Download Performance of Line-start Permanent Magnet Synchronous Motor

Performance of Line-start Permanent Magnet Synchronous Motor with Novel Rotor Structure
Xiaozhuo Xu
Performance of Line-start Permanent Magnet Synchronous Motor with
Novel Rotor Structure
1
Xiaozhuo Xu
School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo,
Henan, P.R.China, [email protected]
2
Yinghua Cui, 3Xudong Wang, 4Haichao Feng, 5Jikai Si
School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo,
Henan, P.R.China
Email:*[email protected],[email protected],[email protected],[email protected]
1
Abstract
The novel Line-start Permanent Magnet Synchronous Motor (LSPMSM) has widely industrial
applications, due to its high efficiency, high power factor and self-starting ability. The starting
characteristics of novel LSPMSM with rotor arc straight inserted permanent magnet are studied based
on the electromagnetic field theory. A finite element model of a 3-phase 8-pole 22kW LSPMSM is
developed under reasonable assumptions as well as the solving region, and the transient
electromagnetic field is calculated by the coupled field circuit method. The effects due to the variation
of rotor structure parameters and stator winding turns and source voltages on performance of starting
torque, current and power factor are analyzed, and the lowest starting voltage is obtained. Under
overall consideration, the optimal motor parameters are confirmed and the performance on rated
condition is calculated. Finally, the prototype experimental results verify the numerical calculating
characteristic of the models.
Keywords: Line-Start, Permanent Magnet Synchronous Motor, New Rotor Structure, Starting
Performance, Finite Element
1. Introduction
In recent years, Line-start Permanent Magnet Synchronous Motor (LSPMSM) has attracted the
attention of a large number of scholars and manufacturers, for its advantages of high efficiency, high
power factor and wide economic operation range [1-3]. The LSPMSM, which inherits the structure
characteristic of induction motor and synchronous motor, consists of permanent magnets and
aluminum winding on its rotor. So it can be started up directly by the asynchronous torque generated
by squirrel cage winding.
Just because of the existence of permanent magnet on the rotor, and asymmetry between rotor d-axis
and q-axis magnetic circuit, many magnetic fields with different speeds exist in the motor air gap. With
the interaction of these fields, driving torque, braking torque and alternating torque are generated,
which make the starting process of LSPMSM very complex [4]. Generally, permanent magnets are arc
surface-mounted or rectangular straight inserted [5-7] in traditional LSPMSM rotor, as shown in Figure
1. the former provides nice air gap field but cuts down the motor starting capability, while the latter has
good starting capability but provides weaker electromagnetic characteristic. In this paper, a 22Kw
LSPMSM with arc straight inserted permanent magnet (ASI-LSPMSM), a new type of magnet which
can provide both good starting capability and nice electromagnetic characteristic at meantime are
designed, the influence of structure size on starting torque ratio and starting current ratio is compared.
Then performance on rated condition is analyzed with the method of finite element numerical analysis,
and the starting performance and starting torque are calculated [8, 9]. Finally, influence of supply
voltage on starting performance is researched and the lowest supply voltage is obtained.
International Journal of Digital Content Technology and its Applications(JDCTA)
Volume7,Number6,March 2013
doi:10.4156/jdcta.vol7.issue6.139
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Performance of Line-start Permanent Magnet Synchronous Motor with Novel Rotor Structure
Xiaozhuo Xu
permanent
magnet
permanent
magnet
rotor slot
rotor slot
(a)Rectangular straight inserted
(b)Surface-mounted
Figure1. Classical permanent magnet structure
2. LSPMSM Electromagnetic Field Analysis
The novel rotor structure, arc straight inserted permanent magnet and combination of flux barrier
and air slot are adopted in the motor designed in this paper, and the structure parameters and chart are
shown in table 1 and figure 2 respectively.
Rated power
Table 1. Motor structure parameters
22Kw
Number of stator slot
54
Rated voltage
Rated speed
Insulation class
Exciting mode
380V
750r/m
B
Parallel
48
368mm
259mm
0.5mm
Number of rotor slot
Stator out diameter
Stator inner diameter
Air gap length
(a) Whole structure
(b) Novel rotor structure
Figure 2. LSPMSM Structure
2.1. Assumption and solving region
Supposing the electromagnetic field is quasi-static, which means displacement current is ignored.
Electromagnetic field is disposed as two-dimensional field, which means motor axial length is kept
constant and motor end winding is ignored. Materials used in motor is supposed to be isotropy,
hysteresis effect of the ferromagnetic material is ignored. Permanent magnet is simulated with
equivalent surface current. Conductivity and permeability are just related to the material properties,
irrespective of the temperature variation. Eddy currents of the stator core, rotor core and source current
region are ignored [10-13].
The field is depicted with magnetic vector potential A, and the transient electromagnetic field
definition solution problem can be described as,
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 1 A
 1 A
dA

 S : x (  x )  y (  y )  ( J z   dt )

1 : A  0

1 A 1 A
 2 :

 s

2 n

1 n
(1)
Where, S is solving region, 1 is the first species boundary condition,  2 is permanent boundary
condition, A is magnetic vector potential,  s is permanent boundary equivalent surface current density,
dA
is eddy current density.
 is permeability, J z is axial current density, 
dt
2.2. Finite element calculation of LSPMSM
During the process of PMSM finite element analysis and solution, formula (1) is taken as Euler
equation of a function, the differential equation corresponding functional of the PMSM mathematic
model is obtained, with which the conditional variation problem is constituted and solved, and then
each motor field quantity can be obtained. With weighted residual method, finite element discretization
equation is established. Taking weight function equal to shape function, formula (2) can be got with
taking formula (1) weighted integral.
1 A
 1 A
dA
T 
T
T
(2)
Se ( N [ x (  x )  y (  y )]  N J z  N  dt )dxdy  0
Taking surface integral as the sum of unit integral, formula above is dispersed, if first order linear
triangle unit is adopted, the integral of formula (2) first term is,

Se
(N T [
Where, N e  [ N ie
N 1 Ae
N 1 A
 1 A
 1 A
1 A
(
) (
)]dxdy   ( e
) e (
)dxdy   N eT (
)dl
Se
le
x  x y  y
x  x
y  y
 n
N ej
(3)
N me ]T
The line integral of formula (3) can be disposed by boundary condition. If first order linear triangle
unit is adopted, the right of formula (3) first term is,
 bi bi  ci ci
b j bi  c j ci
bm bi  cm ci   Ai 
1 
 
(4)



b
b
c
c
b
b
c
c
b
i j
i j
j j
j j
m b j  cm c j   A j    K e Ae
4 
bi bm  ci cm b j bm  c j cm bm bm  cm cm   Am 


The integral of formula (2) second term is,
T
Se N J z dxdy  J z Se  Ni
Nj
T
N m  dxdy 
N e I
1 1 1  Ce I e
3aAb
T
(5)
Where, a is number of winding branches in parallel, N e is number of turns in series of one coil
side in slot. Ab Is a half slot area(double-layer winding). And,
T
 N e N e N e 
Ce  diag 
 , Ie   I I I 
 3aAb 3aAb 3aAb 
The integral of formula (2) third term is,
dA
dA
dAe
(6)
Se  N T  dt dxdy   dt Se  N T N e Ae dxdy  Te dt
 1/ 6 1/ 12 1 /12 
Where, Te   1/ 12 1/ 6 1 /12 
1/ 12 1/ 12 1/ 6 

dt
, the discretization equation of formula (1)
Combining all the formulas above and making A 
dA
can be got as below,

KA  T A  CI
(7)
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2.3. Starting process calculation and analysis on rated condition
The motor is designed with field-circuit combination method, and transient magnetic field is
calculated with finite element method to research starting process of the AIS-LSPMSM. Mechanical
motion equation is shown as follow.
d
J
 Tem  TL
(8)
dt
Where, J is rotary inertia, TL is load torque, which is a approximate constant when motor is on
stable operation, Tem is electromagnetic torque,  is angular speed.
To get the transient performance curve, mechanical motion equation and transient electromagnetic
field must be solved simultaneously during the FEM analysis. The solution procedure is that, supposing
rotor spins  in t , with which motor angular speed  at a time can be ascertained. Then finite
element equation is solved and magnetic field distribution and electromagnetic torque can be obtained.
Taking electromagnetic torque solved above as known conditions, finite element equation is solved to
get angular speed  . If error between calculation value  and assumption value  is less than
allowable value, the process is continued to calculate  at t  t . Otherwise, rotary angular 
must be revised and the former two steps be repeated. With repeated iteration and solution, the
performance analysis curve of the LSPMSM can be obtained.
Magnetic field distribution plot on initial starting stage and lock-in synchronism stage are shown in
Figure 3. Comparison of those two figures shows that no saturation happens in stator core, while
saturation happens in the rotor core over against the flux barrier and rotor slot at 0.2s. The reason is
that when motor is locked-in synchronism, rotor current is close to zero and stator current is approach
to rated current, so the magnetomotive force(MMF) generated by stator and rotor current is small,
while rotor core over against flux barrier is very thin, only a little MMF can make the core be saturated.
Figure 3.a shows that saturation happens not only in the rotor core over against the flux barrier and
rotor slot but also in stator slot teeth at 0.03s. The reason is that at this moment, rotor is at a standstill
while currents both in stator and rotor are very large, values of which can be 10 times that of stator
rated current. As the MMF is proportional to current, the core in leakage magnetic circuit is highly
saturated for the sake of large MMF. Meanwhile, with the adoption of the distributed winding, the
direction of the leakage magnetic field in teeth caused by current in adjacent slots is opposite.
Saturation in the addendum and tooth tip is more serious comparing with teeth part.
(a)0.03s
(b)0.2s
Figure 3. Magnetic field distributions
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Performance of Line-start Permanent Magnet Synchronous Motor with Novel Rotor Structure
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Figure 4. Electromagnetic torque and speed curve
Figure 5. Stator and rotor current curve
It can be seen in figure 4 and 5 that motor starting stage is in 0-0.2s. With the effect of asynchronous
torque, which is caused by interaction of stator field and field induced by rotor current, rotor speed
rises slowly, currents both in the stator winding and rotor are large, and electromagnetic torque is
unstable. After 0.2s, motor is in stable operation, armature current presents periodically oscillation, if
the harmonic magnetic field is ignored, rotor current is close to zero, and electromagnetic torque is
close to rated load torque, these results show that the motor with novel structure owns good starting
performance and electromagnetic performance.
3. Starting performance analysis with different structure parameters
The definition of starting torque in the LSPMSM is same with that in induction motor, it is the
torque generated when rotor keeps stable when slip ratio is 1, it can be shown as follows.
mp
U 2 R2
(9)
Tst 
2 f ( R1  c1 R2 ) 2  ( X 1  c1 X 2 )
From formula (9), it can be seen that starting torque depends on external voltage, stator and rotor
resistance and lekage reactance which is influenced by the extent of the magnetic circuit saturation.
3.1. Influence of winding turns
Figure below shows the influence of winding turns on starting torque ratio and starting current ratio.
(a) Starting torque ratio and starting current ratio
(b) power factor
Figure 6. Stator per-phase winding turns variation
From figure 6, it can be seen that with the increase of winding turns, starting torque ratio and
starting current ratio both reduce, while starting current ratio reduces more rapidly, the reason is that
starting current is proportional to resistance, with the increase of winding turns, winding resistance
increases, and current reduces. With consideration of the power factor, 10 are adopted as stator winding
turns per phase.
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3.2. Rotor slot height variation
(a) Starting torque ratio and starting current ratio
(b) power factor
Figure 7. Rotor slot height variation
Figure 7 shows the influence of rotor slots height variation on starting torque ratio, starting current
ratio and power factor, it can be seen in the figure that with the increase of the rotor slot height, starting
torque ratio and starting current ratio both increase, power factor increases at first,then it decreases. As
the increase of slot height, rotor resistance increases, and rotor lekage inductance reduces, so the
starting torque increases. Considering the motor specifications, and 6.8mm are adopted as rotor slot
height.
3.3. Height of rotor permanent magnets
(a) Starting torque ratio and starting current ratio
(b) power factor
Figure 8. Permanent magnet thickness variation
Keeping pole arc coefficient a constant; permanent magnet (PM) thickness is changed. It can be
shown in Figure.8 that, in a certain range, with the increase of the permanent magnet thickness, power
factor reduces, starting torque ratio increase, the reason is that magnetic saturation increase with the
PM thickness, and leakage reactance reduces gradually. While after the PM thickness increase to
9.4mm, starting torque ratio decrease slightly with the thickness increase, the reason is that when
magnetic circuit is approach to saturation, leakage reactance decreases no longer, and the penetrate rate
of the flux on silicon steel is greatly influenced by saturation, which also makes starting performance
reduce.
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Performance of Line-start Permanent Magnet Synchronous Motor with Novel Rotor Structure
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3.4. Height of air gap variation
(a) Starting torque ratio and starting current ratio
(b) power factor
Figure 9. Air gap length variation
Figure.9 shows that with the increase of air gap length, starting torque ratio, starting current ratio
and power factor all reduce when the length is large than 0.4mm. In the LSPMSM,
anti-demagnetization ability can be enhanced, leakage flux between poles be reduced, air gap effective
flux be enhanced, back electromotive force starting torque be enhanced finally with small air gap
length, while if the length is too small, air gap harmonic magnetic field will be enlarged, stray loss and
noises be increased, the maximum torque and starting torque be reduced, even friction between stator
and rotor will appear. So air gap length has great influence on starting performance.
4.Torque Analyses with Different Supply Voltage
Average torque Tav of ASI-LSPMSM during the starting process includes asynchronous torque Tc
and power generation torque Tg, both of which are explained as follows.
(10)
mpu 2 R2/ s
Tc 
2 f [( R1  c1 R2 / s ) 2  ( x1  c1 x2 ) 2 ]
(11)
R12  xq2 (1  s ) 2
R E 2 (1  s ) 2
mp
Tg  
 2 1 0

2 f (1  s) R1  xd xq (1  s ) 2 R12  xd xq (1  s) 2
Where, R1 , X1 are stator resistance and leakage reactance respectively, R2 , x2 are rotor
resistance and leakage reactance converted to stator side respectively, c1  1  x1 / xm is a factor, and
Xm is excitation reactance, E0 is the back EMF. Equations above show that asynchronous torque is
relative to supply voltage.
(a) Effect of voltage on asynchronous torque
(b) Effect of voltage on resultant torque
Figure 10. Comparison of electromagnetic torque with different work voltage
Figure 10 a) and b) show that with the decrease of voltage, both asynchronous torque and resultant
torque reduce a lot. With the existence of power braking torque, resultant torque waveform sinks
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Xiaozhuo Xu
obviously when the ratio slip is close to 1. If the torque in this period is smaller than rated load torque,
motor will not be started up with rated load. The lowest starting voltage is 290V, when voltage is
inferior to 290V, large pulsating torque and small asynchronous torque emerge with the interactions of
stator rotary magnetic field and permanent magnetic field, and the electromagnetic torque all is
assumed as pulsating torque, the motor will not start up.
Figure 11. New rotor type and motor Prototype of 22Kw LSPMSM
Experiment is done with the prototype shown in Fig.11. Results show that when voltage increases
from 320V to 440V, starting time decreases 52 percentage, and armature current decreases 11.6
percentage. It verifies that LSPMSM characteristics are greatly influenced by voltages in industrial
application.
5. Conclusions
Through the method of finite element analysis, the model of a 22Kw LSPMSM designed with novel
rotor structure is built. Influence of structure parameters on starting performance is researched, along
with proper increase of stator winding turns per phase, starting torque ratio and starting current ratio
reduce. While with increase of rotor slot height, starting torque ratio and starting current ratio also
increase. The performance of motor on rated condition is researched, which shows it has good
characteristic. Torque on different voltages is also calculated, and the lowest voltage is obtained.
Experimental facility is established. The results verify that good matching attributes are got. The
foundation for widely industrial application of this LS-PMSM with novel rotor structure is established
with performance research done above.
6. Acknowledgment
This work was supported by the National Natural Science Foundation of China (NO.61074095,
51277054), Ministry of Education Research Fund for Doctoral Program of Higher
Education(NO.20114116110003), and Henan Province Key Project (NO.122102210121), Ministry of
Education Scientific Research Foundation for Chinese Overseas Returnees, Science and Technology
Research Project of Henan Province Education Department (13A470337, 12B470003), Natural Science
Program of Henan province (2011A470003) , Henan Province Key subjects of Control engineering
(KG2011-05), especially the Innovation Talents Foundation of Henan Province (104200510021).
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Performance of Line-start Permanent Magnet Synchronous Motor with Novel Rotor Structure
Xiaozhuo Xu
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