configuration, sizing and control of power-split hybrid vehiclesavahidi/wp-content/uploads/... ·...

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

32008 ACC HEV workshop-

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%

42008 ACC HEV workshop-

Split Hybrids Dominate Current Market

http://bioage.typepad.com/./photos/uncategorized/2008/01/09/milsales2_2.png

split

52008 ACC HEV workshop-

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(?)

62008 ACC HEV workshop-

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.

72008 ACC HEV workshop-

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

82008 ACC HEV workshop-

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)

92008 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

102008 ACC HEV workshop-

Modeling of a Power-Split Hybrid Vehicle

Power SplitCVT

Vehicle

Engine

M/G2

M/G1

Battery

Driver SupervisoryController

112008 ACC HEV workshop-

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

132008 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

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

142008 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

152008 ACC HEV workshop-

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?

162008 ACC HEV workshop-

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 ⎡ ⎤=⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦⎣ ⎦⎣ ⎦

172008 ACC HEV workshop-

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

−⎡ ⎤⎢ ⎥+⎢ ⎥⎢ ⎥− −⎢ ⎥− −⎢ ⎥⎢ ⎥+ +⎣ ⎦

182008 ACC HEV workshop-

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.

192008 ACC HEV workshop-

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

202008 ACC HEV workshop-

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

212008 ACC HEV workshop-

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

222008 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

232008 ACC HEV workshop-

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× + × =

242008 ACC HEV workshop-

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

−⎡ ⎤ ⎡ ⎤= −⎢ ⎥ ⎢ ⎥

⎣ ⎦ ⎣ ⎦

252008 ACC HEV workshop-

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= − − ⋅

262008 ACC HEV workshop-

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

−⎡ ⎤⎢ ⎥+ +⎢ ⎥=⎢ ⎥− −⎢ ⎥−⎣ ⎦

282008 ACC HEV workshop-

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

292008 ACC HEV workshop-

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)

342008 ACC HEV workshop-

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

352008 ACC HEV workshop-

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.