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Research on instantaneous optimal control of the hybrid electric vehicle with planetary gear sets

  • Shaohua WangEmail author
  • Sheng Zhang
  • Dehua Shi
  • Xiaoqiang Sun
  • Jianqiang He
Technical Paper
  • 53 Downloads

Abstract

Power-split hybrid electric vehicle (HEV), mainly adopting the planetary power coupling mechanism, is superior in improving the fuel economy because the engine speed and torque are decoupled from those of the wheels. Focusing on a power-split HEV with dual-planetary gear sets, this paper establishes an instantaneous optimal control to regulate its power flow. Firstly, simulation-oriented models are established, including the coupling mechanism, the engine, the electrical machines and the battery. Secondly, feasible operation modes of the vehicle are analyzed. Also, the torque and speed equations between the engine and motors are obtained. On the basis of the above, the instantaneous optimization strategy, adaptive equivalent fuel consumption minimization strategy (A-ECMS), is designed, which is developed from the equivalent fuel consumption minimization strategy. The optimization strategy is of high robustness to different driving cycles. To realize the engine speed tracking, a PI controller is introduced. At last, the control effects of A-ECMS are compared with the effects of the engine optimal operating line control strategy. The effectiveness and rationality of two strategies are tested in the dSPACE real-time simulator. Test results under different driving scenarios prove that the A-ECMS is of better performance in ensuring the HEV fuel economy and the battery charging sustainability.

Keywords

Power-split HEV Planetary power coupling mechanism Energy management A-ECMS 

Abbreviations

A-ECMS

Adaptive equivalent minimization fuel consumption strategy

C1

Carrier gear of the first planetary gear set

C2

Carrier gear of the second planetary gear set

ECMS

Equivalent minimization fuel consumption strategy

GM

General motors

HEV

Hybrid electric vehicle

HIL

Hardware in the loop

IO

In/out interface

MG1

Electric machine 1

MG2

Electric machine 2

NEDC

New European Driving Cycle

OOL

Engine optimal operation line

P1

The first planetary gear set

P2

The second planetary gear set

PMP

Pontryagin’s minimum principle

R1

Ring gear of the first planetary gear set

R2

Ring gear of the second planetary gear set

S1

Sun gear of the first/second planetary gear set

S2

Sun gear of the second planetary gear set

SOC

Battery state of charge

SUV

Sport utility vehicle

THS

Toyota hybrid system

UDDS

Urban Dynamometer Driving Schedule

List of symbols

A

Vehicle frontal area

CD

Air drag coefficient

Cp

Correction factor

F1

Internal force on the pinion gear

F2

Internal force on the pinion gear

f

Coefficient of rolling resistance

Ieng

Lumped inertia of the engine

Ifd

Lumped inertia of the main reducer

IMG1

Lumped inertia of MG1

IMG2

Lumped inertia of MG2

Iw

Wheel inertia

IBatt

Battery output current

ISOC

Correction current

i0

Ratio of the final drive

K1

Characteristic parameter of P1

K2

Characteristic parameter of P2

k

Discrete time point

m

Vehicle mass

\(\dot{m}_{\text{Batt}}\)

Battery equivalent fuel consumption rate

\(\dot{m}_{\text{eng}}\)

Engine fuel consumption rate

Peng

Engine power

Peng_max

Engine maximum power

PMG1

MG1 power

PMG1_max

MG1 maximum power

PMG2

MG2 power

PMG2_max

MG2 maximum power

Preq

Required driving power

Pb

Battery power

Q

Battery capability

Qlhv

Low heat value of gasoline

Rw

Wheel radius

Rin

Battery internal resistance

r1

Radius of R1

r2

Radius of R2

\({\text{S}}\mathop {\text{O}}\limits^{.} {\text{C}}\)

Derivative of battery SOC

SOCmin

Lower limit of the battery SOC

SOCmax

Upper limit of the battery SOC

SOCref

Reference SOC

SOChist

Final battery SOC

s1

Radius of S1

s2

Radius of S2

s

Equivalence factor

schg

Charging equivalence factor

sdis

Discharging equivalence factor

Teng

Engine torque

Teng_min

Minimum torque of the engine

Teng_max

Maximum torque of the engine

TMG1

MG1 torque

TMG1_min

Minimum torque of MG1

TMG1_max

Maximum torque of MG1

TMG2

MG2 torque

TMG2_min

Minimum torque of MG2

TMG2_max

Maximum torque of MG2

Treq

Required torque

Tout

Load torque

Tf

Friction braking torque

Teng_ideal

Ideal engine torque

T1

Internal torque between MG1 and S1

\(T_{1}^{'}\)

Internal torque between MG1 and S1

T2

Internal torque between MG2 and S2

\(T_{2}^{'}\)

Internal torque between MG2 and S2

T3

Internal torque between the engine and C1

\(T_{3}^{'}\)

Internal torque between the engine and C1

tf

Time of a selected fragment

Voc

Battery open-circuit voltage

VBatt

Load voltage

xSOC

Correction SOC

ωeng

Engine speed

ωeng_min

Minimum speed of the engine

ωeng_max

Maximum speed of the engine

ωMG1

MG1 speed

ωMG1_min

Minimum speed of MG1

ωMG1_max

Maximum speed of MG1

ωMG2

MG2 speed

ωMG2_min

Minimum speed of MG2

ωMG2_max

Maximum speed of MG2

ωout

Output speed of the power coupling device

ωeng_ideal

Ideal engine speed

ωeng_act

Actual engine speed

ηMG1

Efficiency of MG1

ηMG2

Efficiency of MG2

ηchg

Charging efficiency of the battery

ηdis

Discharging efficiency of the battery

ϕ1

Map for MG1 efficiency

ϕ2

Map for MG2 efficiency

Γ

Map for engine fuel flow rate

ρ

Air density

ψ

State factor

γSOC

Weight factor

Notes

Acknowledgements

This study was supported by the National Nature Science Foundation of China (Grant Nos. 51475213, U1764257), the Foundation for Jiangsu Key Laboratory of Traffic and Transportation Security (Grant No. TTS2018-01) and the ‘333 Project’ of Jiangsu Province (BRA2018178).

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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  • Shaohua Wang
    • 1
    Email author
  • Sheng Zhang
    • 1
  • Dehua Shi
    • 2
  • Xiaoqiang Sun
    • 2
  • Jianqiang He
    • 1
  1. 1.School of Automotive and Traffic EngineeringJiangsu UniversityZhenjiangChina
  2. 2.Automotive Engineering Research InstituteJiangsu UniversityZhenjiangChina

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