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ECE 8830 - Electric Drives
Topic 12: Scalar Control of AC Induction
Motor Drives
Spring 2004
Introduction
Scalar control of an ac motor drive is only
due to variation in the magnitude of the
control variables. By contrast vector control
involves the variation of both the
magnitude and phase of the control
variables.
Voltage can be used to control the air gap
flux and frequency or slip can be used to
control the torque. However, flux and
torque are functions of frequency and
voltage, respectively but this coupling is
disregarded in scalar control.
Introduction (cont’d)
Scalar control produces inferior dynamic
performance of an ac motor compared to
vector control but is simpler to implement.
In variable-speed applications in which a
small variation of motor speed with loading
is tolerable, a scalar control system can
produce adequate performance. However, if
precision control is required, then a vector
control system must be used.
Speed Control
Three simple means of limited speed
control for an induction motor are:
1) Reduced applied voltage magnitude
2) Adjusting rotor circuit resistance
(suitable for a wound rotor machine
and discussed earlier)
3) Adjusting stator voltage and frequency
These are discussed in section 9.2 Ong
text and are not presented further here.
Constant Air Gap Flux
Generally, an induction motor requires a
nearly constant amplitude of air gap flux
for satisfactory working of the motor.
Since the air gap flux is the integral of the
voltage impressed across the magnetizing
inductance, and assuming that the air gap
voltage is sinusoidal,
ag   vag dt   Vag sin  tdt  
Vag

cos  t
Thus a constant volts/Hz ratio results in a
constant air gap flux.
Constant Air Gap Flux (cont’d)
The torque-speed curves with a constant
air gap flux at different excitation
frequencies are shown below:
Constant Air Gap Flux (cont’d)
From the curves on the previous slide, it
can be seen that we will obtain the same
torque at the same value of slip speed if
we operate at a constant air gap flux. This
is the basis for constant volts/Hz control
of an induction motor. This type of control
may be implemented either in open loop
or in closed loop.
Constant Air Gap Flux (cont’d)
A set of 6-step voltage waveforms
illustrating constant volts/Hz is shown below:
Ref: D.W. Novotny and
T.A. Lipo, “Vector
Control and Dynamics
of AC Drives”
Open Loop Volts/Hz Control of a
Voltage-Fed Inverter
Three regions of operation for the induction
motor are possible:
1) Holds slip speed constant and regulates
stator current to obtain constant torque.
2) Holds stator voltages at its rated value
and regulates stator current to obtain
constant power.
3) Holds stator voltage at its rated value
and regulates slip speed just below its
pull-out torque value.
Open Loop Volts/Hz Control of a
Voltage-Fed Inverter (cont’d)
Open Loop Volts/Hz Control of a
Voltage-Fed Inverter (cont’d)
Open Loop Volts/Hz Control of a
Voltage-Fed Inverter (cont’d)
The open loop volts/Hz control of an induction
motor is very popular because of its simplicity.
A block diagram of such a control system is
shown below:
Open Loop Volts/Hz Control of a
Voltage-Fed Inverter
The power circuit comprises:
1) A diode rectifier supplied by either a
single-phase or three-phase supply
2) An LC filter
3) A PWM voltage-fed inverter.
The primary control variable is the frequency
er. The commanded phase voltage Vs* is
generated by a gain stage based on the
speed e to maintain a constant air gap flux.
Open Loop Volts/Hz Control of a
Voltage-Fed Inverter (cont’d)
As the frequency becomes small at low
speed, the voltage drop across the stator
resistance can no longer be neglected
and so a boost voltage V0 needs to be
supplied allowing the rated flux (and thus
the full torque) to be available down to
zero speed. The effect of the boost
voltage is negligible at higher
frequencies.
Open Loop Volts/Hz Control of a
Voltage-Fed Inverter (cont’d)
The drive’s steady state performance for a
fan or pump-type load (TL=Kr2) is shown
below:
Open Loop Volts/Hz Control of a
Voltage-Fed Inverter (cont’d)
As the frequency is increased the speed
increases almost proportionally and we
move along the load torque curve from
points 1->2->3 … etc. moving smoothly
through the different operating modes of
the induction motor.
Open Loop Volts/Hz Control of a
Voltage-Fed Inverter (cont’d)
Let us now look at the effects of dynamic
variations in load torque and line voltage.
Suppose the load torque is changed from
TL to TL’ for the same frequency
command, the speed will drop slightly
from r to r’. This type of speed variation
can easily be tolerated by a fan or pump.
Now suppose the operating point is a and
the line voltage drops so that the
operating point moves to b. Again the
speed is tolerable for some applications.
Open Loop Volts/Hz Control of a
Voltage-Fed Inverter (cont’d)
The safe acceleration/deceleration
characteristics are shown below:
Open Loop Volts/Hz Control of a
Voltage-Fed Inverter (cont’d)
Assume a pure inertia type load and the
motor initially operating at point 1. A small
step increase in command frequency will
initially move the operating point to point 2
(the rated torque) and then steadily increase
to point 3. The frequency can then be
decreased slightly to achieve the steady state
operating point 4. All of these transitions are
done in a gradual manner to prevent the
machine from becoming unstable.
Decrementing the frequency command in a
step will shift the operating point from 1 to 5
due to a negatively developed torque.
Open Loop Volts/Hz Control of a
Voltage-Fed Inverter (cont’d)
The motor torque and speed are related by:
Te  TL
r  
dt
J
where
J = moment of inertia,
Te = torque developed by motor,
and TL = load torque
With the rated Te the slope of the
acceleration curve dr/dt is determined by J.
The higher J, the smaller the slope.
Open Loop Volts/Hz Control of a
Voltage-Fed Inverter (cont’d)
Typical Volts/Hz drive performance is shown
below:
Energy Savings with Variable
Frequency Drives
Considerable energy savings can be
achieved with variable frequency drives
compared to constant frequency drives
(see figure below and text).
Closed Loop Volts/Hz Control with
Slip Regulation
An improvement over open loop Volts/Hz
control is closed loop Volts/Hz control with
slip regulation (see block diagram below).
Closed Loop Volts/Hz Control with
Slip Regulation (cont’d)
Here the speed loop error generates a slip
command sl* via a proportional-integral
controller and limiter. This slip command
is added to the feedback speed signal r
to get the frequency command e* which,
in turn, generates the voltage command
through a volts/Hz function generator.
Since slip is proportional to torque at
constant flux, this approach may be
considered as open loop torque control
within a speed control loop.
Closed Loop Volts/Hz Control with
Slip Regulation (cont’d)
If a step-up speed command is provided,
the motor accelerates freely until a slip limit
(corresponding to the motor’s torque limit)
is achieved and then settles down to the
steady state load-limited torque.
If r* is stepped down, the drive behaves as
a generator and decelerates with constant
negative slip - sl*. However, the value of sl* must be limited to a safe margin below
the slip speed corresponding to the pull-out
torque point.
Closed Loop Volts/Hz Control with
Slip Regulation (cont’d)
Since the slip speed is relatively small
compared to the rotor speed, this mode of
operation requires precise measurement
of the rotor speed. Also, in negative slip
mode of operation, the regenerated power
must either be dissipated in a braking
resistor or fed back to the ac mains.
One disadvantage of this approach is that
the flux may drift due to load torque or
supply voltage variations.
Closed Loop Volts/Hz Control with
Slip Regulation (cont’d)
A speed control system with closed loop
torque and flux control is shown below.
However, additional feedback control loops
increases system complexity and potential
stability problems.
Current-Regulated Voltage-Fed
Inverter Drive
Instead of controlling inverter voltage by
the flux loop, the stator current can be
controlled which has the benefit of
providing inherent overcurrent protection
to the switching devices as well as
achieving direct control of the motor
torque and air gap flux.
A current-regulated VSI drive, with torque
and flux control in an outer loop and
hysteresis-band current control in the inner
loop, is shown on the next slide.
Current-Regulated Voltage-Fed
Inverter Drive (cont’d)
Flux control loop -> stator current amplitude
Torque control loop -> frequency command
Only need 2 current sensors since ia+ib+ic =0
(for an isolated motor neutral).
Current-Regulated Voltage-Fed
Inverter Drive (cont’d)
The performance of the drive for subway
traction application is shown below:
Traction Drives with Parallel
Machines
Multiple voltage-fed inverters can be
operated in parallel. An example of such a
system for a locomotive drive is discussed
in the Bose text, pp. 348-349.
Current-Fed Inverter Control
Some of the same principles for control
of voltage-fed inverters can be applied to
current-fed inverters. However, the
current-fed inverter cannot be operated
open loop.
The simplest implementation of a closed
loop control system for a current-fed
inverter, allowing independent control of
dc link current Id and slip sl, is shown on
the next slide.
Current-Fed Inverter Control (cont’d)
Current-Fed Inverter Control (cont’d)
In this implementation, the fed back rotor
speed r and command slip sl* are added to
give the command frequency e*. The dc link
current Id is controlled by a feedback loop
that controls the output voltage of the
rectifier, Vd.
With +ve slip, acceleration occurs; with -ve
slip, Vd and VI both become -ve and power is
fed back to the source.
The torque can be controlled either by Id or
sl. However, no flux control is possible with
this control scheme.
Current-Fed Inverter Control (cont’d)
Speed and flux control can be achieved in
a current-fed inverter using the below
control system.
Current-Fed Inverter Control (cont’d)
In this case the speed control loop
controls the torque by slip control (as
before) but also controls the current Id*
by a pre-computed function generator to
maintain a constant flux. This open loop
approach is satisfactory but the machine
flux may still vary with parameter
variations. An independent flux control
loop (as shown earlier for the voltage-fed
inverter) can be implemented for tighter
flux control if desired.
Current-Fed Inverter Control (cont’d)
A volts/Hz implementation for a current-fed
inverter is shown below:
A particular advantage of this approach is
that the motor flux is unaffected by line
voltage variation.
Efficiency Optimization Control by
Flux Program
Normally a motor is operated at its rated
flux because the developed torque is high
and the transient response is fast. Under
light loads, this can lead to poor efficiency
of the drive. The rotor flux can be lowered
at light loads so that the motor losses are
reduced and the conversion efficiency of
the drive optimized. See text pp. 352-254
(Bose) to see how this may be achieved.