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ECE 8830 - Electric Drives


Title: Microelectromechanical Devices Author: Ankineedu Maganti Last modified by: Pritpal Singh Created Date: 8/4/2003 1:49:55 AM Document presentation format – PowerPoint PPT presentation

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Title: ECE 8830 - Electric Drives

ECE 8830 - Electric Drives
Topic 3 Induction Motor Modeling -
Steady State Spring 2004
  • Induction machines are the most widely used of
    all electric motors. They offer the following
    attractive features
  • Generally easy to build and cheaper than
    corresponding dc or synchronous motors
  • Rugged and require little maintenance
  • Offer reasonable asynchronous performance
  • A manageable torque-speed curve
  • Stable operation under load
  • Generally satisfactory efficiency
  • Range in size from few Watts to several MW

Introduction (contd)
  • Some disadvantages of induction motors are
  • Speeds not as easily controlled as dc motors
  • Draw large starting currents, typically 6-8 x
    their full load values
  • Operate with a poor lagging power factor when
    lightly loaded

Introduction (contd)
  • New designs for high performance induction
    machines, such as in high speed motors for gas
    compressors, will be required to have new
    characteristics from existing machines, it is
    important to have a good fundamental
    understanding of these types of machines.
  • Goal To develop a simple model for the
    induction machine that is useful for control and

Structure of an Induction Machine
  • Two types of induction machine
  • Wound rotor or squirrel cage rotor

Rotating Magnetic Field and Slip
  • We previously showed that a balanced set of
    three-phase currents flowing in a set of
    symmetrically placed, three-phase stator windings
    produces a rotating mmf given by
  • eq. (6.1) Ong, eq. (2.9) Bose
  • where ?ae is the electrical angle measured
    from the a-phase axis and ?e is the angular speed
    of the stator mmf in electrical radians/second.

Rotating Magnetic Field and Slip (contd)

Rotating Magnetic Field and Slip (contd)
  • In mechanical radians/sec. the synchronous
    speed is related to the electrical speed by
  • If the rotor is rotating at an angular speed
    ?rm the slip speed is simply equal to ?sm - ?rm.
    The slip,s, is the normalized slip speed and is
    given by

Torque Production
  • The torque produced by an induction motor may
    be derived and expressed by the following
    equation (see ref. 1 in Bose)
  • where P of poles
  • l axial length of motor
  • r radius of motor
  • Bp peak air-gap flux density
  • Fp peak value of rotor mmf
  • and

Per-Phase Equivalent Circuit Model
  • A per-phase transformer-like equivalent
    circuit is shown below

Per-Phase Equivalent Circuit Model (contd)
  • Synchronously rotating air gap flux wave
    generates a counter emf Vm. This in turn is
    converted to a slip voltage in the rotor phase,
    Vr nsVm, where nrotorstator turns ratio, and
    snormalized slip.
  • Stator terminal voltage, Vs Vm VRs VLls
  • where VRsvoltage drop across stator
    resistance (Rs) and VLlsvoltage drop across
    stator leakage inductance (Lls).

Per-Phase Equivalent Circuit Model (contd)
  • Excitation current, I0 Ic Im
  • where Ic is core loss current (Vm/Rm)
  • and Im is magnetizing current (Vm/ )
  • Rotor-induced voltage, Vr VRr VLl
  • where VRr voltage drop across rotor resistance
  • and VLl voltage drop across rotor leakage
  • inductance
  • The induced voltage in the rotor leads to a rotor
  • current Ir at slip frequency ?sl.

Per-Phase Equivalent Circuit Model (contd)
  • The stator current, IS I0 Ir
  • where Ir is the rotor-reflected current
    induced in the stator.

Per-Phase Equivalent Circuit Model (contd)
Per-Phase Equivalent Circuit Model (contd)

Per-Phase Equivalent Circuit Model (contd)
  • Torque expression can be written as
  • where peak value of air gap flux
  • linkage/pole
  • and peak value of rotor current

Per-Phase Equivalent Circuit Model Power
  • Input Power where cos? is input PF
  • Stator copper loss
  • Rotor copper loss
  • Core loss
  • Power across air gap
  • Output power
  • Shaft Power where PFw is friction and
    windage power loss

Per-Phase Equivalent Circuit Model Torque
  • The torque can be expressed as
  • where is the rotor
  • mechanical speed (radians/sec.)

Per-Phase Equivalent Circuit Model Torque
Expression (contd)
  • Using a little algebra (see Bose) it can
  • be shown that the torque may be further
  • expressed as
  • where .
  • This torque expression is similar to that for
  • a dc motor, where Im magnetizing
  • component of stator current and Ia
  • armature component of stator current.

Simplified Per-Phase Equivalent Circuit
  • A simplified circuit dropping Rm and shifting
    Lm to the input is applicable to integral
    horsepower machines.
  • Performance of this equivalent circuit is
    typically within 5.

Simplified Per-Phase Equivalent Circuit Model
  • The current Ir in this circuit is given by
  • The torque of the motor using this circuit
  • is given by

Example of Calculating Efficiency of an Induction
  • Example 5.1 Krishnan

Flowchart for Computing Steady State Performance
of Induction Motor

Ref R. Krishnan, Electric Motor Drives
Torque-Speed Curve of Induction Motor
  • The torque-speed curve as a function of slip
    can be calculated from the equation two slides

Torque-Speed Curve of Induction Motor (contd)
  • Three regions in torque-speed curve
  • 1) Plugging (braking) region (1ltslt2)
  • Rotor rotates opposite to direction of air
    gap flux. Can happen, for example, if stator
    supply phase sequence reversed while rotor is
  • 2) Motoring region (0ltslt1)
  • Te0 at s0. As s increases (speed decreases),
    Te increases until max. torque (breakdown torque)
    is reached. Beyond this point, Te decreases with
    increasing s.

Torque-Speed Curve of Induction Motor (contd)
  • 3) Regenerating Region (slt0)
  • Here the induction machine acts as a
    generator. Rotor moves faster than air gap flux
    resulting in negative slip.

Torque-Speed Curve of Induction Motor (contd)

Ref R. Krishnan, Electric Motor Drives
Performance Characteristics of Induction Motor

Ref R. Krishnan, Electric Motor Drives
Starting Torque of Induction Motor
  • The starting torque of an induction motor is
    given by substituting for s1 and is given by

Starting Torque of Induction Motor (contd)
  • This torque can be enhanced for line start
    motors (ones started directly with full line
    voltage) by increasing the rotor resistance. This
    can be achieved by connecting external resistors
    in the case of slip ring rotors. However, with
    squirrel cage rotors where the rotor is shorted,
    deep bar or double-cage rotors can be used to
    increase starting torque.

Characterizing Induction Motors
  • One way to characterize an induction motor is
    with the No-load/blocked rotor tests which yield
    the per-phase equivalent circuit model shown
    earlier (see figure below).

Characterizing Induction Motors (contd)
  • We can characterize an induction motor with
    the variables Rs, Lls, M, Llr, Rr determined
    through lab tests using balanced 3? excitation.
    This circuit described the impedance perceived
    per phase on a line-neutral connected machine.
    Everything in the dashed box is a rotor quantity
    that has been referred to the stator by the
    ideal transformer in the machine model. From now
    on, assume that Llr, Rr and iar are referred to
    the stator.

Characterizing Induction Motors (contd)
  • No-Load Test (s0)
  • Equivalent circuit

Ref R. Krishnan, Electric Motor Drives
Characterizing Induction Motors (contd)
  • No-Load Test (s0) yields
  • In sinusoidal steady state, ignoring
  • But -ias (ibsics)
  • ?
  • From transformer model

Characterizing Induction Motors (contd)
  • Blocked rotor test (s1) yields estimates of Lls
    and Llr. Equivalent circuit at standstill is
    shown below

Ref R. Krishnan, Electric Motor Drives
Characterizing Induction Motors (contd)
  • Ohmmeter/Power loss tests give Rs
  • and Rr.
  • So, with Llr, Rr and all irs understood as
  • referred rotor quantities, the stator-side
  • tests identify all the model parameters for
  • the induction motor.

Example of Determining Induction Motor Model
  • Example 5.2 Krishnan

NEMA Classification of Induction Motors
  • The National Electrical Manufacturers
    Association (NEMA) has classified induction
    motors based on their torque-slip
    characteristics. (see text for details)

Circuit Model of a Three-Phase Induction Machine
(State-Space Approach)

Voltage Equations
  • Stator Voltage Equations

Voltage Equations (contd)
  • Rotor Voltage Equations

Flux Linkage Equations

Model of Induction Motor
  • To build up our simulation equation, we could
    just differentiate each expression for ?, e.g.
  • But since Lsr depends on position,
  • which will generally be a function of time,
    the trig. terms will lead to a mess!
  • Parks transform to the rescue!

first row of matrix