« Energetic Macroscopic Representation (EMR) · two pictograms background: orange contour: red upstream I/O vectors (dim n) downstream I/O vectors (dim p) Possible tuning input vector

EMR’12

Madrid

June 2012

Joint Summer School EMR’12

“Energetic Macroscopic Representation”

« Energetic Macroscopic

Representation (EMR) »

Prof. Daniel HISSEL

FEMTO-ST Energy Department, FCLAB, University of Franche-Comte,

[email protected]

Dr. Walter LHOMME, Prof. Alain BOUSCAYROL

L2EP, University of Lille 1,

[email protected], [email protected]

mailto:[email protected]









EMR’12, Madrid, June 2012 2

« Energetic Macroscopic Representation »

- Outline -

1. EMR basic elements

• General principles

• Source, accumulation and conversion elements

• Coupling elements

2. EMR of a whole system

• Action and tuning path

• Association rules

• Example

3. Conclusion



EMR’12

Madrid

June 2012

« EMR basic elements »

7


EMR’12, Madrid, June 2012

Interaction principle

Each action induces a reaction

action

reaction

S2 S1

Power exchanged between S1and S2 = action x reaction

power

- Interaction principle -

Example

battery load

Vbat Vbat

iload

load battery Vbat

iload

P=Vbat iload

8



area xdt

knowledge

of past evolution

OK in

real-time

Principle of causality

physical causality is integral input output

cause effect

t1

t

x

knowledge

of future evolution

slope

dt

dx

?

impossible in

real-time

- Causality principle -

9



- State variable (1/3) -

Energy is the integrative of power

t

dPowertEnergie0

).()(

System

Power 1 Power 2

Energy

A system can store energy : in this case power1(t) ≠ power2(t)

Energy cannot vary instantaneously !

)()( tEnergydt

dtPower we would obtain Power(t) In fact, as :

Physically impossible

10




Energy varies thus « slowly », according to the charge and the discharge of the

energy storage devices Examples :

- filling the tank of a car

- energy storage in the capacitors

- energy storage in flywheels

- thermal energy storage in a heater

- compressed air storage

- …

Variable linked to the stored energy Example :

- energy stored in a capacitor (value C) :

variable linked to energy = voltage V

the voltage V of a capacitor cannot vary instantaneously

2.2

1VCE

v

i2 i1

C

11




State variable = Energy linked variable

Variable representing the stored energy Example :

- energy stored in a flywheel (moment of inertia J) :

variable linked to the energy = angular speed Ω

angular speed Ω of a flywheel cannot vary instantaneously

angular speed directly represents the energetic state of the flywheel system

2.2

1 JE

J

C2

C1

12



- Different elements -

An energetic system:

Energy sources

Energy storage elements

Energy conversion elements

Energy distribution elements

Energy storage element versus energy conversion element:

Different in view of control – state variable control

The state of a energy storage element can not change

instantaneously

13



Source oval pictogram

background: light green

contour: dark green

1 output vector (dim n)

1 input vector (dim n)

- Energetic sources -

terminal elements which represent

the environment of the studied system

generator and/or receptor of energy

power system

reaction

action

upstream

source

downstream

source x1

y1

x2

y2

p1= x1. y1 p2= x2. y2

direction of

positive power

(convention)

n

i

ii yx

1

11

14



i1

u13

u23

i2

grid

VDC

i Bat.

VDC

i

- Energetic sources: examples (1) -

structural

description

EMR

(functional

description)

p=VDC i

Battery Electrical grid

p=u i

u

i

23

13

u

uu

2

1

i

ii

2 independent currents

2 independent voltages

15



pload

qwind

wind

qwind [m3/s]

Pload [Pa]

bulb I

u

I

u

Wind

(air flow source)

Energy generator

VDC

i Bat

VDC

i

- Energetic sources: examples (2) -

Battery

(voltage source)

generator and

receptor of energy

Ligthing bulb

Energy receptor

IC engine

(torque source)

Energy generator Tice

ICE

Tice

17



Accumulator rectangle with an oblique bar

background: orange

contour: red

upstream I/O vectors (dim n)

downstream I/O vectors (dim n)

- Accumulation elements -

internal accumulation of

energy (with or without

losses)

reaction

action x1

y

y

x2

p1= x1. y p2= x2. y

causality principle

output(s) = input(s)

dtxxfy ),( 21

y = output, delayed from

input changes

18



i1 L, rL

u’13

u’23

i2 u13

u23

)'(21

12

3

1uuiri

dt

dL L

v1 v2

i

L, rL

2 1 L v v i r i dt

d L

v1

v2

i

i

- Accumulation elements: examples (1) -

inductor 3-phase line

structural

description

EMR (causal

representation)

mathematical

Model

i

i

u

u’

19



inductor

v1

v2

i

i

v1 v2

i

L

v

i2 i1

C

capacitor

i1

i2

v

v

inertia

J

T2 T1

T1

T2

stiffness

k 1 2

T T

1

2

T

T

2 2

1iLE

2 2

1 JE

2 1

2

1T

kE

2 2

1vCE

- Accumulation elements: examples (2) -

20



conversion

element two pictograms

background: orange

contour: red

upstream I/O vectors (dim n)

downstream I/O vectors (dim p)

Possible tuning input vector (dim q)

- Conversion elements -

action /

reaction x1

y1

y2

x2

p1= x1. y1 p2= x2. y2

z

tuning vector

conversion of energy

without energy

accumulation

(with or without

losses)

),(

),(

21

12

zxfy

zxfyno delay!

upstream and downstream

I/O can be permuted

(floating I/O)

21



- Conversion element pictograms -

Circle = electromechanical conversion

Square = electrical conversion

Triangle = mechanical conversion

Circle = multiphysical conversion

Square = monophysical conversion

For multiphysical systems

22



- Conversion element pictograms -

VDC

iconv

uconv

iload

VDC uconv

iload

m

iconv

loadconv

DCconv

imi

Vmu

m: modulation function of the converter

cycleduty Dm

Circle = multiphysical conversion

Square = monophysical conversion

23



- Conversion elements: examples -

dcmdcmdcm euiridt

dL

VDC uconv

iload iconv

VDC

iconv

uconv

s

iload

s

i

u DCM

gear

Tgear T1

2

2

T3

kgear

3gear2 TTdt

dJ

ke

ikT

dcm

dcmdcm

idcm

u idcm

edcm

Tdcm

k

gear

T1

2

Tgear

2

T3

2geargear

1geargear

k

TkT

m

loadconv

DCconv

imi

Vmu

Bat

24



- Coupling elements -

coupling

elements

overlapped pictograms

background: orange

contour: red

electro

mechanical

coupling

electrical

coupling

mechanical

coupling

distribution

of energy

no tuning

vector

coupling

elements


background: orange

contour: red

multiphysical

coupling

Monophysical

coupling

25



Bat

- Coupling elements -

VDC

icoup

i1

i2

vcoup1 = VDC

vcoup2 = VDC VDC

icoup

i1

i2

vcoup1

vcoup2

21coup

DC

iii

commonV

parallel connexion

distribution

of energy

no tuning

vector

coupling

elements


background: orange

contour: red

multiphysical

coupling

Monophysical

coupling

26



- Coupling elements: examples -

2

TTT

gearrdifldif

iarm

uarm DCM

iexc

uexc

excdcm

armexcdcm

ike

iikT iarm

uarm

iexc

uexc

iarm

earm

Tdcm

eexc

iexc

Field winding DC machine

Mechanical differential

diff

Tgear

lwh

rwh

Tldiff

Trdiff

Tldiff

rwh

Trdiff

lwh Tgear

diff 2

ΩΩΩ rwllwh

diff

28



« EMR of a whole system »

EMR’11

Lausanne

July 2011



29



- Example of an electromechanical conversion system -

PE Bat. Fres EM

S1 S2

upstream

source

downtream

source

x1 x2 x3 x4 x5 x6 x7

y1 y2 y3 y4 y5 y6 y7

z23 z45 z67

upstream

source

downtream

source

Convention: direction of positive power flow

(could be negative for bidirectional system)

electromechanical

conversion electrical

conversion mechanical

conversion

energy storage =

power adaptation

31



- Tuning path -

PE Bat. Fres EM

S1 S2

upstream

source

downtream

source

x1 x2 x3 x4 x5 x6 x7

y1 y2 y3 y4 y5 y6 y7

z23 z45 z67

Tuning path:

Technical requirements: action on z23 and x7 to be controlled

x3 x4 x5 x6 x7

z23

The tuning path is independent

of the power flow direction

(e.g. velocity control in acceleration AND regenerative braking)

33



OK y2

x2

- Association rules: direct connection -

x2

y2 y1

x1 x3

y3

direct connection if:

Out(S1) = In (S2)

In(S1) = Out(S2)

S1 and S2 any sub-systems

Bat

VDC

iL

u

VDC VDC

iL iL

iL

u

L iL

VDC

iL

iL

u

Bat

uVidt

dL DCL

i state variable

Example

34



x1

x1 y2

y2

x1

y1 x1

y3

- Association rules: merging rule -

NO

2 accumulation elements

would impose the same

state variable x1

Conflict of association

merging

x1

y3 x1

y1

1 equivalent function for

2 elements / systemic

35



- Merging rule: example -

DC machine and

smoothing inductor

u

i

u2

Lf rf

u i u2

iruudt

diL f2f

Lm rm

u2 i e

ireudt

diL m2m

i

u2

u

i e i

u2 i

i)rr(eudt

di)LL( mfmf

Leq+Lm rf +rm

u i e

i

e

u

i

Assumption: Lf, Lm constant

36



x2

y2 y1

x1 x3

y3

x’2

y’2 y1

x1 x3

y3

- Association rules: permutation rule -

permutation possible if same global behavior:

strictly the same effects (y1 and x3) from the same causes (x1 , y3 and z)

z z x2

y2 y1

x1 x3

y3

z

37



1

1

T2

T1 2

T3

- Permutation rule: example -

Shaft + gearbox

1

T2 T1

1

2

T3

J

211 TTdt

dJ

12

32

k

TkT

1

T’2 T1 2

T3 2

J/k2 3222

' TTdt

d

k

J

21

32

1

1

k

Tk

T

variable

change

no assumption

strict equivalence

(same model)

‘ 1

38



Assumptions:

J1 , J2 constant

no backslash

- Interest of rules -

1 1

T2

T3

2

T1

T4

2 J1

J2

1

1

T2

T1 J1 2

T3 2

2

T4

T3 J2

to solve conflict

of association

k

J1/k2

1

T’2 T1 2

T3 2 2

2

T4

T3 J2

permutation

k

22

1eq J

k

JJ

1

T’2 T1

2

T4 2

Jeq merging

k

40



- Lift example: EMR -

Tm Ls, rs

uch

um

ich

VDC

im

inductor shaft pulley DCM chopper supply

counter

weight

cage

Tpul

vcage

filter

uc

iL Lf, rf

C

VDC iL

iL uC

Bat Env

m

ich

uC

im

uch

em

im

Tm Fpul

vcage

vcage

Fres

filter chopper DC machine pulley cage+CW

merging permutation

and merging

41



up down

- Lift example: tuning path -

Tm Ls, rs

uch

um

ich

VDC

im

inductor shaft pulley DCM chopper supply

counter

weight

cage

Tpul

vcage

filter

uc

iL Lf, rf

C

VDC iL

iL uC

Bat Env

m

ich

uC

im

uch

em

im

Tm Fpul

vcage

vcage

Fres

filter chopper DC machine pulley cage+CW

tuning path



EMR’12

Madrid

June 2012

« Conclusion »



x1

x1 y2

y2

- EMR and systemic -

I/O are independent

of power flows

Tuning paths:

• defined by the technical requirements

• independent of the power flow direction

EMR describes energetic

functions

EMR is adapted for control design

x1

y1 x1

y3

x1

y2 x1

y3

Priority to the function

by keeping the physical causality

(systemic)

EMR respects natural

integral causality



« BIOGRAPHIES AND REFERENCES »

EMR’11

Lausanne

July 2011





- Authors -

Prof. Daniel HISSEL

University of Franche-Comte, FEMTO-ST, FCLAB, MEGEVH,

France

Director, FCLAB CNRS Research Federation

Head, Hybrid & Fuel Cell Systems Research Team, FEMTO-ST

PhD in Electrical Engineering at University of Toulouse (1998)

Research topics: Modeling, control, diagnosis of hybrid and fuel

cell systems

Prof. Alain BOUSCAYROL

University of Lille 1, L2EP, MEGEVH, France

PhD in Electrical Engineering at University of Toulouse (1995)

Research topics: EMR, EVs and HEVs

Dr. Walter LHOMME

L2EP, University Lille1, MEGEVH, France

PhD on Hybrid Electric Vehicles at University Lille1, 2007

Engineer at AVL (UK) (2007-2008) Associate Prof. at Univ. Lille1 (2008)

Research topics: EMR, EVs and HEVs



- References -

A. Bouscayrol, & al. "Multimachine Multiconverter System: application for electromechanical drives", European

Physics Journal - Applied Physics, vol. 10, no. 2, May 2000, pp. 131-147 (common paper GREEN Nancy, L2EP Lille

and LEEI Toulouse, according to the SMM project of the GDR-SDSE).

A. Bouscayrol, "Formalism of modelling and control of multimachine multiconverter electromechanical systems” (Texte

in French), HDR report, University Lille1, Sciences & technologies, December 2003

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, December 2006, vol. 53, no.

6, p. 1799-1806 (common paper of L2EP Lille and LEEI Toulouse).

Boulon, L., Hissel, D., Bouscayrol, A., Pape, O., Péra, M.C., “Simulation model of a military HEV with a highly

redundant architecture”, IEEE Transactions on Vehicular Technology, vol. 59, n°6, pp. 2654-2663, 2010.

P. Delarue, A. Bouscayrol, A. Tounzi, X. Guillaud, G. Lancigu, “Modelling, control and simulation of an overall wind

energy conversion system”, Renewable Energy, July 2003, vol. 28, no. 8, p. 1159-1324 (common paper L2EP Lille and

Jeumont SA).

Boulon, L., Hissel, D., Bouscayrol, A., Péra, M.C., “From Modeling to Control of a PEM Fuel Cell Using Energetic

Macroscopic Representation”, IEEE Transactions on Industrial Electronics, vol. 57, n°6, pp. 1882-1891, 2010.

W. Lhomme, “Energy management of hybrid electric vehicles based on energetic macroscopic representation”, PhD

Dissertation, University of Lille (text in French), November 2007 (common work of L2EP Lille and LTE-INRETS

according to MEGEVH network).

Documents

« Energetic Macroscopic Representation (EMR) · two pictograms background: orange contour: red upstream I/O vectors (dim n) downstream I/O vectors (dim p) Possible tuning input vector