Absfmct- Permanent magnet (PM) motors are attracting growing at- tention for a wide variety of industrial applications. In traction and spindle drives, constant power operation and wide speed range are de- sirable. With dc motor drives, these are achieved by the appropriate reduction of the field current as the speed increases. In the PM mo- tor, direct control of the magnet flux is not available. The air-gap flux, however, can be weakened by the direct axis armature current. In this operation, magnet demagnetization due to the direct axis armature reac- tion must be prevented, because the magnet torque decreases irreversibly if this demagnetization is very large. The current vector control method of PM motors is examined to expand the operating limits considering the inverter capacity. This control method is optimum in the sense of deriving maximum output torque within the voltage and current con- straints. The effects of motor parameters are examined by the computer simulation. The operating limits are examined considering the demag- netization of the permanent magnet.
Trang 1866 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL 26, NO 5 , SEPTEMBERIOCTOBER 1990
Magnet Motor by Current Vector Control
Considering Inverter Capacity
Absfmct- Permanent magnet ( P M ) motors are attracting growing at-
tention for a wide variety of industrial applications In traction and
spindle drives, constant power operation and wide speed range are de-
sirable With dc motor drives, these are achieved by the appropriate
reduction of the field current as the speed increases In the P M mo-
tor, direct control of the magnet flux is not available The air-gap flux,
however, can be weakened by the direct axis armature current In this
operation, magnet demagnetization due t o the direct axis armature reac-
tion must be prevented, because the magnet torque decreases irreversibly
if this demagnetization is very large The current vector control method
of P M motors is examined t o expand the operating limits considering
the inverter capacity This control method is optimum in the sense of
deriving maximum output torque within the voltage and current con-
straints The effects of motor parameters are examined by the computer
simulation The operating limits are examined considering the demag-
netization of the permanent magnet
I INTRODUCTION RMANENT MAGNET (PM) motors are attracting
p" growing attention for a wide variety of industrial appli-
cations The maximum steady-state torque of the PM motor
depends on the continuous armature current rating The maxi-
mum speed attainable at this torque is limited by the available
output voltage of the inverter
In traction and spindle drives, constant power operation and
wide speed range are desirable With dc motor drives, these
are achieved by the appropriate reduction of the field current
as the speed increases In the PM motor, direct control of
the magnet flux is not available The air-gap flux, however,
can be weakened by the demagnetizing current in the direct
axis [ 11-[4] This control method is called "flux-weakening.''
In this operation, magnet demagnetization due to the direct
axis armature reaction must be prevented because the magnet
torque decreases irreversibly if this demagnetization is very
large
In this paper, the armature current control method expand-
ing the operating limits is examined under the constant inverter
capacity The effects of motor parameters such as d- and q-
Paper IPCSD 90-2 1, approved by the Electric Machines Committee of the
IEEE Industry Applications Society for presentation at the 1989 Industry Ap-
plications Society Annual Meeting, San Diego, CA, October 1-5 Manuscript
released for publication March 6, 1990
S Morimoto, Y Takeda, and T Hirasa are with the De7artment of Elec-
trical Engineering, College of Engineering, University of Osaka Prefecture,
4-804 Mom-Umemachi, Sakai, 591 Japan
K Taniguchi is with the Department of Electrical Engineering, College of
Engineering, Osaka Institute of Technology, 5-16-1 Omiya, Asah-ku, Osaka,
535 Japan
IEEE Log Number 9037046
d - a x i s
Fig 1 Basic vector diagram for PM motor
axis inductances, flux linkage of the permanent magnet, and
so on are examined by computer simulation Furthermore, the control method and the output characteristics are examined considering the demagnetization of the permanent magnet due
to the direct axis armature reaction
11 BASIC EQUATIONS OF PM MOTOR
In the d-q coordinates which rotate synchronously with an electrical angular velocity w , the steady-state voltage equation
is expressed as follows:
d- and q-axis components of armature current,
d- and q-axis components of terminal voltage,
flux linkage of permanent magnet per-phase (rms),
armature resistance,
d- and q-axis components of armature self-
inductances
=
Erom ( l ) , the basic vector diagram shown in Fig 1 is ob- tained The d- and q-axis components of the armature current are represented as
i d = -Ia sin0 i, = I a cos0 (2)
where I a = die, I, is the armature current per-phase (rms), and /3 is the leading angle of armature current from the q-axis The power P and the terminal voltage V a are given by
P = + ( L d - L q ) i d i g } (3)
V a - - J (W$a + W L d i d + Ri,)2 + ( -wLqiq + R i d ) * (4)
0093-9994/90/09OO-0866$01 OO 0 1990 IEEE
Trang 2To examine the demagnetization of the permanent magnet due
to the d-axis armature reaction, the demagnetizing coefficient
C: is defined as the ratio of the d-axis armature reaction flux
to the permanent magnet flux linkage [6];
If E is large and the coercivity of the magnet is not enough,
then the permanent magnet demagnetization may create a se-
rious problem and the magnet torque decrease irreversibly
In the per-unit expression, these basic equations are rewrit-
ten as follows, where the armature resistance is neglected as
the PM motor is used comparatively in high speed range and
I
- " -
Voltage-I imit Current-limit
el I ipse
-_ -.*
Increasing swed
-
Current-limit circle and voltage-limit ellipse for interior
tor
magnet mo-
Fig 2 shows the current-limit circle and the voltage-limit el- lipse in the id-iq plane The voltage-limit ellipse becomes
small as the speed w increases The armature current vector
i(id, i q ) satisfying both conditions of the current limit and the
voltage limit must be inside the current-limit circle and the voltage-limit ellipse For example, the available armature cur- rent vector at w = W O is inside ABCDEF (hatched area) in
(7)
where
resents its rated value
The salient coefficient p represents the saliency of the PM
motor[6] As the relative permiability of a permanent magnet
is very nearly unity, the magnet space behaves like an air
The surface magnet motor exhibits negligible saliency, so that
interior magnet motor exceeds the d-axis inductance; hence
p > 1 In this paper, the surface magnet motor and the interior
magnet motor are examined
III ARMATURE CURRENT VECTOR CONSIDERING INVERTER
CAPACITY Considering the inverter capacity, the armature current I,
and the terminal voltage Vu are limited as follows:
The current limit I l h is decided by the continuous armature
current rating and the available output current of the inverter
The voltage limit Vlim is decided by the available maximum
output voltage of the inverter In this paper, the current and
voltage limits are set as the ratings ( I l h = 1.0 pu, VI^ = 1.0
pu) for the simulation From (2) and (9), the current-limit
circle is given by
i i + i i = I:,
IV OPTIMUM CURRENT VECTOR CONTROL From (6), the torque is represented as
From this equation, the armature current vector il(id1, i q l )
producing maximum torque per current is derived as follows
[51:
(14)
id1 = 0 i q l = I , ,
where
* ( 1 5 ) -Eo + JE; + 8 ( p - 1)2X:Zi
01 =sin-'
The maximum torque-per-ampere current vector trajectory is shown in Fig 3 If the armature current I, is limited by I l i m ,
the maximum torque is obtained at point A1 in Fig 3 The d-
and q-axis components of this point are derived by substituting
reaches its limited value Vlim at w = w1, the motor can be accelerated by this maximum torque This maximum speed of the constant torque operation is given by
From (7) and ( l o ) , the voltage-limit ellipse is given by From (6) and (12), the armature current vector i2(id2, iq2)
producing maximum output power under the voltage-limit condition is derived as follows, where the current-limit con-
Trang 3868 IEEE TRANSACTIONS O N INDUSTRY APPLICATIONS, VOL 26, NO 5 SEPTEMBERIOCTOBER 1990
itaxiaua Voltage-1 iaited
aaximm-output 2 o'q torque-per-amp trajectory , J/ trajectory
P =1.0
Voltage-1 imi t
- 2 0 1
(a)
Uax i mu
torque-per-aap
trajectory 2 0Iq Voltase- I imi ted\
P =2.0
Eo'O 6 Xd=0.75
e l l i p s e A4(-EO/Xd.0)
-2.0
(b)
Fig 3 Maximum torque-per-ampere current vector trajectory and voltage-
limited maximum-output current vector trajectory for Eo < X,Jlirn (a)
Surface magnet motor ( p = 1) (b) Interior magnet motor ( p > 1)
dition is not considered,
where
I P f l
The current vector trajectory of the voltage-limited maximum-
output is shown in Fig 3 The current vector approaches the
point A4 ( i d = -Eo/Xd,iq = 0 ) as the rotor speed increases
and reaches the current-limit circle at w = w2 (point A2 in Fig
3) The rotor speed w1 is the maximum speed for the constant
torque operation with the maximum torque considering the
current limit The rotor speed w2 is the minimum speed for the
voltage-limited maximum-output operation Below this speed,
the voltage-limited maximum-output operating point cannot
be reached, because the voltage-limited maximum-output tra-
jectory intersects the voltage-limit ellipse outside the current-
Lxiaua torque-per-aap 2 0 7 trajectory
Yo I tage-1 imi ted
a x i a u r o u t p u t
x , 4 5
e l l i p s e
- 2 0 1
Fig 4 Maximum torque-per-amp current vector trajectory and voltage- limited maximum-output current vector trajectory for Eo > Xdlli,,,
DC S U P P ~ Y Inverter
Fig 5 Scheme of flux-weakening control system
limit circle To produce the maximum output power in all speed ranges considering the conditions of both the current and the voltage limits, the optimum current vector is choosen
as follows
(14) The current vector is fixed at A1 in Fig 3
point of the current-limit circle and the voltage-limit ellipse The current vector moves from A1 to A2 along the current- limit circle as the rotor speed increases
current vector moves from A2 to A4 along the voltage-limited
maximum-output trajectory
Region I corresponds to Z , = Z l i , , Vu < Vlim Region
I1 corresponds to Z , = Z l i m , Vu = Vlim Region I11 corre-
sponds to I , < Z l i r n , Vu = I / l i m If &/Xd is larger than Zlimr
the voltage-limited maximum-output trajectory is outside the current-limit circle (see Fig 4) Therefore, Region I11 does
not exist, and the output power becomes zero at w = w3 (point
A3 in Fig 4):
(19) Fig 5 shows the scheme of the flux-weakening control sys- tem in which the current vector is controlled according to the
Vlim
w3 =
Trang 4U2
Region II I Region 111 I
0
- 0 5
, ; '
I
1:b Speed 2 w (PU) 3:O 4
Fig 6 Output power characteristics for surface magnet motor - with
flux weakening; - - - without flux weakening
foregoing algorithm The relationships between the current
commands iC;, i;, the torque command T * , and the rotor speed
w are preliminarily obtained by the simulation based on the
knowledge of the motor parameters These relationships are
stored in the memory of the microprocessor as a lookup table
The current commands are decided by the torque command
and the detected speed using the lookup table The commands
iC; and i; are transformed to the phase current commands i;
and i: using the rotor angle feedback 0 The closed-loop cur-
rent controller is responsible for controlling the PWM volt-
age excitation so that the instantaneous phase currents follow
their commanded values The current commands are always
kept inside the voltage-limit ellipse and the current-limit cir-
cle Therefore, the current regulators are not saturated in all
operating regions, and the resultant currents follow the com-
manded currents
Fig 6 shows the output power characteristics for the sur-
face magnet motor (nonsalient machine: p = 1) The motor
parameters used in Fig 6 are the same in Fig 3(a) The
terminal voltage reaches its limited value at w = w1 Below
this speed, the torque is kept constant and the output power
is proportional to the rotor speed The output power without
the flux-weakening control (id = 0 control) decreases rapidly
over this speed (see the broken lines) On the other hand, the
output power with the flux-weakening control is large and kept
almost constant by controlling the d- and q-axis components
of the armature current according to the rotor speed (see the
solid lines) The operating limits are greatly enlarged by the
optimum current vector control
V EFFECTS OF MOTOR PARAMETERS
Fig 7 shows the effects of the motor parameters such as
Eo and X d If Eo 5 XdZlim (Xd = 0.7, 0.8 in Fig 7), the
output power does not decrease at high speed If EO > XdZlim
(Xd = 0.5, 0.6 in Fig 7), the output power decreases as the
rotor speed increases In the speed range of Fig 7 (w 5 4.0
pu), it can be seen that the output characteristics for x d = 0.6
is the best The same results are obtained in case of the interior
magnet motor ( p > 1) From Fig 7, it has been seen that
the ideal constant power operation can be obtained with the
condition of Eo 2 [7]
Xd=O 6 1.0
b
B 0 6
c
B
d 0.4 0.2
0 1.0 2 0 3 0 4 0
Speed w (PU)
Fig 7 Effects of motor parameters
b
0 6
*:
0.4
0.2
1.0 U4
4
a 0.5 .O
8
L
O O 1.0 2.0 3 0 4 0
S e e d w (PU)
Fig 8 Effects of saliency
Fig 8 shows the effects of saliency The output powers of
the different type motors are nearly the same at high speed range (w > 2.0), but the output power of the interior magnet motor ( p = 2 O or 3 O) is larger than that of the surface magnet motor ( p = 1 O) at low speed range because the reluctance torque is available in the interior magnet motor The maximum values of the demagnetizing coefficient are about 0.8 In some
cases, the permanent magnet is demagnetized irreversibly by the flux-weakening control
VI DEMAGNETIZATION OF PERMANENT MAGNET
If the PM motor is controlled by the foregoing flux- weakening control method, which uses the negative d-axis armature current, it is very important to examine the demagne- tization of the permanent magnet, because the magnet torque decreases irreversibly if the demagnetization is very large Fig 9 shows the equivalent d-axis magnetic circuit for the
PM motor The following nomenclature applies in Fig 9:
po permeability of air,
p r
P u
P l m
P l a
recoil permeability ( G! po)
= P u I m / A r n , where Pu = p O A g / I g , permeance of air gap,
= P / m l m / A m , where P l m = leakage permeance of magnet,
= P I a I m / A m , where p i o = leakage permeance of ar- mature,
Trang 5870 IEEE TRANSACTIONS O N INDUSTRY APPLICATIONS, VOL 26, NO 5 SEPTEMBERIOCTOBER 1990
B Air gap B, B,
Permanent magnet
Armature reaction
Fig 9 Equivalent d-axis magnetic circuit for PM motor
B Load l i n e
.=urllc
Fig 10 Demagnetization curve for rare-earth permanent magnet
I , magnet length,
Am magnet area,
I , air gap length,
A , effective gap area,
H , coercivity,
H , magnetic field intensity by armature reaction
Fig 10 shows the demagnetization curve for a rare-earth
permanent magnet where the sign of magnetic field intensity
H is reversed With the permanent magnet that has a straight
demagnetization curve, such as a rare-earth permanent mag-
net, the recoil line coincides with the demagnetization curve
Therefore, the operating point of the magnet moves along the
demagnetization curve Using the demagnetizing coefficient
C; defined in (8), the operating point ( H , , B,) is given as
follows:
where
x
Ho, Bo
( p u + p l , , ) / p , , leakage factor of MMF, operating point at no-load,
The d-axis armature current can be safely increased until
the resultant flux density at the trailing edge of the magnet
becomes approximately zero This safe operating condition is
represented as follows:
- : without demagnetization-limit
_ _ _ - - : E I i m = o a
-
0 '2.0
-1.0 1.0 2.0 3 0 4 0
Speed w (PU)
Fig 1 1 Output characteristics c0nsiderir.g demagnetization limit
From (8) and (22), the d-axis armature current considering
the demagnetization is limited as follows:
The demagnetization-limit C;lim is given by substituting Bm = 0
in (21):
The leakage factors U , h are larger than 1.0; therefore, Elirn > 1.0 If the demagnetization curve is not straight, the demagnetization-limit Elim may be smaller than 1 O &im must
be carefully desided according to the permanent magnet ma- terial and the design of magnetic circuit
Fig 1 1 shows the output characteristics considering the de-
magnetization limit The d-axis armature current id is limited according to the demagnetization limit As a result, the out- put power decreases at high speed range as the demagnetizing limit decreases Therefore, a magnet material that has a linear demagnetization curve must be used for the PM motor if wide speed range or constant power operation is desirable
VII CONCLUSION
In this paper, the current vector control method for ex- panding the operating limits is examined under the constant inverter capacity On the basis of the simulation, the following conclusions can be obtained
1) The operating limits are greatly expanded by controlling the d- and q-axis components of the armature current accord- ing to the rotor speed
2) The output characteristics are affected by the parame-
ters such as Eo and X d If Eo X d l l i m , the operating limits become very large When Eo X d l l i m , the ideal output char- acteristics can be obtained If Eo > X d l l i m , the output power
is large in the low speed range but the wide speed range cannot
be obtained
3) In the interior magnet motor, in which the q-axis induc-
tance is larger than the d-axis inductance, the large output torque can be obtained as the positive reluctance torque is available
Trang 64) The control method considering the demagnetization-
limit is analyzed If the permanent magnet has a straight de-
magnetization curve, as does a rare-earth permanent magnet,
the PM motor can be safely operated until the demagnetiz-
ing coefficient becomes 1.0 If wide speed range or constant
power operation is desirable, the permanent magnet with a
high coercivity and a linear demagnetization curve must be
used for the PM motor
REFERENCES [l] B Sneyers, D W Novotny, and T A Lipo, “Field weakening in
buried permanent magnet ac motor drives,” IEEE Trans Ind Appl.,
vol IA-21, pp 398-407, Mar./Apr 1985
T Sebastian and G R Slemon, “Operating limits of inverter-driven
permanent magnet motor-drives,” IEEE Tins Ind A p p l , vol IA-
23, pp 327-333, Mar.lApr 1987
T Jahns, “Flux-weakening regime operation of an interior permanent-
magnet synchronous motor drive,” IEEE Trans Ind A p p l , vol IA-
B K Bose, “A high-performance inverter-fed drive system of an in-
terior permanent magnet synchronous machine,” IEEE Trans Ind
Appl., vol IA-24, pp 987-997, Nov./Dec 1988
T M Jahns, G B Kliman, and T W Neumann, “Interior permanent-
magnet synchronous motor for adjustable speed drives,” IEEE Trans
Ind A p p l , vol IA-22, pp 738-747, JulylAug 1986
Y Takeda and T Hirasa, “Current phase control methods for per-
manent magnet synchronous motors considering saliency,” in PESC
Conf RE., Apr 1988, pp 409-414
R Schiferl and T A Lipo, “Power capability of salient pole permanent
magnet synchronous motors in variable speed drive applications,” in
IEEE IAS Annu Meeting Conf R e , 1988, pp 23-31
[2]
[3]
23, pp 681-689, July/Aug 1987
[4]
[5]
[6]
[7]
Shigeo Morimoto was born on June 28, 1959 He
received the B.E and M.E degrees from Univer- sity of Osaka Prefecture, Japan, in 1982 and 1984, respectively
He joined the Mitsubishi Electric Corporation, Tokyo, Japan, in 1984 Since 1988, he has been
a Research Associate in the Department of Electri- cal Engineering at the University of Osaka Prefec- ture, engaged in research on inverter systems and
ac servo control systems
Mr Morimoto is a member of the Institute of Electrical Engineers of Japan, the Society of Instrument and Control Engi-
neers of Japan, and the Japan Society for Power Electronics
Yoji Takeda was born in Osaka, Japan, on Novem-
ber 10, 1943 He received the B.E., M.E., and Ph.D degrees from the University of Osaka Prefec- ture, Japan, in 1966, 1968, and 1977, respectively
In 1968, he joined the Department of Electncal Engineering, University of Osaka Prefecture He is presently an Associate Professor
Dr Takeda is a member of the Institute of Elec- trical Engineers of Japan, the Institute of Systems, Control and Information Engineers, and the Japan Society for Power Electronics
Taka0 Hirasa (M’85) was born on May 13, 1930
He received the B.E and Ph.D degrees from the University of Osaka Prefecture, Japan, in 1958 and
1965, respectively Since 1953, he has been with the Department of Electrical Engineenng at the University of Osaka Prefecture, where his areas of interest are power system stability, motor controls, and power elec- tronics applications Since 1976 he has been a Pro- fessor of Electrical Engineering
Dr Hirasa is a member of the Institute of Elec- trical Engineers of Japan, the Institute of Systems, Control and Information Engineers, and the Japan Society for Power Electronics
Katsunori Taniguchi (M’75) was born in Na-
gasalu, Japan, on April 21, 1943 He received the B.S degree in electrical engineering from Osaka In- stitute of Technology, Osaka, Japan, and the M.S and Ph.D degree from University of Osaka Pre- fecture, Osaka, Japan, in 1966, 1970, and 1974, respectively
Since 1966, he has been with the Department of Electrical Engineering, Osaka Institute of Technol- ogy, where he is currently a Professor He is en- gaged in research on PWM power conversion sys- tem and its application to the motor control
Dr Taniguchi is a member of the Institute of Electrical Engineers of Japan, the Society of Instrumentation and Control Engineers, and Japan Society for Power Electronics