# PMdrives part2

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Advance AC Drives 2009

Department of Electrical and Electronic Engineering

Advanced AC Drives

Permanent Magnet Machine Drives

Dr. Chris Gerada

chris.gerada@nottingham.ac.uk

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Part II

Permanent Magnet Synchronous

Machines Types, Geometry andConstruction

PMSM Topologies Torque and Machine Size

Pole Number

Rotor Topologies Stator Windings

Back EMF

Armature Reaction Effects Torque and Torque Density

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PM Synchronous machine types

PMSM come in various forms. Whilst allmachines can be represented by thesame equivalent circuit and aregoverned by the same principles ofoperation, different machine topologies

have different properties. Generally speaking PMSM construction

fall into one of three categories(according to the flux direction) :

Radial most common form of PM

machine type. They can either have aninterior rotor structure or an outer rotorin applications such as wheel motors.

Axial an attractive alternative due toits pancake shape, compactconstruction and high power density.

Particularly suitable for electrical andhybrid vehicles and wind generators.They can be designed as double-sidedor single sided machines with or withoutarmature slots.

Transverse this is when the velocityvector is transversal to the fluc path.This machine is ideal for low speedgenerators (high pole numbers)

In this Course we will be looking at radial type PMSM

Radial

Axial

Transverse

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PM machine construction basic definitions

Consider the 3 phase 2 pole motor shown.

Construction details: Interior rotor

Laminated Stator with a stacking factor of 0.9

Solid Rotor

Surface mount magnets

Non-salient machine Ld=Lq

Parallel magnetisation

2 poles (1 pole pair) 1mm air gap length

48 slots or 8 slots/pole/phase

Single layer wound

magnet span

No of conductors per slot = 26

Conductors per phase : 26*8*2 = 416

Turns per phase : 416/2 = 208

Slot fill = Copper area in slot / slot area

wtooth width t

wtooth pitch

26 conductors per slot

magnet span

magnet thickness air gap length

d

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PM machine basics of torque production

Diagram

Construction details:

Ad AC D i 2009

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Power Rating and Size

The most basic question one needs to answer when specifying a machine for a particularapplication is what rating need it be? And how big will it be?

The most universal way to describe the output from a machine is via its power.

Power :

Thus if we want more power from a given motor the simplest thing to do is to make it runfaster!

Having the machine running faster will imply a larger BEMF and thus an appropriateconverter able to handle the voltage. There will be more iron losses in the machine andhigher converter switching losses. The maximum speed a motor can reach is also limited

by the mechanical integrity of the system.

To match the motor speed to the application requirements mechanical gearing is used.Whilst mechanical gears are much more torque dense than electrical machines, the higherthe gear ratio the lower will be the transmission efficiency and the reflected motor inertiawill be proportional to the gear ratio squared.

Increasing the torque implies a higher current supplied to the machine. The maximumcontinuous current is obviously limited by the maximum temperature the various machinecomponents can withstand.

Starting from basics, we will derive the torque and power produced by an electricalmachine in terms of its geometry to define the relationship between torque produced and

the main dimensions of a machine.

P T =

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Machine Loadings

Magnetic Loading : Bpk

Defined as the peak radial flux density in the air-gap of the machine. This is for the fundamental, spatial flux density. Ie. harmonics neglected.

This is typically around 0.8T. having a tooth width half the tooth pitch and a typical B in theteeth of 1.6T (limited by magnetic steel saturation)

Current Loading or Electric Loading :Arms

Defined to be the total rms current per unit length of the airgap periphery.

D = air gap diameter

2mNphI = Nph turns per phase * m number of phases (3) * 2 conductors per turn * RMS current This is generally limited to 30-80kA/m, depending on machine size and cooling method.

2 phrms

m N IA

D

=

Current Density : Jrms Density of current in windings.

This is typically limited to around 4-6A/mm2

We will derive the output torque equation in terms of the machine geometry. We willassume a sinusoidal winding and air gap flux distribution, in other words this analysis isvalid for sinusoidally excited machines such as IM and PMSM.

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Torque Produced

Assuming a sinusoidal distribution of flux density and current we canexpress them as :

From Lorentz equation, force on acurrent carrying conductor in anorthogonal field is :

T BL I r =

T

I Ar = F BIL= And the torque produced at a radius r

is :T BILr=

Consider the figure shown :

( ) sing pkB B =

( )gB ( )I

Then we can express the torque developed by the machine as :

( ) ( )2

0

m gT B I L r d

=

being the phase shiftbetween the flux and currentwaveforms

( ) ( )2

2

0

2 sin sinm ms pkT A B L r d

= +

( ) ( )2 sinrmsI A r = +

( )22 cosm rms pkT A B r L =

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Torque Produced

The torque equation can be written as :

( )22 cosm rms pkT A B r L =

Torque = k * Electrical Loading * Magnetic Loading * Rotor Volume

The torque per rotor volume (TRV) is thus : 2 rms pkTRV A B= assuming 0 =

The TRVis related to the air gap shear stress . This is defined as the tangential (torqueproducing) force per unit swept rotor surface area. Thus, for a cylindrical rotor we canwrite:

( ) 2m rT D L r V = =

2mTTRVV

= =

2

rms pkA B

=thus

The air gap shear stress is measuredin kN/m2 .

It can be noted that the only wayhow to increase the TRV or the shearstress is by increasing either thecurrent or magnetic loading. Theseare limited by the cooling capabilityand saturation of the magnetic

material. Typical values are :222 /kN m =

344 /TRV kNm m=

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Maximum TRV

The TRV can thus be improved by : Increasing B

Flux density is limited by the magnetic material saturation. Magnetic saturation in thestator teeth limits the tooth flux density to approx 1.6T so that the air gap flux densitydoesnt exceed 0.8T independent of machine size. One way of increasing this is by using

more exotic magnetic steels such as Cobalt Steel. This is only used in highperformance motors such as those for aerospace. Saturation flux densities above 2.2Tcan be reached.

Increasing A Increase the slot depth (for a given current density): increases slot leakage, increases

tooth mmf drop, increases machine outside diameter

Widen the slots (for a given current density): reduces slot leakage but reducesmagnetic loading as the teeth become narrower

Increase current density J increases I2R loss. Better cooling required.

Improving machine cooling by using forced convection or direct liquid cooling canconsiderably improve the TRV by 4 to 5 times

The values given so far relate to continuous rating. The peak torques a machine canachieve can be considerably higher than these. This in general depends on the dutycycle involved. This is again related to the thermal limit of the machine. Other

limitations might be magnet demagnetisation due to the armature reaction field if thecurrent is very high, converter ratings or to the mechanical integrity of the machineitself.

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Pole number

With inverter driven PMSM machines thechoice of the number of poles is not obviousas with other traditional machines andapplications.

Induction motors have generally low polenumber due to the otherwise very lowmagnetising inductance, power factor andefficiency. This is not the case for PMmachines as there is no need for anexcitation current. High pole numbermachines are thus ideal for low speed, direct

drive applications. Using a higher number of poles allows an

increase in the air gap diameter for thesame stator outer diameter since less spaceis needed for the stator yoke (Torque airgap diameter2)

Consider a 2 and a 16 pole machine of sameouter stator dimensions.

Higher torque (more force producing surfacearea acting on a larger radius)

Less stator copper losses as end windinglength is reduced.

Mo