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Battery State-of-Health Perceptive Energy Management for Hybrid Electric Vehicles

This paper presents a causal optimal control-based energy management strategy for a parallel hybrid electric vehicle (HEV). This strategy not only seeks to minimize fuel consumption while maintaining the state-of-charge of the battery within reasonable bounds but to minimize wear of the battery by penalizing the instantaneous battery usage with respect to its relative impact on battery life as well. This impact is derived by means of a control-oriented state-of-health model. The results indicate that the proposed causal strategy effectively reduces battery wear with only a relatively small penalty on fuel consumption. Ultimately, in terms of cost of fuel and battery replacements, the total cost of ownership over the entire life of the vehicle is significantly reduced.

Implementation of Dynamic Programming for

Many optimal control problems include a continuous nonlinear dynamic system, state, and control constraints, and final state constraints. When using dynamic programming to solve such a problem, the solution space typically needs to be discretized and interpolation is used to evaluate the cost-to-go function between the grid points. When implementing such an algorithm, it is important to treat numerical issues appropriately. Otherwise, the accuracy of the found solution will deteriorate and global optimality can be restored only by increasing the level of discretization. Unfortunately, this will also increase the computational effort needed to calculate the solution. A known problem is the treatment of states in the time-state space from which the final state constraint cannot be met within the given final time. In this brief, a novel method to handle this problem is presented. The new method guarantees global optimality of the found solution, while it is not restricted to a specific class of problems. Opposed to that, previously proposed methods either sacrifice global optimality or are applicable to a specific class of problems only. Compared to the basic implementation, the proposed method allows the use of a substantially lower level of discretization while achieving the same accuracy. As an example, an academic optimal control problem is analyzed. With the new method, the evaluation time was reduced by a factor of about 300, while the accuracy of the solution was maintained.

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Particle swarm optimization (PSO) is rapidly gaining popularity but an official implementation of the PSO algorithm in Matlab is yet to be released. In this paper, we present a generic particle swarm optimization Matlab function. The syntax necessary to interface the function is practically identical to that of existing Matlab functions such as fmincon and ga. We demonstrate our PSO function by means of two examples: the first example is an academic test problem; the second example is a simplified problem of optimizing the gear ratios in a hybrid electric drivetrain. The PSO function is available online.

-Dimensional Optimal Control Problems With Final State Constraints

Currently, many different topologies are designed with different transmission technologies such as automated manual transmission (AMT) and continuously variable transmission (CVT). The choice of topology determines the energy-flow efficiency between the hybrid system, the engine, and the vehicle wheels. The optimal topology minimizing fuel consumption is influenced by the transmission technology. Therefore, an AMT (high efficiency) and a push-belt CVT (moderate efficiency), are used in this research for comparison. In addition, a controlled switching topology is introduced as a benchmark, where controlled coupling with additional clutches of the electric machine before or after the transmission minimizing transmission losses and improving hybrid performance is investigated. The results showed that a switching topology can significantly improve CO2 emission reduction (average relative improvements between 2% and 7%), particularly for CVT-based hybrid vehicles. Moreover, in case of an AMT, a precoupled topology is preferable, and in the case of a CVT, a postcoupled is preferable for full-hybrid vehicles. For these cases, selecting the optimal fixed topology can improve the relative CO2 emission reduction between 2% and 8%.

A generic particle swarm optimization Matlab function

Electric hybridisation of vehicles aims at reducing fuel consumption but increases production costs. Hence, automobile manufacturers are confronted with the multi-objective optimisation problem of sizing the drive-train components. In this paper, we evaluated Particle Swarm Optimisation (PSO) for solving this problem. The results showed that PSO performs significantly better than competing methods. Parameter sensitivities indicated that the optimal solution, the vehicle performance constraints, and the preference between fuel consumption and production cost are intimately coupled. Finally, a Pareto analysis confirmed that a relatively small increase in cost accounts for a majority of the total fuel saving potential.

Topology Optimization for Hybrid Electric Vehicles With Automated Transmissions

This paper studies convex optimization and modelling for component sizing and optimal energy management control of hybrid electric vehicles. The novelty in the paper is the modeling steps required to include a battery wear model into the convex optimization problem. The convex modeling steps are described for the example of battery sizing and simultaneous optimal control of a series hybrid electric bus driving along a perfectly known bus line. Using the proposed convex optimization method and battery wear model, the city bus example is used to study a relevant question: is it better to choose one large battery that is sized to survive the entire lifespan of the bus, or is it beneficial with several smaller replaceable batteries which could be operated at higher c-rates?

Particle swarm optimisation for hybrid electric drive-train sizing

In this paper, we apply a methodology to select the cost and fuel-optimal topology of a set of topologies for hybrid electric vehicles (HEVs). For each topology, the optimal component sizes are determined by optimizing a weighted sum of fuel consumption and powertrain costs. Vehicle performance constraints are imposed to ensure a minimum level of drivability. The constrained optimization problem is solved using Particle Swarm Optimization (PSO), and deterministic Dynamic Programming (DP) is used to calculate the optimal fuel consumption. The methodology is applied to a torque-assist and a full-parallel HEV with each three degrees of freedom, i.e. the size of the engine, the motor and the battery. Moreover, we consider two driving cycles: the New European Driving Cycle (NEDC) and a driving cycle with considerable elevation changes. We found that in case of the NEDC, the sizing problem can be reduced to one degree of freedom, whereas in case of the other driving cycle, all three degrees of freedom are required. The latter observation is related to the relative importance of the maximum battery capacity compared with the maximum battery power, but also to the size of the electric motor maximizing energy recuperation.

Including a Battery State of Health model in the HEV component sizing and optimal control problem

Recently, the Formula 1 propulsion system has evolved from being a conventional combustion engine toward a highly integrated hybrid electric powertrain. Since 2014, the vehicles have been equipped with an electric motor for extra boosting and regenerative braking, and an electrified turbocharger to improve the engine’s torque response and to recover waste heat from the exhaust gas. The powertrain is controlled with a dedicated energy management system, which significantly influences the vehicle’s acceleration performance as well as its fuel and electric energy consumption. Therefore, the strategy must be carefully optimized. In this paper, we propose a computationally efficient method to evaluate the theoretic, optimal energy management strategy leading to the best possible lap time. Since the driving path cannot be influenced by the energy management strategy, but is rather determined by the driver’s steering’s input, we separate the optimization of velocity profile and energy management from the problem of finding the optimal driving path. By carefully introducing convex approximations and relaxations, we formulate the problem as a convex optimal control problem that can be solved efficiently using dedicated numerical solvers. The proposed method allows parameter studies to be conducted within a reasonable time frame of a few minutes, while the optimization results serve as a benchmark for any real-time energy management strategy ultimately to be used during a real race.

Cost and fuel-optimal selection of HEV topologies using Particle Swarm Optimization and Dynamic Programming

In this paper, we adopted a simple yet useful capacity fade model of a Li-ion battery for a hybrid electric vehicle application. Its simple structure permitted us to embed it in the formulation of the optimal energy management control problem, which we solved using dynamic programming. In this way, we were able to study the trade-off between globally optimal fuel economy and battery life. This trade-off was quantified in terms of total cost of fuel and battery projected to the entire vehicle life. Furthermore, a sensitivity analysis was performed to investigate the influence of time-varying fuel and battery prices on total cost of ownership.Copyright

Time-optimal Control Strategies for a Hybrid Electric Race Car

Since 2014, the Formula 1 car has been a hybrid electric vehicle with a turbocharged gasoline engine and electric motor/generator units connected to the axle, for kinetic energy recovery and boosting, and to the shaft of the turbocharger, mainly to recover waste heat from the exhaust gases. This system offers a new degree of freedom, namely, the power split, which is the ratio of power delivered by the electric traction motor in comparison to the overall propulsive power. In the straights, where the driver usually requests 100% acceleration, regulations allow the implementation of a thrust controller, since only by limiting the acceleration power, the maximum allowed fuel consumption of 100 kg gasoline per race can be achieved. The decisions of the corresponding energy management controller strongly influence the achievable lap time, and thus need to be carefully optimized. Furthermore, there exist several operational constraints imposed by the regulations that need to be tracked. This paper proposes a real-time implementable energy management strategy minimizing the lap time, by deriving the optimal control policy analytically. Optimality of the proposed controller is verified by comparing the results obtained with a benchmark simulator against the global optimal solution, while implementability and compatibility with the regulations are demonstrated using a high-fidelity nonlinear simulator.