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.
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Abbreviations
- A :
-
bus frontal area
- C d :
-
drag coefficient
- D HM :
-
displacement of the hydraulic motor
- D HP :
-
displacement of the hydraulic pump
- EM:
-
electric motor
- E max :
-
maximum energy stored in the battery
- F ad :
-
aerodynamic force
- F g :
-
gravity force
- F rr :
-
rolling resistance
- F t :
-
tractive force
- g :
-
gravity acceleration
- H :
-
Hamiltonian function
- HM:
-
hydraulic motor
- HP:
-
hydraulic pump
- I CE :
-
internal combustion engine
- m :
-
mass of the bus
- m f :
-
fuel flow rate
- P BAT :
-
power delivered by the battery
- P EM :
-
power consumed by the electric motor
- P F :
-
instantaneous power of the fuel
- Q LHV :
-
lower heating value of the fuel
- SLR :
-
static loaded radius of the wheel
- SOC :
-
battery state of charge
- SOE :
-
battery state of energy
- T HM :
-
torque of the hydraulic motor
- T ICE :
-
torque of the engine
- T wheel :
-
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
- η mHM :
-
mechanical efficiency of the hydraulic motor
- η mHP :
-
mechanical efficiency of the hydraulic pump
- η vHM :
-
volumetric efficiency of the hydraulic motor
- η vHP :
-
volumetric efficiency of the hydraulic pump
- η BAT :
-
efficiency of the battery
- θ :
-
slope of the road
- λ :
-
slope of the road
- λ 0 :
-
initial values of the costate
- λ max :
-
maximum values of the costate
- λ min :
-
minimum values of the costate
- μ rr :
-
rolling resistance coefficient
- ξ :
-
maximum hydraulic torque variation rate
- ρ :
-
density of the air
- ρ 1, ρ 2 :
-
gearbox’ reduction ratios
- ω HM :
-
rotational speed of the hydraulic motor
- ω ICE :
-
rotational speed of the engine
- ω wheel :
-
rotational speed of the wheel
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Ouddah, N., Adouane, L. & Abdrakhmanov, R. From Offline to Adaptive Online Energy Management Strategy of Hybrid Vehicle Using Pontryagin’s Minimum Principle. Int.J Automot. Technol. 19, 571–584 (2018). https://doi.org/10.1007/s12239-018-0054-8
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DOI: https://doi.org/10.1007/s12239-018-0054-8