A Novel Stator Hybrid Excited Doubly Salient Permanent Magnet Brushless
Machine for Electric Vehicles
Xiaoyong Zhu1, 2, Ming Cheng1
1 Department of Electrical Engineering, Southeast University, Nanjing 210096, P.R. China
2 School of Electrical and Information Engineering, Jiangsu University, Jiangsu, 212013, P.R. China
Phone: 86-25-83794152 Fax: 86-25-83791696
E-mail: mcheng@seu.edu.cn
optimizing control is essential for long EV driving range.
Abstract—In this paper, a novel stator hybrid excited
doubly salient permanent magnet (SHEDS-PM) brushless
machine with a special magnetic bridge is proposed for the
first time. The originality of this machine is purposely to add
a magnetic bridge in shunt with each PM pole, which not
only maintains the stator lamination in its entireness, but
also amplifies the effect of dc field flux on PM flux. An
equivalent magnetic circuit is presented to clarify the novelty
and the finite element analysis is adopted to determine the
machine characteristics. The corresponding results on a
prototype machine illustrate that the proposed machine is
promising for application to electric vehicles.
I.
rotor
pole
N
N
armature
winding
stator
pole
magnetic
bridge
shaft
INTRODUCTION
N
N
S
Recently, there is an increasing tendency to study
hybrid excitation machines, which combine the
advantages of PM machines with the possibility of
controllable magnetic flux by auxiliary dc windings [1].
The initial research has revealed that the hybrid excitation
permanent magnet (HEPM) machines can offer the
advantages of high power density, high efficiency and
robust rotor structure. Moreover, the most attractive
performance is its special ability of the flux weakening in
the operation of constant power, which is very important
for electric vehicles (EV) [2].
In this paper, a novel stator hybrid excited doubly
salient permanent magnet (SHEDS-PM) brushless
machine with a special magnetic bridge is proposed for
the first time. The operation principle of the SHEDS-PM
machine is described. On the basis of theoretical study in
SHEDS-PM machine by using 2-D finite element method,
the corresponding static characteristics, including selfinductance, mutual inductance and static torque are
deduced in the paper. An equivalent magnetic circuit is
also presented to clarify how the magnetic bridge
amplifies the effect of dc field flux on PM flux.
II.
dc excited
winding
S
S
S
permanent
magnet
Fig. 1. Cross-section of the SHEDS-PM machine.
φm
θw
φmax
φmin
0
θ1
θ2
θ3
θ4
θ
θoff −
θ
i
Im
0 θ on +
−
θoff + θon
− Im
Fig. 2. Theoretical flux and current waveforms.
The originality of this topology is to purposely add an
extra flux path in shunt with each PM pole, the so-called
magnetic bridge. This magnetic bridge not only maintains
the stator lamination in its entireness, but also amplifies
the effect of dc field flux on PM flux.
The theoretical waveforms of PM flux φ m and phase
current i with respect to the rotor position are shown in
Fig. 2. When a rotor pole is entering the region occupied
by a conductive phase, the flux is increasing, if a positive
current is applied to the winding, a positive torque will be
produced. When the rotor pole is leaving the stator pole
from the aligned position, the flux is decreasing and also a
positive torque will be produced if a negative current is
applied to the winding. Thus, two possible torque
producing zones are fully utilized [5]-[8].
MACHINE TOPOLOGY AND OPERATION PRINCIPLE
Fig. 1 shows the proposed topology, which is a
three-phase 12/8-pole machine. It consists of two types of
stator windings, a three-phase armature winding and a dc
excitation winding. The function of the armature winding
is the same as that for a DSPM machine [3]-[4], whereas
the dc field winding not only works as an electromagnet
but also as a tool for flux weakening and/or efficiency
optimization, Notice that flux weakening operation is
necessary for high-speed EV cursing, whereas efficiency
The work was supported by NSFC Project 50337030, 503377004.
412
III. MANNETIC CIRCUIT ANALYSIS
⎫
− 1) FPM ⎪
Φg 0
⎪
(7)
⎬
Φg −
⎪
′
) FPM
Fdc − = (1 −
Φg 0
⎪⎭
If (Φg+/Φg0) =2 and (Φg-/Φg0) =1/2 are wanted, the
MMF of dc excitation can be derived as following when
selecting (Rmb/RPM) =1/3:
F ⎫
Fdc + = PM ⎪
4 ⎪
(8)
⎬
FPM ⎪
Fdc − =
8 ⎪⎭
To clarify how the magnetic bridge amplifies the
effect of dc field flux on PM flux, an equivalent magnetic
circuit model of the proposed machine is presented.
Fig. 3 (a) shows the equivalent magnetic circuit of the
machine with magnetic bridge, and Fig. 3 (b) illustrates
the circuit of the machine without magnetic bridge at
no-load.
In Fig. 3 (a), the airgap flux Φg can be expressed as:
F ( R + RPM ) + F PM Rmb
Φ g = dc mb
(1)
Rmb Rg + RPM Rg + Rmb RPM
Fdc′ + = (
where Fdc is the magnetic motive force (MMF) of dc field
winding excitation, FPM is the PM excitation. RPM is the
reluctance of the PM pole. Rmb is the reluctance of the
extra magnetic bridge, and Rg is the reluctance of the
airgap. When there is no dc field winding excitation,
Fdc=0, so that the corresponding flux is given by:
FPM
Fdc
Φg
Similarly, the dc excitation required to achieve the same
flux variation for the Fig. 3(b) can also be obtained as:
Fdc′ + = FPM ⎫
⎪
F ⎬
Fdc′ − = PM ⎪
2 ⎭
R PM
R PM
Rmb
Fdc
FPM
Φg
Rg
(a) With a magnetic bridge
Rg
(b) Without magnetic bridge
F PM Rmb
Rmb Rg + RPM Rg + Rmb RPM
IV. MAGNETIC FIELD ANALYSIS AND STATIC
CHARACTERISTICS
By using the 2-D FEM, the static characteristics of the
machine are analyzed. In order to assess the performance
of the proposed machine more accurate, its iron core and
magnetic saturation, leakage flux and armature reaction
are taken into account. Fig. 4 shows the flux distributions
of the proposed machine under different dc wingding
excitation currents.
(2)
When a positive dc field winding excitation is applied,
Fdc=Fdc+ so that the corresponding airgap flux is given by:
F ( R + RPM ) + F PM Rmb
(3)
Φ g + = dc + mb
Rmb Rg + RPM Rg + Rmb RPM
A. PM Flux Linkage and back EMF
When a negative dc field winding excitation is applied,
Fdc=Fdc- so that the corresponding airgap flux is given by:
F ( R + RPM ) + F PM Rmb
Φ g− = dc− mb
(4)
Rmb Rg + RPM Rg + Rmb RPM
When the machine operates at a constant speed with
no-load, the corresponding flux linkages with respect to
the rotor position under different dc excitation currents
are simulated as shown in Fig. 5. When the dc excitation
MMF reinforces the PM MMF, this extra flux path will
assist the effect of flux strengthening. On the other hand,
if the dc field MMF opposes the PM MMF, this extra flux
path will weaken the PM flux leakage. Compared with
Fig. 5 (a) and (b), the reluctance of the extra path is much
less than that of PMs without magnetic bridge, hence the
existence of magnetic bridge amplifies the effect of flux
weakening, which agrees with the previous results from
magnetic circuit analysis. The induced back EMF is given
by:
dψ m dψ m 2πn
e=
=
⋅
(10)
dt
dθ
60
Fig. 6 shows the theoretical waveform of the back EMF
of the 12/8-pole machine at the rated speed of 1500 rpm.
With (2), (3) and (4), it yields:
Φg +
Fdc +
−1
Φg 0
FPM
=
RPM
+1
Rmb
1−
and
Fdc − =
(5)
Φg−
Φ g0
RPM
+1
Rmb
FPM
(9)
Compared with (8) and (9), it illustrates that, for the
machine with magnetic bridge, (Φg+/Φg-)=4 only needs a
small change in dc excitation, namely 25% of FPM during
flux strengthening, and 12.5% of FPM during flux
weakening, whereas 100% and 50% of FPM are needed in
dc excitation of the machine without magnetic bridge.
Fig. 3 Equivalent magnetic circuits at no load
Φg 0 =
Φg +
(6)
Similar results can be derived from Fig. 3(b) where there
is no magnetic bridge, namely Rmb is set to infinite:
413
0.25
0A-turns
600A-turns
-600A-turns
Flux linkage(Wb)
0.2
0.15
0.1
(a) PMs only
0.05
0
0
5
10
15
20
25
30
Rotor angle(degree)
35
40
45
(a) With magnetic bridge
0.25
0A-turns
600A-turns
-600A-turns
0.2
Flux linkage(Wb)
(b) PMs and Fdc=600A-turns
0.15
0.1
0.05
0
(c) PMs and Fdc=-600A-turns
Fig. 4. Flux distributions of different dc excitations
5
10
15
20
25
30
Rotor angle(degree)
35
40
45
(b) Without magnetic bridges
Fig. 5 Flux linkages at different dc excitation currents
100
B. Inductance
80
40
20
0
-20
-40
-60
When keeping the dc excitation current a constant,
the armature current +ia and -ia are applied respectively,
the flux linkage of one phase is:
(12)
ψ + = ψ pm + La ia + Laf i f
ψ − = ψ pm − La ia + Laf i f
60
NO-load back EMF (V)
In the calculation of inductance, the cross-coupling
between the PM flux, armature flux and dc excitation flux
should be taken into account. As the PM, armature current
and dc excitation current act together, the flux linkage of
one phase is given by:
(11)
ψ = ψ pm + La ia + Laf i f
-80
-100
0
5
10
15
20
25
30
Rotor angle (degree)
35
40
45
Fig. 6 Simulated no-load back EMF waveform
(13)
Then, the self-inductance can be derived from (12) and
(13) as:
ψ −ψ −
(14)
La = +
2ia
C. Static Torque
Based on the resulted PM flux linkage and inductance,
the electromagnetic static torque for one-phase-on
condition can be deduced by using the co-energy method
as:
∂W ′(ia , i f ,θ )
Te =
∂θ
dLaf dWPM
dψ PM 1 2 dLa
= ia
+ ia
+ ia i f
−
dθ
2 dθ
dθ
dθ
= TPM + Tr + T f − Tcog
(16)
Similarly, when keeping ia=0, the mutual inductance
is given by:
(ψ − ψ pm )
Laf =
(15)
if
The self-inductance and mutual inductance characteristics
are shown in Fig. 7 and Fig. 8, respectively.
Where TPM is the reaction torque due to the interaction
between PM fluxes and winding current, Tr is the
reluctance torque due to the variation of the inductance, Tf
414
is the dc excitation torque and Tcog is the cogging torque.
Fig. 9 shows the total electromagnetic static torque
and its components when ia=±3A and if=-1A.
V. CONCLUSION
This paper proposes a novel stator hybrid excited
doubly salient permanent magnet brushless motor. An
equivalent magnetic circuit of the machine has been
presented, which reveals the advantageous feature of the
machine. The finite element analysis has been carried out.
Based on the parameters resulting from the finite element
analysis, the static characteristics, namely inductance,
flux linkage, back EMF and torque, are deduced. Based
on the theoretical study in SHEDS-PM machine by using
2-D FEM and the equivalent magnetic circuit, the
following conclusion may be drawn:
a) The novelty of this machine is addition of an extra
flux path in shunt with each PM pole, hence amplifying
the effect of flux weakening for constant power operation.
Thus, the proposed machine not only offers the
advantages of a DSPM machine, but also a very wide
speed range that is essential for EV application.
b) The hybrid excitation machine provides an
additional degree of freedom with respect to the flux
weakening method by means of armature current control
alone. It also allows to avoid the constraints and
drawbacks associated with the armature current vector
control method and to widen the speed range at
constant-power operation mode.
c) In addition to the attractive performance of its
special ability of the flux weakening in the operation of
constant power, the machine can also be used to reinforce
the magnetic flux and to increase the maximum torque.
0.024
PM+3A,if=-1A
PM-3A, if=-1A
0.022
Self-inductance (H)
0.02
0.018
0.016
0.014
0.012
0.01
0.008
0.006
0
5
10
15
20
25
30
Rotor angle (degree)
35
40
45
Fig. 7 Phase self-inductance versus rotor angle
0.018
if=-1A, ia=0A
Mutual inductance (H)
0.016
if=-2A, ia=0A
if=-3A, ia=0A
0.014
0.012
0.01
0.008
0.006
REFERENCE
0.004
0.002
[1]
0
5
10
15
20
25
30
Rotor angle (degree)
35
40
45
Fig. 8 mutual inductance between dc excited windings and
the armature windings
[2]
[3]
[4]
2
1.5
[5]
Torque (N*m)
1
[6]
0.5
0
-1
0
[7]
total torque Te
Tcog
Tpm
Tr
Tf
-0.5
5
10
15
20
25
30
Rotor angle (degree)
35
40
[8]
45
Fig. 9 Total torque and its components
415
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