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Design of a high-speed permanent-magnet brushless generator for microturbines

ELECTROMOTION 12 (2005) 86-91
86
Design of a high-speed permanent-magnet
brushless generator for microturbines
J.F. Gieras and U. Jonsson
Abstract – The design process of modern high speed permanent magnet (PM) generators for microturbines has bee
discussed. The following design issues and requirements have been emphasized: volume and mass, power losses and
efficiency, stator core, stator winding, cooling, PM excitation, rotor mechanical stresses, shaft dynamics, consequences of
higher time harmonics and role of inductance in A.C. generator circuit. The paper is ended with a case study: design
specifications and performance characteristics of a 90-kW, 27,000-rpm PM brushless generator.
1. Introduction
1
2
3
45
345
6
Fig. 1. Longitudinal section of a PM high speed brushless
generator for Organic Rankine Cycle Turbo Generator:
1 - stator stack with 3-phase winding, 2 - PM rotor with
retaining sleeve, 3 – rotor laminated stack of radial
magnetic bearing, 4 - rotor of magnetic bearing sensor,
5 - additional rolling bearings, 6 - rotor of microturbine.
The current trend toward distributed
generation has increased interest for various
concepts of small-scale power generation
equipment in the 30 to 200 W range [1,5].
Technologies that are under development that
utilize high speed turbo machinery include small
Brayton cycle gas turbines, miniature steam co-
generation plants and organic Rankine cycle
plants. The small size of these machine drive
operating speeds to a range of 10,000 rpm up to
150,000 rpm in order to be able to operate at
optimum specific speed. An example of such unit
intended for a organic Rankine cycle plant is
shown in Fig. 1. This machine is a small, single-
shaft vapour expander where the rotor is
integrated with high speed electric generator
rated at 90 kW output power at 27,000 rpm.
The gas turbine cycle (Brayton cycle) consists
of four internally reversible processes: (a)
isentropic compression process, (b) constant-
pressure combustion process, (c) isentropic-
expansion process and (d) constant-pressure
cooling process. Unlike the Rankine cycle, micro
turbines use the exhaust gas pressure from the
burning process to turn the shaft directly. Basic
components of micro turbines are: turbine
compressor, combustor, recuperator, generator
and output solid state converter to provide 50 or
60 Hz electrical power. Commonly, micro
turbines burn natural gas but are also used with
liquid fuel or by landfill or sewage plant digester
gas. It is common that the high-grade exhaust
heat is recovered in heating processes to improve
the plant overall economy.
Water is the most common working fluid in
the Rankine cycle for large-scale power plants
operating at high temperatures. Water is not a
suitable fluid for small-scale power plants due to
the inherent risk of compressed steam requiring
operators and substantial maintenance. By using
organic working fluids it is possible to design
organic Rankine cycle plants that require a
minimum of maintenance and can operate
unattended for extensive times enabling
commercial viability of small plants. Typical
working fluids are hydrocarbons such as toluene
and various chloro and fluorocarbons.
© 2005 – Mediamira Science Publisher. All rights reserved.
J.F. Gieras, U. Jonsson / Design of a high-speed permanent-magnet brushless generator for microturbines
87
2. Requirements
Owing to high efficiency and power density,
permanent magnet (PM) brushless generators are
the best machines for distributed generation. The
electromagnetic design of PM high speed
brushless generators is aimed at meeting the
following requirements [2,3,4,6]:
compact design and high power density;
ability of the PM rotor to withstand high
temperature;
minimum number of components,
optimal cost/efficiency to minimize
system cost/kW;
high reliability (the failure rate shall be
< 5% within 80,000 h);
high efficiency over the whole range of
variable speed (frequency);
acceptable power factor over the whole
range of speed;
low total harmonics distortion (THD).
3. Design
Volume and mass. The power per volume of an
electrical machine is proportional to the line
current density, intensity of the cooling system,
air gap magnetic flux density and rotational
speed [3]. The higher the speed (frequency), the
higher the power density (power output-to-mass
or power output–to-volume). High frequency PM
brushless generators for microturbines have
small rotor diameter (a few centimeters). It is
sometimes very difficult to accommodate the
required volume of PM and retaining sleeve.
Power losses and efficiency.
A high speed PM
slotted brushless generator dissipates the
following power losses: (a) stator (armature)
winding losses, (b) stator core losses, (c)
windage losses (friction of rotor and cooling
gas), (d) bearing losses, (e) losses in the rotor
retaining sleeve due to higher harmonic magnetic
fields if a conductive material is used, (f) losses
in rare earth PM magnets. All losses, especially
the windage losses must be predicted with high
accuracy at the early stage of design. The
windage losses depend on the cooling gas, its
pressure, temperature and rotor diameter. At
constant armature current the efficiency
decreases with the frequency. To optimise the
overall value it is important to correlate
efficiency improvements with overall plant cost
in $/kW. A typical plant can cost 500-
3,000 $/kW.
Laminations
. The stator core losses can achieve
high values in high frequency and high power
density generators. If the maximum variable
frequency does not exceed 400 Hz, the optimum
thickness of laminations is 0.2 mm. A frequency
above 700 Hz usually requires laminations
thinner than 0.1 mm. Non-oriented silicon steels
(3% Si, 0.4% Al, 96.6% Fe) with low specific
losses or amorphous alloys are used.
Stator conductors.
The most intensive cooling
system is a direct liquid cooling system with
hollow conductors or oil spray system. However,
high frequency winding losses in hollow
conductors are higher than those in stranded
wires (Litz wires). Direct cooling system
increases the stator outer diameter and is too
expensive for generators rated below 200 kW.
Generator cooling.
High speed generators use air,
working fluid, oil or water as cooling media. To
obtain cycle efficiency, reliability and overall
economy it is often desirable to integrate the
generator cooling with the cycle and recover the
heat back to the cycle.
Excitation system
. Since the turbine end or hot
end of the shaft can reach the temperature over
+150
0
C, sintered NdFeB PMs are not
recommended. Currently available SmCo PMs
can withstand continuous operating temperature
up to +350
0
C.
Rotor mechanical stresses. The maximum
tangential stress occurs at the inner diameter of
the rotor. To secure acceptable rotor stresses, the
rotor diameter – to - length aspect ratio must be
properly selected. It is also critical to consider
possible over speed events caused by loss of
generator load where speeds in excess of 200%
can occur.
Rotor retaining sleeve.
Rotors with surface PMs
require retaining sleeves (cans). A good retaining
sleeve material must have a high permissible
J.F. Gieras, U. Jonsson / Design of a high-speed permanent-magnet brushless generator for microturbines
88
stress and low specific mass density. Carbon
fibre, glass fibre, titanium alloy TA6V or
nonmagnetic steel are the best materials. To hold
PMs and sleeve on the shaft, two solutions are
possible [4]: (a) to control the shaft expansion in
such a way as to achieve the same expansion of
the shaft and sleeve; (b) to decrease the sleeve
expansion. Both two solutions are technically
difficult.
Shaft dynamics
. Critical speeds and rotor
eccentricity should be carefully considered. The
speed–dependent rotor eccentricity affects the air
gap and must be accounted for in the generator
design. The selection of rotor diameter–to–rotor
length aspect ratio is frequently in conflict with
critical speed and windage losses minimization.
4. Performance characteristics
The phasor diagram of a salient pole
synchronous generator with RL load is shown in
Fig. 2. The input voltage projections on the d and
q are
11
11
sin
cos
aq sq ad
fadsdaq
VIXIR
VEIXIR
δ
δ
=−
=−
(1)
and
1
1
sin
cos
ad L aq L
aq L ad L
VIRI
VIRI
X
X
δ
δ
=−
=+
(2)
where V
1
is the output phase voltage, I
ad
is the d-
axis stator (armature) current, I
aq
is the q-axis
stator current, R
1
is the stator winding resistance
per phase, X
sd
is the d-axis synchronous
reactance per phase, X
sq
is the q-axis
synchronous reactance per phase, R
L
is the load
resistance per phase and X
L
is the load reactance
per phase. The load angle
δ
between the voltage
V
1
and EMF E
f
can be determined, e.g., from the
first eqn (2)
=
1
arcsin
V
XIRI
LaqLad
δ
(3)
Combining eqns (1) and (2), the d and q axis
currents are independent of the load angle
δ
, i.e.,
2
1
)())((
)(
LLsqLsd
Lsqf
ad
RRXXXX
XXE
I
++++
+
= (4)
2
1
1
)())((
)(
LLsqLsd
Lf
aq
RRXXXX
XRE
I
++++
+
= (5)
The short circuit current can be found by
putting R
L
= 0 and X
L
= 0. The ratio of the short
circuit–to–rated current ratio for high frequency
generators for microturbines is usually from 1.5
to 2.5.
The angle
Ψ
between the stator current I
a
and
q-axis and the angle
ϕ
between the current I
a
and
voltage V
1
are, respectively,
+
=
=Ψ
22
arccosarccos
aqad
aq
a
aq
II
I
I
I
(6)
I
ad
R
1
I
aq
R
1
I
a
R
1
V
1
I
a
jI
aq
X
sq
jI
ad
X
sd
E
f
q
d
I
ad
I
aq
V
1
I
a
R
L
jI
ad
X
L
jI
aq
X
L
jI
a
X
L
I
aq
R
L
I
ad
R
L
d
I
a
q
Fig. 2. Phasor diagram of an overexcited salient pole
synchronous generator.
=
=
L
LLa
Z
R
V
RI
arccosarccos
1
ϕ
(7)
where
I
a
=
(I
ad
2
+I
aq
2
). The output electrical
power on the basis of the phasor diagram (Fig. 2)
and eqn (1) is
11
2
1
3cos 3(cos sin
3[ ( ) ]
out a aq ad
faq adaq sd sq a
PVI VI I
EI I I X X IR
)
ϕ
ϕδ
=
=+
=−
(8)
Including only the stator winding losses
P
1w
= 3I
a
2
R
1
and stator core losses
P
1Fe
, the internal
electromagnetic power of the generator is
11
1
3[ ( )]
elm out w Fe
faq adaq sd sq Fe
PP P P
EI I I X X P
=
+∆ +∆
=− +
(9)
J.F. Gieras, U. Jonsson / Design of a high-speed permanent-magnet brushless generator for microturbines
89
In practical calculations eqn (9) requires
accurate estimation of the stator core losses
P
1Fe
.
5. POWER CONVERSION SYSTEM
The power plant solid state converter must
convert the generator high frequency output to a
low frequency sinusoidal output compatible with
utility grid requirements. The block diagram of
the power conversion components are shown in
Fig. 3.
3-phase
generato
r
passive
or
active
rectifier
output
inverter
filtering
C
d.c. voltage
link
transmission
line impedance
3-phase
utility grid
v
o
l
tage
Fig. 3. Block diagram of power conversion components.
Consequences of higher time harmonics in
generator current:
(a).
efficiency decreases;
(b).
parasitic electromagnetic torques appear;
(c).
rotor PMs can get overheated due to eddy
currents induced in conductive material of
PMs by higher harmonic fields
.
Role of inductance in A.C. generator circuit
(a)
Neglecting the commutation effect, if the
synchronous reactance is low, there is no
series additional inductance and generator is
loaded with a diode rectifier, the shape of the
generator current is approximately rectangular
(Fig. 4a) and, consequently, there is a large
content of the 5
th
and 7
th
harmonics (Fig. 4b).
(b)
An additional inductance (in some cases the
value of the generator synchronous inductance
is sufficient), improves the rectangular current
waveform to be more or less trapezoidal
function. The content of the 5
th
and 7
th
harmonics is reduced.
A high synchronous inductance is
recommended because it can sufficiently damp
the 5
th
and 7
th
harmonics in the case of a diode
(passive) rectifier and LC filter at the D.C. side.
The efficiency of 95% can be achieved and there
is no danger that the rotor can be overheated.
6. Case study
A 90-kW, 27,000-rpm, 4-pole PM brushless
generator for an organic Rankine cycle turbo
generator with hydrofluorocarbon working fluid
cooling system have been studied and designed.
Table 1 shows specifications of the generator,
i.e., design data, rated parameters, dimensions of
magnetic circuit and parameters of windings. A
four pole rotor with bread loaf shaped SmCo
PMs and non-magnetic retaining sleeve has been
used (Fig. 5). The stator winding is located in
semi-closed oval slots. To reduce the winding
losses, stator coils have been wound using
stranded conductors.
300
200
100
0
100
200
300
400
500
600
700
700
(a)
300
V
av
Iline
z
v
rect
z
LastPoin
0
z
N
N
S
S
1
2
3
Fig. 5. Cross section of four-pole PM rotor: 1 – PMs,
rotor core, 3 – retaining sleeve.
Fig. 4. A three-phase 900-Hz PM brushless generator
loaded with RL load via passive rectifier: (a) line current
(solid line) and rectified voltage (dashed line);
(b) harmonic contents in the line current (peak values
versus harmonic numbers).
(b)
J.F. Gieras, U. Jonsson / Design of a high-speed perman
ent-magnet brushless generator for microturbines
90
Table 1. Specifications of a 90-kW, 27,000-rpm, 4-pole
PM brushless generator.
Rated input frequency, Hz 900
Rated voltage (line-to-line), V 465
Winding temperature,
0
C 75
SmCo PM temperature,
0
C 150
Total non-magnetic gap, mm 4.2
Air gap (mechanical clearance) mm 1.1
Thickness of non-magnetic sleeve, mm 3.1
Length of stator stack, mm 120
Stator inner diameter, mm 95
Stator outer diameter, mm 146
Diameter of shaft, mm 40
Air gap magnetic flux density, T 0.70
Number of turns per phase 18
Radial thickness of PM (one pole), mm 19.8
Conductor diameter, mm 0.405
Winding resistance at 75
0
C per phase,
0.02502
Number of parallel wires 63
Number of parallel paths 1
Windage losses (HFC cooling medium), W 419.5
Bearing losses (magnetic bearings), W 49.8
Stator winding losses, W 1103
Stator core losses, W 2074
Eddy current losses in PMs, W 291
Efficiency for motoring 0.958
Efficiency for generating 0.961
Output power for generating, W 96 960
Power factor for generating 0.956
Synchronous reactance in the d-axis,
0.585
Synchronous reactance in the q-axis,
0.501
Mass of active materials, kg 18.52
Mass of PMs (SmCo), kg 4.58
First critical speed, rpm approx.
43,900
Overall sound power level at no load, dB(A) 67.8
0 200 400 600
0
0.2
0.4
0.6
0.8
1
speed, rev/s
1
0
pf n
i
()
η
g
n
i
()
585
0
n
s
n
i
Fig. 7. Power factor and efficiency versus speed at load
resistance: R
L
= 2.2 , and inductance L
L
= 0.00012 H.
power factor, efficiency
0 100 200 300 400 500
1
0.83
0.67
0.5
0.33
0.17
0
0.17
0.33
0.5
0.67
0.83
1
magnetic flux density excited by PMs
1.0
1.0
1
4〈〉
i
N0i
Fig. 6. Distribution of the normal component of the
magnetic flux density in the air gap.
B
PM0
i
B
PM
()
B,
T
Fig. 6 shows the distribution of the normal
component of the magnetic flux density in the
air gap, Fig. 7 shows efficiency and power factor
curves and Fig. 8 shows the sound power level
spectrum under load. Electromagnetic
calculations have been performed analytically
with some support of the 2D FEM. For stress
analysis and rotor dynamics analysis a structural
3D FEM package has been used. Temperature
distribution along the longitudinal section has
been simulated using a thermal resistance
network.
10
20
30
40
50
60
70
80
sound power level spectrum (dB vs Hz)
80
SPL_dB
0〈〉
0 1000 2000 3000 4000 5000 6000 7000 8000
0
0
80000
SPL_dB
1〈〉
Fig. 8. Predicted sound power level spectrum due to
radial magnetic forces at rated load.
It was rather impossible to reduce the
thickness of the nonmagnetic retaining ring
below 3.1 mm. Lower thickness would reduce
the volume of PM material; however the
expansion and thermal compatibility of different
rotor materials create difficult manufacturing
problems.
The 1.1-mm air gap is the minimum
mechanical clearance from radial expansion and
rotor eccentricity point of view. The total
nonmagnetic air gap equal to 4.2 mm (sleeve and
J.F. Gieras, U. Jonsson / Design of a high-speed permanent-magnet brushless generator for microturbines
91
mechanical clearance) requires about 4.6 kg of
good quality SmCo PMs.
The stator core losses (over 2 kW) are almost
twice as high as the stator winding losses. The
remaining power losses (windage, bearing and
losses in PMs) are less than 20% of the total
losses.
The efficiency curve is flat in the wide range
of speed and power factor slightly decreases as
the speed increases (Fig. 7). The predominant
acoustic noise frequency (Fig. 7) is 1800 Hz, i.e.,
double the input frequency.
7. Conclusions
In designing high speed PM brushless
generators, a careful attention must be given to
many new technical issues, including
electromagnetic, thermal, structural and
economical analysis. The most important are:
number of poles, rotor diameter, magnetic
loading, electric loading, power losses and
efficiency, laminations, armature conductors,
cooling system, rotor mechanical stresses, higher
harmonics generated by the power electronics
converter and related parasitic effects, vibration,
expansion of rotor retaining sleeve, shaft
dynamics, reliability and fault tolerance.
References
1. Aglen, O., “A High Speed Generator for
Microturbines”, Int. Conf. on Electr. Eng. And
Technology ICEET01, Dar es Salaam, Tanzania,
2001.
2. Consterdine, E., Hesmondhalgh, D.E., Reece, A.B.J.,
and Tipping, D., “An assessment of the power
available from a permanent magnet synchronous
motor which rotates at 500,000 rpm”, Int. Conf. on
Electr. Machines ICEM’92, Manchester, U.K., 1992,
pp. 746-750.
3. Gieras, J.F. and Wing, M., “Permanent Magnet Motors
Technology – Design and Applications”, 2
nd
edition,
Marcel Dekker, New York - Basel, 2002.
4. Lieutaud, P., Brissonneau, P., Chillet, C., and
Foggia, A.: “Preliminary Investigations in High
Speed Electrical Machines Design”, Int. Conf. on the
Evolution and Modern Aspects of Synchronous
Machines SM100, 1991, Zurich, Switzerland, Part 3,
pp. 840-844.
5. Puttgen, H.B., MacGregor, P.R., and Lambert, F.C.,
“Distributed Generation: Semantic Hype or the Dawn
of a New Era?”, IEEE Power and Energy Magazine,
Vol. 1, No. 1, 2003, pp. 22-29
6. Takahashi, T., Koganezawa, T., Su, G., and
Ohyama, K.:, “A Super High Speed PM motor Drive
System by a Quasi-Current Source Inverter”, IEEE
Trans on IA, Vol. 30, No. 3, 1994, pp. 683-690.
Received June 2, 2005
Dr. Jacek F. Gieras
Dr. U. Jonsson
United Technologies Research Center
411 Silver Lane, East Hartford
CT 06033, U.S.A.
Book
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Preliminary Investigations in High Speed Electrical Machines Design
  • P Lieutaud
  • P Brissonneau
  • C Chillet
  • A Foggia
Lieutaud, P., Brissonneau, P., Chillet, C., and Foggia, A.: " Preliminary Investigations in High Speed Electrical Machines Design ", Int. Conf. on the Evolution and Modern Aspects of Synchronous Machines SM100, 1991, Zurich, Switzerland, Part 3, pp. 840-844.
An assessment of the power available from a permanent magnet synchronous motor which rotates at 500,000 rpm
  • E Consterdine
  • D E Hesmondhalgh
  • A B J Reece
  • D Tipping
Consterdine, E., Hesmondhalgh, D.E., Reece, A.B.J., and Tipping, D., " An assessment of the power available from a permanent magnet synchronous motor which rotates at 500,000 rpm ", Int. Conf. on Electr. Machines ICEM'92, Manchester, U.K., 1992, pp. 746-750.