Fuel-Optimal Power Split and Gear Selection Strategies for a Hybrid Electric Vehicle

Ritzmann, Johannes; Christon, Andreas; Salazar, Mauro; Onder, Christopher H.

doi:10.4271/2019-24-0205

Cited by 27 publications

(19 citation statements)

References 19 publications

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“…This method may lead to the interpolation error and deterioration in the optimization in terms of accuracy of the result. Ritzmann et al [24] optimized the torque split and gear selection based on a mixed-integer convex problem and a non-smooth PMP to improve the computation efficiency; however, frequent gear switching is not properly penalized. Steinbuch et al [25] utilized a numerical PMP to optimize the gearshift command by directly adding a penalty function.…”

Section: Literature Reviewmentioning

confidence: 99%

“…To further show the fitting results, the engine fuel rate fitting curve is created by the piecewise linear approximation, as shown in Figure 5. Similarly, the approximation of SOC derivative ( SOC  ) is simplified by piecewise linear approximation, which can be presented as Equation (24).…”

Section: A Models Approximationmentioning

confidence: 99%

“…Similarly, the approximation of SOC derivative (S . OC) is simplified by piecewise linear approximation, which can be presented as Equation (24).…”

Section: A Models Approximationmentioning

confidence: 99%

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Computationally Efficient Energy Management in Hybrid Electric Vehicles Based on Approximate Pontryagin’s Minimum Principle

Zhang

Wang

Coşkun

et al. 2020

WEVJ

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This article presents an energy management method for a parallel hybrid electric vehicle (HEV) based on approximate Pontryagin’s Minimum Principle (A-PMP). The A-PMP optimizes gearshift commands and torque distribution for overall energy efficiency. As a practical numerical solution in PMP, the proposed methodology utilizes a piecewise linear approximation of the engine fuel rate and state of charge (SOC) derivative by considering drivability and fuel economy simultaneously. Moreover, battery aging is explicitly studied by introducing a control-oriented model, which aims to investigate the effect of battery aging on the optimization performance in the development of the HEVs. An approximate energy management strategy with piecewise linear models is then formulated by the A-PMP, which targets a better performance for the Hamiltonian optimization. The gearshift map is extracted from the optimal results in the standard PMP to hinder frequent gearshift by considering both drivability and fuel economy. Utilizing an approximated Hamilton function, the torque distribution, gearshift command, and the battery aging degradation are jointly optimized under a unified framework. Simulations are performed for dynamic programming (DP), PMP, and A-PMP to validate the effectiveness of the proposed approach. The results indicate that the proposed methodology achieves a close fuel economy compared with the DP-based optimal solution. Moreover, it improves the computation efficiency by 50% and energy saving by 3.5%, compared with the PMP, while ensuring good drivability and fuel efficiency.

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Section: Literature Reviewmentioning

confidence: 99%

Section: A Models Approximationmentioning

confidence: 99%

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Computationally Efficient Energy Management in Hybrid Electric Vehicles Based on Approximate Pontryagin’s Minimum Principle

Zhang

Wang

Coşkun

et al. 2020

WEVJ

View full text Add to dashboard Cite

show abstract

“…The problems of frequent active constraints or integer decisions are typically addressed by direct transcription and then solved numerically. Common examples are the multiple shooting and collocation methods for smooth nonlinear programs [7], [8] or DP and branch, bound and cut techniques for mixed-integer programs [9], [10], [11] that involve decoupling the speed optimization from power-split and gear optimization or by assuming that the speed profile is known a priori.…”

Section: Introductionmentioning

confidence: 99%

Real-Time Predictive Energy Management of Hybrid Electric Heavy Vehicles by Sequential Programming

Ghandriz

Jacobson

Murgovski

et al. 2021

IEEE Trans. Veh. Technol.

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With the objective of reducing fuel consumption, this paper presents real-time predictive energy management of hybrid electric heavy vehicles. We propose an optimal control strategy that determines the power split between different vehicle power sources and brakes. Based on model predictive control (MPC) and sequential programming, the optimal trajectories of the vehicle velocity and battery state of charge are found for upcoming horizons with a length of 5-20 km. Then, acceleration and brake pedal positions together with the battery usage are regulated to follow the requested speed and state of charge, which is verified using a high-fidelity vehicle plant model. The main contribution of this paper is the development of a sequential linear program for predictive energy management that is faster and simpler than sequential quadratic programming in tested solvers and provides trajectories that are very close to the best trajectories found by nonlinear programming. The performance of the method is also compared to that of two different sequential quadratic programs.

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“…For feedback control, equivalent consumption minimization strategies have been applied for fuel consumption minimization [16,17] considering also pollutant emissions [18], the battery state of health [19] or turbocompounding [20,21]. Furthermore, the integer nature of gears and the engine on/off choice were tackled with iterative algorithms [7], Pontryagin's minimum principle [22,23], dynamic programming [8,23], outer convexification [24][25][26][27][28] and shooting or bisection methods [29,30]. However, all these approaches mainly rely on quasi-static system models and ignore the dynamic behavior of the internal combustion engine, e.g., the intake manifold or the turbocharger dynamics.…”

Section: Introductionmentioning

confidence: 99%

Time-Optimal Low-Level Control and Gearshift Strategies for the Formula 1 Hybrid Electric Powertrain

et al. 2020

Self Cite

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Today, Formula 1 race cars are equipped with complex hybrid electric powertrains that display significant cross-couplings between the internal combustion engine and the electrical energy recovery system. Given that a large number of these phenomena are strongly engine-speed dependent, not only the energy management but also the gearshift strategy significantly influence the achievable lap time for a given fuel and battery budget. Therefore, in this paper we propose a detailed low-level mathematical model of the Formula 1 powertrain suited for numerical optimization, and solve the time-optimal control problem in a computationally efficient way. First, we describe the powertrain dynamics by means of first principle modeling approaches and neural network techniques, with a strong focus on the low-level actuation of the internal combustion engine and its coupling with the energy recovery system. Next, we relax the integer decision variable related to the gearbox by applying outer convexification and solve the resulting optimization problem. Our results show that the energy consumption budgets not only influence the fuel mass flow and electric boosting operation, but also the gearshift strategy and the low-level engine operation, e.g., the intake manifold pressure evolution, the air-to-fuel ratio or the turbine waste-gate position.

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Fuel-Optimal Power Split and Gear Selection Strategies for a Hybrid Electric Vehicle

Cited by 27 publications

References 19 publications

Computationally Efficient Energy Management in Hybrid Electric Vehicles Based on Approximate Pontryagin’s Minimum Principle

Computationally Efficient Energy Management in Hybrid Electric Vehicles Based on Approximate Pontryagin’s Minimum Principle

Real-Time Predictive Energy Management of Hybrid Electric Heavy Vehicles by Sequential Programming

Time-Optimal Low-Level Control and Gearshift Strategies for the Formula 1 Hybrid Electric Powertrain

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