rotor in a dc generator. The field winding is housed in a rotor poles.

It is more usually convenient, advantageous to place the field winding on rotating part (rotor) and armature winding on stationary part (stator).



Difference between DC & AC Generator:-

Advantages of stationary armature:- The field winding of an alternator is placed on the rotor and connected to dc supply through the slip ring. The 3- armature winding is placed on the stator. This arrangement has the following advantages.

1. “Easier to insulate the stationary winding” for high voltages because they are not subjected to centrifugal force and extra space is available on stator.

2. “Stationary 3- armature winding is directly connected to the load” without giving through large, unreliable slip-rings and brushes.

3. “One (or) two slip-rings are required for dc supply to the field winding on the rotor”. Since exciting current is small, the slip rings and brush gear required are of light construction”.

4. “Due to simple and robust construction of the rotor”, higher speed of rotating dc filed is possible so that output electrical power increased.

5. Stationary armature windings can be cooled more efficiently. 6. “Rigid and convenient construction” because stationary armature winding is capable of handling

high voltage and current. In addition, water cooling can be installed more conveniently on stator rather than

rotor by flexible water tube connection. 7. “Lesser rotor weight” because field winding requires less amount of copper. Reduces the inertia

due to low-priced bearings and also longer life because of “minimum wear and tear”. The above are the major advantages of the stationary armature windings. Note: All Alternators above 5KVA employs Stationary Armature, Rotating Filed

DC GENERATOR ALTERNATOR Faradays law of electromagnetic

induction. Fleming’s right hand rule. Stationary field. Rotating armature. Conductors cut the flux. Yoke. Prime mover as IC engine.

Faradays law of electromagnetic induction.

Fleming’s right hand rule. Rotating field. Stationary armature. Flux cuts the conductor. Stator. Prime mover Turbines.



Construction:- An alternator has 3- armature winding on the stator and dc field winding on the rotor. Stator:- It is the stationary part of the machine and is built up of sheet steel laminations having slots on its inner periphery. A 3- winding is placed in these slots and serves as the armature winding of alternator. The armature winding is always connected in star and the neutral is connected to the load because,

For star connection,

𝑉𝑝𝑕 =𝑉𝑙

√3

Since the emf is proportional to number of turns, so that it requires less number of turns than Delta. Neutral protects the system in case of ground faults. Rotor:- The rotor carries a field winding which is supplied with direct current (dc) through two slip rings by a separate dc source.

Depending on the construction of rotor the alternators are classified in to two types. i. Salient / projecting pole type.

ii. Non-Salient / Cylindrical / Wound type.

(i). Salient (or) projecting pole type:- In this type, salient (or) projecting poles are mounted on a large steel (circular type) frame

which is fixed to the shaft of an alternator as shown in figure. The individual field pole windings are connected in series in such a way that when a field

winding is energized by the dc exciter, adjacent poles have opposite polarities. Low and medium speed alternators (120 –

400) such as those driven by diesel engines (or)water turbines have salient pole rotors due to the following reasons: a) The salient field poles would cause an

excessive windage loss if driven at high speed and would tend to produce noise.

b) Salient-pole construction cannot be made strong enough to withstand the mechanical stresses to which they may be subjected at higher speeds.



Since a frequency of 50Hz is required, we must use a large number of poles (P) on the rotor of slow speed (N) alternator.

(NS =120∗f

P Ns 1/P)

Low speed rotors always posses a large diameter to provide the necessary space for the poles. Consequently, salient pole type rotors have large diameters and short axial lengths.

(ii). Non – Salient pole type / cylindrical / wound rotor:-

In this type, the rotor is made of smooth solid forged steel radial cylinder having a number of slots along the outer periphery.

The field windings are embedded in these slots

and are connected in series to the slip – rings through which they are energized by the dc exciter. It is clear that the poles formed are non-salient

i.e., they do not project out from the rotor surface. High-Speed alternator’s (1500 or 3000 rpm) are

driven by steam turbines and use of non-salient pole rotor’s due to the following reasons:

a) The type of construction has mechanical robustness and gives noise less operation at high

speeds. b) The flux distribution around the periphery is nearly a sine wave and hence a better emf

wave form is obtained rather than salient pole rotor.

Since steam turbine runs at high speed and a frequency of 50Hz is required, we need a small number of poles i.e., 2 and 4. For a 2-pole it is 3000rpm and 4-pole it is 1500rpm.

It possesses small diameter and very long axial lengths because high speed of rotation produces strong centrifugal forces which impose an upper limit on the diameter. Therefore, high-power & high speed rotors have to be very long.



Operation of an Alternator:-

The rotor winding is energized from the dc exciter and alternate ‘N’ and ‘S’ poles are developed on the rotor. When the rotor is rotated in anti-clockwise direction by a prime mover, the stator (or) armature conductors are cut by the magnetic flux of rotor poles.

Consequently, emf is induced in the armature conductors due to electromagnetic induction. The induced emf is alternating since ‘N’ and ‘S’ poles of rotor alternately pass the armature conductors.

The direction of induced emf can be found by Fleming’s right hand rule and frequency is given by,

F = NP/120

Where, N = speed of rotor (rpm) P = number of rotor poles.

The above figure shows star-connected armature winding and dc field winding. When the rotor is rotated, a 3- voltage is induced in the armature winding. The magnitude of the induced depends upon the speed of rotation and the dc exiting current.

The magnitude of emf in each phase of the armature winding is the same. However, they differ in phase by 1200 electrical as shown in the phasor diagram.

Supply Frequency:- The frequency of induced emf in the armature conductors depends upon speed and number of the poles. Let, N = rotor speed (rpm) P = number of rotor poles F = Frequency of emf (Hz)



Consider a stator conductor that is successively swept by ‘N’ and ‘S’ poles of the rotor. If a positive voltage is induced when a N-pole sweeps across the conductor, a similar negative voltage is induced when a ‘S’ – pole sweeps by. This means that one complete cycle of emf is generated in the conductor as a pair of poles passes

it. i.e., one N-pole and the adjacent following S-pole. The same is true for every other armature conductor.

We know that from graphical representation of graphical plot, the rotating field travels a distance covered by 2-poles.

Number of cycles for one revolution = P/2 for ‘P’ pole machine.

Number of revolution /second = 𝑁

60 (sec)

Number of Cycles / second = 𝑁𝑜 .𝑜𝑓 𝑐𝑦𝑐𝑙𝑒𝑠

𝑅𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠 × 𝑁𝑜 .𝑜𝑓 𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛

𝑆𝑒𝑐𝑜𝑛𝑑

= 𝑃

2 ∗

𝑁

60

But number of cycles / second is its emf’s frequency.

F = Frequency = 𝑃𝑁

120

It may be noted that ‘N’ is the synchronous speed. For a given alternator, the number of rotor poles is fixed and therefore, the alternator must be run at synchronous speed to give an output of desired frequency. For this reason, an alternator is sometimes called synchronous generator. Note:- In other words, the synchronous machines doubly excited energy – conversion devices. In general, the generated induced emf is depends on the relative motive between the field flux lines and armature conductors. If it is working as a motor, the field winding is energized from a dc source and its armature

winding is connected to ac source. Finally the synchronous machine delivers (or) exports ac power.



Differences between Salient and Non-Salient pole type rotors:-

S.No SALIENT POLE TYPE ROTOR NON – SALIENT POLE TYPE ROTOR

1. This type of rotor is having large diameters and small axial length.

This type of rotor is having large diameters and long axial length.

2. Poles are separately projected to the large cylindrical steel frame.

Poles are in-built to the solid forged steel radial cylinder.

3. Simple in construction, N = 150 to 1500rpm Robust in construction, N=1500 to 3000rpm

4. Low and medium operating speed. (120 to 400rpm)

High operating speed (1500,3000rpm)

5. Somewhat noisy operation due to air-gap between the poles, air friction is maximum.

Noiseless operation and air friction is minimum.

6. These are employed with hydraulic turbines and diesel engines.

Employed with steam turbines i.e., turbo type.

7. The emf wave form is not a exact one, large diameter, short axial length.

Better emf wave form will obtained, small diameter & large axial length.

8. Poles are laminated to reduce the eddy current loss.

Less windage (air resistance) loss.

9. Rotor surface is not smooth. Rotor surface is smooth.

Conductor :- A length of wire which is used for energy–conversion process is called conductor. Turn :- One turn consists of two conductors. In a figure the AB and DE is a coil side / conductors form a turn. Coil :-



One coil consists of number of turns. One coil has one turn shown in fig. (a) One coil has two turns shown in fig. (b) Multi turn coil has shown in fig. (c) i.e. one coil has more than two turns. Coil side:- One coil with any number of turns having two coil sides (or) conductors i.e. PQ is one coil side one turn and ST is another will side. Pitch:- The term pitch indicates a particular method of measurement in terms of soil sides the teeth. Pole pitch:- A pole pitch is defined as the distance between two adjacent poles. Pole pitch is always 1800

electrical.

Coil span (or) coil - pitch:- The distance between two coil sides of coil is called coil-span (or) Coil-Pitch. It is usually measured in terms of teeth’s, slots. Full –pitched winding:- If pole pitch is equal to coil-span / coil-pitch then that type of winding is called full-pitched winding. Short-pitched winding:- If the winding has pole pitch is not equal to coil span (or) coil span is less than pole-pitch is called known as short-pitch winding.



Back-pitch (YB):- The distance measured in between two coil sides of a turn is called known as back pitch. (YB) Front pitch (YF):- The distance between the second conductor of one coil and first conductor of second coil is called front pitch (YF) Resultant Pitch (YR):- The distance between the beginnings of one will and the beginning of the next coil to which it is connected called resultant pitch. (YR) Armature windings:- The armature windings of dc machines are usually closed circuit windings but alternators winding may be either closed giving delta connections (or) open giving star connections. These are classified as follows.

Distributed and concentrated windings. Closed and opened windings. Single layer and double layer winding. Full-pitched and short-pitched windings. Integral and Fractional-slot windings.

(i)Distributed and concentrated windings;-

In concentrated type winding, all the winding turns are wound together in series to form one multi turn coil. This type of windings is used as field windings in salient pole synchronous machine as well as dc machines.

In concentrated coils, all the turns have some magnetic axis. The primary and secondary windings of transformers are of concentrated type.



If one slot per pole (or) slots equal to number of poles are employed, then concentrated winding in obtained.

Concentrated windings give maximum induced emf’s for a given number of conductors but the wave form of induced emf is not exactly of sinusoidal form.

If the conductors are placed in several slots under one pole, the type winding is called distributed winding.

Otherwise, all the turns are arranged in several full-pitch (or) fractional-pitch coils. These coils are then housed in the slots spread around the air-gap periphery to form phase or commutator winding.

Stator and rotor of induction machines, the armatures of both synchronous and dc machines have of distributed type windings.

Advantages of distributed windings:-

a) The harmonic emf is reduced and so the wave form is improved. b) It diminishes armature reaction and armature reactance. c) The core is better utilized as a number of small slots evenly spaced.

(ii)Closed and Open windings:-

The closed windings are only used for commutator machines i.e., such as dc and ac commutator machines. For this there is a closed path, if one starts from any point on the winding and traverses it, one again reaches the starting point from one where had started.

It should be housed at outset of armature always using the double layer windings. Each coil in double layer winding has its one coilside in top layer and its other will side on bottom layer.

The closed type windings are two types. a. Simplex lap winding. b. Simplex wave winding.

The major difference between above two is depends on the manner connecting the coil ends to the commutator segments.

For lap winding, the two coil-ends of a coil are connected to the two adjacent commutator segments.

For wave winding, the two coil-ends of a coil are bent in opposite directions and connected to commutator segments which two pole-pitches (3600) apart.



The open-windings are used only for ac machines like synchronous machines, induction machines, etc. open windings terminate at suitable number of slip-rings (or) terminals. Open windings are always of star type connection. Close windings are of - type connection.

(iii). Single layer and Double layer windings:-

If the winding of one coil-side occupies the total slot area, then it is called single layer winding.

Advantages:-

The following are the advantages of single layer winding.

Higher efficiency and quite operation because of narrow slot openings. Space factor for slots is higher due to absence of inter layer separator.

The number of coils, the number of turns per coil, the coil pitch, the number of circuits and the connection of the phases are give the desired emf wave form.

In case the slot contains even number of coil sides in two (or) double layers, than the winding is called as double layer winding.

The winding may be arranged to be connected either Y (or) , with leads brought out from both ends of each phase to make this possible.

Advantages:-

Ease in manufacture of coils and lower cost of winding. Less number of coils is required as spare in the case of winding repairs. Fractional slot windings, pitch coils are employed. Lower leakage reactance and therefore better performance and more economical.

Modern practice all over the world favors use of double layer windings. Single layer winding is only employed for small rating ac machines and where as double layer windings are more common above 5KW machines.



(iv) Full-pitch and short-pitch / chorded windings:-

If the coil-span /coil-pitch are equal to the pole-pitch then the winding is termed as “full-pitch winding” shown in fig.

If the coil-span / coil-pitch is less than the pole-pitch (1800) then the winding is termed as “short-pitch / chorded winding” as shown in fig.

If there are ‘S’ slots (or teeth’s) and ‘P’ poles, then pole pitch = S

P slots per pole.

α = Short-Pitch angle If Coil-Pitch = S

P , it results in full-pitch winding

If Coil-Pitch < S

P , then it results in Short-pitch winding

Advantages of short-pitch / Fractional-pitch / Chorded winding:-

The ends of the coils are shorter, which means less copper loss due to less total length. The end coils can be formed more compactly. The end belts will need less winding space

resulting in a shorter unit. Improved emf wave form due to reduction of harmonics. Fractional number of slots per pole in a turn reduces the tooth/teeth ripples. Mechanical strength of the coil is increased.

Since all ac equipments are designed to operate on a pure sine wave, the generation of harmonics is to be avoided. This is especially so when the factor that achieves it is otherwise desirable.

The major disadvantage of short-pitch coils are, the total voltage around the coil is somewhat reduced. Because the voltages induced in the two sides of the short-pitched coil are slightly out of phase, their resultant vectorial sum is less than their arithmetic sum.

(v)Integral slot windings:- (m = integer)

To maintain uniform magnetic reaction throughout the surface of armature, the armature conductors should be properly distributed. Integral means forming a whole. If the number of slots/phase/pole (m) is a while (or) integer

number then that type of winding is said to be integral slot winding.



The number of slots in an ac machine should always be integral multiples of three. However, the number of slots per pole per phase may be integer (or) a fraction. The winding may be single layer (or) double layer.

Assure that the full-pitch (or) pole-pitch of a winding is 6 slots per pole.

If the coil-pitch is taken to be equal to pole-pitch, then the upper coil-side in slot-1 should be

connected to bottom coil side in slot ‘7’(=1+6).

Since there are 6 slots per pole of 1800, the slot angular pitch = = 1800

6 = 300

Upper coil-side in slot-2 must be connected to bottom coil-side in slot-8 (2+6 = 8). The winding is further completed for phase-‘R’ only shown in figure.

For a 3- machine, from the above figure the slots 7, 8, 13, 14 contain coil sides belonging to the same phase-‘R’. In general, it can be stated that for full-pitch integral slot winding, each slot contains coil-sides belonging to the same phase.

(v) Fractional slot winding:- (m = fractional) The number of slots per phase per pole is a fractional then it is known as “fractional-slot winding”. But the total number of slots must be multiples three (3). This helps to maintain symmetrical winding. The advantages of these windings are,

o Reduces the high-frequency harmonics in the emf and mmf wave forms. o This winding permits the use of already existing slotting nos. for the armature

laminations. o Allows choice of coil-pitch.

The restrictions of this winding are, It can be used only with double-layer windings.



The number of parallel circuits is limited . Let ‘S’ be the total number of slots and ‘P’ be the number of poles. Then slot per pole per phase, for a 3- winding are ‘(S/3)/P’. If ‘K’ is highest common factor between S/3 and ‘P’ the slots / pole/ phase can be,

𝑆/3

𝑃 = 𝐾∗𝑆𝐾

𝐾∗𝑃𝐾 = 𝑆𝐾

𝑃𝐾

Where, Sk = 𝑆/3

𝐾

Pk = 𝑃𝐾

The ratio Sk / Pk is called the ‘characteristic’ ratio of the fractional slot winding.

Difference between Fractional and Integral Slot winding:- S.No INTEGRAL SLOT WINDING FRACTIONAL SLOT WINDING

1. Number of Slots/Phase/Pole (m) should whole / integral number.

Number of Slots/Phase/Pole (m) should be an fractional number.

2. Number of slots is integral multiples of three.

Number of slots is integral multiples of three.

3. Applicable for both single and double layer winding. Practicable only with double layer arrangement.

4. Integral slot winding may not appear to be complicated. It may appear to be little complicated.

5. Manufacturing in little complicated. Easier to manufacture and the cost is low.

6. Obtained lesser power density compared to fractional slot winding. It is obtained higher power density.

7. Longer non-over-lapping emf turns. Shorter non over-lapping emf turns.

Pitch factor / chording factor: - (Kp (or) Kc) Pitch factor is defined as the ratio of emf with short-pitch coil to the emf with full-pitch coil. Already we know that, pole-pitch is the distance between the centre lines of adjacent ‘N’ and ‘S’

pole measured along the circumference of armature surface. When two sides of a coil are full pole pitch apart, it is called “full-pitched coil”. The emf in coil side of a full-pitched coil is in phase.

In practice, coil pitch is less than pole pitch and hence emf’s in the coil sides have a phase difference. The resultant emf in the coil will be less than that of full-pitched coil. Therefore, for full-pitch coil, Kp = 1 while for short-pitch coil, Kp<1.



Let us consider the coil sides are housed in slots ‘1’ and ‘7’ gives the full-pitched coil. If the coil-sides are placed in slots ‘1’ and ‘6’ gives short/fractional pitched winding because coil span < pole-pitch (<1800) (or) equal to 5/6th pole-pitch.

It falls short by pole-pitch (or) by 1800

6 = 300 (or) 5/6 × one pole pitch

5/6 × 1800 = 1500 (coil span).

Short pitch angle = Pole pitch – coil span = 1800 − 1500 = 300

The advantages and disadvantages as we know refer page No. 9.

Therefore,

KP (or) Kc = Vector sum of the induced emfs per coil

arithmatic sum of the induced emfs per coil

It is always less than unity. Let ‘Es’ be the induced emf in each side of the coil. If the coil were full-pitched i.e., its two coil sides were one-pole pitch (1800) apart.

Then total induced emf of arithmetic sum is 2Es → 1



If it is short pitched by 300 (∝), their resultant ‘Er’

which is the Vector sum of two voltages with 300

electrical (Es)

From the Vector diagram, ∠OQR = 1800 − 300

∠OQS = 1/2 [∠OQR]

= 1/2 (1800 − 300 ) = 750 .

∠OQS = 900 − 150 = 750

Er = OR = OS+SR

= OQ cos300

2 + QR cos

300

2

= Es cos 150 + Es cos 150

Er = 2Es cos 150

∴ Kp (or) Kc = emf with short − pitched coil

emf with full− pitched coil

= 2𝐸𝑠 cos 150

2𝐸𝑠

Kp = cos 150 = 0.966.

In general, if the coil span falls short of full pitch by angle ‘’ i.e., short-pitch angle is denoted ‘’

(electrical).

∴ Kp (or) Kc = cos∝

2

Distribution / Breadth / Winding / Spread factor:- (Kd)

Distribution factor is defined as the ratio of emf with distributed winding to the emf

with concentrated winding denoted by ‘Kd’

R, Y, B, R1, Y

1, B

1, are three-phase windings displaced

by 1200 electrical.

From the diagram we can say that it is having 36 slots,

3- winding with distributed winding because coils are not concentrated (or) bunched in one slot, but are distributed in a no. of slots to form a polar groups under each pole. Obviously it is having 3 slots/pole/phase because it is 3- winding, single layer winding, 4-pole machine. Now, these three coils which regress one polar group are not bunched in one slot but in three different slots.



9 = no. of slots per pole ( 36

4 = 9)

∴ Angular displacement between any two adjacent slots = 1800

9 = 200

If the 3-coils are bunched in one slot (concentrated winding),

then the total induced emf induced in the three coil sides of the coil is

arithmetic sum of three emf’s. Let ‘Es’ be magnitude of each coil side.

i.e., 3Es → 1

For distributed winding the three coils are displaced 200 in three different slots. Then the vector sum is, OC = Er = OE cos 200 + ED + DC cos 200 = Es cos 200 + Es + Es cos 200 = 2Es cos 200 + Es = 2Es. 0.9397 + Es = 2.88Es → 2

∴ Kp = 21

= 𝑒𝑚𝑓 𝑤𝑖𝑡 𝑕 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑒𝑑 𝑤𝑖𝑛𝑑𝑖𝑛𝑔

𝑒𝑚𝑓 𝑤𝑖𝑡 𝑕 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑒𝑑 𝑤𝑖𝑛𝑑𝑖𝑛𝑔

= 2.88𝐸𝑠

3𝐸𝑠 = 0.96

Kd = 0.96 ≤ 1 General case:-

Let ‘𝛽’ be angular displacement between the slots. Its value,

𝛽 = 1800

𝑁𝑜 .𝑜𝑓 𝑠𝑙𝑜𝑡𝑠 / 𝑝𝑜𝑙𝑒 = 180 0

𝑛

M= no. of slots/pole/phase. m 𝛽 = spread angle. Then the resultant emf in one polar group is ‘mEs’ (i.e., m × AE) Es = voltage induced in one coil side. The method for finding the vector sum of ‘m’ voltages each of value ‘Es’ and having mutual phase difference

of ‘𝛽’. (if m is large, then the curve ABCDE will become part of a circle of radius – r)



∴ AB = Es = 2r sin𝛽

2

Arithmetic sum = mEs = m × 2r sin𝛽

2 → 1

∴Vector sum = AE = Er = 2r sin𝛽

2 → 2

∴Kd = 𝑉𝑒𝑐𝑡𝑜𝑟 𝑠𝑢𝑚 𝑜𝑓 𝑒𝑚𝑓𝑠 𝑖𝑛 𝑎 𝑐𝑜𝑖𝑙

𝑎𝑟𝑖𝑡 𝑕𝑚𝑎𝑡𝑖𝑐 𝑠𝑢𝑚 𝑜𝑓 𝑒𝑚𝑓𝑠 𝑖𝑛 𝑎 𝑐𝑜𝑖𝑙

= 2

1 =

2r sin 𝑚𝛽

2

m × 2r sin𝛽

2

∴Kd = sin

𝑚𝛽2

m sin𝛽2

Induced emf equation of a 3-∅ Alternator:-

Let

= flux per pole (cub)

N = rotor speed (rpm)

F = frequency of induced emf (Hz)

P = no. of poles

Z = no. of conductors/coil sides in series / phase

= 2T

T = no. of turns [one turn = 2coil sides (or) conductors]

Kd = distribution factor = sin

𝑚𝛽2

m sin𝛽2

Kp = Pitch factor = cos∝

2

Kf = form factor = 1.11 for sinusoidal

For one revolution of the rotor it takes a time of 60

𝑁 sec

Each stator conductor cut by flux of ‘’.



∴ change in flux / pole = d = p

Change in time = dt = 60

𝑁

∴ d

𝑑𝑡 = p

60𝑁

= NP

60 = Average induced emf / conductor → 1

Now, we know that f = PN

120 N =

120 f

𝑃 → 2

2 in 1 as

Avg. emf per conductor = NP

60

2 = NP

60 . 120 f

𝑃

= 2f (volts) If there are ‘z’ conductors in series / phase, Then average induced emf/conductor = 2fz = 2f(2T) = 4fT We know, Form factor = Kf = 𝑎𝑣𝑔

𝑟𝑚𝑠 = 1.11

Then, RMS value of emf/ph = 1.11 × avg. = 1.11 × 4fT Eg(rms) = 4.44fT volts. But the above equation is not being so, the actual available voltage is reduced in the ratio of two factors i.e., Kp and Kd. ∴ Actual available voltage/ph = 4.44 Kp Kd fT (volts)

If alternator is star connected, then emf is √3 times of phase emf. Winding factor:- It is the product of the distribution and pitch factors. i.e., Kw = Kp × Kd

It is denoted by ‘Kw’

Documents

UNIT-Ieeeaitsrajampet.com/files/a924mUNIT - 1.pdf · 2019. 12. 17. · Non-Salient / Cylindrical / Wound type. (i). Salient (or) ... Operation of an Alternator:- The rotor winding