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Electromechanical Systems

Asinchronous (induction) machines

- Types of machines with alternating current
- Types of induction machines with alternating

current - Components of asinchronous (induction)

machines, (squirel cage and slip-ring induction

machines) - How does it works!
- Mathematical model
- Equivalent circuit
- Vector (phasor diagram)

Literature

- R. Wolf Osnove elektricnih strojeva, Školska

knjiga, Zagreb, 1991. (72-95, 107-117, dijelovi

181-220), in Croatian - B. Jurkovic Elektromotorni pogoni, Školska

knjiga, Zagreb, 1985. (Staticka stanja

elektromotornih pogona s asinkronim motorima,

str.49-62), in Croatian - 3. D. Ban Mirna, pulzirajuca i okretna

magnetska polja, predavanja (pogledati dodatnu

literaturu na web stranicama), in Croatian

Electrical machines- types

Stator with 3 phase winding

Stator with winding

Rotor, squirel cage or slip-ring type

Rotor with permanent magnets

Stator with winding on the pole

Stator with electromagnet or permanent magnet

Rotor with winding, (armature winding)

Iron rotor different reluctance in different

axces !

ASINCHRONOUS (INDUCTION) MACHINES

- Induction machine (IM)
- Stator with three symetrical (balanced)

distributed phases , a, b. c ( windings)

Stator windings

Rotor winding

air gap

Fig.1.Cross section of IM a), Spatial stator

winding distribution, b)

ASINCHRONOUS MACHINES industrial construction

Fig.2. Two types of induction motors industrial

products

ASINCHRONOUS induction machines

- Squirel cage Induction machine (motor), IM
- - squirrel cage construction, the rotor winding

consists of a number of rotor bars, short-cut

by rings from both rotor side, see figures below

ring

ring

bars

bars

ring

ring

a)

b)

Fig. 3. Squirrel cage rotor of induction motor,

rings and bars a), squirrel cage rotor industrial

product b).

ASINCHRONOUS induction machines

- Slip-ring asynchronous (induction, IM) machine
- stator is identical as squirrel cage induction

motor - rotor has clasical winding, not a bars
- usualy 3 windings (phases) on the rotor
- rotor winding ends connected to the stationary

rings, see figure below

rings

resistors

Fig. 4. Stator and rotor connections of a

slip-ring a), squirrel cage rotor industrial

product b).

Stator Sliced iron, slices electrically isolated

from conductors (windings) placed in slots. There

are 3 isolated balanced phase (windings), spaced

with 120 (for 2-pole machine). 3-phase

symmetrical stators winding is supplied by

3-phase symmetrical voltage supply 120

Rotor Sliced iron, slices electrically isolated

from rotor conductors (windings), placed in

rotor. Rotor winding is usually 3-phase, in

star connection. The ends of 3-phase winding

are short connected altogether from one side in

one point. Three others ends of windings are

usually connected , to three slip rings, see Fig.

4. Those rings are connected then on stator

connection box. For squirrel cage type rotor,

conductors are made from cooper (Cu) or aluminium

(Al).

Air gap It must be as small as possible, taking

into account bearings specifications, as well as

a mechanical stress. Smaller air gap resulting in

small magnetizing current needed for magnetic

field. That field is important for effective

electromechanical conversion.

Physical concept of IM

- Three phase (3f) IM motor supplied from stator

side by symmetrical 3f voltage supply, results

with SYMMETRICAL ROTATING FIELD. This field

rotate with synchronous speed ?s (1) - Rotational field is cutting rotor conductors

by relative speed ?s- ? (slip, (2), inducing in

conductors (windings) voltage E2sE20 , (3) - In short connected rotor winding (squirrel cage

rotor) induced voltage (3) will generate

current, which will together with rotational

field produce tangentional force on the rotor,

ie. torque. - Developed torque will accelerate rotor, and

after reaching desired speed, (steady state),

rotor speed will be close to the synchronous

speed, (1)

slip ()

(2)

slip

Synchronous speed

(1)

p?number of pole pairs (see explanation at the

end)

Rotor voltage dependence of slip

- When rotor is blocked (s1, speed0), rotational

field induce in rotor winding voltage E20 , see

Fig.5. - When rotor start to move, relative speed is

changing, as well as relative speed between

rotational (stator) field against rotor, and

voltage E2 is changing according (3) - When the relative speed is zero, ie. s0, there

is no voltage in rotor winding, no current, nor

force, no torque!! It means that motor cannot

work when s0. Conclusion is that motor can work

only when different speed between rotor and

rotational speed exist!!! This phenomena define

term ASINCHRONOUS MACHINE.

(3)

Fig.5. Rotor voltage vs rotor speed

Rotor current frequency vs slip

- Rotor voltage and current frequencies are

depending of relative speed between rotor and

rotational (stator) field. i.e. slip. Those

variables have frequency determined by

relative speed between rotor and rotational

(stator) field.

Reminder !!!!

- Rotor speed vs. slip

The sam units are used for the synchronous speed

ns

- rotor rotates with synchronous speed ? s 0
- rotor blocked , zero speed ? s1
- rotor rotates faster than rotational speed ? s lt

0 - rotor rotates opposite than rotational field

speed ? s gt 1

Number of pole pairs- Explanation

- The term 1 pair poles defines the region in

the stator of machine where three windings

(phases) are simetrically spaced inside stator

slots. It is said that the angle between axces

of the phases are 120?geometricly , Fig.1. a) - In the a) this space is 360?, in b) it is 180?

geometricly. - For one supply stator voltage period, rotating

field always passing 1 pair poles space!!!.

That means, for one cycle T, rotating field will

pass in case a) 360?, but in case b) only half

space, i.e. 180? geometricly - Conclusion 1 rotating field speed in case a) is

2 times larger than in case b) - Conclusion 2. In the machine with p-pole pairs,

rotating field will pass in one T cycle 360?/p

parts of machine stator space.

a) 1par polova

c) 2 para polova

b) 1par polova

Number of pole pairs- Explanation

- Physical process with one pole pairs machine

doesnt changed increasing the number of poles.

In that case, all analysis can be performed on

one pair poles machines. - In this case the term electrical angle (?el),

is defined and it is identical to the geometric

angle (?g) for 2-pole machine, p1. - Generally, for the case of p- pair poles

machine, relation between electrical and

geometric angle is

(4)

INDUCTION MACHINE HOW DOES IT WORK

Initial position of pulsating field is maximal

field (maximal current) (maximal sinusoid) the

circles are maximal red, vector is maximal

right oriented. When the field is zero, vector

is in the middle of circle (point!), "circles

are red, current in conductors is zero. Next

position is maximum fields in another (left)

side, vector is maximal and on the left, circles

are red (maximal negative current)

Fig.6. Animation of PULSATING field

INDUCTION MACHINE HOW DOES IT WORK

Thru each of 3 winding SYMMETRICAL Y spaced in

stators slot (namot A, B i C) flow one of the 3f

currents, (delayed each other in120). The

picture shows that each of the fields are

PULSATING, only the amount is changing in one

position. Resulting field is ROTATIONAL field,

(BLACK), the sum of pulsating fields of all 3

phases, with maximal amount 50,greater than

maximum of one phase pulsating field.

Fig.7. Animation of SYMMETRICAL ROTATIONAL field

(black) and PULSATING fields of each phase

(red, green, blue)

INDUCTION MACHINE HOW DOES IT WORK

Fig.8. Animation of ROTATIONAL field (black) and

PULSATING fields of each of the 3 phase of IM

INDUCTION MACHINE HOW DOES IT WORK

- The principle of work is based on the force

(i.e. torque) generation - Torque is result of rotational field and rotor

current . Rotor voltage is induced by rotational

stator field - Questions Why rotor cannot reach the speed of

rotational field? How rotor could reach the

speed of rotational field? Explain!

Fig. 9. Rotational field speed (ns), rotor speed

(n), and rotor speed relative to rotational field

speed (ns -n)

Induction machine equivalent circuits

- One phase equivalent induction machine circuit

E1,I1 - induced stator voltage and current U, U1

- stator voltage (supply voltage) R1 - stator

winding (coil) resistance R2 - rotor winding

resistance X?1 - stator leakage reactance X?2 -

rotor leakage reactance E2 - inducied rotor

voltage, E20 - induced rotor voltage, (rotor

locked, stator connected to suply voltage, U)

f1 - stator voltage frequency, f2 - rotor

voltage frequency, N1, N2- stator and rotor

number of coils

Induction machine equivalent circuits

Fig.10. Equivalent circuit per phase of

induction motor with rotor parameters relative to

the stator side

- Recalculation of rotors parameters to the

stator side with parameter (k)

(5)

Explanation of the main and leakadge path -

transformer

Leackage path

Fig.11.

Magnetic field generated from primary side and

coupled with secondary side and magnetic field

generated from secondary side and coupled with

primary side are the main (coupled) magnetic

field (?12 or ?21). Magnetic field which couple

only primary winding is leakage field ??1.

Magnetic field which couple only secondary

winding is leakage field ??2 .

Induction machine_ vector-dijagram with k1

Fig.12. Vector diagram of induction machine

Rotor current and leakage reactance

- Rotor current is defined by induced voltage E2

and rotor impedance Z2

(6)

- In standstil E2 E20 , see (3)
- This formalism can be applied on leakage

reactance, X2s,, so, - X2s0 is leakage reactance in standstil, n0.
- Leakage reactance is defined for 50Hz

(standstill), and influence of the frequency f2

can be involved multiplying by slip s.

- For s0, rotor current is I2(s)0 (SYNCRONISM

!!!)

Electromagnetic torque-dependence of a voltage

and frequency

- How torque is changing by stator voltage and

frequency?

- Assumption Magnetic (rotating) field in the air

gap induce in stator winding voltage e1,

defined by

neglect

- For small slip and small current (load) it can

be wrote

Electromagnetic torque - derivation

Electromagnetic torque Mem can be expressed as

(10)

(11)

Torque speed characteristics-derivation

- Machine torque dependence of voltage supply can

be described using energy balance,

(12)

- Detailed derivation can be found in course

textual material on the web pages

- Primary impedance Z1R1jXs1 is neglected in

equivalent circuits. - It shoud be emphasized that motor torque in each

working point is proportional to the square of

the motor voltage

(13)

Machine torque characteristics-Kloss equation

- Kloss equation describes general torque-speed

characteristics of induction machine. - Functionally, Kloss equation involving two

working points arbitrary working point and

working point with maximal slip. - In the example below, developed torque at

maximal and nominal (rated) torque are used for

calculation

(14)

(15)

Which simplification is used in Kloss-equation?

Torque vs speed characterestics of IM (It

doesnt worth for motors less than 1kW)!!

Fig.13. Motor torque vs speed induction motor

(IM) characteristics

- important 3 points
- s 1, n0 - standstil torque, Mk
- s sn, n nn - rated (nominal) torque, Mn
- s smax, n nmax - maximal torque, Mmax (Mpr)

Electromagnetic torque-dependence of a voltage

and frequency

- Derivation for torque (1) (4) has been done

with assumption that recalculation factor , see

(5), is k1

- From (10)(13) it can be seen quadratic relation

between torque and magnetic field (voltage). - Expression (14), represent simplified

Kloss-equation and can be used for slip-ring

motors and squirrel-cage motors without skin

effect in rotor slots. If the skin effect is

present, Kloss equation (14) can be used only in

the region of the small slip.

Fig.14. Simulation results given from

mathematical model

speed rpm

Induction machine energy balance

Fig.15. Energy balance in induction motor

P1 is electrical power (power supply)

P2 is power on the motor shaft (mechanical

Power)!!!

Nominal data- Total, Active and Reactive power of

IM

Example of motor Data 3f induction motor, P

1000 kW Voltage 6000 V, frequency 50

Hz nominal speed1485 ,(rpm), cosf0,88,

?0.8 nominal current 115 A

- For magnetic field getting, IM taking reactive

power - Total power of IM is
- Active power (on the motor shaft!) PP2 .
- m1 is the number of phases

Induction motors - Slip and Losses

- The amount of slip is directly indicator of the

amount of losses in induction motors (see energy

balance). - It is needed to set working point in the way that

slip must be very low.

- Nominal slip is usually between 0.1 i 5 . Low

power machine (up to cca 1kW), has larger slip.

Take into account the problem of overheating

.High losses means high heating, conductors

isolation getting badly, it is possible

dielectric breakdown!

Working range of induction squirel cage motor

Fig.16. 4-quadrant operation

END