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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 =

    Advance AC Drives 2009

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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