ELECTRIC VEHICLE - EMRwebsite€¦ · 2 11 21 12 22 ss 1 ss 1 Switching functions: •...

Aalto UniversityFinlandMay 2011

« Energy Management of EVs & HEVs usingEnergetic Macroscopic Representation »

Aalto University

«« MMODELLING AND ODELLING AND EMREMR OF ANOF AN

EELECTRIC LECTRIC VVEHICLE EHICLE »»

Dr. Walter LHOMMEL2EP, University Lille1, MEGEVH network

[email protected]

Prof. Alain BOUSCAYROLL2EP, University Lille1, MEGEVH network

[email protected]

HEVs & EMR, Aalto, May 20112

«« Modelling and EMR of an EV Modelling and EMR of an EV »»

- Outline -

1. EMR of an EV with a separately-excited DCM

2. Use other electric machines• Permanent Magnet DC Machine• Permanent Magnet Synchronous Machine• Squirrel Cage Induction Machine

3. Simulation Session: EMR of an EV with a PMDCM



Aalto University

«« EMREMR OF AN OF AN EVEV WITH AWITH A

SSEPARATELYEPARATELY--EEXCITED XCITED DCDC MMACHINE ACHINE »»


[email protected]


[email protected]



Assumptions:ideal power switchesseparately-excited DC machine without saturationinertia of the wheels neglectedcontact wheel/ground without lossno use of the mechanical brake

- Studied EV traction system -

Tgear

rwh

lwh

Tldiff

Trdiff

vveh

Fenv

diffJsh

Tdcm

gear

Tload

gearfsh

ich-auch-a

ia

ubat

if uch-f

ich-f

itot

choppers DC machine Trans- wheels chassis environ.battery shaft



- Modelling and EMR of the battery -

Principally two kinds of model:• energetic model• dynamic model

Both parameters (OCV and R) depend of:• the State Of Charge (SOC)• the temperature• the current level• the ageing

OCV+

_

ibat

ubat=

R

OCV: Output Circuit Voltage



- Modelling and EMR of the battery: OCV -

Data sheets usually give the battery voltage versus SOC (≠ OCV vs SOC) for different currents

Curve for low current (eg. C/5 = 3 A) is close to OCV

Source : Serge Pelissier (IFFSTAR), Batteries for electric and hybrid vehicles: State of the art, Modeling, Testing, Aging,Tutorial, VPPC’2010, Lille, September 2010



- Modelling and EMR of the battery: simulation session -

OCV+

_

ibat

ubat=

R

OCV and R are modelled by means of map with a dependency of:• the State Of Charge (SOC)• the temperature• the use of the battery (charge or discharge)

OCV: Output Circuit Voltage

BAT

ubat

ibat

bat batu OCV R i



- Modelling and EMR of the chopper -

s11 s12

v1 v2

s21 s22

ubat

idcm

uch-a

Four-quadrant chopper:• reversible in current (torque)• reversible in voltage (speed)

ich-a

i1 i2

11 21

12 22

s s 1s s 1Switching functions:

• complementarity of switches

1 11 bat

1 11 dcm

v s ui s i

2 12 bat

2 12 dcm

v s ui s is11 s12

ubat

ich-a

BAT

mch-a

uch-a

DCMidcm

ch a ch a batch a 11 12

ch a ch a dcm

u m uwith m s s

i m i

mch-a: modulation function

ch a 1 2 11 12 bat

ch a 1 2 11 12 dcm

u v v s s ui i i s s i



- Modelling and EMR of the separately-excited DC machine -

JshTdcm

gear

Tload

gearfsh

ich-auch-a

ia

ubat

if uch-f

ich-f

itot

Basis of the separately-excited DC motor:• the field current of the stator if creates a magnetic field• the armature current ia is supplied to the rotor via brush and commutator• the interaction of the magnetic field and the armature current in the rotor produces a torque Tdcm• the motor starts to turn and reaches the speed gear to balance the load torque Tload and develops a back EMF




ia

uch-a

ra

edcm

La

Basis of the separately-excited DC motor:• the field current of the stator if creates a magnetic field• the armature current ia is supplied to the rotor via brush and commutator• the interaction of the magnetic field and the armature current in the rotor produces a torque Tdcm• the motor starts to turn and reaches the speed gear to balance the load torque Tload and develops a back EMF

ra: armature resistor ()La: armature inductor (H)edcm: motor back EMF (V)

if

uch-f

rfLf

rf: field resistor ()Lf: field inductor (H)

dcm f gear i f gear

dcm f a i f a

e k k iT k i k i i

Tdcm: motor torque (Nm)f: magnetic fluxki and k: motor constants (V.s/A and V.s/Wb)

Equivalent circuitEquivalent circuit




ch a dcm a a a adu e r i L idt

edcm

ia

ia

uch-a

ch f f f f f fdu e r i L idt

uch-f if

efif

Tdcm

gear

ia

uch-a

ra

edcm

La ra: armature resistor ()La: armature inductor (H)edcm: motor back EMF (V)

if

uch-f

rfLf

rf: field resistor ()Lf: field inductor (H)

dcm f dcm i f gear

dcm f a i f a

e k k iT k i k i i

Tdcm: motor torque (Nm)f: magnetic fluxki and k: motor constants (V.s/A and V.s/Wb)

Equivalent circuitEquivalent circuit



- Modelling and EMR of the shaft’s DCM -

JshTdcm

gear

Tload

gearfsh

dcm load sh gear sh geardT T f Jdt

fsh: viscous friction (Nm.s)Jsh: moment of inertia (kg.m2)

gear

gear

Tload

Tdcm



- Global EMR: part 1 -

itot

BATubat ea

ia

DC machine

if

ef

shaft

Tdcm

gear

gear

Tload

choppers

mch-f

uch-f

ia

if

mch-a

uch-a

ubat

parallel connection

ubat

ich-f

ich-a

bat

tot ch a ch f

common ui i i

JshTdcm

gear

Tload

gearfsh

ich-auch-a

ia

ubat

if uch-f

ich-f

itot



gear

Tload

diff

Tgear

gear

pgear gear load

gear gear diff

T k T

k

Tload

gear

Tgear

diff

kgear

- Modelling and EMR of the gearbox -

gear diffgear diff gear

load gear

Tif T 0 p 1

T

gear diffgear diff

gear load gear

T1if T 0 p 1T

gear ≈ 98 % for a gear

kgear is constant for a simple gearbox

Tload

gear

Tgear

diff



Source : HowStuffWorks, How Differentials Work,http://auto.howstuffworks.com/differential2.htm

planet gear

ring gear

side gear (wheels)

trans. shaft

- The mechanical differential -



diff

Tgear

diffldif rdif

rwh lwhwh

TT T2

2

- Modelling and EMR of the mechanical differential -

Tldiff

diff

rwh

Trdiff

Tgear lwhTdiff

wh

lwh

rwh

Tldiff

Trdiff

pdiff diff diff gear

diff diff wh

T k Tk

kdiff is a ratio of the differential



Tdiff

wh

Fwh

vwh

wh diff wh

wh wh wh

F T / Rv / R

Rwh: wheel radius

- Modelling of the wheels -

vwh

Fwh

wh

Tdiff



vveh

Fenv

veh veh tot envdM v F Fdt

vveh

Ftot

Fenv

vveh

Flwh

Frwh

vrwh

vrwh

vev

Ftot

Rt

FFF

vR

2/lRv

vR

2/lRv

rwhlwhtot

evt

evtrwh

evt

evtlwh

lev

Rt

Rt: turning radiuslev: EV width

- Modelling of the chassis -



2aero air x veh

roll roll

grade

1F A C v2

F k M g cos( )F M g sin( )

env aero roll gradeF F F F

ENVvveh

Fenv

A Ftot

M g

The slope is most of the time small⇨ sin() ≈ tan() = gradient = h/L⇨ cos() = sin() / tan() ≈ 1

Faero

- Modelling of the environment -

L

hFroll



- Global EMR: part 2 -

rwh

lwh

Tldiff

Trdiff

vveh

Fenv

diff

Tgear

Tload

gear

Flwh

Frwh

vrwh

vlwh

wheels

ENVvvehFtot

Fenvvveh

Rt

chassis environ.

Tgear

diff

Tload

gear

gearbox

Tldiff

lwh

rwh

Trdiff

Tdiff

wh

differential



- Global EMR -

rwh

lwh

Tldiff

Trdiff

vveh

Fenv

diff

Tgear

JshTdcm

gear

Tload

gearfsh

ich-auch-a

ia

ubat

if uch-f

ich-f

itot

Flwh

Frwh

vrwh

vlwhENV

vvehFtot

Fenvvveh

Rt

Tgear

diff

Tload

gear

Tldiff

lwh

rwh

Trdiff

Tdiff

wh

wheels chassis environ.gearbox differential

ea

ia

if

ef

Tdcm

gear

gear

Tloaduch-f

ia

uch-a

DC machine shaft

if



- EMR: permutation and merging -

permutation

permutation

p p 2gear gear dcm gear sh gear gear gear

dk T T J kdt

Flwh

Frwh

vrwh

vlwhENV

vvehFtot

Fenvvveh

Rt

Tgear

diff

Tload

gear

Tldiff

lwh

rwh

Trdiff

Tdiff

wh

wheels chassis environ.gearbox differential

ea

ia

if

ef

Tdcm

gear

gear

Tloaduch-f

ia

uch-a

DC machine shaft

if

Flwh

Frwh

vrwh

vlwhENV

vvehFtot

Fenvvveh

Rt

Tgear

diff

Teq

diff

Tldiff

lwh

rwh

Trdiff

Tdiff

wh

ea

ia

if

ef

Tdcm

gear

diff

Tgearuch-f

ia

uch-a

if



- EMR: permutation and merging -

Flwh

Frwh

vrwh

vlwhENV

vvehF

Fenv

Rt

Tgear

diff

Tldiff

lwh

rwh

Trdiff

Tdiff

wh

ea

ia

if

ef

Tdcm

gear

vveh

Ftotuch-f

ia

uch-a

vveh

Ftot

vveh

merging

Flwh

Frwh

vrwh

vlwhENV

Ftot

Rt

Tgear

diff

Tldiff

lwh

rwh

Trdiff

Tdiff

wh

ea

ia

if

ef

Tdcm

gear

vveh

Fenvuch-f

ia

uch-a

vveh

if

itot

BATubat

mch-f

mch-aubat

ubat

ich-f

ich-a

wheels chassisgearbox differentialDC machinechoppersparallel

connection

2gear diffp p

eq veh sh gear diffwh

k kM M J

R



- EMR: simplification -

Flwh

Frwh

vrwh

vlwhENV

Ftot

Rt

Tgear

diff

Tldiff

lwh

rwh

Trdiff

Tdiff

wh

ea

ia

if

ef

Tdcm

gear

vveh

Fenvuch-f

ia

uch-a

vveh

if

itot

BATubat

mch-f

mch-aubat

ubat

ich-f

ich-a

If the vehicle drives in a straight line (Rt = ∞), an equivalent wheel is sufficient

ENVFtotTgear

diff

Tdiff

wh

ea

ia

if

ef

Tdcm

gear

vveh

Fenvuch-f

ia

uch-a

vveh

if

itot

BATubat

mch-f

mch-aubat

ubat

ich-f

ich-a

wheels chassisgearboxdifferential

ratioDC machinechoppersparallel

connection

tot diff wh

wh veh wh

F T / Rv / R

Rwh: wheel radius

combination



- Global EMR -

rwh

lwh

Tldiff

Trdiff

vveh

Fenv

diff

Tgear

JshTdcm

gear

Tload

gearfsh

ich-auch-a

ia

ubat

if uch-f

ich-f

itot

ENVFtot

ea

ia

if

ef

Tdcm

gear

vveh

Fenvuch-f

ia

uch-a

vveh

if

itot

BATubat

mch-f

mch-aubat

ubat

ich-f

ich-a

chassistransmissionDC machinechoppersparallel

connection

gear diffp ptot gear diff diff

wh

gear diffwh veh

wh

k kF T

Rk k

vR



Aalto University

«« UUSE OTHER SE OTHER EELECTRIC LECTRIC MMACHINESACHINES »»


[email protected]


[email protected]



- Use of a Permanent Magnet DC Machine -

if uch-f

ich-f

rwh

lwh

Tldiff

Trdiff

vveh

Fenv

diff

Tgear

JshTdcm

gear

Tload

gearfsh

ich-auch-a

ia

ubat

itot

Basis of the permanent magnet DC motor:• the field windings are replaced by permanent magnets• the magnetic flux is created by the permanent magnets at the stator

ia

uch-a

ra

edcm

Ladcm f dcm dcm

dcm f a a

e k KT k i K i

f = constantK: motor constant (V.s)



- Use of a Permanent Magnet DC Machine -

Basis of the permanent magnet DC motor:• the field windings are replaced by permanent magnets• the magnetic flux is created by the permanent magnets at the stator

ia

uch-a

ra

edcm

Ladcm f dcm dcm

dcm f a a

e k KT k i K i

f = constantK: motor constant (V.s)

ch a dcm a a a adu e r i L idt

edcm

ia

ia

uch-a Tdcm

gear

ch f f f f f fdu e r i L idt

uch-f if

efif

edcm

ia

ia

uch-a

dcm f f dcm

dcm f f a

f

e k iT k i ie 0

Tdcm

gear



- Global EMR with a Permanent Magnet DC Machine -

ea

ia

ia

uch-a

BATubat

mch-a

ich-a

chassistransmissionDC machinechopper

ENVFtotTdcm

gear

vveh

Fenvvveh

rwh

lwh

Tldiff

Trdiff

vveh

Fenv

diff

Tgear

JshTdcm

gear

Tload

gearfsh

ich-auch-a

ia

ubat

itot



- Use of a Permanent Magnet Synchronous Machine -

rwh

lwh

Tldiff

Trdiff

vveh

Fenv

diff

Tgear

JshTdcm

gear

Tload

gearfsh

ich-auch-a

ia

ubat

itot

uinv23

battery PMSMinverter

uinv13

ism1

ism2

s11s12s13

s21s22s23

ubat

iinv

JshTsm

gear

Tload

gearfsh



- Difference between a single-phase and a 3-phase system -

3-phase system (without neutral):• 3 cables• 2 independent currents• 2 independent voltages

1 2 3

1 2 3 12 31 23

i i i 0v v v 0 u u u 0

star or delta connection

single-phase system:• 2 cables• 1 independent current• 1 independent voltage

LoadGenerator

i

iu

LoadGenerator

i1i2i3

u12

u23

u31

v1 v2 v3

N

v1

v2v3

u31

u23

u12

N

1

23

phase separation ofone-third cycle (2/3)



- Modelling and EMR of the inverter -

inv13 1 3 11 13inv bat

inv 23 2 3 12 13

11 13inv1inv inv bat bat bat

12 13inv 2

u v v s su u

u v v s s

s smu m u u u

s sm

1 sm1

inv 2 11 12 13 sm2

3 sm3

sm1inv 11 12 13

sm2

Tinv inv sm inv1 inv 2 sm

i ii 1 1 1 i s s s i

i i

1 0i

i s s s 0 1i

1 1

i m i m m i

ubat

iinv

BAT SM

invu

smi

invm

inv inv13 sm1 inv 23 sm2p u i u i

sm1 sm2 sm3

1 2 3

i i i 0v v v 0

inv 1 sm1 2 sm2 3 sm3p v i v i v i

inv13 1 3

inv 23 2 3

u v vu v v

s13s12s11

s23s22s21

ubat

iinv

uinv23

uinv13

ism1

ism2v1

v2

v3

s11 s12 s13



- Modelling and EMR of the PMSM -

uinv23

battery PMSMinverter

uinv13

ism1

ism2

s11s12s13

s21s22s23

ubat

iinv

JshTsm

gear

Tload

gearfsh

Basis of the Permanent Magnet Synchronous Motor:• the armature winding (stator) is excited by 3-phase AC current• this supplying creates a rotating magnetic field inside the motor• the rotor, equipped of permanent magnets, creates a constant magnetic field• the interaction between both magnetic fields creates a torque Tsm: the motor rotates• the constant magnetic field is in synchronization with the rotating magnetic field



isd

d/s

isq

vsd

vrd

vsq

vrq

ird

irq

d

q

rotorrotor

ism1vsm1

stator

1s

2s

3s

ism3

vsm3

ism2vsm2 rotor1r

2r

3r

p

S

N

modelling simplifications:0i if sd sqr2sm ikT reduced current magnitude

for same produced torque

isd

d/s

isq

vsd

vrd

vsq

vrq

ird

irq

d

q

rotorrotor

isdisqvsd

vsq

= d

q

d axis oriented on rotor axis 1r

1s

rotor

stator

1r

Park’s transformation

123,rr/ddq,r

123,ss/ddq,s

x)(Px

x)(Px

- Park’s model of the PMSM -d, q rotating reference frame:- DC current- interaction simplification

3-phase system axis:- difficult to control AC currents (sinusoidal)- strong interaction between phases



Stator windings in (d,q)

sdqsdqsdqssdqs eviRidtdL

sm 2 r sq

sd ,q sd sq

T k i

e f ,i ,i

invu

smis dqi

s dqv

transformations

sdqsm

rectsdqi)]('K[i

u)](K[v

- EMR of the PMSM -

invu

smi

smi

sme gear

Tsm

r

s dqe

s dqi

relationships withouttime-dependence

PMSM

invu smi

smi sme gear

Tsm



- Global EMR with a Permanent Magnet Synchronous Machine -

uinv23

uinv13

ism1

ism2

s11s12s13

s21s22s23

ubat

iinv

rwh

lwh

Tldiff

Trdiff

vveh

Fenv

diff

Tgear

JshTsm

gear

Tload

gearfsh

BATubat

ich-a

chassistransmissionPMSMinverter

ENVFtotTsm

gear

vveh

Fenvvveh

invu

smi

smi

smeinvm



- Use of a Squirrel Cage Induction Machine -

rwh

lwh

Tldiff

Trdiff

vveh

Fenv

diff

Tgear

JshTdcm

gear

Tload

gearfsh

ich-auch-a

ia

ubat

itot

uinv23

batteryinductionmachineinverter

uinv13

iim1

iim2

s11s12s13

s21s22s23

ubat

iinv

JshTim

gear

Tload

gearfsh



- Modelling and EMR of the SCIM -

Basis of the Induction Motor:• the armature winding (stator) is excited by 3-phase AC current• this supplying creates a rotating magnetic field inside the motor• the conductor of the rotor is subjected to a sweeping magnetic field, which induces rotor currents• the interaction between both magnetic fields creates a torque Tim: the motor rotates• if the rotor is rotating at synchronous speed (i.e. frequency of the 3-phase at the stator), no currents will be induced in the rotor then no torque

uinv23

batteryinductionmachineinverter

uinv13

iim1

iim2

s11s12s13

s21s22s23

ubat

iinv

JshTim

gear

Tload

gearfsh



rotorrotor

is1vs1

stator

1s

2s

3s

is3

vs3

is2vs2

1s

rotor

stator

1r

r/s

Park’s transformation

123,rr/ddq,r

123,ss/ddq,s

x)(Px

x)(Px

Modelling simplifications:

sqr2im

sd1rikT

ik

isd

d/s

isq

vsd

vrd

ird

vsq

vrqirq

d

q

rotor1r

2r

3r

p

r/s

- Park’s model of the squirrel cage IM -

d, q rotating reference frame:- DC current- interaction simplification

3-phase system axis:- difficult to control AC currents (sinusoidal)- strong interaction between phases



urotor=0

gear

Tim

is-dq

es-dqis-dq

vs-dq

istator

ustator

r

ir-dq

er-dqir-dq

vr-dq

irotor

d/s

Park’s transformations

Rotor windings in (d,q)

Stator windings in (d,q)

sqr2im

sd1rikT

ik

Coupling device

- EMR of the squirrel cage IM -

d/r



- EMR of the squirrel cage IM -

gear

istator Tim

istator estator

Squirrel cagepermutation of windings and transformationconcatenation of EM conversion and transformation

ustator

Simplified EMR

BATubat

ich-a

chassistransmissioninduction machineinverter

ENVFtotTim

gear

vveh

Fenvvveh

invu

imi

imi

imeinvm



Aalto University

«« SSIMULATION IMULATION SSESSION:ESSION:

EMREMR OF AN OF AN EVEV WITH A WITH A PMDCMPMDCM »»


[email protected]


[email protected]



rwh

lwh

Tldiff

Trdiff

vveh

Fenv

diff

Tgear

JshTdcm

gear

Tload

gearfsh

ich-auch-a

ia

ubat

itot

- Simulation Session: EMR of an EV with a PMDCM -

Assumptions:ideal power switchespermanent magnet DC machine without saturationinertia of the DC machine shaft neglectedinertia of the wheels neglectedcontact wheel/ground without lossideal gearbox and differential (gear = diff = 1)no use of the mechanical brake



- Simulation Session: EMR of an EV with a PMDCM -

? ? ? ?

Target: Develop the EMR of the systemand implement it in MATLAB by usingthe graphical toolbox Simulink



- References -

[1] W. Lhomme, Ph. Delarue, Ph. Barrade, A. Bouscayrol, “Maximum Control Structure of a series hybrid electric vehicle using supercapacitors”, EVS'21, Monaco, April 2005.

[2] W. Lhomme, P. Delarue, P. Barrade, A. Bouscayrol, “Design and control of a supercapacitors storage system for traction applications”, IEEE-IAS'05, Hong-Kong (China), October 2005.

[3] A. Bouscayrol, W. Lhomme, P. Delarue, B. Lemaire-Semail, S. Aksas, “Hardware-In-the-Loop simulation of electric vehicle traction systems using Energetic Macroscopic Representation”, IEEE-IECON'06, Paris (France), November 2006.

[4] A. Bouscayrol, M. Pietrzak-David, P. Delarue, R. Peña-Eguiluz, P. E. Vidal, X. Kestelyn, “Weighted control of traction drives with parallel-connected AC machines”, IEEE Transactions on Industrial Electronics, Vol. 53, no. 6, p. 1799-1806, December 2006.

[5] A. Bouscayrol, A. Bruyère, P. Delarue, F. Giraud, B. Lemaire-Semail, Y. Le Menach, W. Lhomme, F. Locment, “Teaching drive control using Energetic Macroscopic Representation - initiation level”, EPE'07, Aalborg (Denmark), September 2007.

[6] K. Chen, P. Delarue, A. Bouscayrol, R. Trigui, “Influence of control design on energetic performances of an electric vehicle”, IEEE-VPPC'07, Arlington (U.S.A.), September 2007.

[7] K. Chen, A. Bouscayrol, W. Lhomme, “Energetic Macroscopic Representation and Inversion-based control: application to an Electric Vehicle with an electrical differential”, Journal of Asian Electric Vehicles, vol. 6, no.1, p. 1097-1102, June 2008.

[8] K. Chen, A. Bouscayrol, A. Berthon, P. Delarue, D. Hissel, R. Trigui, W. Lhomme, “Global energetic modelling of different architecture Hybrid Electric Vehicles”, ElectrIMACS'08, Québec (Canada), May 2008.



- Modelling and EMR of the battery -

Source : Battery Management Systems, Philips Research, 2008, Volume 9, 1-9, DOI: 10.1007/978-1-4020-6945-1_1

Energy density of the hydrocarbon fuels:- gasoline and diesel oils ≈ 10 000 Wh/liter



- Modelling and EMR of the battery: hysteresis effect -

chargeOCV

SOC(%)

discharge

OCVmean

1000

SOC: State Of ChargeOCV: Open Circuit Voltage

The hysteresis effect depends on the type of the battery:• strongly for Ni-MH• lightly for Li-ion

Source : Thèse de Maxime Montaru, Contribution à l’évaluation du vieillissement des batteries de puissance utilisées dans les véhicules hybrides selon leurs usages, Institut Polytechnique de Grenoble, juillet 2009

The evolution of the OCV vs SOC is different according to the use of the battery (charge or discharge)




s11 s12

v1 v2

s21 s22

ubat

idcm

uch-a

Four-quadrant chopper:• reversible in current (torque)• reversible in voltage (speed)

ich-a

i1 i2

ubat

ich-a

BAT

Kirchhoff's current law:

bat

ch a 1 2

u commoni i i

11 21

12 22

s s 1s s 1 Switching functions:

1 11 bat

1 11 dcm

v s ui s i

2 12 bat

2 12 dcm

v s ui s i

Kirchhoff's voltage law:

dcm

ch a 1 2

common iu v v

ubat

i1

ubat

i2

s11

v1

idcm

s12

v2

idcm

uch-a

DCMidcm

s11 s12




ubat

ich-a

BAT

ubat

i1

ubat

i2

s11

v1

idcm

s12

v2

idcm

uch-a

DCMidcm

1 11 bat

2 12 bat

v s uv s u

ch a 1 2u v v Kirchhoff's voltage law:

ch a 1 2 11 12 batu v v s s u

1 11 dcm

2 12 dcm

i s ii s i

Kirchhoff's current law: ch a 1 2i i i

ch a 1 2 11 12 dcmi i i s s i

ubat

ich-a

BAT

mch-a

uch-a

DCMidcm

ch a ch a batch a 11 12

ch a ch a dcm

u m uwith m s s

i m i

mch-a: modulation function




uinv23

uinv13

ism1

ism3

s13s12s11

s23s22s21

ubat

iinv

ubat

ich-a

BAT

ubat

i1

ubat

i2

s11

v1

ism1

s12

v2

ism2

SM

ubat

i3s11

v1

ism3

ism2

invu

smi

Kirchhoff's current law: bat

inv 1 2 3

common ui i i i

inv13 1 3inv

inv 23 2 3

u v vu

u v v

sm1sm1

sm2 sm smsm2

sm3

i 1 0i

i 0 1 i with ii

i 1 1

Kirchhoff's voltage law:

sm1 sm2 sm3i i i 0

star or delta connection




uinv23

uinv13

ism1

ism3

s13s12s11

s23s22s21

ubat

iinv

ism2

ubat

iinv

BAT SM

invu

smi

invm

inv13 1 3 11 13inv bat

inv 23 2 3 12 13

11 13inv1inv inv bat bat bat

12 13inv 2

u v v s su u

u v v s s

s smu m u u u

s sm

1 sm1

inv 2 11 12 13 sm2

3 sm3

sm1inv 11 12 13

sm2

Tinv inv sm inv1 inv 2 sm

i ii 1 1 1 i s s s i

i i

1 0i

i s s s 0 1i

1 1

i m i m m i



- Base Elements of the EMR -

i

v1 i

v2

v1 v2

i

L, r

21 vvirdtdiL

Electromechanical conv.

Electrical converter

Mechanical conv.

Converter without energy accumulation

VDC

mi

u

f

fis

VDC

i

u

isf

ES

s

DC

ifiVfu

VDC

i

VDC

iES

ES : Electrical Source



action - reaction principle

electromechanical coup.electrical coupling mechanical coup.

21

DC21

iiiVvv

VDC

i

VDC

i

i1

i2 v1v2

i1

i2

v1

v2ES

parallel electriccircuit

p=VDC i

- Base Elements of the EMR: the coupling -

Date post:	12-Jun-2020
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ELECTRIC VEHICLE - EMRwebsite€¦ · 2 11 21 12 22 ss 1 ss 1 Switching functions: •...

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