lMBp2`bBiû/2h2+?MQHQ;B2/2*QKTB ;M2 S`û/B+iBQM …
Transcript of lMBp2`bBiû/2h2+?MQHQ;B2/2*QKTB ;M2 S`û/B+iBQM …
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ψ0
ψ1
∆Eb,min
∆Eb,max
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Mvd
dtv(t) = Ft(t)− Fr(t),
Fr
Fr(t) = Fa(t) + Ff (t) + Fg(t) + Fd(t).
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Fd Fa
Ft
Fg
mv .g
v
Ffα
Mv v
Ft
Tt
Ft =Tt
rroue,
rroueFa
Fa =1
2ρSCxv
2rel,
ρ Cx
S vrel
Fg
Fg = mvg (α),
αFf
Ff = Cfmvg (α),
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Cf
Fd
FLDR(t) = a+ bv(t) + cv2(t)
a b c
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µ
Thermiquesconventionnels
(ICEV)
Micro-Hybrides (µHEV)
Hybrides Electrique (HEV)
Plug-In Hybrides Electriques
(PHEV)
100% Electriques (EV)
Quantité d’énergie électrique
Electrique avec Range Extender
(REEV)
Taux
d’hyb
ridation
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Moteur Machine
BatterieRéservoir
Générateur
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Moteur
MachineBatterie
Réservoir
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Moteur
Machine 1
BatterieRéservoir
Machine 2
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0 500 1000 1500 20000
50
100
150
Vite
sse
[s]
Temps [s]
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Modèle longitudinal
Gestion d’énergie
Modèle GMP simplifiéProfil de Vitesse Couple
RégimeCarburantCO2SOC/SOE
Consignes GMP:- répartirions couple électrique/thermique- démarrage/arrêt moteur
État GMP
Gestion d’énergie
Modèle dynamique GMPProfil de Vitesse Demande
de CoupleCarburantCO2SOC/SOE
Consignes GMP:- répartirions couple électrique/thermique- démarrage/arrêt moteur
État GMP+
-Modèle
conducteur
Vitesse véhicule
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0 200 400 600 800 10000
50
100
150
Vite
sse
[km
/h]
0 200 400 600 800 10004550556065
Temps [s]
SOE
[%]
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0 1000 2000 3000 4000 50000
50
100
150
Vite
sse
[km
/h]
0 1000 2000 3000 4000 50000
20406080
100
Temps [s]
SOE
[%]
Pmi
Pmi = ωiTi,
Tmi ωmi
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0 1000 2000 3000 4000 50000
50
100
150
Vite
sse
[km
/h]
0 1000 2000 3000 4000 50000
20406080
100
Temps [s]
SOE
[%]
ηmi
ηmi
ηmi =ωiTi
Pf,
Pf
Pf = mfHPCI ,
HPCI
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242
245245
250
250
250
255
255
255
260
260
26027
0270
270
270270
280
280280
280
300
300
325325
325
350
350
400
400
450
450
500
500
600600
Consommation spécifique [g/kWh]
Régime [tr/min]
Cou
ple
[N.m
]
1000 2000 3000 4000 5000 60000
20
40
60
80
100
120
140
160
mf ≈ a1(ωmi)Tmi + a0(ωmi),
a0 a1
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ηme Pme
Pe
Te ωe
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ηme =ωeTe
Pe, ωeTe > 0 ,
ηme =Pe
ωeTe, ωeTe < 0 .
−6000 −4000 −2000 0 2000 4000 6000−200
−150
−100
−50
0
50
100
150
200
0
0
0
0
5050 50508080
8080
90
90
90
90
92
9292
92
93
9393
93
94
94
94
94
Régime [tr/min]
Cou
ple
[N.m
]
Rendement [%]
Pe ≈ e2(ωme)T2me + e1(ωme)Tme + e0(ωme),
e0 e1 e2
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Energie spécifique Wh/kg
Puis
sanc
e sp
écifi
que
W/k
g
Vocv
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I∗b
SoC(t) = SoC(t0) +1
QnomNcell
∫ t
t0
−I∗b (t)dt,
Qnom Ncell
ηC
I∗b (t) =
{Ib(t) Ib ≥ 0ηCIb(t) Ib < 0.
0 20 40 60 80 1002.6
2.8
3
3.2
3.4
3.6
3.8
4
SOC [%]
V OCV
[V]
LiMn2O4
Vocv
Ri
Ri
Ib Vb
Vb =Vocv(SoC)
2+
√Vocv(SoC)2 − 4Ri(SoC, sign(Ib))Pb
2,
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Ib =Vocv(SoC)
2Rint(SoC, sign(Ib))−
√V 2ocv(SoC)− 4Ri(SoC, sign(Ib))Pb
4R2i (SoC, sign(Ib))
,
Pb
Rint
VbVocv
+
-
Pb = Ib Vb
Ib
SoC = f(VOCV )
Eb Emax
SoE(t) =Eb(t)
Emax
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ωsec =ωprim
rk,
Tsec =
{ηtTprim Tprim ≥ 0rkTprim/ηt Tprim < 0,
ωprim ωsec
Tprim Tsec
rk k
ηt
Tprim = Tmi + Tme.
u = Tmi/Tprim u = 0 uu ≥ 1
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x
u
x(t) = f(x(t), u(t)),
f
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J =
∫ tf
t0
mf (x(t), u(t), t)dt,
mf
uJ = Φ(x(tf ), xf ) +
∫ tf
t0
L(x(t), u(t), t)dt
x(t0) = x0
x(t) = f(x(t), u(t))
x(t) ∈ X (t), ∀t > 0
u(t) ∈ U(t), ∀t > 0
Φ X Ux
x(tf ))xf
Φ
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ux
U
X
X U
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Approches de gestion d’énergie d’un GMP hybride
Approches heuristiques
Instantanées Prédictives
Approches d’optimisation
Temps-réels Globales
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×
K PK × P
xk+1 = F (xk, uk), k = 0, . . . , K − 1,
F
xk ∈ Xk uk ∈ Uk
k
∈ RK×P
Φ
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Jk(xp) ≡
u∈U{lk(xp, u) + Jk+1(x
p + F (xp, u))},
lk(xp, u) uxp Jk(xp)
xp k
Jk
uN u∗
Jk
u∗k(x
p) =un∈U
{l(xp, un) + Jk+1(xp + F (xp, un))}.
uxpk+1 = xp
k + F (xp, uk)
Jk+1(xp+F (xp, uk))
xf = 50
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Temps [s]
SOE
[%]
Coût optimal J* [g]
0 200 400 60030
40
50
60
70
0
500
1000
1500
2000
2500
3000
3500
Temps [s]
SOE
[%]
Commande optimale U* Tmi [N.m]
0 200 400 60030
40
50
60
70
0
50
100
150
k
x
u
U∗k (x
p) = un∈U{l(xp, un) + Jk+1(xp + F (xp, un))}Jk(xp)
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J
O(K.P p.Nn) p N
K
p n
K × P
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f( )
gi( ) ≤ 0, i = 1, . . . ,m
hi( ) = 0, i = 1, . . . , p.
f gi hi
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u∗(t)
H
H(x(t), u(t),λ(t), t) ≥ H(x(t), u∗(t),λ(t), t), ∀u = u∗, t ∈ [t0, tf ],
H
H(x(t), u(t),λ(t), t) = L(x(t), u(t), t) + λT (t)f(x(t), u(t)),
λ(t)
L(x(t), u(t), t)f(x(t), u(t))
λ
λ(t) = − ∂
∂xH(x(t), u(t),λ(t), t).
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t
u∗(t) =u
{H(x(t), u(t),λ(t), t)}.
tfu
λ0x(tf ) = xf λ0
λ0
x(tf )λ0
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Heq
Heq(x, u, s, t) = Pf (u, t) + s(t)Pe(x, u, t),
Pf = HPCImf
mf HPCI
Pe = Voc.Qnom.f(x, u, t)s
sλ
Heq
Heq
u∗
u∗(t) =u
{Heq(x, u, s, t)}.
sxref s
xref
s(x(ti+1)) = s0 +Kp(xref (ti)− x(ti)) +Ki
∫ t
0
(xref (ti)− x(ti))dt,
Kp Ki
s0
s0
xref
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0 20 40 60 800
50
100
150
Vite
sse
[km
/h]
0 20 40 60 80200
300
400
Altit
ude
[m]
Distance [km]
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0 20 40 60 800
20
40
60
80
100
Distance [km]
SoE
[%]
Optimale (DP)D−M (DP)Cible
20
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mf
ηth[ ]
ηme mot[ ]
ηme gen[ ]
0 20 40 60 800
0.5
1
1.5
2
2.5
3
Distance [km]
Cons
omm
atio
n ca
rbur
ant [
l]
Optimale (DP)D−M (DP)
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ηth
ηme mot
ηme gen
0 20 40 60 80 100 1200
5
10
15
20
25
30
|Ibat| [A]
Pour
cent
age
de te
mps
[%]
Optimale (DP)D−M (DP)
I2
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u(t)∗ = uve = 1
0 20 40 60 800
50
100
150
Vite
sse
[km
/h]
0 20 40 60 8010
20
30
40
50
60
70
Distance [km]
SoE
[%]
Libre (DP)VE (DP)Cible
LibreVE
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0 20 40 60 800
20
40
60
80
100
Distance [km]
SoE
[%]
Mixte (ECMS)D−M (ECMS)Cible (DP)
Système d’optimisation énergétique
Gestion des flux de
puissance
Gestion de l’énergie
électrique - SoEref- Mode VE
- Profil de mission- Position
- Puissance à la roue - Consignes GMP
- Limitations GMP
VéhiculeSystème de Navigation
Conducteur
- Consommation énergétique- Style de conduite
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SoEref
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ψ0
ψ1
∆Eb,min
∆Eb,max
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Type
Distance
Vitesse
Distance
Extra Urbain
Urbain
Autoroute
110
70
50
30
Pente
Segments
+10
+5
0
-5
-10
1 2 3 4 5 6 7 8 9
Distance
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u
u
uu = 0 u > 1
Ef
Eb
u = 1
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−400 −300 −200 −100 0 100 200 3000
2
4
6
8
10
12
14
ΔEb [Wh/km]
E f [l/1
00km
]
Approche DPApproche Ucst
Ef = f(∆Eb)
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∗
Temps [s]
SOE
[%]
Coût optimal J* [g]
0 200 400 60030
40
50
60
70
0
500
1000
1500
2000
2500
3000
3500
∗ t = 0
Ef = f(∆Eb)
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RechargeDécharge
Recharge maximale
Maintien de la charge
Mode EV
∆Eb
Ef (∆Eb) = ψ2∆E2b + ψ1∆Eb + ψ0,
∆Eb,min ≤ ∆Eb ≤ ∆Eb,max.
ψ0 ψ1 ψ2
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−300 −200 −100 0 100 200 3000
2
4
6
8
10
12
14
16
ΔEb [Wh/km]
E f [l/1
00km
]
ARTEMIS EmbouteillageARTEMIS Extra−UrbainARTEMIS AutorouteARTEMIS Urbain
ψ0
ψ0
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ψ1
λ∗
(∂H/∂Pb)∗ = 0
λ∗ =
(∂Pf
∂Pb
)∗
ψ1
ψ2
ψ2
∆Eb,min ∆Eb,max
∆Eb,min ∆Eb,max
∆Eb,max
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cce = [ψ0,ψ1,ψ2,∆Eb,min,∆Eb,max]T .
ψ0 ψ1
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ψ0 ψ1 ∆Eb,max
ψ2
∆Eb,min
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ψ0
ψ0
ψ0
ψ0
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0 50 100 1500
2
4
6
8
10
12
DRV_VR_AVG [km/h]
ψ0 [l
/100
km]
ψ0
ψ0
−200 0 200 400 600 8000
5
10
15
20
25
Δ Eb [Wh/km]
E f [l/1
00km
]
δψ0(v) = ψ0(v)− ψ0|v,
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v ψ0
v ψ0
ψ0
δψ0
δψ0
ψ0
ψ1
∆Eb,max
∆Eb,max
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ψ0 δψ0 ψ1 ∆Eb,max
1 2 3 4 5 6 70
20
40
60
80
100
Composantes Principales
Pour
cent
age
de V
aria
nce
Expl
iqué
e [%
]
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−0.5 0 0.5−0.4
−0.2
0
0.2
0.4
0.6
0.8
NAV_ATS
DRV_VR_AVGNAV_GAS
DRV_V_MAX
NAV_SL
DRV_V_AVG
Axe 1
DRV_RPADRV_PKE
Axe
2
ψ2
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ψ0
ψ0
v∗
rpaT
rpa(t) =1
d
∫ t
t−T
a(τ)+v(τ)dτ,
d va+
ψ0
v∗ rpaψ0 = f(v∗, rpa)
ψ0
R2 = 0.82
ψ0(v∗, rpa) =
∑
0<i<N0<j<M
pi,j(v∗)i(rpa)j
pi,j
ψ0
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20 40 60 80 100 1200
0.1
0.2
0.3
0.4
0.5
DRV_VR_AVG [km/h]
DR
V_R
PA [m
s2 ]
20 40 60 80 100 1200
0.50
5
10
15
DRV_VR_AVG [km/h]DRV_RPA [ms2]
ψ0 [l/100km]
−3 −2 −1 0 1 2 30
200
400
600
Résidus [l/100km]
0 2 4 6 8 10 12 14
ψ0
−600 −400 −200 0 200 400 6000
0.05
0.1
0.15
0.2
0.25
0.3
ΔEb [Wh/km]
E f [l/k
m]
ARTEMIS Urbain
Pente: −10%Pente: −7%Pente: −5%Pente: 0%Pente: 5%Pente: 7%Pente: 10%
ψ0
ψ0
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Kg
ψg0
ψg0 = ψ0 +Kg.G
G
-15 -10 -5 0 5 10 15Pente [%]
-0.1
0
0.1
0.2
0g [
l/km
]
Données brutesModèle du premier ordre
ψ0
ψ0
Eaux =Paux
v∗
Paux
ψ0
ψa0 = ψ0 + ψ1Eaux + ψ2E
2aux.
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−200 −100 0 100 200 3000
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16ARTEMIS Urbain
ΔEb [Wh/km]
E f [l/k
m]
Paux: 0WPaux: 500WPaux: 1000WPaux: 1500WPaux: 2000W
ψ1
ψ1
ψ1 = f1(v∗)f1
0 20 40 60 80 100 120 1402.8
2.9
3
3.1
3.2
3.3
3.4
3.5x 10−4
DRV_V_AVG [km/h]
ψ1 [l
/Wh]
ψ1
ψ1
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ψa1 = ψ1 + ψ1Eaux + 2ψ2Eaux.
∆Eb,min
∆Eb,min
∆Eb,min = fmin(ψ0,ψ1,ψ2) =−ψ1 +
2√ψ21 − 4ψ2ψ0
2ψ2.
∆Eb,min
∆Eab,min = ∆Eb,min − Eaux.
∆Eb,max
∆Eb,max
∆Eb,max = fmax(v∗)ψ1 fmax
∆Eb,min ∆Eb,max
∆Eab,max = ∆Eb,max − Eaux.
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0 20 40 60 80 100 120 140 160 1800
100
200
300
400
500
DRV_V_AVG [km/h]
ΔE b,
max
[Wh/
km]
∆Eb,max
Jsim =Nt∑
i=1
liEf (∆Eib)
∆Eib,max ≤ ∆Ei
b ≤ ∆Eib,max
Eb,max ≤ Eib ≤ Eb,max
i = 1, . . . , Nt,
Ef (∆Eib) Nt
i li∆Ei
b
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αi ≥ 1 Ef
Jgen =Nt∑
i=1
αiliEf (∆Eib)
αi i
Ef (∆Eb,min)i = 0
f( ) =1
2TQ + T
A ≤
Q hi,i = 2 ∗ψ2,i
ci = ψ1,i
APb ∆SoE
Eb
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A =
⎡
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
+1 0 · · · 0−1 0 · · · 0
+1 0 · · · 0−1 0 · · · 0l1 0 · · · 0−l1 0 · · · 0
−l1 l2 · · · lN−l1 −l2 · · · −lN
⎤
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦
=
⎡
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
x1,max
−x1,min
xN,max
−xN,min
ymax − y0−ymin + y0
ymax − y0−ymin + y0
⎤
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦
,
li xi,max x1,min
∆Eb,max ∆Eb,min i ymax ymin
y0
N = 100
∆SoE N P
N P ∗ U∗
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∗ ∗
N = 100P = 101
f ∗ νn
f(νn) = g(νn) + h(νn),
g(νn) νn h(νn)
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νn
νpνs h∗
∀νs νp : h∗(νp) ≤ cνp→νn + h∗(νs),
cνp→νn νp → νn
h∗1 h∗
2
∀ νn, h∗1(νn) > h∗
2(νn) h∗1 .
gh
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νi ←νc ←
νi
f
ν∗ ←ν∗
νi νc
νs ν∗
g(νs) ← ν∗ cν∗→νs
νs
νs
νs
νs
hνs) ← hνs→νc
f(νs) ← g(νs) + h(νs)
νs
ν∗
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νi,pνi,f i li
c(νi,p, νi,f ) = li(ψ2,i∆Eb(νi,p, νi,f )2 + ψ1,i∆Eb(νi,p, νi,f ) + ψ0,i)
∆Eb(νi,p, νi,f ) =SoE(νi,f )− SoE(νi,p)
li.
g
g(νn,f ) =i=n∑
i=1
c(νi,p, νi,f ),
νi,p = νi−1,f
h(νn,p) =i=N∑
i=n
liEf (∆SoE(νn,p, νC)).
h Ef
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SoE [%]
Distance [km]
100100
50
10
𝒍𝟏 𝒍𝟐 𝒍𝟑 𝒍𝒊 𝒍𝑵
i
C
1234
65
7𝒈𝑺𝟒
𝒈𝟒𝟔
𝒉𝟔𝑪
X Dans open
X Dans closed
i Initial
C Cible
X Meilleur
1 2 3 …i… N
f
f
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Gestion de l’énergie électrique
Manageur Global
Gestion des segments de route
Estimation des paramètres CCS
Optimisation A*
Données Historique
Calcul du SoE cible
Données Véhicules
𝑺𝒐𝑬𝒄𝒊𝒃𝒍𝒆 (𝐯𝐞𝐫𝐬 𝐒𝐆𝐅𝐏)
Attributs de la route
Position du véhicule
Statu du système de Navigation
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0 500 1000 1500 2000 2500 3000 35000
20
40
60
80
100Trajectoire SoE
Temps [s]
SoE
[%]
0 500 1000 1500 2000 2500 3000 35000
20
40
60
80
100
Temps [s]
SoE
[%]
Régulation SoE
0 500 1000 1500 2000 2500 3000 35000
1
2
3
4
5
6
7
Temps [s]
E f [l]
Consommation
DP: CCSDP: SOESGEE
DP: CCSDP: SOESGEED−M
DP: CCSDP: SOESGEED−M
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0 10 20 30 40 50 60 700
20
40
60
80
100
120
140
v [k
m/h
]
vitesse véhiculeNAV_V_AVGNAV_V_LIM
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0 10 20 30 40 50 60 700
50
100
SoE
[%]
optimisé SGEErégulation SGFPcible minimale
0 10 20 30 40 50 60 70
0
100
200
Distance [km]
T th [%
]
maximalréalisé
0 10 20 30 40 50 60 700
50
100
SoE
[%]
régulation SGFPcible minimale
0 10 20 30 40 50 60 70
0
100
200
Distance [km]
T th [%
]
maximalréalisé
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0 10 20 30 40 50 60 700
0.5
1
1.5
2
2.5
3
Distance [km]
E f [l]
Optimisé SGEED−M SGFP
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0 10 20 30 40 50 60 700
20406080
100So
E [%
]
optimisé SGEErégulation SGFPcible minimale
0 10 20 30 40 50 60 70
0
100
200
Distance [km]
T th [%
]
maximalréalisé
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0 10 20 30 40 50 60 700
20406080
100
SoE
[%]
optimisé SGEErégulation SGFPcible minimale
0 10 20 30 40 50 60 70
0
100
200
Distance [km]
T th [%
]
maximalréalisé
0 10 20 30 40 50 60 70 800
0.5
1
1.5
2
2.5
3
3.5
4
Distance [km]
E f [l]
sans contrainte EVavec contrainte EV
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0 10 20 30 40 50 60 700
50
100
150
v [k
m/h
]
vitesse véhiculeNAV_V_AVGNAV_V_LIM
0 10 20 30 40 50 60 70−5
0
5
10
Distance [km]
pent
e [%
]
pente mesuréeNAV_SLOPE_AVG
0 10 20 30 40 50 60 700
50
100
SoE
[%]
régulation SGFPcible minimale
0 10 20 30 40 50 60 70
0
100
200
Distance [km]
T th [%
]
maximalréalisé
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0 10 20 30 40 50 60 700
50
100
SoE
[%]
optimisé SGEErégulation SGFPcible minimale
0 10 20 30 40 50 60 70
0
100
200
Distance [km]
T th [%
]
maximalréalisé
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0 10 20 30 40 50 60 70 800
1
2
3
4
5
6
7
Distance [km]
E f [l]
OptimiséeD−M
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0 10 20 30 40 50 60 700
50
100
150
v [k
m/h
]
vitesse véhiculeNAV_V_AVGNAV_V_LIM
0 10 20 30 40 50 60 700
500
1000
1500
P aux [%
]
Distance [km]
0 10 20 30 40 50 60 700
50
100
SoE
[%]
optimisé SGEErégulation SGFPcible minimale
0 10 20 30 40 50 60 70
0
100
200
Distance [km]
T th [%
]
maximalréalisé
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0 10 20 30 40 50 60 700
50
100
SoE
[%]
optimisérégulationcible
0 10 20 30 40 50 60 70
0
100
200
Distance [km]
T th [%
]
maximalréalisé
Niter,max
Topt,max
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Niter,max Topt,max
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0 200 400 600 800 1000Temps [s]
0
10
20
30
40
Vite
sse
[km
/h]
0 200 400 600 800 1000Temps [s]
0
20
40
60
Vite
sse
[km
/h]
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0 200 400 600 800 1000Temps [s]
0
20
40
60
80
100
120
Vite
sse
[km
/h]
0 200 400 600 800 1000 1200Temps [s]
0
50
100
150
200
Vite
sse
[km
/h]
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0 500 1000 1500 2000Temps [s]
0
50
100
150
Vite
sse
[km
/h]
0 200 400 600 800 1000 1200Temps [s]
0
20
40
60
80
100
120
Vite
sse
[km
/h]
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1x
∫va+
x
a−
PKE =∑
(v2f−v2i )
xdvdt > 0
dvdt < 0
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