Electric Machines and Power Systems, 28:277–288, 2000
C opyright s c 2000 Taylor & Francis
0731-356X / 00 $12.00 + .00
Performance A nalysis of Split-W inding Doubly
Salient Permanent M agnet M otor for
W ide Speed Operation
MING CHENG
K. T. CHAU
C. C. CHAN
Department of Electrical & Electronic Engineering
The University of Hong Kong
Hong Kong, China
E. ZHOU
Department of Electrical Engineering
Southeast University
Nanjing 210096, China
In this paper, various ux-weakening techniques available for wide speed operation of the doubly salient permanent magnet (DSPM) motor are reviewed.
A new split-winding topology capable of widening the speed range is proposed,
which is valid not only for the DSPM motor with stationary PMs, but also for
that with rotary PMs. Based on the parameters obtained by Žnite element analysis, the performance of the proposed DSPM motor is analyzed. The results
show that this motor combines the features of wide speed range, high e ciency,
simple structure, and low cost.
1
Introduction
At present, there is an increasing tendency to consider brushless motors with permanent magnet (PM) excitation for industrial and electric vehicle applications.
Recently, a viable brushless topology, named as the doubly salient permanent magnet (DSPM) motor, has been introduced. This DSPM motor essentially adopts
the same structure as a switched reluctance (SR) motor but with PMs placed in
the stator or the rotor. Recent literatures have already illustrated that the DSPM
motor is of high e ciency, high power density, and simple structure (Chau et al.,
1999; Cheng et al., 1998; Li and Lipo, 1995; Liao et al., 1995; Liao and Lipo, 1994;
Radulescu et al., 1995; Shakai et al., 1993).
In our preceding paper (Chau et al., 1999), a new 8/ 6-pole DSPM motor was
proposed and its steady-state and dynamic performances were analyzed, revealing
that the 8/ 6-pole DSPM motor takes advantages over the 6/ 4-pole one, namely
higher power density, wider speed range, less torque ripple, and lower current magManuscript received in Žnal form June 23, 1999.
Address correspondence to Dr. K. T. Chau.
277
278
Cheng et al.
nitude. However, similar to most of PM brushless motors, the constant power operation range of the DSPM motor is very limited due to the fact that the Želd
control capability of PM excitation is more di cult to achieve than that of wound
Želd excitation. In general, ux-weakening techniques are employed to extend its
constant power operation range. Section 2 will give a brief review on the available ux-weakening methods for the DSPM motor and their limitations will be
discussed. Theory of the DSPM motor will be presented in Section 3. A new splitwinding DSPM motor capable of widening the operation range will be proposed in
Section 4. In Section 5, performance analysis of the newly proposed split-winding
DSPM motor will be carried out.
2
2.1
Flux-W eakening M ethods
M echanical M ethods
Three mechanical methods for weakening the PM Želd of the DSPM motor were
introduced by (Shakai et al., 1993), which are illustrated in Figures 1 to 3. As shown
in Figure 1, the Žrst method is to partially short-circuit the PM ux path by placing
two pieces of ferromagnetic material around the protruding ears (which house the
PMs). To position the V-shape ferromagnetic plates accurately, two actuators are
usually required.
The second method is to slide the PMs out from the stator in the axial direction
as shown in Figure 2. Because each set of PMs requires two actuators, the DSPM
motor shown in Figure 1 totally requires four actuators for such purpose. Also, a
large force must be provided by the actuators to pull out the PMs from the stator.
The third method is to use a rotatable magnetic/ nonmagnetic collar mounted
on the stator surface as shown in Figure 3. Initially, the nonmagnetic section is
in contact with the PMs, the reluctance seen by the PMs is large, and thus most
of the ux passes through the air-gap, thereby linking the stator windings. When
the collar is rotated by an actuator, the magnetic section begins to short-circuit
the PM ux path. If the collar is properly rotated, the PM ux will be completely
short-circuited.
Figure 1. Flux-weakening by using movable magnetic plates.
Split-Winding Doubly Salient Magnet Motor
279
Figure 2. Flux weakening by sliding magnets axially.
Figure 3. Flux weakening by using rotatable magnetic/ nonmagnetic collar.
Because the mechanization of the above three methods will involve bulky and
costly setups, they are not attractive for practical applications.
2.2
Electrical M ethod
Figure 4 shows a DSPM motor capable of ux weakening by electrical means (Li
and Lipo, 1995). Besides the phase windings in the stator poles, an additional
Želd winding is placed in the space between the arc-shape PMs. By controlling
the magnitude of the Želd winding current, the ux-weakening operation can be
achieved. However, because of a large eŒective air-gap imposed by the PMs, a large
number of ampere turns are necessary, leading to extra copper loss and hence low
280
Cheng et al.
Figure 4. Flux weakening by controlling Želd winding current.
e ciency during ux weakening. Also, the Želd winding and its current controller
increase both complexity and cost.
It should be noted that the aforementioned four methods of ux weakening are
valid only for those DSPM motors with the PMs located in the stator, but not for
those with rotary PMs.
3
M otor Theory
Figure 5 shows the cross section of a newly proposed 4-phase 8/ 6-pole DSPM motor
with stationary magnets. Its theoretical PM ux Ám and stator current i with
Figure 5. Schematic of 8/ 6-pole DSPM motor.
Split-Winding Doubly Salient Magnet Motor
281
Figure 6. Theoretical ux and current waveforms.
respect to the rotor position angle µ are shown in Figure 6. The corresponding
torque can be produced by applying either a positive current to the winding when
the PM ux is increasing or a negative current when the ux is decreasing.
The system matrix equation describing this 4-phase 8/ 6-pole DSPM motor is
expressed as
dY ¯
V̄ = R̄ I¯ +
,
(1)
dt
where V̄ = [º1 , º2 , º3 , º4 ] is the phase voltage matrix, R̄ = diag [r 1 , r 2 , r 3 , r 4 ] is the
resistance matrix, I¯ = [i1 , i2 , i3 , i4 ]T is the phase current matrix, Y ¯ = L̄ I¯ + Y ¯ m is
the total ux linkage matrix, L̄ = L x y (x = 1 ~ 4, y = 1 ~ 4) is the inductance
matrix, and Y ¯ m = [Y m 1 , Y m 2 , Y m 3 , Y m 4 ]T is the PM ux linkage matrix. When
L̄ and Y ¯ m are considered to be spatially dependent only and independent of the
stator current, it yields
T
dY ¯
dt
= L̄
dI¯
dt
+
dL̄ ¯
dY ¯ m
dI¯
d L̄ ¯
dY ¯ m
I +
= L̄
+
I !r +
!r ,
dt
dt
dt
dµ
dµ
(2)
where !r = dµ=dt is the rotor angular speed. Thus, the dynamic equation given by
equation (1) can be rewritten as
d I¯
dt
= L̄
1
"
R̄ +
d L̄
dµ
!r
#
I¯ + L̄
1
"
V̄
dY ¯ m
dµ
!r
#
.
(3)
By employing the coenergy method, the torque expression of the motor is obtained
as
¢
"
#
1 ¯T ¯ ¯ T ¯
1
Te =
=
I L̄ I + Y m I = I¯T
@µ
@µ 2
2
@W
@
³
@
@µ
L̄
´
I¯ +
³
@ ¯
Y m
@µ
´T
I¯ = T r + T m ,
(4)
where T r = 12 I¯T ( @L̄ =@µ) I¯ represents the reluctance torque due to the variation of
inductances, and T m = ( @Y ¯ m =@µ) T I¯ is the reaction torque due to the interaction
between the winding current and the PM ux.
282
Cheng et al.
Computer simulation can readily be performed by numerically solving the dynamic equation given by equation (3). Hence, the output torque can be simulated
by using equation (4). Besides using numerical techniques, an analytical solution
of equation (3) is highly desirable, which can provide the designer physical insight
into the motor performance.
By neglecting the mutual inductances L x y (x =
/ y ) of the motor, or assuming
that only one phase is conducted at any time, equation (3) can be decoupled among
phases and is given by
di
dt
³
1
=
r+
L
dL
dµ
!r
´
i+
³
1
dªm
U
L
dµ
!r
´
(5)
,
where r , L , and U are the resistance, self-inductance, and applied voltage of each
phase winding, respectively. Taking L as its average value in one stroke, the analytical solution of equation (5) can thus be obtained as
i=
³
U
dªm
dµ
!r
´«
1
exp
"
1
L
³
r+
dL
dµ
!r
´ #¼
t
Hence, the steady-state phase current is given by
³
I = U
dªm
dµ
!r
´
¯³
r+
dL
dµ
!r
¯³
´
r+
dL
dµ
!r
´
.
(6)
(7)
.
According to the operation principle of the DSPM motor, a positive current should
be applied to the phase winding when the corresponding ux linkage is increasing,
and vice versa. To keep a positive current at the Žrst stroke and a negative current
at the second stroke, the following condition is necessary:
u u
udªmu
u
|U | u
u dµu!r ³ 0.
(8)
It illustrates that for a given supply voltage, there is a speed limit !r max as represented by
!r max
u
¯u
udª u
= |U | u
u
u = |U |
m
dµu
u´
¯³u
udÁ u
wu
u
u «
m
dµu
|U |
¯³
w
D Ám
µw
´
,
(9)
Á0 is
where w is the number of winding turns in series per phase, D Ám = ÁM
the amplitude of PM ux, and µw = µ2 µ1 is the angular displacement of stroke.
From Figure 6, it yields
D Ám = ÁM
Á0 «
0 .87ÁM = 0 .87k d ¯ s
Di
2
le B ± = k B ± ¯s ,
(10)
where k d is the PM ux leakage factor, ¯ s is the stator pole arc, D i is the stator
inner diameter, l e is the stack length, B ± is the air-gap ux density, and k is a
constant governed by the motor dimensions (Chau et al., 1999). Since the rotor
pole arc ¯r is generally greater than ¯ s and ¯ s = µw , equation (9) can be deduced
as
!r max
=
|U |
wk B ± ¯ s =µw
=
|U |
k wB ±
.
(11)
Split-Winding Doubly Salient Magnet Motor
4
283
Split-W inding M ethod
Equation (11) reveals that there are two ways to extend the speed range of the
DSPM motor: one is to weaken the magnetic ux, as discussed in Section 2, while
another is to reduce the number of turns per phase. The latter is suitable to all
PM motors in theory but not practical for those normal PM motors, such as PM
synchronous motors, because they adopt distributed windings and the corresponding change of the winding turns is di cult. However, the DSPM motor with concentrated windings can allow changing the number of turns by employing split
windings. Figure 7 shows the schematic connection of the proposed split windings.
When the switch K 1 is on, the whole windings are functional, whereas the switch
K 2 can be turned on so that the winding turns per phase are reduced to 60%. These
switches may be electronic, electrical, or even mechanical according to the requirements of application and cost. Figure 8 shows a simple control strategy, where a
relay is used to change the connection of split windings. When the speed of the motor is below the critical speed, the transistor switch T is oŒ, the NC (normal close)
contacts are closed, and NO (normal open) contacts are open, so that the whole
windings are active. When the speed is above the critical speed, T will be turned
on, making the NC contacts open and the NO contacts closed, hence only 60% of
the whole windings are active. In this scheme, only one relay and one transistor
switch are required for changing the number of turns, therefore the cost is low.
5
Performance A nalysis
Finite element analysis of the proposed 8/ 6-pole DSPM motor is carried out in
which magnetic saturation has been taken into account (Cheng et al., 1999). The
Želd distribution of this motor at no-load is illustrated in Figure 9. Hence, the
PM ux and self-inductance of the motor can be deduced. Figure 10 shows the
corresponding characteristics in variation of the rotor position angle.
By using the parameters derived from Žnite element analysis and the derived
equation given by equation (4), the torque T e and output power P characteristics
versus speed with two diŒerent numbers of winding turns based on the same turn-
Figure 7. Schematic connection of split windings.
284
Cheng et al.
Figure 8. Schematic of the DSPM motor drive with split windings.
on angle µon and turn-oŒangle µoŒ are shown in Figure 11. They illustrate that
the constant power operation range is substantially extended from 2650 rpm to
5000 rpm by reducing the winding turns from 100% to 60%. For comparisons,
the characteristics of torque T e and output power P with two diŒerent ux levels,
namely 100% and 60%, based on the same turn-on and turn-oŒangles are shown
Figure 9. Field distribution at no-load.
Split-Winding Doubly Salient Magnet Motor
285
Figure 10. PM ux and self-inductance.
Figure 11. Characteristic under diŒerent winding turns (µon = 3° , µoŒ = 25°).
286
Cheng et al.
Figure 12. Characteristics under diŒerent PM ux levels (µon = 3° , µo Œ = 25°).
in Figure 12. It can be found that the constant power operation range achieved
by ux weakening is much shorter than that by decreasing the number of winding
turns based on the same conditions, namely the same conduction angle and the
same PM ux linkage ªm = wÁm . This is because a reduction of the PM ux
only causes a decrease of the PM ux linkage without having any eŒect on the
inductances, whereas the reduction of the number of winding turns leads to not
only a proportional decrease of the PM ux linkage, but also a square decrease
of the inductances. Hence, as shown in Figure 13, the current rise during ux
weakening is more sluggish, thereby achieving lower power. The corresponding RMS
current versus speed is given in Figure 14, showing that the current at w of 60% is
signiŽcantly higher than that at Ám of 60% with ªm unchanged.
Moreover, since the winding resistance decreases proportionally with the reduction of the winding turns, the copper loss for reduced winding turns is smaller
than that for reduced PM ux, as shown in Figure 15, in which the extra copper
loss of Želd winding for ux weakening is not yet taken into account. So, higher
e ciency is expected when adopting the reduction of winding turns instead of ux
weakening.
Split-Winding Doubly Salient Magnet Motor
Figure 13. Current waveforms at 4000 rpm.
Figure 14. Characteristics of RMS current versus speed.
Figure 15. Copper loss versus torque.
287
288
6
Cheng et al.
Conclusion
In this paper, the ux-weakening principle and basic theory of DSPM motors have
been presented. Then a new DSPM motor with split windings capable of widening
the constant power operation range has been proposed. The corresponding performance analysis has been carried out. It has shown that the newly proposed
split-winding DSPM motor has a number of advantages over the available DSPM
motors using ux-weakening control:
·
·
·
·
Higher capability of widening the range of constant power operation
Valid not only for those motors with stationary PMs but also for those with
rotary PMs
No additional Želd winding loss and lower copper loss, hence higher e ciency
Neither extra Želd windings nor complicated auxiliary equipment, hence simple structure and low cost
All of these advantageous features make this motor a competitive candidate
for those applications desiring high e ciency, high power density, and wide speed
operation, such as electric vehicles.
A cknowledgments
The work was supported in part by the Committee on Research and Conference
Grants of the University of Hong Kong, the Hong Kong Research Grants Council under Project HKU7128/ 99E, and the National Natural Science Foundation of
China under Project 59507001.
References
Chau, K. T., Cheng, M., and Chan, C. C., 1999, Performance analysis of 8/ 6-pole doubly
salient permanent magnet motor, Electric Machines and Power Systems, Vol. 27,
No. 10, pp. 1055–1067.
Cheng, M., Chau, K. T., and Chan, C. C., 1998, A new doubly salient permanent magnet motor, Proceedings of International Conference on Power Electronics Drives and
Energy Systems for Industrial Growth, pp. 2–7.
Cheng, M., Chau, K. T., and Chan, C. C., 1999, Static characteristics of a new doubly
salient permanent magnet motor, Proceedings of IEEE International Electric Machines and Drives Conference, pp. 22–24.
Li, Y., and Lipo, T. A., 1995, A doubly salient PM motor capable of Želd weakening,
Proceedings of IEEE Power Electronics Specialists Conference, pp. 565–571.
Liao, Y., Liang, F., and Lipo, T. A., 1995, A novel permanent magnet motor with doubly salient structure, IEEE Transactions on Industry Applications, Vol. 31, No. 5,
pp. 1059–1078.
Liao, Y., and Lipo, T. A., 1994, A new doubly salient permanent magnet motor for adjustable speed drives, Electric Machines and Power Systems, Vol. 22, No. 1, pp. 259–
270.
Radulescu, M. M., Martis, C., and Biro, K. 1995, A new electronically-commutated doublysalient permanent-magnet motor, Proceedings of IEE International Conference on
Electrical Machines and Drives, pp. 213–216.
Shakai, A., Liao, Y., and Lipo, T. A., 1993, A permanent magnet AC machine structure
with true Želd weakening capability, Proceedings of IEEE International Conference
on Industrial Electronics, pp. 19–24.