Transcript The 10th IEEE International Conference on Power Electronics and

The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
Magnet Losses of Fractional Number
Slots Per Pole PMSM in Flux Weakening
Operation
Istvan Szenasy
Dept. of Automation
Szechenyi University
Hungary
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
Magnet Losses of Fractional Number Slots Per Pole PMSM in Flux
Weakening Operation
Abstract
•
An applied control of PMSM is the flux weakening operation for extending the region over
nominal speed but on nominal voltage.
•
This paper deals with these questions and its impacts.
•
These impacts and its reduction need several investigations. In literature there are some
sophistically elaborated control methods to achieving the needed points of operation
increasing in speed and power regarding the available torque [1],[3],[6],[7].
•
The proved method is increasing the torque angle and with this the d axis directed component
of the stator current vector for reduce the main flux, but the loss developing in magnets may
became significant.
•
Nowadays to apply an electrical drive for vehicle demands a PMSM having extended speed
range possibility with high efficiency and a good torque-ampere ratio.
•
Vector control method provides an adequate possibilities for realise the tasks mentioned in
the PM synchronous motor
•
Our work indicates the possibilities and limits of flux-weakening for a given PMSM, and a
usable control strategy.
Magnet Losses of Fractional Number Slots Per Pole
PMSM in Flux Weakening Operation
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
I. Introduction
We had developed of a 110 kW PMSM for a citybus of 12 t driven by battery in 2011 see Fig. 1.
The nominal voltage, current, torque, speed are 650 V, 240A, 1100 Nm and 1000 rpm respectively.
The maximum torque is 2500 Nm under 900 rpm and the maximum speed is 2500 rpm with good
features, it can be shown in Fig. 2-3-4-5.
The maximum efficiency is higher then 95%, the active mass is of 71.1 kg, and the mass of magnet is of
4.9 kg only.
The outer type rotor has
surface-mounted NeFeB
magnets.
For achieve a lower cogging
torque we chosen a
fractional number of slots
per pole.
Mmax=2600 Nm
Mnévl=1100 Nm
nmax =2500/p
UDC =650 V
We have some experiences
in this aria throughout
building some PMSM by
lower power.
Figure 1. Detail from the stator, rotor and winding of our outer rotor and fractional slot per pole type motor
Magnet Losses of Fractional Number Slots Per Pole
PMSM in Flux Weakening Operation
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
The main features of our PMSM
We were studying to achieve the
possible most appropriate rate of
pole and slot numbers, magnet
shape and thickness, its remanence,
the airgap length, stack length,
winding type, and the shape and
measure to all detail of the slot
Figure 2. The main features of PMSM by near1 % reluctance torque
Magnet Losses of Fractional Number Slots Per Pole
PMSM in Flux Weakening Operation
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
Electromagnetic features of PMSM
The Ld/Lq rate is low as typical for this type of surface-mounted PMS motor
Figure 3. Electromagnetic features of PMSM
Magnet Losses of Fractional Number Slots Per Pole
PMSM in Flux Weakening Operation
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
Regenerative braking
High speed regenerative braking at nominal current in Fig.4. The torque angle is 125 o,
the speed is 2500 rpm. The braking torque (red line) is near constant. The input power
and the total losses are waved
Figure 4. High speed regenerative braking. The braking torque (red line) is near
constant
Magnet Losses of Fractional Number Slots Per Pole
PMSM in Flux Weakening Operation
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
II. Investigations
For realize this results we suppose a motor control has available flux-weakening operation. In
Figure 6 can be shown these known current and voltage vectors, setting by torque angle.
We have done several simulations by Infolytica based FEA for investigate some main
characteristics of this PMSM in this region namely the power factor, the loss of magnet eddy
current, one of stator teeth hysteresis and other losses. The functions of results are fitted by
Matlab.
The eddy current loss induced in the permanent magnets of BLDC or BLAC machines were
often neglected long ago but several researcher dealt with it in [4],[5],[6],[7].
The cogging torque is lower then 0.69 Nm,
Figure 6. Current and voltage vectors
under field-weakening operation
Figure 5. The cogging torque is 0.7 Nm, i.e. 0.07 % of nominal torque
Magnet Losses of Fractional Number Slots Per Pole
PMSM in Flux Weakening Operation
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
The eddy-current losses in magnet
They worked out very accurate analytical models for predicting losses in rotor magnets of
machines have a fractional number of slots per pole too, and they validated it
compared their results by finite-element analysis (FEA). Eddy currents will be induced
in magnets by rotating MMFs and due to the higher conductivity of rare-earth
magnets the loss of magnets can be significant. The losses by analytical method [6]
are:
Here Jm eddy current, A vector magnetic potential, the ρ is resistivity, p the pair
of pole, r radial, θ angular coordinate, t time, ω speed.
The power loss in magnet may cause high, non permitted temperature raise and
result in partial irreversible demagnetization of magnets especially with a high
rotational speed and high pole number or under higher electric loading.
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
Magnet Losses of Fractional Number Slots Per Pole
PMSM in Flux Weakening Operation
The eddy current loss in magnet v. torque angle at constant output power
These features are well shown in the results due our investigations from those we present one
series when the value of speed were higher, 1500, 2000, 2500 and 3000 rpm and the values of
power was held at 108 kW of these speeds by the torque of 686, 517, 413 and 343.8 Nm
For each investigation there was signed one point of work at the same speed and the setting
were realized by different values of advanced angle. The angle that is a degree over the q axis
in rotor coordinates was varied and the torque or the power was set to the same value by tuned
of the stator current.
108 kW at 1500, 2000, 2500 and 3000 rpm
6.5
Each on the four curves the
power is constant at speeds of
motor 1500, 2000, 2500 and
3000 rpm.
The power, the torque and the
value of speed are the same on
any curve.
This magnet loss is calculated
by Infolytica with its FEA
method.
6
5.5
magnet eddy current loss kW
•
5
4.5
2500
4
3000
2000
3.5
1500
3
2.5
2
25
30
35
40
45
50
55
60
advanced angle
Figure 7. The magnet eddy current loss v. advanced angle at
P=108kW and speeds are 1500, 2000, 2500 and 3000 rpm
65
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
Magnet Losses of Fractional Number Slots Per Pole
PMSM in Flux Weakening Operation
The power factor and the loss of stator teeth hysteresis v. advanced angle
The power factor was very sensitive to setting of advanced angle, as can be shown in Fig.
8. The high power factor is demanded to reduce the losses of inverter.
It is observable that at constant speed 1000 rpm and current 280A the power factor versus
the advanced angle may be varied in a large domain. The maximum value of the function is
0.98 and there is at about 31 degrees of advanced angle.
Fig. 9 shows the loss of stator teeth hysteresis vs. advance angle at speed 2000 rpm and
280 A motor current. In Fig. 9 shows it by varied motor current at constant speed 1000 rpm
and at 26 degrees. It is observable increasing the current the hysteresis losses is
decreasing until we reach about 340 A which is the maximum planned current in this motor.
1
0.75
data 1
data 1
4th degree
cubic
0.7
0.9
0.65
0.8
power factor
4
3
stator teeeth hysteresis (kW)
0.6
2
y = - 1.96e-008*x + 8.75e-007*x - 9.84e-005*x + 0.006*x + 0.893
0.7
0.6
0.5
0.55
3
2
y = 2.78e-007*x + 5.79e-006*x - 0.00755*x + 0.718
0.5
0.45
0.4
0.35
0.4
0.3
0.25
0
10
20
30
40
50
60
70
80
advanced angle (degree)
Figure 8. The power factor at speed 1000 rpm, current 280 A
0
10
20
30
40
50
60
70
80
advanced angle (degree)
Figure 9. The loss of stator teeth hysteresis vs. advance
angle. Speed 2000 rpm, Imot 280 A
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
Magnet Losses of Fractional Number Slots Per Pole
PMSM in Flux Weakening Operation
The stator voltage functions v. advanced angle
Fig. 10 shows the stator voltage functions v. advanced angle at constant power Pout=108
kW and at speeds of motor 1500, 2000, 2500 and 3000 rpm.
The power and the value of speeds are constant along any curve so the torque is the
same also. To increasing the advanced angle at the same torque needs to increase the
motor current.
An increased value of current provide more effective flux weakening and with this
decreases the MMF so it will be sufficient a lower voltage of battery to supply the PMSM.
108 kW at 1500, 2000, 2500 and 3000 rpm
650
600
3000rpm
550
stator voltage (V)
For this PMSM the
planned maximum speed
is 2500 rpm and
achieving this by 550 V
DC the needed angle is
58.5 degrees. By 700 V
DC the needed advanced
angle is 47.9 degrees
only.
2500rpm
700V DC
500
450
600V DC
550V DC
400
2000rpm
350
1500rpm
300
25
30
35
40
45
50
55
60
65
advaced angle (degree)
Figure 10. The stator voltage v. advanced angle at P=108 kW and varied speeds
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
Magnet Losses of Fractional Number Slots Per Pole
PMSM in Flux Weakening Operation
The motor current v. advanced angle at Pout=108 kW
In Fig. 11 it be shown the motor current v. advanced angle at Pout=108 kW. The power,
the torque and the value of speed on one curve are the same.
At speed 1500 rpm the needed advanced angle is 25 degrees by the current 163 A.
To achieving speed 3000 rpm at 550 V DC the needed angle is 64.3 degrees, and at 700
V DC is 57.7 degrees. The curves of constant voltages of 550 V DC, 600 V DC and 700 V
DC show the actually achievable work points in the curves of constant speeds.
108 kW at 1500, 2000, 2500 and 3000 rpm
220
2500rpm
2000rpm
180
stator current (A)
In this figure may be
read the possible
region due an
actually voltage of
battery.
1500rpm
200
550V DC
160
600 V DC
140
700 V DC
3000rpm
120
100
25
30
35
40
45
50
55
60
65
advanced angle (degree)
Figure 11. The current v. advanced angle by P= 108 kW at varied speeds
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
Magnet Losses of Fractional Number Slots Per Pole
PMSM in Flux Weakening Operation
Magnet eddy current losses
Drawn the curves of constant battery voltage we can see in Fig. 12 that at 550 V DC
and at speed of 3000 rpm the magnet loss is 6 kW. At 2500 rpm the loss is 4.2 kW in
magnets as heat, that it is needed to transport away by a cooling system. At 700 V
battery voltage will be developed the magnet losses 4.28 kW at 3000 rpm, and at 2500
rpm 3 kW, that needs much lower cooling power.
108 kW at 1500, 2000, 2500 and 3000 rpm
6.5
6
Figure 12. Magnet
eddy current v.
advanced angle at
Pout=108 kW by
varied speeds and
the constant battery
voltages of 550 V
and 700 V
magnet eddy current loss (kW)
5.5
550V DC
5
4.5
4
2000rpm
3.5
3
700 V DC
1500rpm
3000rpm
2.5
2500rpm
2
25
30
35
40
45
50
advanced angle (degree)
55
60
65
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
Magnet Losses of Fractional Number Slots Per Pole
PMSM in Flux Weakening Operation
The total losses v. torque angle
In Fig. 13 it can be shown the total losses v. advanced angle at Pout= 108 kW at the same
circumstances. The curves are very similar to ones of magnet loss because this is the main
loss-component. The curves of total loss determine the efficiency curves. At 700 V DC
voltage of battery the losses are the least, and at 550 V DC the losses are the highest. This
different may be 40 %.
108 kW at 1500, 2000, 2500 and 3000 rpm
10
2500rpm
9
550V DC
8
total loss (kW)
600V DC
7
1500rpm
6
700V DC
3000rpm
5
2000rpm
4
3
25
30
35
40
45
50
55
60
advanced angle (degree)
Figure 13. Total losses v. advanced angle at P=108 kW by varied speeds
and the constant battery voltages of 550 V, 600 V and 700 V
65
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
Magnet Losses of Fractional Number Slots Per Pole
PMSM in Flux Weakening Operation
Efficiency v. torque angle in field-weakening
Efficiency v. advanced angle curves can be shown in Fig. 14 with 108 kW output power
at constant speeds. It is observable that the points due to actually maximum of
efficiency all are above of 95 %. Three curves goes in over the value of efficiency 96 %.
The decreasing of efficiency comes with the increasing of current and advanced angle to
achieving reduction of MMF.
108 kW at 1500, 2000, 2500 and 3000 rpm
97
96
1500rpm
efficiency (%)
With a battery voltage of 550
V at speed of 2500 and 3000
rpm it will be achievable 93.8
and 92.5 % efficiency but with
700 V battery voltage these
values increased to 95.3 and
94.6 %.
The voltage of battery may
change the efficiency only by
about 2 % at 2500 and 3000
rpm and Pout=108 kW
between 700 V and 550 V, but
the developed heat in
rotormagnets will be higher
about 50 % and that should be
critical.
98
95
550V DC
3000rpm
2000rpm
94
700V DC
93
92
25
2500rpm
30
35
40
45
50
55
60
advanced angle (degree)
Figure 14. Motor efficiency v. advanced angle at Pout=108 kW by varied
speeds and the constant battery voltages of 550 V and 700 V
65
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
Magnet Losses of Fractional Number Slots Per Pole
PMSM in Flux Weakening Operation
The power factor v. advanced angle in field-weakening
In Fig. 15 it be shown the power factor v. advanced angle by the same cases as
previously with 1500, 2000, 2500 and 3000rpm, and at output power Pout= 108 kW. The
value of these curves are the highest at speed of 1500, 2000 and 2250 rpm where the
power factor are above 0.95.
At the same time we can see that at 3000 rpm and by a 65 degrees in flux-weakening
the power factor again increases and achieves a value of 0.94.
108 kW at 1500, 2000, 2500 and 3000 rpm
1
2000rpm
1500rpm
power factor
0.95
2500rpm
0.9
3000rpm
0.85
25
30
35
40
45
50
55
60
advanced angle (degree)
Figure 15. Power factor v. advanced angle at P=108 kW by varied speeds
65
Magnet Losses of Fractional Number Slots Per Pole
PMSM in Flux Weakening Operation
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
Magnets from narrower slices
The loss is decreased in ratio of the distribution of magnet-size to more slice according to
the literature on the subject. At the same time there are some disadvantages: the efficiency
of magnet and the mutual inductance will be smaller a little, the cogging torque will be higher
due the increasing the number of slot between magnets, and the cost of manufacturing will
be increased definitely.
We investigated this possibility, as it can shown in Fig. 16. The main parameters here are
Pout = 108 kW, speed 3000 rpm, the torque is 344 Nm, the motor current is 186 A, the
advanced angle is 65 degree and the magnet loss here is Plossmagn =2.58 kW only.
Figure 16. The modified rotor with two-slice type magnets and the decreasing of loss in magnets
Magnet Losses of Fractional Number Slots Per Pole
PMSM in Flux Weakening Operation
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
Distribution of induction at current Imot = 300 %
The distribution of induction by Imot = 300 % that is for a strong overloading can see in
Fig. 17. Even for this utilization the maximum induction is about from 1.9 to 2 Vs/m2 in
teeth.
Figure17. The distribution of induction in the stator core at 300 % overloading
Magnet Losses of Fractional Number Slots Per Pole
PMSM in Flux Weakening Operation
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
III. Investigation and results in fields of current vectors
A circle diagram is a well-known graphical device for determining the adequate fieldweakening control strategy for synchronous motor drives [10]. These drives are usually
current controlled and so its convenient to define the operating point in terms of its
location in the (Id-Iq) plane. The current limit constraint Iqn2+ Idn2 ≤ In2 forms a circle:
Un2 = ωn2 ·[ (Φmn+Ln·Idn)2+(Ln· Iqn)2]
(3)
Tn = Φmn ·Iqn
(4)
Figure 18. The (Id-Iq) plane with the circle diagram for field-weakening control
Magnet Losses of Fractional Number Slots Per Pole
PMSM in Flux Weakening Operation
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
III. Results in fields of current vectors
•
From (3) it can be shown that voltage limit constraint if Vn ≤ 1 defines
a circle whose center is offset from the origin ( see Fig 18). The size of
this circle is inversely proportional to speed.
•
From (4) it can be shown that lines of constant torque form strait lines
parallel to the d-axis in Fig. 18. The size of this circle is inversely
proportional to speed. From (4) it can be shown that lines of constant
torque form strait lines parallel to the d-axis (see Fig. 18).
•
In literature there are several worked out method and strategy to
control a PMSM drive in different applications.
•
Among these methods a maximum efficiency control is very important
in several applications where energy saving may be critical, for
example in hybrid electric and electric vehicle drives [3]. Unfortunately
there is not a simple algorithm for implementing this strategy online. If
the loss is computed for every operating point in advance we can give
an efficient use.
Magnet Losses of Fractional Number Slots Per Pole
PMSM in Flux Weakening Operation
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
Workpoints in field of current vectors
The Fig. 19 shows in field of current vectors summing up the results of our studies and
investigations for our outer-rotor type surface-mounted synchronous motor in its fieldweakening region.
The drawn work-points are the same as were previously: the power is Pout = 108 kW, the
four speeds are 1500, 2000, 2500 and 3000 rpm. The degree and the relative % of
current vectors are described next them.
We drawn three curves
of constant efficiency of
96, 95 and 92 %, the five
curves of power factor of
0.96, 0.97, 0.98, 0.91
and 0.9 values and the
two curves of magnet
losses due of 700 V DC
and 550 V DC battery
voltages.
Figure 19. The field of current
vectors at Pout=108 kW. Curves
of efficiency, power factor and
magnet eddy current losses at
700 and 550 V DC
Magnet Losses of Fractional Number Slots Per Pole
PMSM in Flux Weakening Operation
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
Finding a possible control strategy
•
In Fig. 19 there is a favourable continuous line connecting the speed curves of 1500 and
3000 rpm: this is just the magnet eddy current losses at 700 V, which across the field of
current vectors beeing from 1500 to 3000 rpm. It touches the efficiencies nearby 96 %,
and later the 95 and 94 % and at the same time across the highest values of power
factor region.
•Practically this
red-dotted curve
seems to be the
most adequate line
of an optimum
control strategy for
this motor in fieldweakening region
at case if Pout=108
kW.
Figure 19. The proposed
control strategy in fieldweakening for P=108kW
and 1500 to 3000 rpm
Magnet Losses of Fractional Number Slots Per Pole
PMSM in Flux Weakening Operation
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
Determining of Id and Iq functions for an optimum control strategy
Determined the Id and Iq functions are in Fig. 20 from Fig. 19 to calculate these currents
from actual values of speed, fitted with 4th and 3th orded polynoms, where x is the speed,
[rpm]:
Id= 1.9*10-11x4-1.7*10-7x3+0.00052x2-0.71x+2.5*102
(5)
Iq= -1.83*10-8*x3+1.41*10-4 x2-0.415*x+575
(6)
Figure 20. The function of Id and Iq components v. speed for proposed control strategy
from Fig. 19 for constant 108 kW and at speeds from 1500 to 3000rpm
Magnet Losses of Fractional Number Slots Per Pole
PMSM in Flux Weakening Operation
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
IV Conclusions
•
The result of our work is a possible optimum control strategy in (Id-Iq) plane.
Computing and drawing the curves of magnet losses, efficiency and power
factor, in the field of current vectors it could be find the adequate controlling
line as optimum controlling function.
•
From values of this line can be determined the (5) and (6) functions of Id and
Iq component v. speed, as actual reference current-signals for the control of
PMSM in the field–weakening region, with approximately a possible best
optimum of magnet losses, power factor and efficiency, in case of at a
constant DC voltage supplying.
Acknowledgment
•
„TAMOP-4.2.2.A-11/1/KONV-2012-0012: Basic research for the development
of hybrid and electric vehicles - The Project is supported by the Hungarian
Government and co-financed by the European Social Fund”
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
Magnet Losses of Fractional Number Slots Per Pole
PMSM in Flux Weakening Operation
•
References
•
[1] I. Szenasy.: “Some developing and controlling problems of PMSM motors applied
for modern drives for EV-s.” Presentation in Conference to Drive for Road Vehicle,
MTA, Budapest, 23 01 2012.
•
[2] I. Szenasy : “Investigation some Electromagnetic Characteristics of PMS motor In
Flux Weakening Operation”. Symposium on Applied Electromagnetic 06 23-25 2012
Sopron, Hungary.
•
[3] R. Krishnan.: PMSM and Brushless DC Motor Drives. By Taylor and Francis Gr
LLC 2010. CRC Press 2010. ISBN 978-0-8247-5384—9.
•
[4] J.Wang, K. Atallah, R. Chin, W. Arshad, H. Lendenmann: „Rotor Eddy-Current
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[5] C. Mademlis, J.Xypteras, and N. Margaris: „Loss Minimization in Surface
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[6] D. Ishak, Z. Q. Zhu and D. Howe: „Eddy-Current Loss in the Rotor Magnets of
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IEEE Transaction on Magnetics, Vol. 41, No. 9, September 2005
Magnet Losses of Fractional Number Slots Per Pole
PMSM in Flux Weakening Operation
The 10th IEEE International Conference on Power Electronics
and Drive Systems 22 – 25 April 2013 Kitakyushu, Japan
•
[7] Z. Q. Zhu, K. Ng, N. Schofield, and D. Howe, “Improved analytical modeling
of rotor eddy current loss in brushless machines equipped with surface mounted
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[8] I. Szenasy: New Energy Management of Capacitive Energy Storage in
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[9] Jiabin Wang􀀀, K. Atallah􀀀, R. Chin_, W. M. Arshad_, and H. Lendenmann:
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Sheffield S1 3JD, U.K. ABB Corporate Research, Västerås SE-721 78, Sweden.
IEEE Transaction on Magnetics, VOL. 46, no. 7, July 2010 2701
•
[10] S. Meier: Theoretical design of surface-mounted permanent magnet
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Electronics Stockholm 2001/2002