• Energy Research

Performance and degradation prediction along with control of lithium ion batteries is a critical tool to advance electrification of transportation across the world. In this work, we devise a quadratic battery model which retains the structure of higher fidelity models, thereby allowing for implementation of constraints on internal states to ensure safety and to limit degradation. We validate our model against a pseudo- 2-dimensional partial-differential-equation based model, and demonstrate that our model can achieve high accuracy in spite of its simple nature. Finally, we implement the proposed MPC algorithm in a high-fidelity simulator, demonstrating its ability to charge nearly twice as fast as the most commonly used charging protocols whilst respecting constraints on anode potential, temperature, current, and state of charge. Calculation of the MPC protocol takes less than 0.15 s, meaning it is capable of running in real time.

Abstract The optimal control of Diesel engines remains a challenging task. On the one hand, the number of control inputs is high, resulting in a large optimisation problem. On the other hand, low fuel consumption and low nitrogen oxides (NOx) emissions are conflicting objectives. This means there is no single best solution, but rather a set of Pareto optimal solutions. In this paper, we tackle the steady-state engine calibration problem by directly modelling the Pareto frontiers. This way, the degrees of freedom are reduced, resulting in a much simpler problem. Moreover, because the Pareto frontiers are (close to) convex, we are able to describe them by a convex function. We use lossless constraint relaxations to reformulate the problem as a convex optimisation problem. Solving this problem requires very little computation time and yields the globally optimal solution. The optimal control inputs can be retrieved from the optimal solution in a straightforward manner. We present experimental results to demonstrate the practical feasibility and effectiveness of the proposed approach. Furthermore, we show how the methodology can be readily extended to calculate application-specific calibrations that are tailored to typical in-use operation. Steady-state as well as transient measurements from the engine test-bench prove that significant fuel savings are achievable, while keeping the NOx emissions below the same limit.

We present a modeling and optimization framework to design powertrains for a family of electric vehicles, focusing on the concurrent sizing of their motors and batteries. Whilst tailoring these component modules to each individual vehicle type can minimize energy consumption, it can result in high production costs due to the variety of component modules to be realized for the family of vehicles, driving the Total Costs of Ownership (TCO) high. Against this backdrop, we explore modularity and standardization strategies whereby we jointly design unique motor and battery modules to be installed in all the vehicles in the family, using a different number of these modules when needed. Such an approach results in higher production volumes of the same component module, entailing significantly lower manufacturing costs due to Economy-of-Scale (EoS) effects, and hence a potentially lower TCO for the family of vehicles. To solve the resulting one-size-fits-all problem, we instantiate a nested framework consisting of an inner convex optimization routine which jointly optimizes the modules' sizes and the powertrain operation of the entire family, for given driving cycles and modules' multiplicities. Likewise, we devise an outer loop comparing each configuration to identify the minimum-TCO solution with global optimality guarantees. Finally, we showcase our framework on a case study for the Tesla vehicle family in a benchmark design problem, considering the Model S, Model 3, Model X, and Model Y. Our results show that, compared to an individually tailored design, the application of our concurrent design optimization framework achieves a significant reduction of the production costs for a minimal increase in operational costs, ultimately lowering the family TCO in the benchmark design problem by 3.5\%. 17 pages, 17 figures, 7 tables

In this paper we present models and optimization algorithms to compute the optimal low-level control strategies for hybrid electric powertrains. Specifically, we study the minimum-fuel operation of a turbocharged internal combustion engine coupled to an electrical energy recovery system, consisting of a battery and two motors connected to the turbocharger and to the wheels, respectively. First, we combine physics-based modeling approaches with neural networks to identify a piecewise affine model of the power unit accounting for the internal dynamics of the engine, and formulate the minimum-fuel control problem for a given driving cycle. Second, we parse the control problem to a mixed-integer linear program that can be solved with off-the-shelf optimization algorithms that guarantee global optimality of the solution. Finally, we validate our model against a high fidelity nonlinear simulator and showcase the presented framework with a case-study for racing applications. Our results show that cylinder deactivation and turbocharger electrification can decrease fuel consumption up to 4% and 8%, respectively.

This paper presents models and optimization algorithms to compute the fuel-optimal energy management strategies for a parallel hybrid electric powertrain on a given driving cycle. Specifically, we first identify a mixed-integer model of the system, including the engine on/off signal and the gear-shift commands. Thereafter, by carefully relaxing the fuel-optimal control problem to a linear program, we devise an iterative algorithm to rapidly compute the minimum-fuel energy management strategies including the optimal gear-shift trajectory. We validate our approach by comparing its solution with the globally optimal one obtained solving the mixed-integer linear program and with the one resulting from the implementation of the optimal strategies in a high-fidelity nonlinear simulator.We showcase the effectiveness of the presented algorithm by assessing the impact of different powertrain configurations and electric motor size on the achievable fuel consumption.Our numerical results show that the proposed algorithm can assess fuel-optimal control strategies with low computational burden, and that powertrain design choices significantly affect the achievable fuel consumption of the vehicle.

Modern Formula 1 race cars are hybrid electric vehicles equipped with an internal combustion engine and an electric energy recovery system. In order to achieve the fastest possible lap time, the components’ operation must be carefully optimized, and the energy management must account for the impact of the gearshift strategy on the overall performance. This paper presents an algorithm to calculate the time-optimal energy management and gearshift strategies for the Formula 1 race car. First, we leverage a convex modeling approach to formulate a mathematical description of the powertrain including the gearbox, preserving convexity for a given engine speed trajectory. Second, we devise a computationally efficient algorithm to compute the energy management and gearshift strategies for minimum lap time, under consideration of given fuel and battery consumption targets. In particular, we combine convex optimization, dynamic programming and Pontryagin’s minimum principle in an iterative scheme to solve the arising mixed-integer optimization problem. We showcase our algorithm with a case study for the Bahrain racetrack, underlining the interactions between energy management and gear selection. Finally, we use our approach as a benchmark to evaluate the sub-optimality of a heuristic gearshift rule. Our results show that using an optimized engine speed threshold for upshifts can yield close-to-optimal results. However, already deviations smaller than 4% from the best possible threshold can increase lap time by more than 100 ms, highlighting the importance of jointly optimizing energy management and gearshift strategies. Applied Energy, 282 ISSN:0306-2619 ISSN:1872-9118

This paper presents a framework to estimate the environmental impact of solar electric vehicles, accounting for the emissions caused by photovoltaic system production as well as vehicle use. We leverage a cradle-to-gate life cycle assessment to estimate the greenhouse gas emissions of the vehicle-integrated photovoltaic system, from the raw material extraction to the final panel assembly, including the effect of the electricity mix both at the factory location and in the country of use. %the vehicle's life cycle, considering both Furthermore, we modify an existing optimization framework for battery electric vehicles to optimally design a solar electric vehicle and estimate its energy consumption. We showcase our framework by analyzing a case study where the mono-crystalline silicon extraction and refinement processes occur in China, while the final assembly of the panel is in The Netherlands, generating 118 kg of CO2 equivalents per square meter of solar panel. The results suggest that it is generally beneficial to operate solar electric vehicles in countries with a high irradiation index. However, when the local electricity mix already displays a low carbon intensity, the additional emissions introduced by the panel are unnecessary, requiring a longer vehicle lifetime to reach an advantageous emission balance. Comment: 6 pages, 8 figures, 2024 IEEE Vehicle Power and Propulsion Conference, Best Paper Award

This paper presents an optimization framework to design the components and the controller of a Continuously Variable Transmission (CVT) in an integrated manner. Specifically, we aim at reducing the mass of the transmission and the leakage losses that occur in the system. To do so, we first formulate the joint plant and control design problem including the corresponding objectives and constraints. Thereafter, we propose a proportional integral structure for the design of the CVT ratio control. The combined plant and control design problem is formulated as a nonlinear multi-objective optimization problem, and is simultaneously solved using an interior point optimization method. We evaluate the obtained design on the Worldwide Harmonized Light Vehicles Test Cycle (WLTC) as well as on more aggressive driving scenarios, and demonstrate that the optimized CVT design is always capable of realizing the required driving performance. Additionally, we study the impact of the plant design parameters on the control performance by analyzing the coupling strength between the subproblems. Thereby, the pulley radius is found to have the strongest influence in the resulting leakage losses that occur at the variator level. Finally, leveraging the presented design framework, we show that up to 13% and 18% reduction in the CVT variator mass and on leakage losses, respectively, can be achieved without compromising the desired ratio trajectory over a representative dynamic driving cycle.