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12008 ACC HEV workshop-
Configuration, Sizing and Control of Power-Split
Hybrid Vehicles
Huei PENGProfessor, Department of Mechanical Engineering
Executive Director, Interdisciplinary and Professional Engineering Programs
University of Michigan
Most of the work is based on the research of several Ph.D. students who worked with the author at the University of Michigan: C. Lin, D. Kim, and J. Liu.
22008 ACC HEV workshop-
Power-Split Hybrid Powertrain System
“Transmission” Vehicle
Engine
Motor
Generator
Battery
Power-Split HEV
Series HEV
Parallel HEV
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HEV is ~3% of US Vehicle Sales and Growing
In April 2008, hybrids sale up 46% in the US while overall car market down by 14%
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Split Hybrids Dominate Current Market
http://bioage.typepad.com/./photos/uncategorized/2008/01/09/milsales2_2.png
split
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More Split Hybrids Are Coming• Many GM-BMW-Daimler-Chrysler dual-mode models are or
will be coming to the market.
• Chevrolet Tahoe, GMC Yukon, Chevy Silverado, Saturn Vue, BMW X3 and X6, Dodge Durango(?)
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Popular Split Hybrid Vehicle Configurations
Allison Hybrid SystemClutch 1
EngineM/G 1M/G 2
BatteryPower Bus
Planetary Gear 2Vehicle Mechanical LinkageElectrical Linkage
Planetary Gear 1
Clutch 2
Engine M/G 1 M/G 2
Battery
Power BusPlanetary Gear Set
VehicleMechanical Linkage
Electrical Linkage
Toyota Hybrid System
Holmes, A. G., Klemen, D., Schmidt, M. R., “Electrically Variable Transmission with Selective Input Split, Compound Split, Neutral and Reverse Modes”, U.S. Patent Number 6,527,658 B2, issued Mar. 4, 2003.
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Power-Split Hybrid Powertrain System
Power SplitCVT
Vehicle
Engine
M/G2
M/G1
Battery
Hermance,D. and Abe, S., “Hybrid Vehicles Lesson Learned and Future Prospects”, SAE #2006-21-0027
US Patent 5,931,757US Patent 6,527,658 B2 US Patent 6,478,705
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Major Decisions for Split Hybrid Vehicle Design
• Configurations– Scattered in patents/few papers– A systematic method to search through all possible
configurations (and derive models quickly) has both academic and practical value
• Component sizing– Given performance spec, find proper component sizes
• Control– Dynamic Programming or implemented versions (sub-
optimal)
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Outline
• Introduction
• Dynamic Modeling of Power-Split Hybrid Vehicles
• Automated Modeling of Power-Split Hybrid Vehicles
• Configuration Screening of Power-Split Hybrid Vehicles
• Combined Configuration Design, Component Sizing, and Control optimization of Power-Split Hybrid Vehicles
• Conclusion
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Modeling of a Power-Split Hybrid Vehicle
Power SplitCVT
Vehicle
Engine
M/G2
M/G1
Battery
Driver SupervisoryController
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11111)( SFRFTII ecee ⋅−⋅−=+ω
22 3
2 2 2 2 2( ) ( ) 0.5 ( )tire outout c fb r tire d tire
R m I K F R F S K T mgf R AC RK K
ωω ρ+ = − + − − −
1 1 1 1 1 1( )MG MG s MGI I T F Sω + = + ⋅
1 1 2 1 1 1( )MG MG eS R R Sω ω ω+ = +
2 2 2 2( )MG outS R Sω ω= +
2 2 2 1 2 1 1 2 2( )MG MG s r MGI I I T F R F Sω + + = + ⋅ + ⋅
Ie
Te
Im/g1
Tm/g1
Im/g2
Tf
MM KK
Tm/g2
T, ω +T, ω +
Ground Clutch2Clutch1
F2S2 F1R1
F2R2+F2S2 F1R1+F1S1
F1S1F2R2
Model Derivation of a Dual-Mode Power-Split Powertrain Mechanical Path
Holmes, A. G., Klemen, D., Schmidt, M. R., “Electrically Variable Transmission with Selective Input Split, Compound Split, Neutral and Reverse Modes”, U.S. Patent Number 6,527,658 B2, issued Mar. 4, 2003.Gino
122008 ACC HEV workshop-
Ie
Te
Im/g1
Tm/g1
Im/g2
Tf
MM KK
Tm/g2
T, ω +T, ω +
Ground Clutch2Clutch1
F2S2 F1R1
F2R2+F2S2 F1R1+F1S1
F1S1F2R2
Model Derivation of a Dual-Mode Power-Split Powertrain Mechanical Path
1 1 12
22 2 22
11 1 1
22 1 2 1 2
11 1 1 1
22 2 2
0 0 0 01 0.5 ( )0 0 0 0
0 0 0 00 0 0
0 0 00 0 0 0
ee ce
outtireout fb r tire d tc
MGMG s
MGMG r s
TI I R SR T mgf R AC Rm I R S
K KKI I S
I I I R SFR S S RFR S S
ωωω ρ
ωω
+ +⎡ ⎤⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥ − + ++ + ⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥+ − =⎢ ⎥⎢ ⎥⎢ ⎥+ + − −⎢ ⎥⎢ ⎥⎢ ⎥+ − − ⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦⎢ ⎥+ −⎣ ⎦
3
1
2
00
ire
MG
MG
TT
⎡ ⎤⎢ ⎥
⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦
⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦
Holmes, A. G., Klemen, D., Schmidt, M. R., “Electrically Variable Transmission with Selective Input Split, Compound Split, Neutral and Reverse Modes”, U.S. Patent Number 6,527,658 B2, issued Mar. 4, 2003.Gino
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Ie
Te
Im/g1
Tm/g1
Im/g2
Tf
MM KK
Tm/g2
T, ω +T, ω +
Ground Clutch2Clutch1
F2S2 F1R1
F2R2+F2S2 F1R1+F1S1
F1S1F2R2
Model Derivation of a Dual-Mode Power-Split Powertrain Mechanical Path
1 1 12
2 2 22
11 1 2 1 2
22 1 2 1 2
11 1 1 1
22 2 2 2
0 0 0 01 0.5 (0 0 0 0
0 0 00 0 0
0 0 00 0 0
ee ce
tireout fb r tire dc
MGMG s r
MGMG r s
TI I R SR T mgf R ACm I R S
KKI I I S R
I I I R SFR S S RFR S R S
ωωω ρ
ωω
+ +⎡ ⎤⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥ − + ++ + ⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥+ + − − =⎢ ⎥⎢ ⎥⎢ ⎥+ + − −⎢ ⎥⎢ ⎥⎢ ⎥+ − − ⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦⎢ ⎥+ − −⎣ ⎦
2 3
1
2
)
00
outtire
MG
MG
RK
TT
⎡ ⎤⎢ ⎥
⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦
⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦
Holmes, A. G., Klemen, D., Schmidt, M. R., “Electrically Variable Transmission with Selective Input Split, Compound Split, Neutral and Reverse Modes”, U.S. Patent Number 6,527,658 B2, issued Mar. 4, 2003.Gino
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Outline
• Introduction
• Dynamic Modeling of Power-Split Hybrid Vehicles
• Automated Modeling of Power-Split Hybrid Vehicles
• Configuration Screening of Power-Split Hybrid Vehicles
• Combined Configuration Design, Component Sizing, and Control optimization of Power-Split Hybrid Vehicles
• Conclusion
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Configuration Search
• Let’s limit the scope to a split hybrid with 2 planetary gears.
• Is there a universal model format which enables automatic modeling?
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Universal Format of the Power-Split Powertrain Mode
1 1 12
22 2 22
11 1 1
22 1 2 1 2
11 1 1 1
22 2 2
0 0 0 01 0.5 ( )0 0 0 0
0 0 0 00 0 0
0 0 00 0 0 0
ee ce
outtireout fb r tire d tc
MGMG s
MGMG r s
TI I R SR T mgf R AC Rm I R S
K KKI I S
I I I R SFR S S RFR S S
ωωω ρ
ωω
+ +⎡ ⎤⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥ − + ++ + ⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥+ − =⎢ ⎥⎢ ⎥⎢ ⎥+ + − −⎢ ⎥⎢ ⎥⎢ ⎥+ − − ⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦⎢ ⎥+ −⎣ ⎦
3
/ 1
/ 2
00
ire
m g
m g
TT
⎡ ⎤⎢ ⎥
⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦
⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦
(4 4) (4 2)
(2 4) (2 2)0 0T
J D TD F
× ×
× ×
⎡ ⎤ ⎡ ⎤Ω ⎡ ⎤=⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦⎣ ⎦⎣ ⎦
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Automated Generation of the Input Matrix
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
−−+
1
1
11
RSSR
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
+−−
−+
22
21
1
11
0
00
SRSR
SSR
⇔D
TT EEEEIA 1)( −−=1 1
2 2J AJ T− −Ω =
DJE 21−=
1
3 3
1 2
2 3
1 1 2 2
0 00 0
00
0
RR S
S RS S
R S R S
−⎡ ⎤⎢ ⎥+⎢ ⎥⎢ ⎥− −⎢ ⎥− −⎢ ⎥⎢ ⎥+ +⎣ ⎦
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Rules to Generate the D and J matrix with a Power-Split Powertrain Design
. Generate Kinematical Constraint Matrix D– Rule 1: The number of columns of D is equals to the number of
planetary gears.– Rule 2: The number of rows of D is equals to the number of columns of
D plus two, each representing a node on the lever diagram. – Rule 3: For the power source component(s) at each row, the “node
coefficient” should be entered. The “node coefficient” is equals to: -Si if connected to the sun gear; -Ri if connected to the ring gear; or Ri+Si if connected to the carrier gear. Here the subscript i presents the corresponding planetary gear set.
– Rule 4: Fill all other entries in matrix D with zeros.– Rule 5: Matrix D can be further simplified to 4x2 using the information
on the free-rolling node(s)
. Generate Inertia Matrix J– Diagonal matrix with inertia of power source components.
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Example of Generating Powertrain Model (2PG)
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
−−
++−
2
1
2211
1
00
0
SS
SRSRREngine
M/G 1
M/G 2
Vehicle
PG 1 PG 2
1
1 1 2 2
2
21
0
0R
RR S R S
SS
−⎡ ⎤⎢ ⎥+ +⎢ ⎥−⎢
⎢⎣ ⎦
− ⎥⎥−
Engine
M/G 1
M/G 2
Vehicle
PG 1 PG 2
PG2
PG1
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GM Three Planetary Gears ECVT (Schmidt,
1999)
Timken System (Ai and
Mohr, 2004)
GM Two Planetary Gears ECVT (Holmes et
al. 2003)
Toyota Hybrid System for Lexus GS450 (Hermance and Abe, 2006)
Toyota Hybrid System for Highlander (Hermance and Abe, 2006)
Toyota Hybrid System for Prius (Hermance, 1999)
Design Matrices (Model)Design
⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
−−−
−−+++
−
3
32
21
332211
1
000
0
00
RSS
RSSRSRSR
R
⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
++−−
−−+
−
00
000
00
2211
32
21
33
1
SRSRSS
RSSR
R
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
−−
+−+
2
1
231
11
00
0
SS
SSRSR
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
−−
+−+
2
1
221
11
00
0
SS
SRRSR
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
−−
−−+
2
1
21
11
00
0
SS
RRSR
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
−−+
1
1
11
SR
SR
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
−−
++−
2
1
2211
1
00
0
SS
SRSRR
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
−−−++
−
2
21
2211
1
0
0
SRS
SRSRR
1 1
2 2
1
1 2
00
0
R SR S
SR S
+⎡ ⎤⎢ ⎥+⎢ ⎥⎢ ⎥−⎢ ⎥− −⎣ ⎦
1 1
2 2
1 2
1 2
00
R SR S
S RR S
+⎡ ⎤⎢ ⎥+⎢ ⎥⎢ ⎥− −⎢ ⎥− −⎣ ⎦
Low Speed High Speed
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Model Corresponds To Configuration
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
−−
++−
2
1
2211
1
00
0
SS
SRSRR
PG 1 PG 2Given Configuration
Engine
M/G 1
M/G 2
Vehicle
Given Model
1 1 1
2 2
1
1 2
00
R S RR S
RS S
+ −⎡ ⎤⎢ ⎥+⎢ ⎥⎢ ⎥−⎢ ⎥− −⎣ ⎦
PG 1 PG 2
Engine
M/G 1
M/G 2
Vehicle
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Outline
• Introduction
• Dynamic Modeling of Power-Split Hybrid Vehicles
• Automated Modeling of Power-Split Hybrid Vehicles
• Configuration Screening of Power-Split Hybrid Vehicles
• Combined Configuration Design, Component Sizing, and Control optimization of Power-Split Hybrid Vehicles
• Conclusion
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Configuration Screening Process
• Automatically Generated All Possible Candidates:
Target Vehicle: HMMWV 5400kgEngine: 180 KW
MG1 + MG2 = 60 KW2PG System Design
Candidates: 1152 288 17 2
• Design Objective:
24 24 / 2 24 36 1152× + × =
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Configuration Screening Process _ Step 1
Candidates: 1152 288 17 2
• Check Physical Feasibility
MG1
Ground
VehicleK
Engine
R
R
MG21
1 1 2 2
1 2
0
0 0
RR S R S
S S
−⎡ ⎤⎢ ⎥+ +⎢ ⎥⎢ ⎥− −⎢ ⎥⎣ ⎦
• The Feasibility corresponds to the DOF of the Powertrain
1
2
0e MGT T TEV MG
out MG
D D Dω ωω ω⎡ ⎤ ⎡ ⎤
Ω = + =⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦
1
2
MG eT TMG EV
MG out
D Dω ωω ω
−⎡ ⎤ ⎡ ⎤= −⎢ ⎥ ⎢ ⎥
⎣ ⎦ ⎣ ⎦
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Configuration Screening Process _ Step 2
Candidates: 1152 288 17 2
TMG2_max
TMG2_min
TMG2
THS configurationMG2 is limited to 30KW
TMG2_max
TMG2_min
TMG2
THS configurationMG2 is limited to 90KW
TMG2_max
TMG2_min
TMG2
2PG AHS configurationMG2 is limited to 30KW 2 1 1 2( ) /MG d e MG MG MGT P P T ω ω= − − ⋅
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Configuration Screening Process _ Step 2
Candidates: 1152 288 17 2
TMG2_max
TMG2_min
TMG2
_ min _ _ max
_ min _ _ max
1_ min 1_ 1_ max
1_ min 1_ 1_ max
2_ min 2_ 2_ max
2_ min 2_ 2_ max
e e k e
e e k e
MG MG k MG
MG MG k MG
MG MG k MG
MG MG k MG
T T T
T T T
ω ω ω
ω ω ω
ω ω ω
ω ω ω
≤ ≤
≤ ≤
≤ ≤
≤ ≤
≤ ≤
≤ ≤
• Check Drivability
272008 ACC HEV workshop-
Configuration Screening Process _ Step 3
Candidates: 1152 288 17 2
1
1 1 2 2
1
2
0
00
RR S R S
DS
R
−⎡ ⎤⎢ ⎥+ +⎢ ⎥=⎢ ⎥−⎢ ⎥−⎣ ⎦
MG1
Ground
VehicleK
EngineR1
MG2R2
CL1CL2
• Check Possible Shifting Mode
MG1 Ground
VehicleK
EngineR1 MG2
R2
CL1CL2
1 2
1 1 2 2
1
2
00
mode21
R SR S R S
DS
R
− −⎡ ⎤⎢ ⎥+ +⎢ ⎥=⎢ ⎥−⎢ ⎥−⎣ ⎦
1
1 1 2 2
1 2
2
0
0
mode22
RR S R S
DS S
R
−⎡ ⎤⎢ ⎥+ +⎢ ⎥=⎢ ⎥− −⎢ ⎥−⎣ ⎦
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Configuration Screening Process _ Step 3
Candidates: 1152 288 17 2
• Check Transmission Efficiency (Mechanical Point)
Conlon, 2005, “Comparative Analysis of Single and Combined Hybrid Electrically Variable Transmission Operating Modes”
Vehicle speed v
Engine power Pe
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Configuration Screening Process _ Step 3
Candidates: 1152 288 17 2
• Check Transmission Efficiency (Mechanical Point)
Conlon, 2005, “Comparative Analysis of Single and Combined Hybrid Electrically Variable Transmission Operating Modes”
Vehicle speed v
Engine power Pe
302008 ACC HEV workshop-
Configuration Screening Process _ Step 3
Candidates: 1152 288 17 2
Conlon, 2005, “Comparative Analysis of Single and Combined Hybrid Electrically Variable Transmission Operating Modes”
• Check Transmission Efficiency (Mechanical Point)– Input-split: close to first gear– Compound-split: close to overdrive gear
1
2
MG eT TMG EV
MG out
D Dω ωω ω
−⎡ ⎤ ⎡ ⎤= −⎢ ⎥ ⎢ ⎥
⎣ ⎦ ⎣ ⎦
312008 ACC HEV workshop-
Outline
• Introduction
• Dynamic Modeling of Power-Split Hybrid Vehicles
• Automated Modeling of Power-Split Hybrid Vehicles
• Configuration Screening of Power-Split Hybrid Vehicles
• Combined Configuration Design, Component Sizing, and Control optimization of Power-Split Hybrid Vehicles
• Conclusion
322008 ACC HEV workshop-
Dynamic Programming to Set Fuel Economy Benchmark
Vehicle Dynamics
ωe(k)
v(k)
SOC(k)
ωe(k+1)
v(k+1)
SOC(k+1)
TMG2 Te TMG1
Fuel ConsumptionSOC error
12
0
N
k SOCk
J fuel α−
=
= + Δ∑
_ min _ _ max _ min _ _ max
1_ min 1_ 1_ max 1_ min 1_ 1_ max
2_ min 2_ 2_ max 2_ min 2_ 2_ max
e e k e e e k e
MG MG k MG MG MG k MG
MG MG k MG MG MG k MG
T T T
T T T
ω ω ω ω ω ω
ω ω ω
ω ω ω
≤ ≤ ≤ ≤
≤ ≤ ≤ ≤
≤ ≤ ≤ ≤
• Cost Function
• Constraints
Inputs:
States:
Transitional cost
0 50 100 150 200 250 300 3500
10
20
30
40
50
60vehicle speed (mph)
time (s)
332008 ACC HEV workshop-
17.517.817.8
17.8
17.8
17.9 17.9
17.9
17.9
18
18
18
18
18
18.1
18.1
18.1
18.1
18.2
18.2
18.218.2
18.3
18.3
18.3
18.4
18.4
18.5
18.5
K1K
21.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
)5.25.1( <<= ii
ii KS
RK
18.0918.0218.3518.4318.532.417.9318.0618.1818.5418.432.217.6918.0118.2918.2518.362.017.82 17.7818.2018.2318.171.817.3317.5717.6718.0317.58K2=1.62.42.22.01.8K1=1.6Fuel(mpg)
DP fuel economy results for different gear dimensions on the partial EPA urban cycle (Powertrain #2)
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Effect of the Electric Machine Sizes
0
2
4
6
8
10
12
14
16
18
20
t1 t2 t3 t4 t5
Ever
age
Fuel
Eco
nom
y (m
pg)
MG2(kW) 10 20 30 40 50 50 40 30 20 10 MG1(kW)
Power SplitECVT
Vehicle
Engine
M/G2
M/G1
Battery
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Comparison Between Different Configuration Designs
Fuel efficiency Comparison ResultsTarget Vehicle: HMMWV 5400kg
Engine: 180 KWMG1 + MG2: 60 KW
PT #2
PT #1
K1=1.6K2=1.8
MG1=20 kWMG2=40 kW
K1=1.8K2=2.2
MG1=20 kWMG2=40 kW
362008 ACC HEV workshop-
Outline
• Introduction
• Dynamic Modeling of Power-Split Hybrid Vehicles
• Automated Modeling of Power-Split Hybrid Vehicles
• Configuration Screening of Power-Split Hybrid Vehicles
• Combined Configuration Design, Component Sizing, and Control optimization of Power-Split Hybrid Vehicles
• Conclusion
372008 ACC HEV workshop-
Conclusions
• A universal dynamic model for power-split HEVs, which can be used for exhaustive search of split hybrid configurations.
• A screening process systematically checks the configuration candidates based on optimal design and optimal control results.