dr. philippe barrade*, dr. walter lhomme**, prof. alain...

« Energy Management of EVs & HEVs using Energetic Macroscopic Representation »

Technical University of Graz, April 2012

Dr. Philippe Barrade*, Dr. Walter LHOMME**, Prof. Alain BOUSCAYROL** * LEI, Ecole Polytechnique Fédérale de Lausanne, Suisse

** L2EP, University Lille1, France

2 EMR, Technical University of Graz, April 2012

- Outline -

• Introduction • Modelling and representation of the mechanical part

– Illustration of permutation, merging and combination rules • Modelling and representation of the electrical part

– Considerations on the model level (batteries) – Considerations for the modelling and representation of

power converters – Considerations for the modelling and representation of

electrical machines • Final EMR of an EV


- Studied EV traction system -

Tgear Ωrwh

Ωlwh Tldiff

Trdiff

vveh

Fenv

Ωdiff Jsh Tdcm

Ωgear

Tload

Ωgear fsh

Power Converters

Electrical machine

Trans- wheels chassis environ. batteries shaft


- Goals of the study-

• Allow the EMR of an electric vehicle – Obtained from its modelling – Allow the identification an IBC – Comparisons of various technologies for the electrical

machine

• Assumptions – Ideal power switches for the converters – Non-saturated electrical machines – Inertia of the wheels is neglected – Contact wheel/ground without loss – Mechanical brakes are not considered


- Methodology -

• EMR of each sub-system is deduced from its modelling – And not directly from its structural representation

• EMR of the mechanical subsystems will be made first • EMR of the electrical subsystems will be then operated

– Considering 3 different kinds of electrical machines • DC machines • Induction machines • Permanent magnets synchronous machines

– Comparison of the various EMR will be proposed


- From the shaft to the environment -

Tgear Ωrwh

Ωlwh Tldiff

Trdiff

vveh

Fenv

Ωdiff Jsh Tdcm

Ωgear

Tload

Ωgear fsh

Differential wheels

chassis environ. shaft Gear-box

• Considering that the electrical machine is a torque generator

• Each sub-system is modelled and represented independently • The final EMR is the last step


- Model and EMR of the shaft -

• Model

– Fsh : viscous friction (Nm.s) – Jsh : inertia moment (kg.m2)

• EMR

Jsh Tdcm

Ωgear

Tload

Ωgear fsh

Ωgear

Ωgear

Tload

Tdcm


- Model and EMR of the gearbox -

• Model – kgear : transformation ratio – ηgear : efficiency – p : correction exponent

• EMR

Ωgear

Tload Ωdiff

Tgear

Tload

Ωgear

Tgear

Ωdiff

kgear

Tload

Ωgear

Tgear

Ωdiff

If kgear can be adjusted kgear constant


- Model and EMR of the differential -

• Principle

planet gear

ring gear

side gear

(wheels)

trans. shaft

Ωdiff

Tgear

Ωlwh

Ωrwh

Tldiff

Trdiff


- Model and EMR of the differential -

• Model – kdiff : transformation ratio – ηdiff : efficiency – p : correction exponent

• EMR

Ωdiff

Tgear

Ωlwh

Ωrwh

Tldiff

Trdiff

Tldiff

Ωlwh

Ωdiff

Ωrwh

Trdiff

Tgear Tdiff

Ωwh


- Model and EMR of the wheels -

• Model – Rwh : wheel radius

• EMR

vwh

Fwh

Ωwh

Tdiff

Tdiff

Ωwh

Fwh

vwh


- Model and EMR of the wheels/ground contact -

• Model

» Rt : turning radius » lev : vehicle width

• EMR

lev

Rt

Flwh

Frwh

vrwh

vrwh

vveh

Ftot

Rt


- Model and EMR of the chassis -

• Model – Mveh : mass of the vehicle

• EMR

vveh

Fenv

vveh

Ftot

Fenv

vveh


- Model and EMR of the environment -

• Model – Faero : aerodynamic resistance – Froll : rolling resistance – Fgrade : grade resistance

α

A

α M g

Faero

L

h ½ Froll ½ Froll

Fgrade

If α small (h/L



• Model: Aerodynamic resistance – ρair : density of air (1.223kg/m3 @ 1013hPa, 20°C) – A : frontal area (m2) – Cx : drag coefficient

vehicle Cx drag coefficient convertible 0.33 to 0.50 four-wheel drive 0.35 to 0.50 saloon car 0.26 to 0.35 estate car 0.30 to 0.34 shaped 0.30 to 0.40 headlight and wheels in the fuselage 0.20 to 0.25

kammback 0.23 streamlined shape 0.15 to 0.20

Source: Mémento de Technologie Automobile, 3ème édition, BOSCH drop of water



• Model: Rolling resistance – kroll : coefficient of the rolling (quality of the floor-covering)

floor-covering coefficient of the rolling kroll cobblestones 0.013 concrete, asphalt 0.011 macadam 0.020 / 0.025 dirt track 0.050

Source: Mémento de Technologie Automobile, 3ème édition, BOSCH



• Model: total resistive forces – Once Fenv is known – Requested power can be identified: P=Fenv.vveh – Example for Cx=0.35, A=2m2, kroll=0.02, Mveh=1000kg and h/L=5%


- Global EMR of the mechanical part -

Tgear Ωrwh

Ωlwh Tldiff

Trdiff

vveh

Fenv

Ωdiff Jsh Tdcm

Ωgear

Tload

Ωgear fsh


Tdcm

Ωgear

Ωgear

Tload

shaft

Tgear

Ωdiff

Tload

Ωgear

gearbox

Tldiff

Ωlwh

Ωrwh

Tdiff

Ωwh

differential

Trdiff

Flwh

Frwh

vrwh

vlwh

wheels

ENV vveh Ftot

Fenv vveh

Rt

chassis environ.


- Global EMR of the mechanical part: permutation and merging -

Tdcm

Ωgear

Ωgear

Tload

shaft

Tgear

Ωdiff

Tload

Ωgear

gearbox

Tldiff

Ωlwh

Ωrwh

Tdiff

Ωwh

differential

Trdiff

Flwh

Frwh

vrwh

vlwh

wheels

ENV vveh Ftot

Fenv vveh

Rt

chassis environ.

permutation

Tgear

Ωdiff

Teq

Ωdiff

Tdcm

Ωgear

Ωdiff

Tgear

Tldiff

Ωlwh

Ωrwh

Tdiff

Ωwh Trdiff

Flwh

Frwh

vrwh

vlwh ENV

vveh Ftot

Fenv vveh

Rt Permutation…!..!....


- Global EMR of the mechanical part: permutation and merging -

Tdcm

Ωgear ENV

Tgear

Ωdiff

Tldiff

Ωlwh

Ωrwh

Tdiff

Ωwh Trdiff

Flwh

Frwh

vrwh

vlwh vveh F

Ftot vveh

Rt

vveh Ftot

Fenv vveh

merging

Tdcm

Ωgear ENV

Tgear

Ωdiff

Tldiff

Ωlwh

Ωrwh

Tdiff

Ωwh Trdiff

Flwh

vrwh

vlwh vveh Ftot

Ftot vveh

Rt

Frwh

wheels chassis gearbox differential


- Global EMR of the mechanical part: simplifications (optional) -

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

Tdcm

Ωgear ENV

Tgear

Ωdiff

Tldiff

Ωlwh

Ωrwh

Tdiff

Ωwh Trdiff

Flwh

vrwh

vlwh vveh Ftot

Ftot vveh

Rt

Frwh

ENV Ωdiff Ωwh Ωgear

vveh

Fenv vveh

wheels chassis gearbox differential

ratio

Ftot Tgear Tdiff Tdcm

Rwh: wheel radius

combination


- Global EMR of the mechanical part: simplifications (optional) -

Tgear Ωrwh

Ωlwh Tldiff

Trdiff

vveh

Fenv

Ωdiff Jsh Tdcm

Ωgear

Tload

Ωgear fsh


ENV Ftot Tdcm

Ωgear

vveh

Fenv vveh

chassis transmission


- Global EMR of the mechanical part: key points -

ENV Ftot Tdcm

Ωgear

vveh

Fenv vveh

chassis transmission

• The system has been first modelled • From the model, the EMR has been established

– Permutations and merging are required when conflict of associations are obtained. This is mandatory. It must be done according to the model.

– Simplifications can be made but are optional. In all cases, the model is still valid, except if the simplifications are made following restrictive conditions. Then, adaption of the model is needed . Simplifications depend on the objectives defined for the study.


• Considering that mechanical part is an energy source

• Generalities for modelling and representing – Batteries, Power converters, Electrical machines

• Final EMR comparing the representations of various technologies

Tdcm

Ωgear

- From the batteries to the shaft -


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

• Choice of the model depends on the objectives for the study • Energetic model

– Open Circuit Voltage (OCV): – Internal impedance (R): – State of Charge (SOC):

- Model and representation of the batteries -

OCV +

_

ibat

ubat =

R


• Parameters identification – Directly from datasheets

• identification • Implementation of look-up tables

• From the model to the representation

- Model and representation of the batteries -

BAT

ubat

ibat


• Most of the power converters are made of elementary switching cells – Depending on the switches

• 1 quadrant (is>0) • 2 quadrants (is>0 or


• From the model to the representation

- Model and representation of Power Converters-

t

us ue

T

ue

ie m

us

is

ue

is

Instantaneous model Average model


• Extension to the 4 quadrants DC/DC converters and single phase voltage source inverter – Using 2 parallel elementary converters

– Models for the 2 elementary converters


s11

us1 s12

ue

is ie

i1

m1

s21

s22

i2

us2

us

m2


• 4 quadrants DC/DC converters and VSI – Models for the 2 elementary converters

– Global model


s11

us1 s12

ue

is ie

i1

m1

s21

s22

i1

us2

us

m2


• 4 quadrants DC/DC converters and VSI – From the model to the representation


ue

i1 m1

us1

is

ue

i2 m2

us2

is

ue

ie

us

is


• 4 quadrants DC/DC converters and VSI – Simplification


ue

ie m

us

is

ue

is

Instantaneous model Average model


• 3 phases voltage source inverter – The principle is the same


s31 s21 s11

s33 s22 s12

ue

ie

u23

is1

is2

is3

u13

ue

ie m

us

is

ue

is

Instantaneous model Sliding average model


• Summary

• Warning – Representations of various converter seem to be identical

• Never forget the model hidden behind the representation


ue

ie m

us

is

2Q converter ue

ie m

us

is

ue

ie m

us

is

4Q converter 3 phases VSI


• Main parameters – Armature

• ra: armature resistor (Ω) • La: armature inductor (H) • edcm: motor back EMF (V) • Tdcm: torque (Nm) • Ωgear: angular rotational speed (rad/s) • kΦ: motor constant (V.s/Wb) • Φf: magnetic flux (Wb)

– Excitation • With excitation circuit

– rf: field resistor (Ω) – Lf: field inductor (H) – ki: motor constant (V.s/A)

• With permanent magnets – K: motor constant (V.s)

- Model and representation of DC machines -

ia

uch-a

ra

edcm

La

if

uch-f

rf Lf


• Model – With excitation circuit

• Electrical

• Electro-mechanical

– With permanent magnets • Electrical



ia

uch-a

ra

edcm

La

if

uch-f

rf Lf


• Model – With excitation circuit

• Electrical


– With permanent magnets • Electrical



edcm

ia

ia

uch-a

uch-f if

ef if

Tdcm

Ωgear

edcm

ia

ia

uch-a Tdcm

Ωgear edcm ia

uch-a

• Representation – With excitation circuit

– With permanent magnets

With ef=0 !


• Model – Faraday law

- Model and representation of squirrel cage IM-


• Model: Flux matrix


1 – the position θ is function of time: difficult to control AC currents 2 – strong interaction between phases

solution: use of park’s transformation


• Model: needs in tools for representation – Park’s transformation: 3-phases to 2-phases transformation

• Expressed in a fix reference frame (α,β)

• Transformation in rotating reference frame (d,q)

– For Induction Machines: d axis is oriented along the rotor flux • isd current related to the rotor flux • isq current related to the torque • DC equivalent voltages and current


equivalent DC machine in the (d,q) frame


• Model – Park’s transformation for an Induction Machine


Modelling simplifications:

is1 vs1

stator

1s

2s

3s

is3

vs3

is2 vs2 rotor 1r

2r

3r

pΩ

θr/s

1s

rotor

stator

1r

θr/s

isd

θd/s

isq

vsd

vrd ird

vsq

vrq irq

d

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


• Representation – Step 1


urotor=0

Ωgear

Tim

is-dq

es-dq is-dq

vs-dq

istator

ustator

φr

ir-dq

er-dq ir-dq

vr-dq

irotor

θd/s

Park’s transformations

Rotor windings in (d,q)

Stator windings in (d,q)

Coupling device

θd/r


• Representation – Step 2


Ωgear

Tim

is-dq

es-dq is-dq

vs-dq

istator

ustator

θd/s Stator windings in (d,q)

φr

isd By a variable change, the rotor flux can be expressed in EMR


• Model – Principle is the same than IM, except that rotor is made of

permanent magnets • Rotor angular rotational speed is synchronized with the stator rotating

magnetic field – Same tools: Park’s transformation and expression along the rotor

rotating frame

- Model and representation of PMSM -

isd

θd/s

isq

vsd

vrd

vsq

vrq

ird

irq

d

q

isd

θd/s

isq

vsd

vrd

vsq

vrq

ird

irq

d

q

isd isq vsd

vsq

= d

q 1s

rotor

stator

1r

θ

ism1 vsm1 stator

1s

2s

3s

ism3

vsm3

ism2 vsm2 rotor 1r

pΩ

θ

modelling simplifications: reduced current magnitude for same produced torque


• Model – Main equations

• Electrical


• Representation

- Model and representation of PMSM -

Ωgear

Tsm is-dq

es-dq is-dq

vs-dq

istator

ustator

θ

49 EMR, Technical University of Graz, April 2012 • With DC machines

– With excitation circuit

• With AC machines – Squirrel cage IM

- Global EMR of the electrical part -

- With permanent magnets

- PMSM

Bat ubat

minv iinv

Tdcm

Ωgear

uinv

iim

vsdq

isdq

isdq

esdq

PM synchronous machine inverter

Bat ubat

minv iinv

Tdcm

Ωgear

uinv

iim

vsdq

isdq

isdq

esdq

isd

φr

induction machine inverter

uch-a

ea

ia

ia BAT

ubat

mch-a ich-a

Tdcm

Ωgear

DC machine chopper

ea

ia

if

ef

Tdcm

Ωgear uch-f

ia

uch-a

if

itot BAT

ubat

mch-f

mch-a ubat

ubat

ich-f

ich-a

DC machine choppers parallel

connection


- Global EMR of the electrical part: key points -

• The system must been first modelled

• From the model, the EMR can been established – Never forget the model behind the representation

• The EMR from the batteries to the shaft has been made for different electrical machines

• The comparison of the various EMR shows that strong similarities exist – Thanks to the use of the adequate transformations – Underlined by the EMR

uch-a

ea

ia

ia BAT

ubat

mch-a ich-a

Tdcm

Ωgear

DC machine chopper


- Global EMR (with a DC machine, excitation circuit) -

Ωrwh

Ωlwh Tldiff

Trdiff

vveh

Fenv

Ωdiff

Tgear

Jsh Tdcm

Ωgear

Tload

Ωgear fsh

ich-a uch-a ia

ubat

if uch-f ich-f

itot

ea

ia

if

ef

Tdcm

Ωgear uch-f

ia

uch-a

if

ENV Tgear

Ωdiff

Tldiff

Ωlwh

Ωrwh

Tdiff

Ωwh Trdiff

Flwh

vrwh

vlwh vveh Ftot

Ftot vveh

Rt

Frwh itot

BAT ubat

mch-f

mch-a ubat

ubat

ich-f

ich-a

wheels chassis gearbox differential DC machine choppers parallel

connection



Models = must be defined in function of the objective different models for the same subsystems using different assumptions

EMR = causal way to organize models of different parts highlight energetic properties and conflicts of associations

EV with DC machine = a basic traction system other can be deduced by using the Park’s transformation


- References -

[1] W. Lhomme, "Gestion d’énergie de véhicules électriques hybrides basée sur la Représentation Energétique Macroscopique", Thèse de doctoral de l'Université Lille 1, novembre 2007.

[2] 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.

[3] 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.

[4] 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.

[5] 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.

[6] 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.

dr. philippe barrade*, dr. walter lhomme**, prof. alain...

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