XIX International Conference on Electrical Machines - ICEM 2010, Rome
Investigation of a Three-Phase Flux-Switching
Permanent Magnet Machine for Downhole
Applications
Anyuan Chen, Robert Nilssen and Arne Nysveen
Φ
Abstract – This paper investigates a newly designed fluxswitching permanent magnet machine with 12 stator poles and
14 rotor poles for downhole application where the ambient
temperature is around 150°C. This machine having an outer
diameter of 100 mm and an active axial length of 200 mm can
provide ~ 2.7 kW with an output torque up to 25 Nm, an
efficiency of ~88% and power factor of 0.87. The maximum
temperature in the machine is around 200°C without external
cooling. Additionally, the machine losses, inductance and
magnet demagnetization field are also studied.
Index Terms— Downhole application, finite element method,
flux-switching, high torque, permanent magnet machine.
I. NOMENCLATURE
Acoil
Br
Bt
Do
g
Hrb
Hsb
Ht
Hrt
J
kf
L
lpm
ncoil
ns
Pcu
Pfe
Ppm
S
T
Wrt
Ws
Wst
λ
τr
τs
ωm
ρcu
lend
ψd-max
ψq-max
ψpm
Φd-max
Φq-max
Φpm
αcu
kpm
Coil area
Magnet remanence
Average flux density in stator tooth top at d-axis.
Machine outer diameter
Airgap length
Rotor iron-back thickness
Stator iron-back thickness
Stator tooth height
Rotor tooth height
Current density
Winding factor
Machine active axial length
Magnet thickness
Number of turn of each coil
Number of turn of each phase
Copper loss
Iron loss
Eddy-current loss in magnets
Electrical loading
Torque
Rotor tooth width
Stator slot opening
Stator tooth width
Ratio of stator inner diameter to outer diameter
Rotor pole pitch
Stator pole pitch
Machine synchronous speed
Copper resistivity at room temperature
Copper end winding connection
Peak flux-linkage at d-axis
Peak flux-linkage at q-axis
Flux linkage from magnet only
Peak flux at d-axis
peak flux at q-axis
Flux produced by magnet only
Copper temperature coefficient
Magnet temperature coefficient
This work was supported by Research Council of Norway (NFR).
The authors are with the Department of Electrical Engineering,
Norwegian University of Science and Technology, O.S. Bragstads plass 2E,
level4 (anyuan.chen@elkraft.ntnu.no). (robert.nilssen@elkraft.ntnu.no)
(arne.nysveen@elkraft.ntnu.no).
978-1-4244-4175-4/10/$25.00 ©2010 IEEE
II. INTRODUCTION
T
HE current standard electrical downhole machine is the
induction machine which is relatively inefficient. Today,
with the development of advanced technologies and
applications of high temperature magnets, it is increasingly
interesting for oil and gap industries to develop permanent
magnet (PM) machines for downhole applications where the
machine outer diameter is typically around 100 mm limited
by well sizes and the axial length can be relatively long. Due
to the harsh condition downhole and the high cost for
machine failure replacement the machine reliability is
required high. The authors have compared the performances
of radial flux (RF), axial flux (AF) and transverse flux (TF)
PM machines in [1]. The RFPM machines present the best
characteristics for downhole applications. Conventionally,
the RFPM machines have magnets on the rotor with four
typical types: surface-mounted, inset, interior-radial and
interior circumferential topologies. Disregarding the
different rotor PM arrangements, these machines can offer
the common advantage of high torque density and high
efficiency. However, the magnets on the rotor usually need
to be protected from the centrifugal force by employing a
retaining sleeve, which is made of either stainless steel or
non-metallic fiber. This degrades the cooling capability and
hence limits the power density. Furthermore, these machines
suffer from the possibility of irreversible demagnetization
from armature reaction field, particularly in high temperature
environment, which is the considered case for downhole
applications. Flux-switching permanent magnet (FSPM)
machines have PMs in the stator with a doubly salient stator
and rotor like a reluctance machine as shown in Fig. 1. They
combine the advantages of a conventional PM machine and a
switched reluctance machine, and therefore have high
reliability, high torque /power density and relatively high
efficiency. They are hence preferable reliability premium
applications. Compared with the rotor-PM machines
abovementioned, the FSPM machines have the following
advantages [2]-[7]:
Winding
Magnet
(a)
(b)
Fig. 1. (a) Cross section (b) stator of a 12/14 pole machines.
where Acoil is half the slot area, ncoil is the number of turns of
each coil, it is one fourth the phase-coil turns, ns.
Table I Machine parameters
Optimized value
Parameter
Do
100 mm
L
200 mm
ωm
1000 rpm
g
0.5 mm
λ
0.51
Ps
12
Pr
14
Wrt
3.8 mm
Wst
3.2 mm
Hsb
2.2 mm
Ht
23 mm
Hrt
6.4 mm
lpm
2.4 mm
Br
1.16 T
kf
0.6
J
4 A/mm2
αcu
0.0039K-1
ρcu
1.87x10-8 Ωm
kpm
-0.00045 K-1
Fig. 2. Part of the machine in a plain form.
1) Better cooling capability: PMs in the stator make it
easier to dissipate heat from the stator surface, thereby,
to limit the temperature rise of the magnets.
2) Less de-magnetization field from armature reaction
because the windings and the magnets are magnetically
in parallel. As a result, the electric loading and the
specific torque capability of the FSPM machine can be
higher.
3) Comparative or even better torque capability based on
1) and 2).
4) Only steel on the rotor makes the FSPM machines more
robust.
Additionally, the FSPM machines have concentrated
windings, which result in less copper loss and are also easy
to make.
However, the FSPM machines introduce additional rotor
iron loss caused by the flux variation in the rotor iron. This
may lead to a lower efficiency. But for the relatively low
speed applications here (1000 rpm), the iron loss normally is
minor compared to the copper loss.
In [8] and [9] a FSPM machine with 12 stator poles and
14 rotor poles (12/14 poles) shown in Fig. 1 and Fig. 2 has
been presented. Compared with a 12/10 pole machine, this
machine can provide higher torque density with the same
copper loss and less torque ripple. The magnetic design of a
12/14 pole machine has been presented in [10] and Table I
lists the machine parameters. In this paper this machine is
investigated for downhole applications where the ambient
temperature is assumed to be 150°C and no external forced
cooling available. The maximum temperature in the machine
should not be over 200°C limited by both the PM material
and winding insulation. Firstly, the number of turn and
machine inductance are studied. And then the output torque,
machine losses, power factor and efficiency are investigated
based on finite element method (FEM). Additionally, the
magnet demagnetization field and machine thermal
phenomenon are also presented.
III. INDUCTANCE AND NUMBER OF TURNS
Due to the complexity of the flux paths in the airgap, it is
not easy to analytically evaluate the inductances with an
acceptable accuracy. Additionally, the inductances are
sensitive to iron saturation. So FEM analysis is employed.
Considering the position where the rotor is aligned with
the d- or q- axis of phase a as shown in Fig. 3 and the
injected three-phase currents are
⎧
2 Acoil k f J
cos( Pr ωt )
⎪ia = I max cos( Pr ωt ) =
ncoil
⎪
.(1)
⎨
2 Acoil k f J
⎪
1
cos( Pr ω t )
⎪ib = ic = − 2 I max cos( Pr ωt ) = − 2n
coil
⎩
(a)
(b)
Fig. 3 (a) d-axis position (b) q-axis position of phase a
Then Ld and Lq of each phase can be calculated by [11]
Ld =
ψ d − max −ψ pm
I max
d − axis
⎛ ( Φ d − max − Φ pm ) ⎞
2
⎜
⎟
= ncoil
⎜
⎟
2
A
k
J
coil
f
⎝
⎠ d − axis
or
Lq =
ψ q − max
I max
⎛ Φ q − max
2
⎜
= ncoil
⎜ 2A k J
coil f
q − axis
⎝
⎞
⎟
⎟
⎠ q − axis
.(2)
where Φd-max and Φq-max are respectively the maximum
summary flux in four phase-a coils at d- and q-axis
positions.
As can be seen from (2) the inductances are proportional
to the square of the turn numbers. If assuming the machine
has one-turn coil, its one-turn inductance L1-d/q is directly
given by (2) with Φd-max, Φq-max and Φpm obtained from FEM
simulations as shown in Fig. 4, and Φpm = 3.22 mWb. Then
the inductance with ncoil turns is
2
Ld / q = ncoil
L1− d / q
(3)
where L1-d/q is the phase inductance with one-turn coil in the
d or q-axis.
It is observed from Fig. 4 that due to the iron saturation
the peak flux at the d-position is not symmetrical at the
positive and negative current, so the average between them
is employed.
5
4
Flux at d and q axis(mWb)
ncoil ≤
Fluxd
Fluxq
3
( E1− turn + 8 J ρcu Lcu )2 + ( Pr ωm Acoil k f JL1− q )
(10)
1
0
-1
-3
0
0.5
1
1.5
2
2.5
Time (msec.)
3
3.5
4
4.5
Fig. 4 Flux at d and q axis from FEM analysis
The number of phase-coil turns is limited by the voltage
limitation Vmax of the converter used for the control.
V = E ph + I ph ( jX s + Rs ) ≤ Vmax
(4)
where Eph is the phase back EMF (rms value) proportional
to ncoil, the phase EMF with one-turn coil, E1-turn, is obtained
by FEM simulations shown in Fig. 5 and its rms value is 3.5
V. Rs is the copper resistance and evaluated from (5), Xs is
the phase reactance and calculated by (7). Iph is the phase
current (rms) determined by (8).
Rs =
8ncoil ρcu Lcu
8n 2 ρ ( L + lend )
= coil cu
( Acoil k f / ncoil )
Acoil k f
(5)
5
IV. LOSSES AND MACHINE EFFICIENCY
In order to investigate the machine efficiency and the
thermal behavior, the machine losses that contribute to
heating are studied. The losses considered here are the iron
loss in stator and rotor, the copper loss in the stator winding
including the end parts, (only the ohm loss are considered,
eddy current loss in the copper is neglected) and the magnet
eddy current loss.
A.
Iron losses
The iron loss significantly depends on the iron material.
Fig. 6 depicts the specific losses of M330-35A. The loss is
frequency dependent and the curve in the considered case is
the one at 233 Hz (Prωm). Then the iron loss in each part is
determined by
Pfe = WG
(11)
where W is the specific loss in the corresponding iron part
dependent of the peak flux density that can be obtained by
FEM simulations, and G is the weight of the corresponding
iron part. For calculating the loss in the teeth where the peak
density at the top and bottom may be different, its average
peak value is employed.
Table II lists the peak flux densities and the calculated
loss.
4
3
2
1
0
-1
-2
-3
-4
-5
2
Here Vmax = 415V and ncoil is selected to be 96.
2
-2
Phase EMF of one-turn coil (V)
2
Vmax
0
5
10
15
20
Rotor position in mech. degree
25
30
Fig. 5 phase back EMF with one-turn coil.
where lend is approximated by
lend = π 2 (λ Do + H t ) / 2 ps
X s = Pr ωm Ls
(6)
(7)
Assuming the FSPM machine is controlled to only have
q-axis current Iq (Id=0), and it is determined by
I q = I ph =
Acoil k f J
ncoil
(8)
Substituting (5), (7) and (8) into (4) yields
Vmax ≥ E ph + I q ( jPr ωm Lq + Rs )
≥ E1− turn ncoil + 8ncoil J ρcu Lcu + jPr ωm Acoil k f Jncoil L1− q
The turn number of each coil is limited by
(9)
Fig. 6 Characteristics curve of M330-35A
Loss
(W)
75
35
19
11
Copper loss
The copper loss is calculated at 200 °C and it is
determined by (12). The calculated loss Pcu is 185 W.
B.
2
ph
Pcu = I Rs _ 200
(12)
where Rs-200 is the copper resistance at Tθ = 200°C and given
by
Rs _ 200 = Rs (1 + (Tθ − 20)α cu ) .
(13)
C.
Magnet eddy current loss
The eddy current loss in the permanent magnet is caused
by the flux variation in the magnets. In analysis and design
of PM machine, the eddy-current effect is usually neglected.
For concentrated winding machines, the eddy current loss is
relatively large compared with that in distributed winding
machines due to the wider slot opening [12]. The loss is
investigated by 2D-FEM simulations with conductivity σ =
7.1x105 S/m and presented in Fig. 7. Its average value Ppm is
26 W.
30
O utput torque (N.m )
Table II Peak flux density in iron parts with J = 4 A/mm2
Iron parts
Weight Peak flux Specific
(kg)
density (T)
loss (W/kg)
Stator tooth top /bottom
2.70
1.9 /1.3
28
Stator back iron
0.99
1.7
35
Rotor tooth top /bottom
0.54
1.7/1.7
35
Rotor back iron
0.37
1.6
28
25
20
15
10
5
0
0
5
10
15
20
25
Rotor position in mech. degree
30
35
40
Fig. 8 The output toque from FEM simulations.
VI. MACHINE PERFORMANCE
Table III presents the machine performance parameters
from the investigations.
Table III Performance parameters of the machine
Value
Parameter
V
412 V
Iph
2.88 A
ns
384 turns
Ld
39.4 mH
Lq
48.6 mH
Rs
4.4 Ω
Pout
2.7 kW
T
25.2 N.m
η
87.9%
PF
0.87
Magnet eddy current loss (W)
VII. THERMAL INVESTIGATION
30
25
20
15
10
5
0
0
5
10
15
20
25
Rotor position in mech. degree
30
35
40
Fig. 7. Eddy-current loss from FEM simulations
D.
Machine Efficiency and power factor
The machine efficiency is evaluated by (14).
η = ( 3E ph I ph − Pfe − Pcu − Ppm ) / ( 3E ph I ph )
(14)
The power factor is determined by
PF = ( E ph + I ph Rs _ 200 ) / V .
Insulation is the weakest part of a machine and hence can
be easily destroyed by overheating, which depends on the
maximum winding temperature in the machine. For this
machine, the chosen insulation class of the winding is 200°C
(IEC317-13). Its continuous work temperature is 200°C, and
maximum allowable hot-spot temperature is 320°C.
The machine is installed within an aluminum frame with
1 cm thickness. Since this frame is not an active part of the
machine and has no contribution for torque production, this
part is therefore not considered during the machine design
procedure.
For downhole applications the machine outer surface is
surrounded by liquid and the temperature is assumed to be
constant 150°C. Fig. 9 shows the temperature distribution of
the machine from the static-state FEM simulation with the
calculated losses. The maximum temperature in the coil parts
is around 200°C.
(15)
V. OUTPUT TORQUE
The output toque is obtained from FEM simulations and
shown in Fig. 8, in which the magnet temperature coefficient
has been taken into account by (16) with Tθ = 200°C. The
average torque is 25.2 N.m.
Bm = Br (1 + (Tθ − 20)k pm )
where Bm is magnet flux density used in the FEM
simulations.
(16)
Fig. 9 Temperature distribution in the machine from FEM simulation
VIII. DEMAGNETIZATION FIELD
The torque capability of a PM machine is not only
dependent on the cooling of the machine and the current
capability of the inverter, but also the demagnetization field
that the magnets can withstand. A typical demagnetization
characteristic for Sm-Co magnet material is shown in Fig.
10. As long as the demagnetizing field intensity does not
exceed the magnitude HD, the recoil line will fall along the
original demagnetization line and the torque capability of the
machine will be preserved. The critical point (BD, HD) on the
demagnetization curve is temperature dependent, and BD is
usually lower than 0 at 200°C for Sm-Co magnet materials.
Fig. 10 Demagnetization characteristic of PM material.
To prevent demagnetization of the magnet the stator
current must be limited so that
BD < Bm − Bc
(17)
where Bm is flux density over the magnet at no load
condition, in which the stator current is zero. Bc is the peak
flux density over the magnet with stator current acting alone.
Both the values can be investigated by FEM simulations.
Fig. 11 shows the average flux density along the axial
middle line of the magnet at the different rotor position with
only either magnets or stator current. It is observed that the
minimum Bm = 0.23 T is much higher than the peak value Bc,
0.05 T. So this is no risk to demagnetize the magnet with the
given current density.
X. REFERENCES
[1]
Anyuan Chen, Robert Nilssen and Arne Nysveen, “Performance
comparisons among radial flux, multi-stage axial flux and three-phase
transverse flux PM machines for downhole applications”, IEEE Trans.
Ind. Appl., vol 46, No.2, pp 779-789.
[2] J. Zhang, Z. Chen and M. Cheng, “Design and comparison of a novel
stator interior permanent magnet generator for direct-drive wind
turbines”, IET Renewable Power Generation, December, 2007, Vol.1
pp 203-210.
[3] Z. Q. Zhu, Y. Pang, D. Howe, S. Iwasaki, R. Deodhar, and A. Pride,
“Analysis of electromagnetic performance of flux-switching
permanent magnet machines by non-linear adaptive lumped parameter
magnetic circuit model,” IEEE Trans. Magn, vol.41, No.11, pp. 42774287, November 2005.
[4] Y. Pang, Z. Q. Zhu, D. Howe, S. Iwasaki, R. Deodhar, A. Pride,
“Comparative Study of Flux-Switching and Interior Permanent
Magnet Machines”, the proceeding of ICEMS 2007, Oct. 8-11, Seoul,
Korea.
[5] K. T. Chau, C. C. Chan and Chunhua Liu, “Overview of PermanentMagnet Brushless Drives for Electric and Hybrid Electric Vechicles”,
IEEE Transactions on Inductrial Electronics, vol. 55, no. 6 June 2008.
[6] Fang, Z. X., Wang, Y., Shen, J. X., Huang, Z. W., “Design and
analysis of a novel flux-switching permanent magnet integratedstarter-generator” , PEMD 2008.
[7] Arwyn S. Thomas, Z. Q. Zhu, Richard L. Owen, Geraint W. Jewell
and David Howe, “Multiphase Flux-Switching Permanent-Magnet
Brushless Machine for Aerospace Application”, IEEE Trans. Ind.
Appl., vol. 45, No. 6, pp. 1971-1981, November/December 2009.
[8] J. T. Chen, Z. Q. Zhu, A. S. Thomas and D. Howe, “Optimal
combination of stator and rotor pole numbers in flux-Switching PM
brushless AC machines”, the proceeding of ICEMS,2008, vol. 44, pp.
4659 – 4667.
[9] Anyuan Chen, Njål Rotevatn, Robert Nilssen and Arne Nysveen,
“Characteristic Investigations of a New Three-Phase Flux-Switching
Permanent Magnet Machine by FEM Simulations and Experimental
Verification” in the proceeding of ICEMS2009, 15-18, Nov., 2009
Tokyo, Japan.
[10] Anyuan Chen, Robert Nilssen and Arne Nysveen, “Analytical design
of a high-torque Flux-Switching Permanent magnet machine by a
Simplified Lumped parameter magnetic circuit model”, submitted to
the conference ICEM 2010.
[11] Ping Zheng, Peter Thelin, Anyuan Chen and Erik Nordlund,”
Influence of Saturation and Saliency on the Inductacne of a FourQuadrand Transducer Prototype Machine”, IEEE Trans. Magn. Vol.
42, no.4, april 2006.
[12] Katsum Yamazaki, Yu Fukushima and Makoto Sato, “Loss Analysis
of Permanent-Magnet Motors with Concentrated Windings-Variation
of Magnet Eddy-Current Loss Due to Stator and Rotor Shapes”, IEEE
Trans. Ind. Appl., vol. 45, No.4, July /August 2009.
Average x component of the flux density(T)
XI. BIOGRAPHIES
Anyuan Chen received the B.Sc. degree in electrical engineering from
Wuhan Institute of Technology, Wuhan, China in 1991, and then worked as
(senior) electrical engineer at several companies. In 2004 he received the
M.Sc. in Electrical Power Engineering from the Royal Institute of
Technology (KTH), Stockholm, Sweden. Now he is working toward the
Ph.D. degree in Norwegian University of Science and Technology (NTNU),
Trondheim, Norway.
His research interests include permanent magnet machine design and
electric drives.
Only magnet
Only current
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.05
0
5
10
15
20
25
30
Rotor position in mech. degree
35
40
Fig. 11 Flux density in the magnets from FEM simulations.
IX. CONCLUSIONS
This paper investigates a flux-switching permanent
magnet with 12 stator poles and 14 rotor poles for downhole
application where the ambient temperature is around 150°C.
This machine has an outer diameter of 100 mm and an active
axial length of 200 mm. The investigations show that the
machine can provide ~ 2.7 kW power with the output torque
up to 25 Nm, an efficiency of ~ 88% and a power factor of
0.87. The maximum temperature in the machine is around
200°C without external cooling.
Robert Nilssen received the M.Sc. and Dr.ing from the Norwegian Institute
of Technology (NTH), Trondheim Norway, in 1983 and 1988, respectively,
specializing in the field of Finite Element Analysis.
He was an advisor to Norwegian Research Institute of Energy supply and
SINTEF. Currently he is a professor in Electrical Engineering at the
Norwegian University of Science and Technology (NTNU). He current
research interests include design of electromagnetic components and
electrical machines, optimization and modeling. He is a co-founder of
several companies.
Arne Nysveen (M’00-SM’06) received the M.Sc. degree in Electrical
Power Engineering and the Dr.ing degree from the Norwegian Institute of
Technology (NTH), Trondheim, Norway, in 1988 and 1994, respectively.
From 1995 to 2002, he was a Research Scientist with ABB corporate
Research, Oslo, Norway, where his main research dealt with subsea power
supply and electrical power apparatus. Since 2002, he has been a professor
at the department of Electrical Power Engineering, Norwegian University of
Science and Technology (NTNU), Trondheim. He holds several patents on
subsea power equipment and electric machinery.