From Offline to Adaptive Online Energy Management Strategy of Hybrid Vehicle Using Pontryagin’s Minimum Principle

  • Nadir Ouddah
  • Lounis Adouane
  • Rustem Abdrakhmanov
Article
  • 14 Downloads

Abstract

This paper details the development of an energy management strategy (EMS) for real-time control of a multi hybrid plug-in electric bus. The energy management problem has been formulated as an optimal control problem in order to minimize the fuel consumption of the bus drivetrain for a typical day of operation. Considering the physical characteristics of the studied hybrid electric bus and its well-known daily tour, the Pontryagin’s minimum principle (PMP) is firstly used as the mean to obtain offline optimal EMS. Afterward, in order to adapt the proposed strategy for real-time implementation, the proposed control parameters are adapted online using feedback from the battery state of energy (SOE) which allows us to accurately control the battery SOE in the presence of wide range of uncertainties. The work proposed in this paper is conducted on a dedicated high-fidelity dynamical model of the hybrid bus, that was developed on MATLAB/TruckMaker software. The performance evaluation of the proposed strategy is carried out using a normalized driving cycles to represent different driving scenarios. Obtained results show that among the investigated methods, it is reasonable to conclude that the proposed adaptive online strategy based on PMP is the most suitable to design the targeted EMS.

Key words

Optimal control Heavy hybrid vehicle Energy management Pontryagin’s minimum principle 

Subscripts

A

bus frontal area

Cd

drag coefficient

DHM

displacement of the hydraulic motor

DHP

displacement of the hydraulic pump

EM

electric motor

Emax

maximum energy stored in the battery

Fad

aerodynamic force

Fg

gravity force

Frr

rolling resistance

Ft

tractive force

g

gravity acceleration

H

Hamiltonian function

HM

hydraulic motor

HP

hydraulic pump

ICE

internal combustion engine

m

mass of the bus

mf

fuel flow rate

PBAT

power delivered by the battery

PEM

power consumed by the electric motor

PF

instantaneous power of the fuel

QLHV

lower heating value of the fuel

SLR

static loaded radius of the wheel

SOC

battery state of charge

SOE

battery state of energy

THM

torque of the hydraulic motor

TICE

torque of the engine

Twheel

torque of the wheel

U

admissible control set

v

velocity of the bus

a

acceleration of the bus

γ, σ

lagrange multipliers used to introduce constraints

ηmHM

mechanical efficiency of the hydraulic motor

ηmHP

mechanical efficiency of the hydraulic pump

ηvHM

volumetric efficiency of the hydraulic motor

ηvHP

volumetric efficiency of the hydraulic pump

ηBAT

efficiency of the battery

θ

slope of the road

λ

slope of the road

λ0

initial values of the costate

λmax

maximum values of the costate

λmin

minimum values of the costate

μrr

rolling resistance coefficient

ξ

maximum hydraulic torque variation rate

ρ

density of the air

ρ1, ρ2

gearbox’ reduction ratios

ωHM

rotational speed of the hydraulic motor

ωICE

rotational speed of the engine

ωwheel

rotational speed of the wheel

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Copyright information

© The Korean Society of Automotive Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Nadir Ouddah
    • 1
  • Lounis Adouane
    • 1
  • Rustem Abdrakhmanov
    • 1
  1. 1.Institut Pascal, IMobS3, UCA/SIGMA UMR CNRS 6602Clermont-FerrandFrance

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