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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

t

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, Ω

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, Ω

0.585

Synchronous reactance in the q-axis, Ω

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 Ω, 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

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.