1. Induction Motors
Theory of Operation
Dave Loucks, PE

2. Induction Motors Convert electrical energy to magnetic energy
Convert magnetic energy to mechanical energy
Two types of mechanical energy
Rotational
Linear (won’t cover today)

3. Electrical Force  Mechanical Force
W or J or calories
PL = f(, T, h…)
V, I
(Pe-PL1)(P-PL2)Pm
Pm = f(, T)
Pe = f(V, I, , f)
Motor
3 Electrical Power
Mechanical Power
Equating both:

4. Motor Theory Review Ampere’s Law Ienc = (enclosed) current (amperes)
B = flux density (Teslas)
L = length around closed path
 = permeability of space
= Line integral of a space traced by a closed B field
“Current is proportional to the amount of flux captured by a wire. ” (i.e. a generator) dL
Biot-Savart Law is reverse (if know I, solve for B)

5. What is a Line Integral ( ) anyway?
Just the area enclosed by an arbitrary path B I OR
In this case, it defines a region over which flux is captured

6. What is Permeability ()?
A measure of how densely a space holds a magnetic field
Defined as the slope of the B-H curve.
It is the ratio of how much flux density is produced for a given magnetic field strength
Applied Field Strength
(amperes-turns/meter)
Flux Density
(Teslas)
The material is
more “magnetic” B H
f Ferromagnetic material (Fe, Co, Ni, rare earths) – Keeps magnetism
p Paramagnetic material (W, Cs, Al, Li, Mg, Na) – Magnetic only when field applied
d Dimagnetic (anti-) material (Bi, Sb) – Repels magnetic field

7. Convert Electricity (I)  Magnetic Field ()
Biot–Savart’s Law
Note: field B has direction
Surrounds (but does not cross) straight conductor
B field is artifact of current
Right Hand Rule (#1)

8. Combine Biot-Savart and Ampere’s Laws
For a circular path around thin1 straight conductor I B
If r is in meters and I is in amperes, units of B are in “Teslas”
1 T = Gauss
1Means that conductor length >> conductor radius

9. What Happens in a Coil? N N N N N N N N I N N N N I N N N N
Solenoid
Bar Magnet
Using RHR #1, no matter where current flows in coil, fingers point up inside coil and down outside coil
Image Source:

10. What Happens When B Fields Interact?
We know that with magnets, opposites attract S N S N S N S N I I I I
We also know, like poles repel N N S N N S I I I I

11. Can We Create Motion? Faraday’s Law of Induction V = voltage (volts)
N = # of turns of wire around coil
d/dt = time rate of change of magnetic flux (Telsas / m2 / s)
“The required voltage to operate a motor is proportional to the number of turns of wire multiplied times how fast the rotor spins”

12. Motor Theory Review Lorenz Force Law
Force vector (N)
Current (A)
Magnetic Field (T) L
Length of wire (m)
Force on a current carrying conductor is perpendicular to both the current and the magnetic field.
Good description of Lorenz Force Law:

13. Time to Reintroduce the Cross-Product
Magnitude is equal to the product of the two vectors times the sine of the angle between them times the unit vector perpendicular
Unit Vector Perpendicular has magnitude of 1 and a direction that is perpendicular to both of the two other vectors
sin 0o = 0
sin 30o = 0.5
Sin 90o = 1 

14. Parallel Conductor Forces L
There is no force on a single conductor since the B field never intersects the conductor
There is a force between conductors since the B field from the adjacent conductor intersects the neighboring conductor

15. Magnetic Field Interaction
Parallel conductors with current flowing in the same direction
Attract
Parallel conductors with current flowing in the opposite direction
Repel

16. Magnetic Field Interaction
Perpendicular conductors
Neither attract nor repel
No Force 
(Field induced from I2)
I1 and B2 are parallel (don’t intersect)
F=0 since sin 0o = 0

17. Magnetic Field Interaction
Conductors crossing at an angle have force between them proportional to sin , where  is the angle between the current carrying paths
(Field induced from I1) 

18. Using Lorenz Law to Spin Rotor

19. Magnetic Field Rotational Velocity
Stator field moves from pole to pole
Returns to original pole 360O later
Assume 60 Hz and 2 poles per phase
1/60 second makes 1 revolution, so 60 revolutions / second
1 min makes 60 * 60 = 3600 rev / m
60O

20. Magnetic Field Rotational Velocity
Stator field moves from pole to pole
30O
If 4-pole, then in 1 cycle, moves from one set of poles to the next
But since two sets per rotation, only makes it ½ way around in 1 cycle
Rotational speed proportional to frequency but inversely proportional to number of poles

21. Magnetic Field Rotational Velocity
Magnetic field rotational speed called “Synchronous Speed”
Induction rotor must “cut” lines of flux, so it cannot operate at synchronous speed. This % difference in speed is defined “slip”

22. Slip
Machines produce differing amounts of torque depending on amount of slip
Rotor losses are proportional to slip
50% slip = 50% losses
Reason why VFDs are more popular than wound rotor controllers

23. Current Unbalance
Current produces flux, flux connects stator and rotor
If flux is unbalanced between poles, there are torque “pulsations” as the rotor rotates
You can think of a pulsation as someone “hitting the brakes” or adding “reverse torque”.
30O
“Reverse” or “negative” torque works against the “positive” torque.
“Positive sequence” current produces torque. “Negative sequence” current produces just heat.

24. Reversing Offset phases create rotating magnetic fieldB C 1 2 1 2 3 3 A B C
Reverse any two phases and magnetic field rotates in opposite direction 1 2 3

25. Delta-Wye (Delta-Star)
Delta connection
Wye connection i1 i3 3 1 C B VL VL i2 2 i1 1 A C VP A VP B i3 3 i2 2

26. Enclosures / Mounting Foot Mount Vertical Mount Open Drip Proof (ODP)
Totally Enclosed Blower Cooled (TEBC)
C-Face Mount
Totally Enclosed Fan Cooled (TEFC)
Totally Enclosed Non Vent (TENV)
(Large) Flange Mount
Totally Enclosed Air Over (TEAO)
Totally Enclosed Water Cooled (TEWC)

27. Download these slides …
Contact author: