Time-optimal Control Strategies for Electric Race Cars with Different Transmission Technologies

This paper presents models and optimization methods to rapidly compute the achievable lap time of a race car equipped with a battery electric powertrain. Specifically, we first derive a quasi-convex model of the electric powertrain, including the battery, the electric machine, and two transmission technologies: a single-speed fixed gear and a continuously variable transmission (CVT). Second, assuming an expert driver, we formulate the time-optimal control problem for a given driving path and solve it using an iterative convex optimization algorithm. Finally, we showcase our framework by comparing the performance achievable with a single-speed transmission and a CVT on the Le Mans track. Our results show that a CVT can balance its lower efficiency and higher weight with a higher-efficiency and more aggressive motor operation, and significantly outperform a fixed single-gear transmission.Comment: 5 pages, 4 figures, submitted to the 2020 IEEE Vehicle Power and Propulsion Conferenc

Electric Motor Design Optimization: A Convex Surrogate Modeling Approach

This paper instantiates a convex electric powertrain design optimization framework, bridging the gap between high-level powertrain sizing and low-level components design. We focus on the electric motor and transmission of electric vehicles, using a scalable convex motor model based on surrogate modeling techniques. Specifically, we first select relevant motor design variables and evaluate high-fidelity samples according to a predefined sampling plan. Second, using the sample data, we identify a convex model of the motor, which predicts its losses as a function of the operating point and the design parameters. We also identify models of the remaining components of the powertrain, namely a battery and a fixed-gear transmission. Third, we frame the minimum-energy consumption design problem over a drive cycle as a second-order conic program that can be efficiently solved with optimality guarantees. Finally, we showcase our framework in a case study for a compact family car and compute the optimal motor design and transmission ratio. We validate the accuracy of our models with a high-fidelity simulation tool and calculate the drift in battery energy consumption. We show that our model can capture the optimal operating line and the error in battery energy consumption is low. Overall, our framework can provide electric motor design experts with useful starting points for further design optimization.Comment: 6 pages, 5 figures, final submission for the 10th IFAC Symposium on Advances in Automotive Control, 202

Effective Scaling of High-Fidelity Electric Motor Models for Electric Powertrain Design Optimization

In general, electric motor design procedures for automotive applications go through expensive trial-and-error processes or use simplified models that linearly stretch the efficiency map. In this paper, we explore the possibility of efficiently optimizing the motor design directly, using high-fidelity simulation software and derivative-free optimization solvers. In particular, we proportionally scale an already existing electric motor design in axial and radial direction, as well as the sizes of the magnets and slots separately, in commercial motor design software. We encapsulate this motor model in a vehicle model together with the transmission, simulate a candidate design on a drive cycle, and find an optimum through a Bayesian optimization solver. We showcase our framework on a small city car, and observe an energy consumption reduction of 0.13% with respect to a completely proportional scaling method, with a motor that is equipped with relatively shorter but wider magnets and slots. In the extended version of this paper, we include a comparison with the linear models, and add experiments on different drive cycles and vehicle types.Comment: 4 pages, 2 figures, 2 tables, first submission to the 2023 Vehicle Power and Propulsion Conference in Milano, Italy, accepte

Effective Scaling of High-Fidelity Electric Motor Models for Electric Powertrain Design Optimization

In general, electric motor design procedures for automotive applications go through expensive trial-and-error processes or use simplified models that linearly stretch the efficiency map. In this paper, we explore the possibility of efficiently optimizing the motor design directly, using high-fidelity simulation software and derivative-free optimization solvers. In particular, we proportionally scale an already existing electric motor design in axial and radial direction, as well as the sizes of the magnets and slots separately, in commercial motor design software. We encapsulate this motor model in a vehicle model together with the transmission, simulate a candidate design on a drive cycle, and find an optimum through a Bayesian optimization solver. We showcase our framework on a small city car, and observe an energy consumption reduction of 0.13% with respect to a completely proportional scaling method, with a motor that is equipped with relatively shorter but wider magnets and slots. In the extended version of this paper, we include a comparison with the linear models, and add experiments on different drive cycles and vehicle types

Electric Motor Design Optimization: A Convex Surrogate Modeling Approach

This paper instantiates a convex electric powertrain design optimization framework, bridging the gap between high-level powertrain sizing and low-level components design. We focus on the electric motor and transmission of electric vehicles, using a scalable convex motor model based on surrogate modeling techniques. Specifically, we first select relevant motor design variables and evaluate high-fidelity samples according to a predefined sampling plan. Second, using the sample data, we identify a convex model of the motor, which predicts its losses as a function of the operating point and the design parameters. We also identify models of the remaining components of the powertrain, namely a battery and a fixed-gear transmission. Third, we frame the minimum-energy consumption design problem over a drive cycle as a second-order conic program that can be efficiently solved with optimality guarantees. Finally, we showcase our framework in a case study for a compact family car and compute the optimal motor design and transmission ratio. We validate the accuracy of our models with a high-fidelity simulation tool and calculate the drift in battery energy consumption. We show that our model can capture the optimal operating line and the error in battery energy consumption is low. Overall, our framework can provide electric motor design experts with useful starting points for further design optimization

Optimal Design of Electric Micromobility Vehicles

This paper presents a modeling and optimization framework to design battery electric micromobility vehicles, minimizing their total cost of ownership (TCO). Specifically, we first identify a model of the electric powertrain of an e-scooter and an e-moped consisting of a battery, a single electric motor and a transmission. Second, we frame an optimal joint design and control problem minimizing the TCO of the vehicles. Since this problem is nonlinear w.r.t. the motor size and the total mass of the vehicle, but convex if their value is given, we efficiently solve the problem for a range of motor sizes with an algorithm based on second-order conic programming iterating on the vehicle's mass. Finally, we showcase our framework on custom-created driving cycles for both vehicles on hilly and flat scenarios, providing an in-depth analysis of the results and a numerical validation with high-fidelity simulations. Our results show that the characteristics of the area where the vehicles are employed have a significant impact on their optimal design, whilst revealing that regenerative braking and gear-changing capabilities (as in the case of a continuously variable transmission) may not be worth implementing

Time-optimal Control Strategies for Electric Race Cars with Different Transmission Technologies

This paper presents models and optimization methods to rapidly compute the achievable lap time of a race car equipped with a battery electric powertrain. Specifically, we first derive a quasi-convex model of the electric powertrain, including the battery, the electric machine, and two transmission technologies: a single-speed fixed gear and a continuously variable transmission (CVT). Second, assuming an expert driver, we formulate the time-optimal control problem for a given driving path and solve it using an iterative convex optimization algorithm. Finally, we showcase our framework by comparing the performance achievable with a single-speed transmission and a CVT on the Le Mans track. Our results show that a CVT can balance its lower efficiency and higher weight with a higher-efficiency and more aggressive motor operation, and significantly outperform a fixed single-gear transmission

Time-optimal Control Strategies for Electric Race Cars with Different Transmission Technologies

This paper presents models and optimization methods to rapidly compute the achievable lap time of a race car equipped with a battery electric powertrain. Specifically, we first derive a quasi-convex model of the electric powertrain, including the battery, the electric motor, and two transmission technologies: a fixed-gear transmission (FGT) and a continuously variable transmission (CVT) Second, assuming an expert driver, we formulate the time-optimal control problem for a given driving path and solve it using an iterative convex optimization algorithm. Finally, we showcase our framework by comparing the performance achievable with an FGT and a CVT on the Le Mans track. Our results show that a CVT can balance its lower efficiency and higher weight with a higher-efficiency and more aggressive motor operation, and significantly outperform an FGT