08/07/2016
1
EMR’16
UdeS - Longueuil
June 2016
Summer School EMR’16
“Energetic Macroscopic Representation”
«EMR-based Simulation Tool of a
Multi-train Subway System »
Dr. C. Mayet1, Dr. P. Delarue1, Prof. A. Bouscayrol1
Dr. J.-N. Verhille2, Mr. E. Chattot2
1 L2EP, Université Lille1, France 2 SIEMENS, France
EMR’16, UdeS Longueuil, June 20162
« EMR-based simulation tool of a multi-train subway systems »
- Context and Objective -
Objective: Develop and energetic and flexible simulation tool
SOUS-STATION
Rail positif
Rail de retour
SOUS-STATION
- + - +
Accurate estimation of energy consumptions
Evaluate new solutions to save energy (i.e. ESS), size the system, etc.
- Non-linearities (Non-reversiblity of TPS)
- Structural Variability (trains displacements)
- Coupling of several subsystems (trains, TPS, etc.)
Accuracy of the results
&
Simulation flexibility ?
Main difficulties
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EMR’16, UdeS Longueuil, June 20163
« EMR-based simulation tool of a multi-train subway systems »
- Outline -
1. EMR of Subsystems
• EMR of the supply subsystem
• EMR of the subway subsystem
2. EMR of Mono-train Subway Systems
• EMR of mono-train subway systems
• Experimental validation
3. EMR of Multi-train Subway Systems
• EMR of multi-train subway systems
• Simulation results
4. Conclusion & Perspectives
EMR’16
UdeS - Longueuil
June 2016
Summer School EMR’16
“Energetic Macroscopic Representation”
« EMR of Subsystems »
08/07/2016
3
EMR’16, UdeS Longueuil, June 20165
« EMR-based simulation tool of a multi-train subway systems »
- EMR of the Supply Subsystem -
ON
OF
ON
OF
Petri Net
Models activation
tuteteA railssss 02 :
0:1 tiA ss
A2
Mode bloqué
A1
Mode passant
Off-state
On-state
Non-linear system
iss(t)
ess(t)
i2(t)i1(t)ig(t) L2 R2
Lμ, Rir
mt
Dup1,2,3
Ddo1,2,3
Traction Power Substation
Lr-pos Rr-pos
DC rails LoadGrid
Cbus-eq
ibus-eq(t)
Lr-neg Rr-neg
Modeling of each states
urail(t)
ug(t)
ug(t)
ig(t)
i1(t)
Grid
u20(t)
i2(t)
Load
Rectifier
ess0(t)
iss(t)
ug(t) iss(t)
urail(t)
Transformer
i10(t)
u20(t)
i2(t)
iss(t)
urail(t)
i2(t)
iss(t)
u20(t)
Global non-linear behavior = 2 linear behaviors
iss(t)
ess(t)
L2 R2 Lr-eq Rr-eq
i22(t) L2 R2
i23(t) L2 R2
v201(t)
v202(t)
v203(t)
iss(t)
ess(t)
i21(t) L2 R2 Lr-eq Rr-eq Dup1
i22(t) L2 R2
i23(t) L2 R2 Ddo3
v201(t)
v202(t)
v203(t)
ess0(t)
i21(t)
Mode bloqué (aucune diode ne
conduit)
Mode passant (ex : Dup1 et Ddo3
conduisent)
1
1
1
1
2
2
2
2
3
3
3
3
Dup
Dup
Ddo
Ddo
urail(t)
urail(t) Off-state
On-state
EMR’16, UdeS Longueuil, June 20166
« EMR-based simulation tool of a multi-train subway systems »
- EMR of the Supply Subsystem -
Energy consumption
Average error
Experiment 1.25 Wh 0 %
Simulation 1.12 Wh 1.4 %
Bus DC
Current
source
DC Rails
Rectifier
Transformer
Experimental validation
Tension des rails urail(t) (V)
Temps (s)
Mesure Simulation 0 1 2 3 4 5 6 7 8 9
82
78
74
70
66
Courant AC ig1(t) (A)
Temps (s)
3
2
1
0
-1
-2
-3
Mesure Simulation 0 1 2 3 4 5 6 7 8 9
Courant ibus-eq(t) (A)
Temps (s)
10
8
6
4
2
0
0 1 2 3 4 5 6 7 8 9
Traction Power Substation DC rails LoadGrid
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EMR’16, UdeS Longueuil, June 20167
« EMR-based simulation tool of a multi-train subway systems »
- EMR of the Supply Subsystem -
Models Time step Comp. time Average error
Dynamical 0.05ms 348.3s 0 % (référence)
Averaged static non-linear 1ms 5.2s 0.36 %
Averaged static linear 1ms 5.1s 13.36 %
Courant ig(t) (A) 30
20
10
0
-10
-20
-30
0 5 10 15 20 25 30 35 40 45 50 55
Temps (s) Dynamique instantané non-linéaire Statique moyen non-linéaire Statique moyen linéaire
Courant iss(t) (A) 1200
800
400
0
-400
0 5 10 15 20 25 30 35 40 45 50 55
Temps (s) Dynamique instantané non-linéaire Statique moyen non-linéaire Statique moyen linéaire
Linear : non-reversibility is neglected
Static: transient states are neglected
Averaged: averaged value on 50 Hz
Averaged static non-linear model
3Vg(t)
IPFg(t)
IPF1(t)
IPF10(t)
Grid
3V20(t)
IPF2(t) ess0(t)
iss(t)
iss(t)
3Vg(t)
3Vg(t) 3V20(t)
IPF2(t)
3V20(t)
IPF2(t)
iss(t)
urail(t)
urail(t)
Rectifier Transformer
O F O N
Load
iss(t)
urail(t)
O F O N
EMR’16, UdeS Longueuil, June 20168
« EMR-based simulation tool of a multi-train subway systems »
- EMR of the Subway Subsystem -
Model
urail(t)
isub(t)
Rail Env.
vsub(t) Fwh(t)
vsub(t)
ubus(t)
ivsi(t)
ubus(t)
ibus(t) itrac(t)
ubus(t)
Aux. ubus(t)
iaux(t)
Tsm(t)
Ωsm(t)
uvsi(t)
ism(t)
mvsi(t)
vdq(t)
idq(t) Θ(t)
idq(t)
edq(t)
Brake
Tbk(t) Ωsm(t)
Tbk-ref
Ttrans(t)
Ωsm(t) vsub(t) Fres(t)
Fsub(t)
8 2
Aux. VSI PMSM Brake Trans. Chassis
4
Filter
ibo(t)
ubus(t)
urail(t)
ibo(t)
Ttrans-ref(t) Tsm-ref(t) idq-ref(t) vdq-ref(t) uvsi-ref(t) Fwh-ref(t) KDbk(t)
Fsub-ref(t) vsub-ref(t)
8
Inversion-based control
isub(t)
icar1(t)
ibo2(t)
-
urail(t) Bogie 1
ibo1(t)
Bogie 2
Car 1 icar2(t)
ibo4(t)
Bogie 3
ibo3(t)
Bogie 4
Car 2
+
Subway
iaux(t)
ivsi(t)
ism1(t) ubus(t)
uvsi13(t) Ωsm(t)
Tsm(t)
Ωsm(t) Ttrans(t)
Ωwh(t)
Twh(t)
Aux. VSI Traction system
Cbus
Lf itrac(t) ibo(t)
PMSM
PMSM uvsi23(t)
ism2(t)
Aux.
ibus(t)
Filter
rf
rbus
Energy management strategy
strategy
Voltage-dependent electrodynamic
braking characteristic
ubus (t)
Regenerative braking
Ubus_brk Ubus_MAX
Dissipative braking
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EMR’16, UdeS Longueuil, June 20169
« EMR-based simulation tool of a multi-train subway systems »
- EMR of the Subway Subsystem -
Energy consumption
Average error
Experiment 33.80 kWh 0 %
Simulation 34.15 kWh 3.48 %
Experimental validation
Temps (s)
70
60
50
40
30
20
10
0
Vitesse vsub(t) (km/h) 70
60
50
40
30
20
10
0
Altitude (m)
840 850 860 870 880 890 900 910 920 930
Vitesse mesurée (km/h) Vitesse simulée (km/h) Altitude (m)
Courant isub(t) (A) 1200
900
600
300
0
-300
-600
Temps (s) Mesure Simulation 840 850 860 870 880 890 900 910 920 930
EMR’16, UdeS Longueuil, June 201610
« EMR-based simulation tool of a multi-train subway systems »
- EMR of the Subway Subsystem -
Cte. velocity: accelerations & decelerations
are neglected
Models Step time Comp. time Average error
Dynamic 1ms 185s 0 %
Quasi-static 50ms 1.92s 0.77 %
Static 100ms 0.25s 14.16 %
Cte. velocity 100ms 0.23s 20.54 %
Quasi-static: fast dynamics are neglected
Static: low dynamics are neglected
Dynamique Quasi-statique Static Vitesse moyenne
Energie (kWh)
Temps (s)
40
30
20
10
0 0 500 1000 1500
Courant (A)
Temps (s)
900
600
300
0
-300
-600 0 20 30 40 50 60
Dynamique Quasi-statique Static Vitesse moyenne
urail(t)
isub(t)
Rail Env.
vsub(t) Fwh(t)
vsub(t)
ubus(t)
ivsi(t)
ubus(t)
ibus(t) itrac(t)
ubus(t)
Aux. ubus(t)
iaux(t)
Tsm(t)
Ωsm(t)
Frein Tbk(t)
Ωsm(t)
Tbk-ref(t)
Ttrans(t)
Ωsm(t) vsub(t) Fres(t)
Fsub(t) urail(t)
ibo(t)
8
Ttrans-ref(t)
Tsm-ref(t)
Fwh-ref(t) KDbk(t) Fsub-ref(t) vsub-ref(t)
strategie
4 2
8
Auxiliaire Filtre MSAP Frein méca. Tans. Masse Filter Aux PMSM Brake Trans. Chassis
Quasi-static model
08/07/2016
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EMR’16
UdeS - Longueuil
June 2016
Summer School EMR’16
“Energetic Macroscopic Representation”
« EMR of Mono-train Subway
Systems »
EMR’16, UdeS Longueuil, June 201612
« EMR-based simulation tool of a multi-train subway systems »
urail(t)
isub(t)
Env.
vsub(t) Fwh(t)
vsub(t)
ubus(t)
ivsi(t)
ubus(t)
ibus(t) itrac(t)
ubus(t) Tsm(t)
Ωsm(t)
Brake Tbk(t)
Ωsm(t)
Tbk-ref(t)
Ttrans(t)
Ωsm(t) vsub(t) Fres(t)
Fsub(t) urail(t)
ibo(t)
8
Ttrans-ref(t)
Tsm-ref(t)
Fwh-ref(t) KDbk(t) Fsub-ref(t) vsub-ref(t)
Strategy
4 2
8
Aux. Filter PMSM Brake Trans. Chassis Rectifier Transformater
ubus(t) IPF2(t) 3Vg(t)
IPFg(t)
IPF1(t)
IPF10(t)
Grid
3V20(t)
IPF2(t) ess0(t)
iss(t)
iss(t)
3Vg(t)
3Vg(t)
3V20(t)
IPF2(t)
3V20(t)
iss(t)
ubus(t)
iss(t) O F O N
O F O N
urail(t)
iaux(t)
Aux.
ubus(t)
- EMR of Mono-train Subway Systems -
Grid
uvsi23(t)
uvsi13(t)
ug(t)
iss(t)
ess(t)
i2(t) i1(t) ig(t) L2 R2
Lμ, Rir
u20(t)
mt
Dup1,2,3
Ddo1,2,3
Traction Power Substation
i10(t)
Lr-pos(x) Rr-pos(x)
u2(t)
DC rails
iaux(t)
ivsi(t)
ism1(t) ubus(t)
Ωsm(t)
Tsm(t)
Ωsm(t) Ttrans(t)
Ωwh(t)
Twh(t)
Cbus
itrac(t)
PMSM
PMSM
ism2(t)
Aux.
ibus(t)
rbus
isub(t) ibo(t) Lf rf
urail(t)
Filter Aux. VSI Traction System
Lr-neg(x) Rr-neg(x)
Other bogies
Other bogies
Subsystems connexion
Systemic approach DC bus has to be taken into account
Cartesian approach
Rail voltage
?
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EMR’16, UdeS Longueuil, June 201613
« EMR-based simulation tool of a multi-train subway systems »
Grid
uvsi23(t)
uvsi13(t)
ug(t)
iss(t)
ess(t)
i2(t) i1(t) ig(t) L2 R2
Lμ, Rir
u20(t)
mt
Dup1,2,3
Ddo1,2,3
Traction Power Substation
i10(t)
Lr-pos(x) Rr-pos(x)
u2(t)
DC rails
iaux(t)
ivsi(t)
ism1(t) ubus(t)
Ωsm(t)
Tsm(t)
Ωsm(t) Ttrans(t)
Ωwh(t)
Twh(t)
Cbus
itrac(t)
PMSM
PMSM
ism2(t)
Aux.
ibus(t)
rbus
isub(t) ibo(t) Lf rf
urail(t)
Filter Aux. VSI Traction System
Lr-neg(x) Rr-neg(x)
Other bogies
Other bogies
- EMR of Mono-train Subway Systems -
Env.
vsub(t) Fwh(t)
vsub(t)
ubus(t)
ivsi(t)
ubus(t)
ibus(t) itrac(t)
ubus(t) Tsm(t)
Ωsm(t)
Brake Tbk(t)
Ωsm(t)
Tbk-ref(t)
Ttrans(t)
Ωsm(t) vsub(t) Fres(t)
Fsub(t) isub(t)
ubus(t)
8
Ttrans-ref(t)
Tsm-ref(t)
Fwh-ref(t) KDbk(t) Fsub-ref(t) vsub-ref(t)
Strategy
4 2
8
Aux. DC bus PMSM Brake Trans. Chassis Rectifier Transformer
ubus(t) IPF2(t) 3Vg(t)
IPFg(t)
IPF1(t)
IPF10(t)
Grid
3V20(t)
IPF2(t) ess0(t)
iss(t)
iss(t)
3Vg(t)
3Vg(t)
3V20(t)
IPF2(t)
3V20(t)
iss(t)
ubus(t)
iss(t)= isub(t)
O F O N
O F O N
ubus(t)
xsub(t)
iaux(t)
Aux.
ubus(t)
Impact on strategy
Impact on
switching (on/off)
Strong impact on energy
EMR’16, UdeS Longueuil, June 201614
« EMR-based simulation tool of a multi-train subway systems »
- EMR of Mono-train Subway Systems -
Energy consumption
Average error
Experiment 3.1 kWh0 %
(référence)
Simulation 3.0 kWh 1.9 % Experimental validation
Energie totale de traction (kWh) 3,5
3
2,5
2
1,5
1
0,5
0
Temps (s)
0 20 40 60 80 100 120
Mesure Simulation
Courant total de traction Nbcar/rameNbbo/car itrac(t) (A) 1200
800
400
0
-400
Temps (s)
0 20 40 60 80 100 120
Mesure Simulation
Tension de bus ubus(t) (V) 1000
950
900
850
800
750
700
Mesure Simulation
Temps (s)
0 20 40 60 80 100 120
Vitesse vsub(t) (km/h)
Temps (s)
60
50
40
30
20
10
0
-10
0 20 40 60 80 100 120
Mesure Simulation Altitude (m)
60
50
40
30
20
10
0
-10
Altitude (m)
08/07/2016
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EMR’16
UdeS - Longueuil
June 2016
Summer School EMR’16
“Energetic Macroscopic Representation”
« EMR of Multi-train Subway
Systems »
EMR’16, UdeS Longueuil, June 201616
« EMR-based simulation tool of a multi-train subway systems »
Grid
ug(t)
iss(t)
ess(t)
i2(t) ig(t) L2 R2
Lμ, Rir
u20(t)
mt
Dup1,2,3
Ddo1,2,3
Traction Power Substation
u2(t)
Rail section 1
iaux2(t)
ivsi2(t)
ubus2(t) Cbus
itrac2(t)
PMSM
PMSM
Aux.
ibus2(t)
rbus
isub2(t) Lf rf
Other bogies
Other bogies
iaux1(t)
ivsi1(t)
ubus1(t) Cbus
itrac1(t)
PMSM
PMSM
Aux.
ibus1(t)
rbus
isub1(t) Lf rf
Subway 1
Other bogies
Other bogies
Subway 2
Lrp(x2) Rrp(x2)
Lrn(x2) Rrn(x2)
Rrp(x1) Lrp(x1)
Rrn(x1) Lrn(x1)
urail2(t) urail1(t)
Rail section 2
Grid
ug(t)
iss(t)
ess0(t)
i2(t) ig(t)
Rtps-eq
Rir
mt
Dup1,2,3
Ddo1,2,3
Traction Power Substation
Rail section 1
iaux2(t)
ivsi2(t)
ubus2(t) Cbus
itrac2(t)
PMSM
PMSM
Aux.
ibus2(t)
rbus
isub2(t) rf-eq
Other bogies
Other bogies
iaux1(t)
ivsi1(t)
ubus1(t) Cbus
itrac1(t)
PMSM
PMSM
Aux.
ibus1(t)
rbus
isub1(t)
Subway 1
Other bogies
Other bogies
Subway 2
Rr2-eq(x2) Rr1-eq(x1)
urail2(t) urail1(t)
Rail section 2
ess(t)
rf-eq
- EMR of Multi-train Subway Systems -
08/07/2016
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EMR’16, UdeS Longueuil, June 201617
« EMR-based simulation tool of a multi-train subway systems »
Env. 8
Brake
2 4
Aux.
ibo1(t)
ubus1(t)
ubus1(t)
ibus1(t)
ubus1(t) ubus1(t)
itrac1(t)
ubus1(t)
iaux1(t)
ivsi1(t)
Tsm1(t)
Ωsm1(t)
Ttr1(t)
Ωsm1(t)
Ωsm1(t) Tbk1(t)
Fwh1(t)
vsub1(t) vsub1(t)
vsub1(t) Fsub1(t)
Fres1(t)
Tbk1-ref(t)
Tsm1-ref(t)
8
vsub1-ref(t) Fsub1-ref(t) Fwh1-ref(t) Ttr1-ref(t) KDbk1(t)
Strategy
Subway 1
Traction Power Substation
IPF2(t) 3Vg(t)
IPFg(t)
IPF1(t)
IPF10(t)
Grid
3V20(t)
IPF2(t) ess0(t)
iss(t)
3Vg(t)
3Vg(t)
3V20(t)
IPF2(t)
3V20(t)
O F O N
iss(t)
ess0(t)
Grid
ug(t)
iss(t)
ess0(t)
i2(t) ig(t)
Rtps-eq
Rir
mt
Dup1,2,3
Ddo1,2,3
Traction Power Substation
Rail section 1
iaux2(t)
ivsi2(t)
ubus2(t) Cbus
itrac2(t)
PMSM
PMSM
Aux.
ibus2(t)
rbus
isub2(t) rf-eq
Other bogies
Other bogies
iaux1(t)
ivsi1(t)
ubus1(t) Cbus
itrac1(t)
PMSM
PMSM
Aux.
ibus1(t)
rbus
isub1(t)
Subway 1
Other bogies
Other bogies
Subway 2
Rr2-eq(x2) Rr1-eq(x1)
urail2(t) urail1(t)
Rail section 2
ess(t)
rf-eq
iss(t)
ess0(t)
Rtps-eq
Rail section 1
iaux2(t)
ivsi2(t)
ubus2(t) Cbus
itrac2(t)
PMSM
PMSM
Aux.
ibus2(t)
rbus
isub2(t) rf-eq
Other bogies
Other bogies
iaux1(t)
ivsi1(t)
ubus1(t) Cbus
itrac1(t)
PMSM
PMSM
Aux.
ibus1(t)
rbus
isub1(t)
Subway 1
Other bogies
Other bogies
Subway 2
Rr2-eq(x2) Rr1-eq(x1)
urail2(t) urail1(t)
Rail section 2
ess(t)
rf-eq
- EMR of Multi-train Subway Systems -
.
and and
with
1
222111
22112211
11
22
011
22
xRrxRxRrxR
xRxRxRRxRRxR
tuxRRR
RxRRte
xR
xR
xRti
eqreqfeqeqreqfeq
eqeqeqeqtpseqeqtpseqon
buseqeqtpseqtps
eqtpseqeqtps
sseq
eq
eqonsub
.11 titi subss
TPS is on-state
.11
111
11
22
2211
tutixR
xR
xRxRti busss
eq
eq
eqeqsub
TPS is off-state
.222
1
2
1 2211
0 tixR
RxR
Rtute sub
eq
eqss
eq
eqssbusss
ubus(t)
isub(t)
isub(t)
ubus(t)
isub(t)
O F O N
ubus(t)
ubus1(t)
isub1(t) ubus2(t)
isub2(t)
xsub1(t) xsub2(t)
iaux2(t)
ivsi2(t)
ubus2(t) Cbus
itrac2(t)
PMSM
PMSM
Aux.
ibus2(t)
rbus
Other bogies
Other bogies
iaux1(t)
ivsi1(t)
ubus1(t) Cbus
itrac1(t)
PMSM
PMSM
Aux.
ibus1(t)
rbus
Subway 1
Other bogies
Other bogies
Subway 2
Subway 2
iaux2(t)
ivsi2(t)
ubus2(t) Cbus
itrac2(t)
PMSM
PMSM
Aux.
ibus2(t)
rbus
Other bogies
Other bogies
Env.
vsub2(t) Fwh2(t)
vsub2(t)
ubus2(t)
ivsi2(t)
ubus2(t)
ibus2(t) itrac2(t)
ubus2(t) Tsm2(t)
Ωsm2(t)
Brake Tbk2(t)
Ωsm2(t)
Tbk2-ref(t)
Ttr2(t)
Ωsm2(t) vsub2(t) Fres2(t)
Fsub2(t) ibo2(t)
ubus2(t)
8
Ttr2-ref(t)
Tsm2-ref(t)
Fwh2-ref(t) KDbk2(t) Fsub2-ref(t) vsub2-ref(t)
4 2
8
iaux2(t)
Aux.
ubus2(t)
Strategy
Subway 2
EMR’16, UdeS Longueuil, June 201618
« EMR-based simulation tool of a multi-train subway systems »
- EMR of Multi-train Subway Systems -
Positions (km) 6
4
2
0 0 100 200 300 400 500 600 700 800 900
Subway 1 x1(t)
Subway 2 x2(t)
TPS xss
Velocities (km/h) Time (s) 80
60
40
20
0
0 100 200 300 400 500 600 700 800 900
Subway 1 vsub1(t)
Subway 2 vsub2(t)
Time (s)
Currents (A) 2000
1500
1000
500
0
-500
340 360 380 400 420 440 460 480 500
Subway 1 isub1(t)
Subway 2 isub2(t)
TPS iss(t)
DC voltages (V) Time (s) 1000
900
800
700
600
500 340 360 380 400 420 440 460 480 500
Subway 1 ubus1(t)
Subway 2 ubus2(t)
TPS ess(t)
Time (s)
08/07/2016
10
EMR’16
UdeS - Longueuil
June 2016
Summer School EMR’16
“Energetic Macroscopic Representation”
« Conclusion & Perspectives »
EMR’16, UdeS Longueuil, June 201620
« EMR-based simulation tool of a multi-train subway systems »
- Conclusion & Perspectives -
• EMR of each subsystems (dynamical model, experimental validation, model reduction)
• EMR and experimental validation of mono-train subway systems
- DC bus modelling, real braking strategy
• EMR and simulation of multi-train subway systems
- Switching of models
Conclusion
• Extension for real subway systems (several subways and TPSs)
• Experimental validation of the final simulation tool
- HIL simulation ?
• Study of innovative solutions
- ESS, reversible TPS ?
Perspectives
08/07/2016
11
EMR’16
UdeS - Longueuil
June 2016
Summer School EMR’16
“Energetic Macroscopic Representation”
« REFERENCES »
EMR’16, UdeS Longueuil, June 201623
« EMR-based simulation tool of a multi-train subway systems »
- References -
[Allègre 10] A.-L. Allègre, A. Bouscayrol, P. Delarue, P. Barrade, E. Chattot and S. El-Fassi, “Energy StorageSystem With Supercapacitor for an Innovative Subway”, IEEE Transactions on Industrial Electronics,vol. 57, no. 12, pp. 4001-4012, December 2010 (common paper of L2EP, LEI and Siemens).
[Bouscayrol 12] A. Bouscayrol, J.-P. Hautier, and B. Lemaire-Semail, “Systemic Design Methodologies forElectrical Energy Systems – Chapter 3: Graphic Formalisms for the Control of Multi-physical EnergeticSystems: COG and EMR”, ISTE Ltd and John Wiley & Sons, Inc., 2012.
[Mayet 14] C. Mayet, L. Horrein, A. Bouscayrol, P. Delarue, J.-N. Verhille, E. Chattot and B. Lemaire-Semail, “Comparison of Different Models and Simulation Approaches for the Energetic Study of aSubway”, IEEE Transactions on Vehicular Technology, vol. 63, no. 2, pp. 556-565, February 2014(common paper of L2EP and Siemens).
[Mayet 16a] C. Mayet, P. Delarue, A. Bouscayrol, E. Chattot, and J.-N. Verhille, “Comparison of DifferentEMR-based Models of Traction Power Substations for Energetic Studies of Subway Lines”, IEEETransactions on Vehicular Technology, vol. 65, no. 3, pp. 1021-1029, March 2016 (common paper ofL2EP and Siemens).
[Mayet 16b] C. Mayet, P. Delarue, A. Bouscayrol, E. Chattot, and J. Sanchez, “EMR-based Simulation Toolof a Multi-train Subway System”, IEEE VPPC’16, Hangzhou, China, October 17-20 (common paper ofL2EP and Siemens) (accepted).