Induction Motor by Bullet Points Stator generates rotating sinusoidal BField This field induces current in the rotor cage loops at The stator BField at each rotor wire is such that Torque pushes in direction of field rotation ID: 675874
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Slide1
Induction Motors
Equations, Performance, Electrical Equivalent CircuitsSlide2
Stator Structure: Single Winding and One Turn RotorSlide3
Induction Motor by Bullet Points
Stator generates rotating, sinusoidal B-Field:
This field induces current in the rotor cage loops at
The stator B-Field at each rotor wire is such that
Torque pushes in direction of field rotation!
(That’s it!!)Rotor currents generate triangular B-field rotating in the air gap at slip speed relative to rotor, so at line rate in reference frame!Rotor field reduces field in stator and line current increases to maintain the stator winding voltage and the gap magnetic fieldIncreased line current supplies the mechanical energy and the joule heating of the rotor. Slide4
Fields and Currents:
Stator Field of One Winding:
Three Windings – It Rotates!!
Rotor Moves More Slowly than Field – “Slip” Frequency is
Induces a Current in the Rotor at Slip Frequency
Lorenz Force Produces a Torque: Lots of Vibration!!! Slide5Slide6
Add a Second Loop to Smooth Things Out
Put another loop at right angle to the first
Torque of second loop:
Result is constant torque and power!!
Maximum power comes with small slip.
More pairs of shorted rotor turns add to torque and power directlyHeat generated in rotor by induced current – use aluminum or copper bars to maximize efficiencySlide7Slide8Slide9Slide10
What Next and Why?
Show by an energy argument that the Lorenz force results are correct even with turns sunk into the rotor.
Develop a transformer model of the motor that can have its parameters fit to any given motor
Want to simulate the steady state operation of the motor to test adequate capacity for the application
Need such a model to design a controller for variable speed and highest efficiency operation
I want a lab about a motor and parameter fitting makes a good basisSlide11
Formal Transformer Analogy
Mutual inductance stator to rotor is time dependent
The A, B, C voltages are the line voltages
The rotor voltages are
Given rotor frequency, calculate currents and power, subtract rotor and winding heat to get mechanical power.
Shows all stator voltages and currents are at line frequencyShows magnetizing inductance per phase is Hard to get more useful results!Slide12
Simple Per-Phase Transformer Model
Know that power flow is constant at constant speed (No torque variation!)
Build a per-phase model with constant impedance that is a function of rotor speed
Use basic single-phase transformer model with secondary impedance dependent on rotor speed
Must predict proper dependence of thermal and mechanical rotor power as functions of line voltage and rotor speed
Stator field is zero-slip model because no rotor current at line speedSlide13
Electrical Equivalent Circuit of Stator Alone
Applies when rotor is turning at zero slip
Accounts for wire loss and stator core loss
Derive from DC ( ) and extrapolated zero slip ( ) conditions
Leakage inductance usually larger than for a simple transformer because of air gap and slot shape
Some leakage inductance designed into slot shape to limit inrush current on startupSlide14
Deriving a Rotor Model
Must give thermal and mechanical rotor power correctly
Sum of thermal and mechanical power is
Looks like a voltage source ( ) at line frequency driving an R-L circuit where the resistor ( ) is dependent on slip?
Will use an ideal transformer to match rotor resistance to the impedance at the line connection but have no way to get the turns ratio, so only fit the scaled values
Model becomes:Slide15
Electrical Equivalent Circuit with Ideal Transformer
S is the “slip” or
Rotor inductance is Leakage inductance!
Slide16
Electrical Equivalent Circuit Referred to the Stator
Do not know turns ratio or rotor bar resistance directly
Map rotor “components” to line side and get:
Basis for calculating efficiency, start inrush, etc.
Mechanical energy is electrical loss in ; all else is heat
Measure remaining parameters from locked rotor, low voltage measurementSlide17
Simplify Even More!
Stator magnetizing current small – does not change voltage drop in components in series with the line.
Drop in those components does not change the voltage across
Lprm
enough to change fields significantly – approximate!!Slide18
Things Left Out!
R
CORE
is S dependent – why??
Inrush
current – some leakage inductance designed into stator slots, gap size selection, etc. to limit starting current.No-load mechanical drag from cooling, bearing friction, etc.Add “windage” – subtract fixed mechanical power for bearings, cooling, etc. Design tradeoffs with costSlide19
Single Phase Induction Motors
Big advantage: No three-phase supply – 1-breaker, 2-wires, no possibility of incorrect rotation
Downside: poor efficiency, low power factor
Government efficiency regulation
Recently – March 2015 – applies to
motors from ¼ HPMinimum efficiency requires higher cost capacitor start/run designsSlide20
Try One Winding with Same Rotor Design
Same sinusoidal winding – get B field of one coil:
Two counter-rotating fields mean no net torque – WILL NOT START
Must have a second winding to get it started
Second winding at 90 electrical degrees around stator
Drive stator windings with Passive phase shift problem requires different components for start/run conditionsSplit-phase and capacitor start motors simply disconnect start winding after speed attained.Capacitor run motors have second, permanently connected small capacitor to convert counter-rotating fields into single unidirectional field near operating point.Slide21
Single Split-phase Motor Model:
General model divided by the dotted line into rotor parameters for run direction on left and opposite direction on right. Stator
L
PRM
divided to show magnetic coupling on each side is half of B-field.
The net mechanical power and torque come from the difference in energies delivered to the two rotor resistances.For approximate calculation, it is possible to move the RS and LS components past the R
CORE and LPRM connections.Slide22
Fitting Parameters Experimentally:
Look at locked rotor and synchronous operating conditions
Locked Rotor Condition S = 0 – No-load, Synchronous Operation