«energetic macroscopic - emrwebsite · – interaction principle: each action induces a reaction...

Seminar On EMR Sept. 2014

Seminar Sept. 2014 “Energetic Macroscopic Representation”

«Energetic Macroscopic Representation »

Dr. Philippe Barrade LEI, EPFL, Switzerland

Prof. B. Lemaire-Semail, Dr. W. Lhomme, Prof. A. Bouscayrol University Lille1, L2EP, MEGEVH, France

Seminar on EMR, Sept. 2014 2

« Energetic Macroscopic Representation »

- Outline -

•  Introduction •  Representation: EMR basic elements

–  Sources –  Accumulation –  Conversion –  Coupling

•  Organization: fundamental rules –  Direct connections –  Merging rules –  Permutation rules

•  Analysis for the simulation and the control –  Action and reaction paths –  Tuning path

•  Example: Wind Energy Conversion System •  Conclusion



« Introduction»



- System analysis -

•  Needs in graphical descriptions as valuable intermediary step

real system

system model

system representation

system simulation

model objective

limited validity range

valuable properties

behavior study

organization

prediction



- System analysis -

•  The graphical description is chosen depending on objectives –  real-time control and energy management of energetic systems

systemic (cognitive)

causal models

functional description static or

quasi-static models

causal dynamical models & forward approach



- System analysis -

•  Real-time control and energy management of energetic systems

real system

representation

Model objective: “control”

causal & systemic

organization

Highlight energetic and systems properties

prediction

dynamical models

Real-time control & Energy

management

forward approach



- Objectives of the presentation -

•  Define the key elements of EMR

•  Define the fudamental rules –  For connecting elements –  For solving conflicts of associations

•  Define the notions of –  Action, reaction and tuning paths

•  Assumption –  As EMR is an intermediary step, coming after a modeling activity, one will

consider that models are already defined…



«Representation: EMR basic elements »



- Different elements -

•  Energetic Macroscopic Representation –  Any energetic system –  Energy sources –  Energy storage elements –  Energy conversion elements –  Energy distribution elements

•  Key elements –  energy storage element

•  delay, state variable, closed-loop control –  energy distribution element

•  power flow coupling, control with criteria



- Energy sources -

•  Back to definitions –  System: interconnected subsystems organized for a common objective, in

interaction with its environment. –  Input: produced by environment, imposed to the system –  Output: consequence of the system evolution, imposed to its environment –  Interaction principle: each action induces a reaction

–  Needs in defining an element representing the environment of a system, and its links to the studied system

•  According to the interaction principle

action

reaction

S2 S1

power



- Energy sources -

•  Definition of the environment –  Environment & System must be defined first

system 3

Environment 3 unidirectional

system 1 Environment 1 bidirectional

system 2

Environment 2 bidirectional

i1

u13

u23

i2 v13

v23 vdc

iload

grid line diode rectifier

Border of the system?



- Energy sources -

•  Representation –  Terminal element which represents the environment of the studied system

•  Generator or receptor Source oval pictogram

background: light green contour: dark green 1 input vector (dim n) 1 output vector (dim n)

power system

reaction

upstream source

downstream source x1

y1

x2

y2

p1= x1. y1 p2= x2. y2

direction of positive power (convention)

∑=

=n

iii yx

111

action



- Energy sources - Examples -

pload

qwind

wind

qwind [m3/s]

Pload [Pa]

bulb I

u

I

u Wind

(air flow source) generator energy

VDC

i Bat

VDC

i Battery

(voltage source) generator and

receptor of energy

Ligthing bulb receptor of energy

IC engine (torque source)

generator of energy

Tice

Ω ICE

Tice

Ω

Tice-ref



- Accumulation elements -


interaction with its environment. –  Input: produced by a subsystem, imposed to its close subsystem –  Output: consequence of the subsystem evolution, imposed to its close

subsystems –  Interaction principle: each action induces a reaction –  Internal accumulation of energy (with or without losses)

•  Key transformation for safety and efficiency •  Output(s) is an integral function of input(s), delayer fron input(s) changes •  Causal description: fixes input(s) and output(s)

–  Needs in defining an element representing the accumulation of energy, and the links with its close subsystems

•  According to a causal description, and to the interaction principle



- Accumulation elements -

•  Representation –  internal accumulation of energy (with or without losses)

•  Causality principle

Accumulator rectangle with an oblique bar background: orange contour: red upstream I/O vectors (dim n) downstream I/O vectors (dim n)

∫∝ dtxxfy ),( 21

y = output, delayed from input changes

fixed I/O (causal description)

reaction

action x1

y

y

x2

p1= x1. y p2= x2. y



- Accumulation elements - Examples -

inductor v1

v2

i

i

v1 v2

i

L

v

i2 i1

C capacitor

i1

i2

v

v

inertia

Ω J

T2 T1

Ω

T1

T2

Ω

Ω

stiffness

k Ω1 Ω2

T T

Ω1

Ω2

T

T

2 21 iLE = 2

21

Ω= JE

2 121 Tk

E =2

21 vCE =



- Conversion elements -



subsystems –  Interaction principle: each action induces a reaction –  Conversion of energy without energy accumulation (with or without losses)

•  No delay from input(s) changes •  Non causal description: input(s) and output(s) can be permuted

•  Needs in defining an element representing the conversion of energy, and the links with its close subsystems –  According to a non causal description, and to the interaction principle



- Conversion elements -

•  Representation –  Conversion of energy without energy accumulation (with or without losses)

•  Two possibilities conversion

element Square for monophysical conversion Circle for multiphysical conversion background: orange contour: red upstream I/O vectors (dim n) downstream I/O vectors (dim p) Possible tuning input vector (dim q)

OR

Action/reaction x1

y1

y2

x2

p1= x1. y1 p2= x2. y2 €

y2 = f (x1, z)y1 = f (x2 , z)" # $ %

z

no delay!

upstream and downstream I/O can be permuted

(floating I/O) tuning vector



- Conversion elements - Examples -

kΦ

dcmdcmdcm euiridtdL −=+

VDC uconv

iload iconv

VDC

iconv uconv

s

iload

s

i

u DCM

Ωgear

Tgear T1

Ω2

Ω2

T3

kgear

3gear2 TTdtdJ −=Ω⎩

⎨⎧

=

=

ΩΦ

Φ

keikT

dcm

dcmdcm

idcm

u idcm

edcm

Tdcm

Ω

Ωgear

T1 Ω2

Tgear

Ω2

T3

⎩⎨⎧

=

=

2geargear

1geargear

kTkTΩΩ

m

⎪⎩

⎪⎨⎧

=

=

loadconv

DCconvimiVmu

Bat



- Coupling elements -



subsystems –  Interaction principle: each action induces a reaction –  Distribution of energy without energy accumulation (with or without losses)

•  No delay from input(s) changes •  Non causal description: input(s) and output(s) can be permuted

–  Needs in defining an element representing the distribution of energy in parallel branches, and the links with its close subsystems

•  According to a non causal description, and to the interaction principle



- Coupling elements -

•  Representation –  Distribution of energy without energy accumulation (with or without losses)

•  Two possibilities

Coupling element Overlapped squares for monophysical conversion Overlapped circles for multiphysical conversion background: orange contour: red no tuning input vector

OR

VDC

icoup

i1

i2

vcoup2

VDC

icoup

i1

i2 vcoup1

vcoup2

€

Vcoup1 =Vcoup2 =VDCicoup = i1 + i2

" # $

parallel connexion

vcoup1



- Coupling elements – Examples -

2T

TT gearrdifldif ==

iarm

uarm DCM

iexc

uexc ⎩⎨⎧

=

=

Ωexcdcm

armexcdcm

ikeiikT iarm

uarm

iexc

uexc

iarm

earm

Tdcm

Ω

eexc

iexc

Field winding DC machine

Mechanical differential

Ωdiff

Tgear

Ωlwh

Ωrwh

Tldiff

Trdiff

Tldiff

Ωrwh

Trdiff

Ωlwh Tgear

Ωdiff 2ΩΩΩ rwhlwh

diff+

=



«Organization: fundamental rules»



- Warning -

•  Elements defined and to be used

Coupling element

OR

Monophysical Multiphysical

Conversion element

OR

Monophysical Multiphysical

electro-mechanical conversion

electrical conversion

mechanical conversion

electro-mechanical coupling

electrical coupling

mechanical-coupling

electro-mechanical conversion



- Association rules: direct connection -

•  Systemic: Science for the study of systems, and their interaction –  Considering S1 and S2 any kind of sub-systems

•  The direct connection of S1 and S2 is only possible if

–  out(S1) = in(s2) –  in(S1) = out(S2)

OK y2

x2 x2

y2 y1

x1 x3

y3

Bat

VDC

iL

u

VDC VDC

iL iL

iL

u

L iL

VDC

iL

iL

u

uVidtdL DCL −=

i state variable

Example

Bat



- Association rules: conflicts of association -

•  Example: two inertia linked by a fix ratio gearbox

•  Models

•  Representation

Ω1 Ω1

T2 T3

Ω2

T1 T4

Ω2 J1

J2

€

J1dΩ1dt

= T1 −T2

€

J2dΩ2dt

= T3 −T4

€

Ω2 = K.Ω1T2 = K.T3

# $ %

Ω1

Ω1

T2

T1 J1 Ω2

T3 Ω2

Ω2

T4

T3 J2

k Ω1

T2 causal causal non causal




•  Example: two inertia linked by a fix ratio gearbox –  Direct connection 1:

–  Direct connection 2: •  Use the property of a non causal element to permute inputs and outputs

•  Still conflict of association

Conflict of association

Ω1

Ω1

T2

T1 Ω2

T3 Ω2

Ω2

T4

T3 J2

k

Ω1

Ω1

T2

T1 J1

Ω2

T3

Ω2

Ω2

T4

T3 J2

k Ω1

T2

Ω2

T3 k

Ω1

T2 Ω2

T4

J2

Ω1

Ω1

T2

T1 J1




•  Remain –  The property of a non causal element to permute inputs and outputs can be

efficiently used •  I/Os of a non causal element are fixed by state variables (accumulation

element), does not necessarily solve conflicts of associations •  In case conflicts of association subsist

–  Back to the model

€

J1dΩ1dt

= T1 −T2

€

J1KdΩ2dt

= T1 −K.T3 ⇒J1K 2

dΩ2dt

= T '2 −T3

€

Ω2 = K.Ω1T2 = K.T3

# $ %

€

T '2 =T1K

with

Conflict of association

2 accumulation elements would impose the same

state variable x1

J1/k2

Ω1

T’2 T1 Ω2

T3 Ω2 Ω2

Ω2

T4

T3 J2

k




•  Remain –  Permutation of elements is possible if one obtain the same global behavior:

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

x2

y2 y1

x1 x3

y3

x’2

y’2 y1

x1 x3

y3

z z x2

y2 y1

x1 x3

y3

z

Permutation Rule




•  Remain –  The property of a non causal element to permute inputs and outputs can be

efficiently used –  Permutation rule

•  In case conflicts of association subsist –  Back to the model

€

T '2 =T1K

with

€

J1K 2

dΩ2dt

= T '2 −T3

J2dΩ2dt

= T3 −T4

$

% &

' &

⇒J1K 2

dΩ2dt

= T '2 −J2dΩ2dt

−T4

€

J1K 2

+ J2"

# $

%

& ' dΩ2dt

= T '2 −T4Ω2

T’2 Ω2

T3

J1/K2+J1

1/k Ω1

T1

One has finally merged 2 accumulation elements series connected (same state variable)




•  Remain –  When 2 accumulation elements impose the same state variable

•  Conflict association •  Solution: Merging rule

Merging Rule

x1

x1 y2

y2

x1

y1 x1

y3 NO

merging x1

y3 x1

y1

1 equivalent function for 2 elements / systemic



«Analysis for the simulation and control»



- System analysis

•  Objective: real-time control and energy management of energetic systems

real system

representation

Model objective: “control”

causal & systemic

organization

Highlight energetic and systems properties

prediction

dynamical models

Real-time control & Energy

management

forward approach



- Power flow -

•  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

downstream source

Convention: direction of positive power flow (could be negative for bidirectional system)

electromechanical conversion electrical

conversion mechanical conversion

energy storage = power adaptation



- Action and Reaction paths -


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

P > 0 action path: (e.g. acceleration) reaction path:

x1 x2 x3 x4 x5 x6 x7

y1 y2 … y7

P < 0 action path: (e.g. braking) reaction path: x1 x2 x7

y1 y2 … y7 …

Bidirectional system if: •  bidirectional sources •  bidirectional conversion elements

I/O independent of power flow direction action/reaction dependent of power flow direction



- Tuning paths -


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)



- Tuning paths -


z45

y5

x7

PE Bat. Fres EM

S1 S2

upstream source

downtream source

x1 x2 x3 x4 x5 x6

y1 y2 y3 y4 y6 y7

z23 z67

Tuning path:

Technical requirements: action on z45 and y1 to be controlled

z45

The tuning path depends on the technical requirements

y1 y2 y4 y3



« Example: WIND ENERGY CONVERSION

SYSTEM (WECS)»



- Studied WECS -

•  Chosen WECS for variable speed and variable frequency: –  a squirrel cage IM and two VSI

Voltage Source Inverter

iinv

uinv13

uinv23

Technical requirements: provide the maximum active power P and control the reactive power Q

vwind

wind

utrans13

trans-former

itrans1

itrans2 iline2

line & filter

utrans23

iline1

C

capacitor

ucap

irect


urect13

urect23

induction machine

iim1

iim2

Ωshaft

Cim

shaft & gearbox

blades

Ωgear

Cblade

Ωshaft

Cgear ugrid13

electric grid

ugrid23

WECS control



- EMR of the blades -

2windblade VS

21F ρ=

Ftang

CT

( ) bladeTgtan FCF λ=

wind

shaftblade

windblade

vR

vv

Ωλ ==

vblade

Tblade

Ωshaft

Rblade

⎩⎨⎧

=

=

shaftbladeblade

gtanbladebladeRv

FRTΩ

Fblade

vwind Fblade

vwind

Fblade

Tblade

Ωshaft CT = f(λ)

0

0,02

0,04

0,06

0,08

0 5 10 15



- EMR of the mechanical powertrain -

Ωhs

T2 Ωhs

Tim T1 T2 Ωls T1

Ωls

Tblade T1

Ωls

Ωhs

T2 Tim

Ωhs

1bladelsls1 TTfdtdJ −=+ ΩΩ

Tblade Ωls

slow speed shaft

im2hs2hs2 TTfdtdJ −=+ ΩΩ

high speed shaft

⎩⎨⎧

=

=

lsgearhs

2gear1k

TkTΩΩ

Ωls Ωhs

gearbox



- EMR of the mechanical powertrain -

OK

Element association?

T1

k

Ωhs

T2 Ωhs

Tim T1 T2 Ωls T1

Tblade Ωls Ωls Ωhs

Tim Ωls T1

Ωls

T2

Ωhs

Ωls

T1 1. permutation

Tblade Ωls

2. merging 2 2 1

J J J eq + =

Ωshaft

Tgear

Ωgear

Ωshaft

Tblade

Tim

Equivalent power train



- EMR of the squirrel cage IM -

Φrotor

is1 vs1

stator

1s

2s

3s

is3

vs3

is2 vs2 rotor 1r

2r

3r

pΩ

θr/s

isd

θd/s

isq

vsd

vrd ird

vsq

vrq irq

d

q

1s

rotor

stator

1r

θr/s

Park’s transformation

[ ][ ] 123,rr/ddq,r

123,ss/ddq,sx)(Px

x)(Px

θ

θ

=

=

⎩⎨⎧ ≈

≈ sdiim

sdrT

iφ

Modelling simplifications: ⎩⎨⎧

≈

≈

sqr2im

sd1rikTikφ

φ



- EMR of the squirrel cage IM -

Ωgear

Tim

is-dq

es-dq is-dq

vs-dq

istator

ustator

φr ir-dq

er-dq ir-dq

vr-dq

irotor

urotor=0

θd/r

θd/s

Park’s transformations

Rotor windings in (d,q)

Stator windings in (d,q)

Simplified EMR

Ωgear istator

Tim istator

estator

Squirrel cage permutation of windings and transformation concatenation of EM conversion and transformation

ustator

⎩⎨⎧

≈

≈

sqr2im

sd1rikTikφ

φ

Coupling device



- EMR of the back-to-back VSI -

urect ucap

srect

iinv iline

uinv13

uinv23

⎩⎨⎧

=

=

imtrectrect

caprectrectimi

umu

⎥⎦

⎤⎢⎣

⎡−

−=

1312

1311rect ss

ssm

C ucap

iond

irect iim1

iim2 urect13

urect23

⎩⎨⎧

=(open) 0

(closed) 1s11

iim irect uinv ucap

sinv

Rect Inv

ifilt1

ifilt2

invrectcap iiudtdC −=



- EMR of the grid connection -

ugrid

i3

i3

u3

u2 u3

i2 i3

u1

i1

i1

uinv

u2

i2

i2

u1

grid33333 uuiRidtdL −=+

⎩⎨⎧

=

=

2trans3

3trans2imiumu

1inv1311 uuiRidtdL −=+

212322 uuiRidtdL −=+

uinv13 u13-1 u13-2 u13-3 ugrid-13

i1 i2 i3

filter line 1 Ideal

transformer line 2



- EMR of the grid connection -

OK

iline ugrid utransf

uinv itransf iline i1 u2 i2 ugrid u’3

2. permutation u2 i3 i2

1. merging uinv i1

3. merging 2m3L

2L1LeqLtrans

++=

ugrid

i3

i3

u3

u2 u3

i2 i3

u1

i1

i1

uinv

u2

i2

i2

u1

Element association?



- EMR of the WECS -

vwind

ugrid minv mrect

Fblade

Tblade

Ωshaft Tgear

Ωshaft

Tim

Ωgear

eim

iim

iim

urect

irect

ucap

ucap

iinv

uinv

iline

iline

utransf

itransf


iinv

uinv13

uinv23

vwind

wind

utrans13

trans-former

itrans1

itrans2 iline2

line & filter

utrans23

iline1

C

capacitor

ucap

irect


urect13

urect23

induction machine

iim1

iim2

Ωshaft

Cim

shaft & gearbox

blades

Ωgear

Cblade

Ωshaft

Cgear ugrid13

electric grid

ugrid23

equivalent line & transformer

inverter capacitor induction machine

rectifier equivalent power train

blade

T’ Wind grid



- Tuning paths of the WECS -

minv mrect

⎥⎦

⎤⎢⎣

⎡=

23

13rect m

mm ⎥

⎦

⎤⎢⎣

⎡=

23

13inv 'm

'mm2 freedom degrees 2 freedom degrees

objectives: active power P reactive power Q

constraints: capacitor voltage machine flux

vwind

ugrid Fblade

Tblade

Ωshaft Tgear

Ωshaft

Tim

Ωgear

eim

iim

iim

urect

irect

ucap

ucap

iinv

uinv

iline

iline

utransf

itransf

T’ Wind grid

equivalent line & transformer inverter capacitor

induction machine rectifier

equivalent power train blade



« Conclusion » EMR = multi-physical graphical description based on the interaction principle (systemic)

and the causality principle (energy)

Basic elements = energetic function sources, accumulation, conversion and distribution of energy

Association rules = holistic property of systemic enable keeping physical causality in association conflict

Applications analysis, design, simulation, control structure…



- 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, J. P. Hautier, B. Lemaire-Semail, "Graphic Formalisms for the Control of Multi-Physical Energetic Systems", Systemic Design Methodologies for Electrical Energy, tome 1, Analysis, Synthesis and Management, Chapter 3, ISTE Willey editions, October 2012, ISBN: 9781848213883 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, June issue, 2008, pp. 1097-1102. 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). J. P. Hautier, P. J. Barre, "The causal ordering graph - A tool for modelling and control law synthesis", Studies in Informatics and Control Journal, vol. 13, no. 4, December 2004, pp. 265-283. 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).



« Appendix: normalization of EMR pictograms»



- Colors -

pale green

gold

Power system

Power source

Web X11 colour, standard colours on web pages http://en.wikipedia.org/wiki/Web_colors

•  light green background RGB = (152,251,152) « pale green » •  dark green border RGB = (0,128,0) « greeen »

•  orange background RGB = (255,215,0) « gold » •  red border RGB = (255,0,0) « red »



- EMR pictograms -

element name

Name

No equation number in slides

x1

y1

element name element name

element name element name

power vectors (size b, full arrows)

signal vectors (size b/2, empty arrows)

(radius= a)

borders of power elements = b pt

(a/2 x a) (a x a) (2a x a)

a

2a



- Example -

ich1

ubat

ifield

efield

battery choppers

DC machine

ubat Bat.

itot Env.

uch1

iarm

iarm

earm Tem

Ω gear

Tgear

Ωwh

Fwh

Fres

vev

vev

gearbox

mch1

ifield

uch2

ich2

ubat

parallel connexion wheel

chassis

environment

mch2

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