Trends in Dimensioning PM and Reluctance Machines

©2015 Retrospeed 1Tim Miller FEMAG Anwendertreffen 2015 Leutkirch

17 Trends in Dimensioning PM and Reluctance Machines

Trends in Dimensioning PM and Reluctance Machines

Tim Miller

FEMAG Anwendertreffen 201528. 29.Oktober2015


Dimensions

Size + Shape + Drawing Dimensions + Control Parameters

How big?

Or rather,

How small?

• Shapes• Features• Details

• Diameters• Lengths and widths• Angles

• Priority, hierarchy,dependency,weighting

• Refinement• Optimization

Materials

• Voltage• Current• Phase angles


Motor chart

PM DC WF AC IPM Synchronous Reluctance

Spoke

Universal Induction SPMSwitched

Reluctance

AC drivesClassical Electronicallycontrolled


Synchronous reluctance, PM-assisted synchronous reluctance, IPM machines


Synchronous reluctance motor in smartFEM

Things to discuss

• Dimensioning principles

• Historical review

• Some comments about

• Time-simulation

• Performance calculations

We don't need FEA to determine the numberof poles!


Brushless synchronous reluctance / PM motor rotor lamination

What the electric machine designer sees:• A 4-pole rotor• Paths of easy magnetization defining d-axis— Relatively low flux per pole— Saturates very easily• Delicate mechanical configuration

According to the theory• We must maximize the saliency

What we need• Finite-element analysis

• Mechanical and electromagnetic• Time simulation (for controller design)• A way to evolve an optimum design• Tooling for manufacture

d

d


Saturation of Ld and Lq due to the currents in their own axes

We often see these curves . . .


Saturation and cross-saturation

If current is known, calculate the voltageIf voltage is known, calculate the current

Calculate the mean electromagnetic torque

See Vagati et al[1997,1998]

. . . but !!It can be an advantage to useflux-linkage, and avoid Inductancecompletely.


Energy-conversion diagram for machine with sinusoidal current & flux-linkage

Flux is limited by cross-sectional dimensions of magnetic core,and by saturation

Current is limited by cross-sectional dimensions of winding, and by temperature rise

Magnetization curves

Flux or flux-linkage is useful in sizing, but Inductance isnot very helpful in the sizing process.


Relationship between energy-conversion diagram and dimensions (SR motor)

Y

Aligned inductance depends onairgap length and pole arc— dimensions again

Unaligned inductance depends on space around wound poles in unaligned position— dimensions again

Flux is limited by cross-sectional dimensions of magnetic core,and by saturation

Current is again limited by cross-sectional dimensions of winding, and by temperature rise


• It can be used for preliminary design or sizing• It is directly related to the machine dimensions and material properties

• It requires only a magnetostatic calculation• No time-stepping simulation required• Current waveform is assumed known

• Suitable for 2-D FEA, but end-effects must be added

• It defines the maximum torque per ampere

• The required voltage can be deduced from it

• It shows several figures of merit

• It can easily be scaled according to the number of turns

• Pre-calculated sets of magnetization curves can be used for dynamic simulation (see next slide)

Features of the simple energy-conversion diagram


Stepwise integration. . .

Simple enough by Euler or Runge-Kutta

Numerical model of flux-linkagecurves is much more complex. . .

. . . and we need the inverse

Similar numerical approximationis required to calculate the torque. . .

Voltage equation (1 phase only)

Time-stepping simulation (one phase only)


Electric loading• A common design parameter

Magnetic loading• A common design parameter

Average flux-densityOver stator bore circumference

(How many amps (really, ampere-turns) can we pack into the stator?)

(How much flux can we pack into the stator?)

Torque / Rotor Volume TRV is proportional to the electric and magnetic loadings.This is an engineering formulation of "torque = flux × current".

In AC machines, we need this relationship because the flux is sinusoidally distributed and the induced voltage depends on the fundamental, not the average.

Electric and magnetic loading


Internal power factor and type of rotor

• In general the flux and the ampere-conductor distribution are not orthogonal.

• There is an angle between them, which can be regarded as an internal power-factor angle. It gives rise to an internal power-factor IPF.

• The value of IPF depends on the type of rotor

• Surface PM motor : IPF can be as high as 1• Interior PM motor : 0·8• Induction motor : 0·8• Synchronous reluctance motor : 0·6

• We should de-rate the initial design of the motor by this factor

• Or for the same power output, it will need a bigger inverter than the PM motors or the induction motor


Machine configurations; historical progress

Cruickshank, Anderson, Menzies 1971

Cruickshank A.J.O., Anderson A.F. and Menzies R.W.Theory and performance of reluctance motors with axially laminated anisotropic rotorsProceedings IEE, Vol. 118, No. 7, July 1971, pp. 887-894.


Lawrenson 1965; segmental rotor (line-start)


Essential flux-barriers (Fong and Htsui [1970])


Essential flux-barriers (Fong and Htsui [1970])


SynchroTek 1984

Bak D.J. Rotor Design Minimizes Magnetic Leakage Design News, May 21, 1984, pp. 110-111.(A brief review of the Synchroloc motor of Bogue Mfg. Co., developed by Shekar Rao.)

Rao S.C. Dynamic performance of reluctance motors with magnetically anisotropic rotors IEEE Transactions, Vol. PAS-95, No. 4, July-August 1976, pp. 1369-1376.


El-Antably and Hudson 1985 : 6-pole axially-laminated rotor

El-Antably A. and Hudson T.L. The Design and Steady-State Performance of a High-Efficiency Reluctance MotorIEEE IAS, 1985, pp. 770-776.


Mayer and Weh 1986 ; Boldea 1994 : 2-pole axially-laminated rotor

21/16 Saliency ratio, no-load/full-load

Mayer R., Mosebach H., Schröder U. and Weh H. Inverter-Fed Multiphase Reluctance Machine with Reduced Armature Reaction and Improved Power DensityICEM 1986, Pt. III, pp. 1138-1141

Boldea I., Fu Z.X. and Nasar S.A. High Performance Reluctance GeneratorIEE Proceedings-B, Vol. 140, No. 2, March 1993, pp. 124-130


Soong 1995 : 4-pole axially-laminated rotor

Soong W.L., Staton D.A. and Miller T.J.E.Design of a new axially-laminated interior permanent-magnet motor.IEEE Transactions on Industry Applications, Vol. 31, No.2, March/April 1995, pp. 358-367.


Fratta, Vagati, et al 1993

Oscillation between Figs. 2 and 3 causes flux pulsationwhich causes torque ripple, core loss, and harmonic leakage

Analytical model

Flaring and fairing

Fratta, Vagati et al 1993 : Effects of positions of ends of flux-barriers in generating flux and torque pulsations (including harmonic leakage inductance)

Fratta A., Troglia G.P., Vagati A. and Villata F.Evaluation of Torque Ripple in High Performance Synchronous Reluctance MachinesIEEE IAS 1993 pp. 163-170

It seems Vagati et alestablished the viability of thetransverse-laminated synchronous reluctance motor.After this, the axially laminated concept faded away.


Okuma synchronous reluctance motor, Nikkei Mechanical, 1998.4 No. 523, pp. 26-29

Okuma 1998


“A promising technology for efficient fan systems is the synchronous reluctance motor, which has a winding-free rotor, thus avoiding rotor losses and keeping the motor relatively cool.”

Drives and Controls, July/August 2013

Shaped flux-barriersin transverse lamination,(and not too many of them)Vagati et al, 1995 and earlier

Vagati et al, 1997

ABB

ABB 2013


ABB 2013


Stator : typical integral-kW

WEG


r s 4n n= ±

Vagati US Patent 5,818,140Oct. 6. 1998

Vagati's rule


The R-wave needs to follow the F-wave as closely as possible, to minimize the introduction of spurious harmonics.

This also leads to the principle of equal permeances for the flux-barriers.

Magnetic equivalent circuit

See Vagati et al [1997,1998]


Bianchi N., Bolognani S., Bon D. and Dai Pré M.Rotor Flux-Barrier Design for Torque Ripple Reduction in Synchronous Reluctance and PM-Assisted Synchronous Reluctance MotorsIEEE Transactions on Industry Applications, Vol. 45, No. 3, May/June 2009, pp. 921-928

12th-order torque harmonic from poles 1 & 3 is 180° out of phase with the 12th-order torqueharmonic from poles 2 & 4.

Angles A, B chosen to cancel a given torque harmonic, e.g. the 24th.

Angles a,b also chosen to cancel the same torque harmonic.

Poles 1&3 (AB) and 2&4 (ab) combine to compensate the 12th-order torque harmonic.

Resulting torque ripple < 5% (peak-to-peak).

This is about 1/3 — 1/2 the value in a similar IPM designed as a "control" experiment.

An analytical formulation of the torque rippleis also presented and tested.

Bianchi's "Machaon" rotor combines two different pole geometries in a single lamination.

He also presented a rotor with 2 symmetrical halveshaving different pole geometries ("R & J" type).

Synchronous reluctance motor with different flux-barrier angles


• Simple flux-barrier shapesminimize the number of dimensions

• Achieved similar torque to that of a motor optimized with 20 parameters, but reduced the torque ripple significantly

No. of flux-barriers

No. of dimensions

1 52 83 114 14

Pellegrino G., Cupertino F. and Gerada C., Automatic Design of Synchronous Reluctance Motors focusing on Barrier Shape Optimization, Transactions IEEE, Industry Applications, Vol. 51, No. 2, March/April 2015, pp. 1465-1474

Pellegrino's dimensioning for design optimization


No. of flux-barriers

No. of dimensions

1 162 273 384 49

Even this is not enough:Many details are missing, andthe poles may not all be identical.

Basic dimensioning for parameterized CAD


Detail : end of flux-barrier


(a) (b)

(d)

(c)

(e) (f)

Systematic design of rotor


Synchronous reluctance motor with single-tooth windings?

Grundfos PM motor from the Green Book, used here only to show an example of single-tooth windings. It is not otherwise related to this presentation.

It would seem that single-toothwindings are not appropriate for synchronous reluctancemotors, because of the highharmonic content in the stator ampere-conductor distribution.

However, this technology is well established andautomated, so we maysee attempts in futureto try to develop thesynchronous reluctancemotor with such windings.

An obvious problem is thewinding factor:

2-pole 0·54-pole 0·866

6 stator slots?


Spargo C.M., Mecrow B.C., Widmer J.D., Morton C. and Baker N.J., Design and Validation of a Synchronous Reluctance Motor with Single Tooth Windings, IEEE Trans. on Energy Conversion, Vol. 30, No. 2, June 2015, pp. 795-805

• Cruciform rotor has poor saliency

• Single-tooth winding has high space-harmonic content

Reported by Mecrow:

• Unsaturated saliency ratio 4·4

• Power-factor 0·51

• Torque ripple 44%

• Efficiency 91% (but uses segmented core with 58% slot fill)

Again we see high copper content in the stator, required to allow the high electric loading needed to compete with the induction motor.

See Spargo et al for details of the flux-barrier geometry

Shown with the d-axis aligned with phase C,at the instant of peak current in phase C.

Synchronous reluctance motor with single-tooth windings

Rotor concepts"outside the box" of conventional practice.


Thank you !

Thank you !

Most of the ideas in this presentation are described in detail in this book:"Reluctance Machines" , 2015, 185 pagesSwitched and synchronous reluctance machines, plus IPM and PM-assistedsynchronous reluctance machines and certain flux-switching machines and variants.Extensive bibliographies are included for both types of machine, with full referencesto the published works mentioned in this presentation.

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Trends in Dimensioning PM and Reluctance Machines