Transcript Microelectromechanical Devices

ECE 8830 - Electric Drives
Topic 15: Permanent Magnet Synchronous
and Variable Reluctance Motors
Spring 2004
Introduction
Permanent magnet synchronous motors
have the rotor winding replaced by
permanent magnets. These motors have
several advantages over synchronous
motors with rotor field windings, including:




Elimination of copper loss
Higher power density and efficiency
Lower rotor inertia
Larger airgaps possible because of larger
coercive force densities.
Introduction (cont’d)
Some disadvantages of the permanent
magnet synchronous motor are:




Loss of flexibility of field flux control
Cost of high flux density permanent
magnets is high
Magnetic characteristics change with time
Loss of magnetization above Curie
temperature
Permanent Magnets
Advances in permanent magnetic materials
over the last several years have had a
dramatic impact on electric machines.
Permanent magnet materials have special
characteristics which must be taken into
account in machine design. For example, the
highest performance permanent magnets
are brittle ceramics, some have chemical
sensitivities, all have temperature sensitivity,
and most have sensitivity to demagnetizing
fields. Proper machine design requires
understanding the materials well.
B-H Loop
A typical B-H loop for a permanent magnet
is shown below. The portion of the curve in
which permanent magnets are designed to
operate in motors is the top left quadrant.
This segment is referred to as the
“demagnetizing curve” and is shown on
the next slide.
Demagnetizing Curve
Demagnetizing Curve (cont’d)
The remnant flux density Br will be
available if the magnet is short-circuited.
However, with an air gap there will be
some demagnetization resulting in the
no-load operating point, B’. Slope of noload line is smaller with a larger air gap.
With current flowing in the stator, there is
further demagnetization of the permanent
magnet causing the operating point to
shift to C’ at full load.
Demagnetizing Curve (cont’d)
Transients or machine faults can lead to a
worst-case demagnetization as shown which
results in permanent demagnetization of the
permanent magnet. The recoil line following
the transient is shown and shows a reduced
flux density compared to the original line. It
is clearly important to control the operation
of the magnets to keep the operating point
away from this worst-case demagnetization
condition.
Permanent Magnetic Materials


Alnico - good properties but too low a
coercive force and too square a B-H loop
=> permanent demagnetization occurs
easily
Ferrites (Barium and Strontium) - low cost,
moderately high service temperature
(400C), and straight line demagnetization
curve. However, Br is low => machine
volume and size needs to be large.
Permanent Magnet Materials (cont’d)


Samarium-Cobalt (Sm-Co) - very good
properties but very expensive
(because Samarium is rare)
Neodymium-Iron-Boron (Nd-Fe-B) very good properties except the Curie
temperature is only 150C
Permanent Magnet Materials (cont’d)
PM Motor Construction
There are two types of permanent magnet
motor structures:
1) Surface PM machines
- sinusoidal and trapezoidal
2) Interior PM machines
- regular and transverse
Circuit Model of PM Motor (cont’d)
Based on the recoil line, we can write:
 0
 F  ( F0 )
 Prc
where Prc, the permeance, is the slope of
the line. From this equation we can write:
r  Prc F0
Equivalent Circuit Model of PM Motor
Rearranging the slope equation, we get:
F  F0 

Prc
This equation suggests the following
equivalent circuit for a permanent magnet:
Equivalent Circuit Model of PM
Motor (cont’d)
It can be shown that the mmf, flux and
permeance are the mathematical duals
of current, voltage, and inductance,
respectively. Therefore, the following
electrical equivalent circuits can be used
to represent the magnetic circuit:
Equivalent Circuit Model of PM
Motor (cont’d)
We can now use this equivalent circuit
of the permanent magnets on the rotor
and the previous equivalent equivalent
circuits of the synchronous motor to
develop a set of qd0 equivalent circuits
for the permanent magnet synchronous
motor. Assuming the PM synchronous
motor has damper cage windings but
no g winding, the qd0 equivalent
circuits are as shown on the next slide.
Equivalent Circuit Model of PM
Motor (cont’d)
Equivalent Circuit Model of PM
Motor (cont’d)
Here the PM magnet inductance Lrc can be
lumped with the common d-axis mutual
inductance of the stator and damper
windings, and the combined d-axis mutual
inductance indicated by Lmd. Also, the
current i’m is the equivalent magnetizing
current for the permanent magnet
referred to the stator side.
qd0 Equations for Permanent
Magnet Synchronous Motor
The qd0 equations for a permanent magnet
motor are given in the table below:
qd0 Equations for Permanent
Magnet Synchronous Motor (cont’d)
qd0 Equations for Permanent
Magnet Synchronous Motor (cont’d)
The developed electromagnetic torque
expression has three components:
1) A reluctance component (which is
negative for Ld<Lq)
2) An induction component (which is
asynchronous torque)
3) An excitation component from the
field of the permanent magnet.
qd0 Equations for Permanent
Magnet Synchronous Motor (cont’d)
The mutual flux linkages in the q- and
d-axes may be expressed by:
mq  Lmq (iq  ikq' )
md  Lmd (id  i  i )
'
m
'
kd
The winding currents can be expressed (as
before) as:
'

q  mq
kq  mq
'
ikq 
iq 
'
L
Lls
lkq
id 
d  md
Lls
ikd' 
kd'  md
L'lkd
qd0 Equations for Permanent
Magnet Synchronous Motor (cont’d)
Combining these equations gives:
md
where
 d kd'
' 
 LMD 
 '  im 
 Lls Llkd

1
1
1
1

 ' 
.
LMD Lls Llkd Lmd
Similar expressions for mq and LMQ can
be written for the q-axis.
qd0 Equations for Permanent
Magnet Synchronous Motor (cont’d)
Under steady state conditions where =e as
in the case of Ef in the wound field
synchronous motor, we can express em’ or
xmdim’ by Em, the permanent magnet’s
excitation voltage on the stator side. If the
stator resistance is neglected and the Ef term
in the earlier torque expression replaced by
Em, the torque of a permanent magnet
synchronous motor in terms of the rms phase
voltage Va at its terminal can be written as:

 1
 P  Va Em
1 
2
Te  3 
sin   Va 

 sin 2 



 2 e   X d
 Xq Xd 
Simulation of PM Synchronous Motor
A line-start permanent magnet motor
has magnets embedded in the rotor to
provide synchronous excitation and a
rotor cage provides induction motor
torque for starting. Thus it is a high
efficiency synchronous motor with selfstart capability when operated from a
fixed frequency voltage source.
Simulation of PM Synchronous
Motor (cont’d)
The simulation equations for the PM
synchronous motor are given below:
Simulation of PM Synchronous
Motor (cont’d)
Simulation of PM Synchronous
Motor (cont’d)
The Simulink file s4 in Ch.7 Ong implements a
simulation of a line-start 3 PM synchronous
motor connected directly to a 60Hz, 3 supply
of rated voltage. The overall block diagram is:
Simulation of PM Synchronous
Motor (cont’d)
This slide and the next few slides show the
internal blocks of the Simulink model.
Simulation of PM Synchronous
Motor (cont’d)
Simulation of PM Synchronous
Motor (cont’d)
Simulation of PM Synchronous
Motor (cont’d)
Simulation of PM Synchronous
Motor (cont’d)
Simulation of PM Synchronous
Motor (cont’d)
Simulation of PM Synchronous
Motor (cont’d)
Trapezoidal Surface Magnet Motor
A trapezoidal surface permanent magnet
motor is the same as a sinusoidal PM
motor except the 3 winding has a
concentrated full-pitch distribution instead
of a sinusoidal distribution.
Trapezoidal Surface Magnet Motor
(cont’d)
This 2-pole motor has a gap in the rotor
magnets to reduce flux fringing effects
and the stator has 4 slots per phase
winding per pole. As the machine rotates
the flux linkage will vary linearly except
when the magnet gap passes through the
phase axis. If the machine is driven by a
prime mover, the stator phase voltages
will have a trapezoidal wave shape as
shown on the next slide.
Trapezoidal Surface Magnet Motor
(cont’d)
Trapezoidal Surface Magnet Motor
(cont’d)
An electronic inverter is required to
establish a six-step current wave to
generate torque. With the help of an
inverter and an absolute-position sensor
mounted on the shaft, both sinusoidal
and trapezoidal SPM motors can serve as
brushless dc motors (although the
trapezoidal SPM motor gives closer dc
machine-like performance).
Synchronous Reluctance Motor
A synchronous reluctance motor has the
same structure as that of a salient pole
synchronous motor except that it does
not have a field winding on the rotor.
Synchronous Reluctance Motor (cont’d)
The stator has a 3, symmetrical winding
which creates a sinusoidal rotating field in
the air gap. This causes a reluctance torque
to be created on the rotor because the
magnetic field induced in the rotor causes it
to align with the stator field in a minimum
reluctance position. The torque developed in
this type of motor can be expressed as:

 P   2 ( Lds  Lqs )
Te  3    s
sin 2 


2 Lds Lqs
 2 

Synchronous Reluctance Motor (cont’d)
The reluctance torque stability limit can be
seen to occur at    / 4 (see figure below).
Synchronous Reluctance Motor (cont’d)
Iron laminations separated by non-magnetic
materials increases reluctance flux in the
qe-axis. With proper design, the reluctance
motor performance can approach that of an
induction motor, although it is slightly heavier
and has a lower power factor. Their low cost
and robustness has seen them increasingly
used for low power applications, such as in
fiber-spinning mills.
Variable Reluctance Motors
A variable reluctance motor has double
saliency, i.e. both the rotor and stator have
saliency. There are two groups of variable
reluctance motors: stepper motors and
switched reluctance motors. Stepper motors
are not suitable for variable speed drives.
Ref: A. Hughes, “Electric Motors and Drives”, 2nd. Edn. Newnes
Switched Reluctance Motors
The structure of a switched reluctance
motor is shown below. This is a 4-phase
machine with 4 stator-pole pairs and 3
rotor-pole pairs (8/6 motor). The rotor has
neither windings nor permanent magnets.
Switched Reluctance Motors (cont’d)
The stator poles have concentrated
winding rather than sinusoidal winding.
Each stator-pole pair winding is excited
by a converter phase, until the
corresponding rotor pole-pair is aligned
and is then de-energized. The stator-pole
pairs are sequentially excited using a
rotor position encoder for timing.
Switched Reluctance Motors (cont’d)
The inductance of a stator-pole pair and
corresponding phase currents as a function
of angular position is shown below.
Switched Reluctance Motors (cont’d)
Applying the stator pulse when the
inductance profile has positive slope
induces forward motoring torque.
Applying the stator pulse during the time
that the inductance profile has negative
slope induces regenerative braking
torque.
A single phase is excited every 60 with
four consecutive phases excited at 15
intervals.
Switched Reluctance Motors (cont’d)
The torque is given by:
1 2
Te  mi
2
where m=inductance slope and
i=instantaneous current.
Switched Reluctance Motors (cont’d)
Switched reluctance motors are growing in
popularity because of their simple design and
robustness of construction. They also offer
the advantages of only having to provide
positive currents, simplifying the inverter
design. Also, shoot-through faults are not an
issue because each of the main switching
devices is connected in series with a motor
winding. However, the drawbacks of this type
of motor are the pulsating nature of their
torque and they can be acoustically noisy
(although improved mechanical design has
mitigated this problem.)