Electromechanical Systems

1
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)

2
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

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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 !
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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)
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ASINCHRONOUS MACHINES industrial construction
Fig.2. Two types of induction motors industrial
products
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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).
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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).
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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.
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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)
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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
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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 !!!!
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• 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

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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
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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)
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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
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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)
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INDUCTION MACHINE HOW DOES IT WORK
Fig.8. Animation of ROTATIONAL field (black) and
PULSATING fields of each of the 3 phase of IM
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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)
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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
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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)
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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 .
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Induction machine_ vector-dijagram with k1
Fig.12. Vector diagram of induction machine
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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
  !!!)

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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

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Electromagnetic torque - derivation
Electromagnetic torque Mem can be expressed as
(10)
(11)
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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)
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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?
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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)

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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.

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Fig.14. Simulation results given from
mathematical model
speed rpm
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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)!!!
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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

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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!
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Working range of induction squirel cage motor
Fig.16. 4-quadrant operation
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END