motori per trazione

5-1 Chapter 5 : DC and AC Electric Machines

IIntroduction

Machines used as motors for propulsion and Machines used as motors for propulsion and as generators for braking. as generators for braking.

Can either be DC or AC machinesCan either be DC or AC machines

Instantaneous power rating can be much Instantaneous power rating can be much higher than rated powerhigher than rated power

Capability to provide full torque even at low Capability to provide full torque even at low speedsspeeds


Machine TypesMachine Types

DC: good characteristics but large andDC: good characteristics but large and giving giving maintenance problemsmaintenance problems

AC-induction: complex control, but rugged and widely AC-induction: complex control, but rugged and widely usedused

PM: high energy density, though costly and fault sensitivePM: high energy density, though costly and fault sensitive

EV motors are larger EV motors are larger ⇒⇒ Cost implications are significant Cost implications are significant

HEV motors are smaller HEV motors are smaller ⇒⇒ PM motor performance may PM motor performance may outweigh cost problemoutweigh cost problem

SRM: excellent fault tolerance and ease of construction, SRM: excellent fault tolerance and ease of construction, requires complex controlrequires complex control


Electric Motor and IC Engine Ratings

Power Watts = Torque N −m × Speed rads / s .

HP=Torque ft−lbs ×rpm5252

Comparison Comparison between ICE and between ICE and electric motors:electric motors:

Note:Note:


Electric Motor and IC Engine Ratings

• Rated HP of electric motor is deratedRated HP of electric motor is derated• For short periods, motors can deliver 2 to 3 For short periods, motors can deliver 2 to 3

times rated HPtimes rated HP• Torque can be maximum under stall Torque can be maximum under stall

conditionsconditions• ICE maximum HP is derived under idealized ICE maximum HP is derived under idealized

lab conditionslab conditions• Transmission is essential for ICE to match Transmission is essential for ICE to match

vehicle speedvehicle speed• Electric motor can be directly coupled with Electric motor can be directly coupled with

a single gear.a single gear.


EV/HEV Motor Requirements

Requirements:Requirements:– Flexible drive controlFlexible drive control– Fault tolerance and ruggednessFault tolerance and ruggedness– High efficiencyHigh efficiency– High speedHigh speed– Low acoustic noise and EMILow acoustic noise and EMI– Wide constant power regionWide constant power region– High torque to inertia and power to weight ratiosHigh torque to inertia and power to weight ratios

• Large TLarge Tee/J results in good acceleration /J results in good acceleration

– High peak torque capability (300-400% rated power)High peak torque capability (300-400% rated power)


DC MachinesDC Machines

Characteristics:Characteristics:– Windings at the stator (field) and rotor (armature) Windings at the stator (field) and rotor (armature)

produce two mmf’s in quadrature and generate a Lorentz produce two mmf’s in quadrature and generate a Lorentz forceforce

– Can be operated in different configurations, depending on Can be operated in different configurations, depending on the winding connectionsthe winding connections

– Easy and flexible to control, established manufacturing Easy and flexible to control, established manufacturing technologytechnology

– Low maximum speed, brush maintenance, important EMI Low maximum speed, brush maintenance, important EMI issues and large sizeissues and large size


Separately excited DC machine:Separately excited DC machine:

Independent voltage and field controls are possible in this Independent voltage and field controls are possible in this configurationconfiguration


Electrical ModelingElectrical Modeling

V A=RA iALAA

di A

dte A

e A=K φωm

T e=Kφi A

V F=RF iFLFF

diF

dt

φ= f iF

Armature CircuitArmature Circuit

Field CircuitField Circuit


Magnetic modelingMagnetic modeling

Basic equations:Basic equations: B=μHμ=μ0 μrμ0=4π×10−7

Non linear characteristics with hysteresis effect:Non linear characteristics with hysteresis effect:

ApproximationApproximation

Magnetic CharacteristicsMagnetic Characteristics


Torque-speed characteristicsTorque-speed characteristics

ωm=V A

Kφ−

RA

Kφ 2 T e

Torque-speed equation:Torque-speed equation:

DC Motor CharacteristicsDC Motor Characteristics

• Speed torque characteristics is controlled by varying armature voltage and/or field current


V A=RA I A¿K φω

m¿

⇒V A=RA

KφT ¿K φω

m¿or ω

m¿K 2φ2−V A KφRAT ¿=0

Operating pointOperating point:: VV vs. vs. φφ at operating point at operating point::

Operating PointOperating Point

•For a given (T*,ω*) point, there can several armature voltage or field current


Three-Phase AC MachinesThree-Phase AC Machines

Winding ConfigurationWinding Configuration

3-phase winding:3-phase winding: Sinusoidal distribution:Sinusoidal distribution:


Armature is stationary as opposed to Armature is stationary as opposed to DC machinesDC machines

Rotor circuit generates excitationRotor circuit generates excitation

Can be of two types, induction or Can be of two types, induction or synchronous machinessynchronous machines

No commutator or brushes in the case No commutator or brushes in the case of ac machinesof ac machines

AC MachinesAC Machines


For sinusoidally distributed winding:For sinusoidally distributed winding:

Magnetomotive force:Magnetomotive force:

Winding and MMFWinding and MMF


Phase a winding:Phase a winding: Phase a mmf:Phase a mmf:

4-Pole Machine4-Pole Machine


Vettori di Spazio – sistema di coordinateVettori di Spazio – sistema di coordinate

α=0

ρ

α

ζ

Sia Θ(α,t) la distribuzione della densità angolare di corrente relativa ad un elemento di macchina nel suo riferimento. Dalla teoria delle macchine elettriche, possiamo derivare la Θ(α,t) dalla conoscenza della tensione magnetica Γ(α,t) secondo la legge:

ααα

∂Γ∂=Θ ),(

),(t

t

la Γ(α,t) sarà una distribuzione a gradino. Ciò, indica una distribuzione di densità lineare di corrente lungo la periferia di macchina di tipo impulsivo:

∑=

−=Θm

kkck izpt

2

1

)(),( ααδα

)1()1(2

12 −=−= km

kmk

ππα


Distribuzione di correnteDistribuzione di corrente

kc

m

k

izkm

pt ∑=

−−=Θ

2

1

)1(),(παδα

∑∞

−∞=

Θ=Θh

jphh et αα

.

),(

Applichiamo lo sviluppo in serie di Fourier

Ricordando che il periodo della funzione Θ è T=2p, e quindi che la pulsazione della fondamentale è ω0=p, i coefficienti Θh sono ottenuti come segue:

∑ ∫

∫ ∑∫

=

−

−

=

−

−−=

=

−−==Θ

m

k

jphkc

jphp m

kkc

Tjhp

h

dekm

pizp

deizkm

pp

defT

2

1

2

0

2

0

2

10

)1(2

)1(2

)(1

πα

α

π

α

απαδπ

απαδπ

αα


Vettori di spazioVettori di spazioDalla teoria delle distribuzioni (teorema del campionamento) possiamo calcolare l’integrale precedente: il prodotto della δ di Dirac concentrata nei punti pα-π/p(k-1) per una qualsiasi funzione f(α) è pari alla f(pα- π(k-1)/p) cioè alla funzione originaria campionata nei punti in cui è concentrato l’impulso.Segue quindi: ∑

=

−−=Θ

m

k

km

jh

kch eizp 2

0

)1(

2

π

π

La precedente sommatoria va separata tra correnti uscenti e correnti entranti. Rispetto al riferimento esse saranno sfasate spazialmente di π radianti elettrici (π/p radianti meccanici):

∑∑∑=

−−

=

−−

=

−−=

−+=Θ

m

k

km

jh

kcj

m

k

km

jh

k

m

k

km

jh

kch eizp

eeieizp

1

)1(2

1

)1(2

1

)1(2

22

)(2

ππ

ππ

ππ


Vettori di spazioVettori di spazio

i

c

m

k

km

jp

kc zp

meizp

ππ

π

21

)1(2

1 ==Θ ∑=

−−

∑=

−−=

m

k

km

j

kei1

)1(2

3

2π

i

++=

ππ3

4

33

2

213

2 jjeieiii

( )( )

( )2321

2321

2321

3

23

23

2

aiaii

aa

avavv

++=

++=

++=

i

ψ

v

ψψψ

Dove i è il vettore di spazio associato alla terna di correnti di alimentazione, definito quindi come


Characteristics:Characteristics:

Provides a simple and efficient way of representing Provides a simple and efficient way of representing sinusoidally space distributed variablessinusoidally space distributed variables

Similar to the use of phasorsSimilar to the use of phasors

Gives a compact way of representing machine Gives a compact way of representing machine equationsequations

Facilitates the conversion from a 3-phase system to a Facilitates the conversion from a 3-phase system to a 2-phase system2-phase system

Space Vector RepresentationSpace Vector Representation


Riferimenti di Clarke e di ParkRiferimenti di Clarke e di Park

Riferimento di Clarke: Sistema di assi cartesiani α,β solidali con lo statore

Riferimento cartesiano il cui asse d è ruotato rispetto al riferimento di Clarke di un angolo γ


Trasformazione di Trasformazione di ParkPark

[ ]

⋅=

⋅

−=

−

000 100

0cossin

0sincos

3

2

gg

g

R

gg

g

gg

g

dqq

d

β

α

αββ

αγγγγ

[ ]dqR −αβ [ ]0αβT

Moltiplicando la matrice di rotazione

per quella che rappresenta la trasformazione di Clarke

si ottiene la trasformazione di Park

( ) [ ]

⋅=

+−

−−−

+

−

=

=

⋅

−

−−

⋅

−=

3

2

1

0

3

2

1

0

21

21

21

3

2sin

3

2sinsin

3

2cos

3

2coscos

3

2

21

21

21

23

23

0

21

21

1

100

0cossin

0sincos

32

gg

gT

gg

g

gg

g

dq

q

d

πγπγγ

πγπγγ

γγγγ


Trasformazione inversaTrasformazione inversa

01323211 )(2

3)(

2

1

2

3

3

2iiiijiiiiee −=

−+++−ℜ=ℜ i

02

203

Re

Re

iia

iia

−=

−=

i

i

[ ]

⋅=

⇔

⋅

=

3

2

1

03

2

12

0 2

1

2

1

2

11

3

2

i

i

i

Si

i

i

iaa

i

ii

0032

3iveP iii +ℜ= iv


[ ] [ ] [ ] abcgTg

g

g

g

gg

g

⋅=

⋅

−

−−

=

00

3

2

1

0

2

1

2

1

2

12

3

2

30

2

1

2

11

3

2

αβαβ

β

α

Adoperando la notazione complessa, si può scrivere in maniera equivalente:

g=gα+j gβ = )(2

3)(

2

1

3

232321 ggjggg −++−

,

( )3210 3

1gggg ++=

Trasformazione di ClarkeTrasformazione di Clarke


• Space vector for a balanced set of 3-phase variables has a Space vector for a balanced set of 3-phase variables has a magnitude 3/2 times greater than the magnitude of the magnitude 3/2 times greater than the magnitude of the phase variablesphase variables

• The amplitude of the space vector is constant for a The amplitude of the space vector is constant for a balanced set of variables, but the phase angle is a balanced set of variables, but the phase angle is a function of time.function of time.

• There is a unique set of vectors that would sum up to There is a unique set of vectors that would sum up to give the resultant space vector.give the resultant space vector.

• The multiplication of 2/3 in the previous figure The multiplication of 2/3 in the previous figure represents the relationship between the magnitude of the represents the relationship between the magnitude of the space vector and the peak magnitude of the time varying space vector and the peak magnitude of the time varying phase sinusoid.phase sinusoid.

And the flux-density:And the flux-density:


Types of AC MachinesTypes of AC Machines

Rotor mmf generation technique characterizes an AC machineRotor mmf generation technique characterizes an AC machine

Synchronous machines rotate at synchronous speed; rotor mmf is Synchronous machines rotate at synchronous speed; rotor mmf is produced either by electromagnet (used in utility power generation) or produced either by electromagnet (used in utility power generation) or permanent magnet (can have EV/HEV applications)permanent magnet (can have EV/HEV applications)

Induction machine rotor mmf is induced by the stator currents, and Induction machine rotor mmf is induced by the stator currents, and rotates at a speed close to, but different than the synchronous speedrotates at a speed close to, but different than the synchronous speed


Induction MachinesInduction Machines

Two rotor configurations are possible:Two rotor configurations are possible:Squirrel cage rotors are widely used because of Squirrel cage rotors are widely used because of

their ruggedness and low costtheir ruggedness and low costWound rotors, which can be connected to an Wound rotors, which can be connected to an

external circuitexternal circuit

Squirrel cage Squirrel cage configurationconfiguration


Stator and rotor electrical circuits:Stator and rotor electrical circuits:

Stator and Rotor CircuitsStator and Rotor Circuits


Stator has sinusoidally distributed windingsStator has sinusoidally distributed windings

Balanced sinusoidal currents induce a rotating stator fieldBalanced sinusoidal currents induce a rotating stator field

Currents flow in the short-circuited rotor windings and Currents flow in the short-circuited rotor windings and induce rotor mmf if the difference in speed between stator induce rotor mmf if the difference in speed between stator and rotor is non-zeroand rotor is non-zero

Operation is then comparable to that of a transformerOperation is then comparable to that of a transformer

Interaction of stator and rotor mmf’s produce torqueInteraction of stator and rotor mmf’s produce torque

Induction Machine OperationInduction Machine Operation


Modello in un riferimento qualsiasiModello in un riferimento qualsiasi

=

=

ℑ=

=−

+=

+=

−++=

++=

010

010

'

2

3

)(

rrr

sss

sse

rLe

smrrr

rmsss

rrbr

rrr

sbs

sss

idt

dLv

idt

dLv

mpM

dt

dJMM

LL

LL

jpdt

dR

jpdt

dR

iψ

iiψ

iiψ

ψψ

iv

ψψ

iv

ω

ωω

ω


Motor usually operated at low slip to have a more linear Motor usually operated at low slip to have a more linear characteristic and maximize efficiencycharacteristic and maximize efficiency

Speed-Torque CharacteristicsSpeed-Torque Characteristics


At rated flux:At rated flux:

k M=π rlN S

2

T e=k MBms

Ir′

wherewhere

i r' t =

F r

N S / 2

Ir′=k r

Bms ωslipAnd fromAnd from we getwe get T e=k m k rB

ms2ωslip

Simplified Torque ExpressionSimplified Torque Expression


Two main possibilities:Two main possibilities:

Stator terminal voltage controlStator terminal voltage control

Stator frequency controlStator frequency control

A power electronics converter is usually requiredA power electronics converter is usually required

Speed Control MethodsSpeed Control Methods


Variable stator voltage at fixed frequency:Variable stator voltage at fixed frequency:

Torque-speed profileTorque-speed profile


Variable frequency but constant V/f ratio:Variable frequency but constant V/f ratio:

Torque-speed profileTorque-speed profile


Common mode of operation:Common mode of operation:

Motor driveMotor drive

Torque-speed Torque-speed operating envelopoperating envelop


Regenerating Regenerating BrakingBraking

Feature of electric machines, allows the regeneration of Feature of electric machines, allows the regeneration of kinetic energy back to the electrical form during braking kinetic energy back to the electrical form during braking operationsoperations

Mechanical brakes still required for short transientsMechanical brakes still required for short transients

Extends the range of the vehicle up to 15%Extends the range of the vehicle up to 15%

Induction machine is operated at negative slipInduction machine is operated at negative slip

Part of the four-quadrant operation required by EV/HEVPart of the four-quadrant operation required by EV/HEV


An example of braking:An example of braking:


Cenni di dimensionamentoCenni di dimensionamento

Chapter 5 : DC and AC Electric Machines

Considerazioni di progettoConsiderazioni di progetto

Per le macchine rotanti la Per le macchine rotanti la potenza di dimensionamento è potenza di dimensionamento è sempre una potenza elettrica, sempre una potenza elettrica, assorbita od erogata a seconda assorbita od erogata a seconda che la macchina sia un motore che la macchina sia un motore od un generatore, ed è la od un generatore, ed è la potenza apparente nel caso di potenza apparente nel caso di corrente alternatacorrente alternata


Dimensioni principaliDimensioni principaliD: DiametroD: DiametroPasso polarePasso polare

L: lunghezza del pacco lamiereL: lunghezza del pacco lamiereK: Densità di corrente lineareK: Densità di corrente lineare

2

D

p

πτ =

32

N IK

D

ξπ

=


DimensionamentoDimensionamentoPotenza di Potenza di dimensionamentodimensionamento

Flusso per poloFlusso per polo

Tensione indottaTensione indotta

3dS EI=

2

2med Max Max

DL DLB L B B

p p

πτπ

Φ = = =

2 4.442

E f N fNπ ξ Φ= = Φ


Potenza di dimensionamentoPotenza di dimensionamento

3 22 32

3

d Max

DL DKS fN B

Np

ππ ξξ

= =

=

g

2 fN

p

π ξ2

2 32Max

D L KB

πg Nξ

2n

=

=2 2

60 22Max

D L KB

p

π

22

60 2Maxn B D LK

π

=

=


Potenza di dimensionamentoPotenza di dimensionamento

K Densità di corrente lineareK Densità di corrente lineareJ Densità di corrente superficialeJ Densità di corrente superficialehhcc Altezza di cava Altezza di cavawwcc Larghezza di cava Larghezza di cavakkff Fattore di riempimento Fattore di riempimentoppdd passo di dentatura passo di dentaturanncc numero di conduttori in cava numero di conduttori in cava

c f c c dn I k w h J p K= =


•Perdita per effetto Joule della cava

•Potenza smaltita

•Con kf=0.4, wc/pd=0.5 hc=0.05 J=4E6 A/m2

Si ha K=40 kA/m

Relazioni utiliRelazioni utilic

f c cd

wK k h J h J

p= ﾵ

2J f c cp k w h Jρ=

J c dp pα ϑ=c

JKρϑ

α=


Relazioni utiliRelazioni utiliρρ=0.02E-6 =0.02E-6 ΩΩmmααcc=100 W/(m=100 W/(m22°C)°C)

Si ha Si ha ϑϑ=32°C=32°CCostante di macchina Costante di macchina C=SC=Sdd/(nD/(nD22L)L)(Rapporto fra coppia e volume della (Rapporto fra coppia e volume della macchina)macchina)

Con B=0.8T e K=40kA/m Con B=0.8T e K=40kA/m C=3720 N/mC=3720 N/m33


ConclusioniConclusioni

La potenza di traferro SLa potenza di traferro Sdd di una macchina di una macchina elettrica si può esprimere come:elettrica si può esprimere come:

Con Con BBMM valore massimo dell’ induzione valore massimo dell’ induzione magnetica al traferro, magnetica al traferro, KK densità lineare di densità lineare di corrente di armatura, corrente di armatura, D diametro D diametro di di alesaggio, alesaggio, LL lunghezza attiva di macchina. lunghezza attiva di macchina.

22

60 2d MS n B K D L

π=


ConclusioniConclusioni

Nelle macchine tradizionali, la Nelle macchine tradizionali, la profondità di cava di eccitazione profondità di cava di eccitazione hhee o di armatura o di armatura hhaa sono limitate dalla sono limitate dalla saturazione dei denti. Una saturazione dei denti. Una macchina che non presenta alcuna macchina che non presenta alcuna dentatura non risente, invece, di dentatura non risente, invece, di questi vincoli.questi vincoli.

motori per trazione

Documents