Bài giảng Green Energy Course Syllabus - Chapter 6: Energy storage + Electric vehicles - Nguyễn Hữu Phúc

erential state Equations ;
– existence of derivative causality: Algebro Differential state Equation ;
– systematic equation derivation (state equations, transfer function/ 
matrix) 
3.c) Causality in Bond-Graphs : a prime importance for energetics 
3.d) BG model of a wind turbine driving a equivalent DC generator
MSe:Twt()
I:JTot
1

Wind turbine
Vv 1
I:Lm
R:Rm
f
GY1
R:F
m
I:J
m
GCC
Turbine/Generator Speed
wt
Twt
 the 2 I elements have been gathered : no more causality conflict
 Considering a “direct driven” generator (without multiplier) : OK for low powers
0
C:Cbus
)(....
2
1)( 2  




= CVRSVT vVw
Buck
DC-DC converter
MTF
a,CH VoutVbus
ILIbus
I:L
1
Current control
load
storage
batt
0
 Towards MPPT for better efficiency !!!
3.d) MPPT from power control
Method based on the Cp(λ) 
characterisitc knowledge: power 
control
 power reference:
CP()=CPopt(opt) => Popt = Kopt.opt3
Power – rotation speed characteristic
with
Maximal power obtained if:
 kPref kW



W
s
rad
 WP
 optopt fP W=
1W
1P
2W
2P
3W
3P
opt4 W=W
opt4 PP =
 1
 2
 3  4
λ(opt)
Cp(opt
)
3
3RSoptPC
2
1
optK


=Pref = Kopt.3
Kopt.3
 rot speed reference:
CP()=CPopt(opt) => Popt = Kopt.opt3
3
optK
Pref éol=W
with
Maximal power obtained if:
 kP  3
optK
kP  krefW



W
s
rad
 WP
 optopt fP W=
1W
1P
2W
2P
3W
3P
opt4 W=W
opt4 PP =
 1
 2
 3  4
λ(opt)
Cp(opt
)
3
3RSoptPC
2
1
optK


=
3.d) MPPT from speed control
Method based on the Cp(λ) 
characterisitc knowledge: speed 
c ntrol
Power – rotation speed characteristic
 Torque (current) reference:
CP()=CPopt(opt) => Popt = Kopt.opt3
2.ΩoptKΩ
optPref
emT
==
2W= optK
ref
emT
opt
wtwt
3ref
em TTT ==
opt3 =
( )3
Convergence of algorithm
 2
2W
2wtT
2ref
emT
1wtT
1W
 1
1ref
emT



W
s
rad
 mNT   optopt fT W=
λ(opt)
Cp(opt)
with
3.d) MPPT from torque (current) control
Maximal power obtained if:
Method based on the Cp(λ) 
characteristic knowledge: torque 
c ntrol
3
3
2
1
opt
RSoptPC
optK 
 
=
Torque – rotation speed characteristic
3.d) BG model of a wind turbine driving a equivalent DC generator
MSe:Twt()
I:JWT
1

Wind turbine
Vv 1
I:Lm
R:Rm
f
GY1
R:F
m
I:J
m DCG
wt
Twt
(a) BuckDC-DC converter
MTF
a,CH
0
C:Cbus
VoutVbus
ILIbus
I:L
1
)(....
2
1)( 2  




= CVRSVT vVw
Current control
& MPPT
3
3
2
1
opt
RSoptPC
optK 
 
=
batV
optPref
LI =
= 3.ΩoptKoptP Do it yourself 
& good luck on 20Sim!!!
load
storage
batt
0
Xavier ROBOAM, Guillaume FONTES 
1) Some reminders about Bond-Graphs Basics (X. Roboam)
2) Some examples on Bond graph modeling and 20 Sim simulations (X. Roboam & G. Fontes)
a. Simulation of a current controlled DC DC buck chopper;
b. Simulation of a DC machine : motor generator mode
3) Some reminders about Wind Turbine systems connected to a DC electrical machine;
a. About aerodynamics and energy efficiency of wind turbines
b. Simulating wind turbine torque/speed curves with inertia and defining a load torque
characteristic: to analyze generator / load compatibility;
c. Short reminders about “causality” issues
d. MPPT control of a wind turbine system connected to a current controlled DC generator
4) System study of a wind turbine system connected to a low voltage 48V DC bus (X. Roboam)
a. System description and analysis
b. “DC equivalent modeling” of a PM synchronous generator – diode rectifier device
coupled on low voltage (48V) DC bus
1st Week: Bond Graphs based wind turbine energy system design
4.a) Medium voltage (600V) DC bus coupling of wind & PV hybrid systems
NB: this application is studied by LSE Tunis (Tunisia) in Cooperation with LAPLACE Toulouse (France)
Two structures are convenient
vV
MS
V600
busE
batI
PWM rectifier
MS
dcI
dcU
Diode rectifier
C
E (t)
T (t)
batI
E (t)
T (t)
Boost
chopper
Hacheur 
survolteurBoost
chopper
vV
1 st structure 2 nd structure)
• Very efficient but not cheap!
PV-Gen
PV-Gen
• efficient, reliable and cheap
• considered as better for low power WT (Mirecki
PHD)
Wind Turbine Savonius
V600
busE
4.a) Low voltage (48V) DC bus coupling of wind & PV hybrid systems
NB: this application is studied by LSE Tunis (Tunisia) in Cooperation with LAPLACE Toulouse (France)
Two structures are convenient: 48V is the stadard for stand alone systems
V48
busE
1 st structure
• Very efficient but not cheap!
• efficient, reliable and cheap
• considered as better for low power WT (Mirecki
PHD)
vV
MS
batI
PWM rectifier
E (t)
T (t)
Buck
chopperPV-Gen
2 nd structure)
MS
dcI
dcU
Diode rectifier
C
batI
E (t)
T (t)
Buck
chopper
Buck
chopper
vV
PV-Gen
Wind Turbine
V48
busE
Wind Turbine
First week
4.a) “DC equivalent modeling” of a PM synchronous generator –
diode rectifier device coupled on low voltage (48V) DC bus
NB: this application is studied by LSE Tunis (Tunisia) in Cooperation with LAPLACE Toulouse (France)
Iéol
PM
SM buck
48 V
Battery
diode 
rectifier
DC loads
Iond
IBat
Wind turbine
αw
DC Bus 48V
0 5 10 15 20
temps {s}
Pé
ol
_m
ax
 {W
}
Pé
ol
_M
PP
T 
{W
}
0
200
400
600
800
1000
PWTopt
 JbatmpptE,wtoptE
%4,11%E =
Current control
& MPPT
EWT-opt
Pbatmppt
4.b) DC equivalent model of PM synch generator connected to a 
diode rectifier
Iéol
PM
SM buck
Batterie
s
48 V
diode 
rectifier
DC loads
Iond
DC equivalent
modelling
IBat
Wind turbine
αw
DC Bus 48V
Tem M, ΩM
PMSG (Generator)
Es Rs Ls Is
Vs
Diode 
Rectifier IDC
UDC
Tem M, ΩM
DCG (Generator)
EDC
RDC
LDC
IDC
UDC
4.b) DC equivalent model of PM synch generator connected to a 
diode rectifier
Tem M, ΩM
PMSG (Generator)
Es Rs Ls Is
Vs
Diode 
Rectifier IDC
UDC
Tem M, ΩM
DCG (Generator)
EDC
RDC
LDC
IDC
UDC
Rs Is
Ls cycl
j  Ls cycl    Is
Es Vs 
Rs  Is
Is Vs
Es
Rs Is
j Ls cycl  Is
Es’
Es’
Vector diagram of synchronous generator
With diode rectifier : cos j = 1
4.b) DC equivalent model of PM synch generator connected to a 
diode rectifier
s s ss scycl sV E j.L . .I R .I=    2 2
s s scycl s s sV E (L . .I ) R .I=   
' 2 2
s s scycl sE E (L . .I )=  
DC sf
3 6U V= 

DC sfI I6

= 
2
2
DC s scycl DC s DC
6 6U E L I R I
3 6
 
=        
sDC s
2
DC scycl
2
DC s
3 6E E
6L 3 L
6R 3 R

 = 
 

 
=     

  =     
em M p ex s
s p ex M
C 3 n I cos
E n
=     

=  W
em em M M s sP C 3 E I cos= W =     sDC s p ex M p DC M
emM emM
s DC s
p ex p DC
3 6 3 6E E n n
C C
I I
3 n cos n cos6 6

=  =   W =  W
 

  =  =  =
       
DC ex
3 6
 = 

cos j = 1 
4.b) DC equivalent model of PM synch generator connected to a 
diode rectifier
Electromechanical conversion
 
 
emM p DC sDC
sDC p DC M
C n I cos
E n
 =   

=  WGY
EsDC
I’sDC
CemM
WM
sDC sDCI ' I cos= 
Magnetic reaction
 22sDC sDC DC DCE ' E L I=   sDC sDCE ' E cos=  or
sDC
sDC
I '
I
cos
=

TF
E’sDC
I’sDC
EsDC
IsDC
cos 
4.b) DC equivalent model of PM synch generator connected to a 
diode rectifier
Diode overlapping effect
Equivalent scheme during switchingm: Overlapping time
s DC
3 L I=  
DC
UDµ=ArcCos(1-
max
sDC
E3
LωI2

 ) 'DC sDC s DC
3E E L I=    

emp s
3R L=  

4.b) DC equivalent model of PM synch generator connected to a 
diode rectifier
1 1GYSe : Céol
Céol
ΩM
Cem
ΩM
np.ΦDC
EsDC EsDC’ EDC UDC
IsDC’ IsDC IDC IDC
I : Jtot
R: ftot R: RDC
I : LDC subt
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P.M.S..G
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insert it again.overlapping
Diode rectifier
v(i) v(i)
Mechanical mode
Direct current generator 
(equivalent to SM+Diode Rectifier)
Some REFERENCES
• X. Roboam, S. Astier, ‘’Graphes de liens Causaux pour systèmes à énergie renouvelable’’, Techniques de 
l’Ingénieur, traité Génie Electrique, rubrique « systèmes pour les énergies renouvelables », D3970 (PARTIE 1) & 
D3971 (PARTIE 2), Aout 2006. 
• D. Karnopp, D. Margolis, R. Rosenberg, System Dynamics : Modeling and Simulation of Mechatronic Systems, 
John Wiley & sons, 2000 (3rd edition). 
• S. Astier , R. Saïsset , X. Roboam, Modelling and study of a solar car with embedded photovoltaic array and Li-
ion storage, IMAACA'04, part of SCS I3M conference, Genoa, Italy, October 28-30, 2004.
• M. Dali, J. Belhadj, X. Roboam, ”hybrid wind-photovoltaic power systems: Structure Complexity and Energy 
Efficiency, Control and Energy management”, numéro spécial, ”réseaux isolés” EJEE_RIGE, Volume 12, N°5-6, 
2009, pp 669-700.
• M. Dali, J. Belhadj, X. Roboam, “Hybrid Solar-Wind System with Battery Storage Operating in Grid-Connected and 
Standalone Mode: control and energy management, experimental investigation”, EGY-D-09-00098R1, Elsevier, 
journal of energy conversion and management 
• M. Dali, commande et gestion énergétique des systèmes hybrides pv – éolien, thèse de l’ENIT Tunis, Tunisie, 
soutenue le 24/01/2009
• A. Mirecki, X. Roboam, F. Richardeau, ‘Architecture cost and energy efficiency of small Wind Turbines : which 
system tradeoff?’, IEEE Transactions on Industrial Electronics, Vol 54, N°1, pp 660 – 670, February 2007.