Physics-Based Computationally Efficient Battery Degradation Model and Electric Machine Scaling Strategy for Hybrid Electric Vehicle Design Optimization

Xing Jin, Purdue University


The Hybrid Electric Vehicle (HEV) powertrain design and control optimization is of great importance to maximize the fuel benefits of hybridization for any given application. Component life, sizing, and cost are intimately coupled with each other and critical for system-level optimization. For greater confidence in system-level optimization results, it is desirable to incorporate high-fidelity physically-based component models, especially for the key components: battery and electric machine. However, with higher fidelity and accuracy, comes greater computational cost. The focus of this effort is the development of battery and electric machine models that have the accuracy and computational complexity consistent with model-based control algorithm design and optimization-based powertrain sizing. The novel aspects are: 1) a high-fidelity yet computationally-efficient simplified battery degradation model is developed for use in system-level studies to capture the battery degradation effect; 2) a physically-based electric machine scaling strategy is derived to show how the speed, torque, and efficiency of an electric machine change with geometry scaling factors. Within electrified vehicle powertrains, battery performance degrades with aging and usage, resulting in a loss in both energy and power capacity. As a result, models used for system design and control algorithm development would ideally capture the impact of those efforts on battery capacity degradation, be computationally efficient, and simple enough to be used for algorithm development. This effort provides an assessment of the state-of-the-art in battery degradation models, including accuracy, computational complexity, and amenability to control algorithm development. Three degradation models, a pseudo two-dimensional (2-D) electrochemical model (AutoLion ST, or ALST), a semi-empirical model (from the National Renewable Energy Laboratory) and an empirical model (published in the literature), are compared against four published experimental data sets for a 2.3-Ah commercial graphite/LiFePO4 cell. Based on simulation results and comparisons to experimental data, the key differences in the aging factors captured by each of the models are summarized. The results show that the physically-based model is best able to capture results across all four representative data sets with an error less than 10%, but is 24x slower than the empirical model, and 4000x slower than the semi-empirical model, making it unsuitable for powertrain system design and model-based algorithm development. Despite being computationally efficient, the semi-empirical and empirical models, when used under conditions that lie outside the calibration data set, exhibit up to 71% error in capacity loss prediction. Such models require expensive experimental data collection to recalibrate for every new application. These findings clearly point out that there exists a need for a physically-based model that generalizes well across operating conditions, is computationally efficient for model-based design, and simple enough for control algorithm development. To fill the gap in the existing battery degradation models, a physically-based reduced-order capacity-loss model is derived based upon the salient physical loss mechanisms to improve computational efficiency without sacrificing model fidelity. The model differs from computationally efficient semi-empirical and empirical models as it results from the analytic solution of widely accepted constitutive laws, includes no ad-hoc terms, and can predict degradation accurately across a wide range of operating conditions. More complex electrochemical models couple these same constitutive laws with Li-ion transport PDEs, and as such, capacity loss prediction using those models is computationally expensive. Unlike the electrochemical models, the reduced-order degradation model only requires lumped input information (current vs time and SOC vs time) to predict the capacity loss. Two primary degradation mechanisms that occur in the graphite anode of a typical lithium ion cell are captured in this model: a) capacity loss due to Solid Electrolyte Interface (SEI) layer growth, and b) capacity loss due to isolation of active material. The model matches experimental capacity degradation results within a maximum 20% error. Moreover, the reported model is 2400 times faster than currently existing more complex physically-based electrochemical models that are only slightly more accurate (in some cases). In most system-level vehicle optimization studies, the electrical machine dimensioning is performed simply by linear scaling of the base design. This approximation neglects the key physical phenomena and does not consider the complexity of the electromagnetic fields in the electric machine. To address the problem of oversimplification, a physical two-dimensional (2D) field analysis model is proposed to capture the electromagnetic phenomena and main features of electric machine design. This enables both physical scaling and changes of design parameters that ultimately shape the efficiency map. The fields in the x-y plane are decoupled from those in the z-direction by introducing two independent geometry scaling factors, one in the radial direction and the other in the axial direction. Apart from the geometry scaling factors, there are two scaling factors: speed range scaling factor, and number-of-turns scaling factor. (Abstract shortened by ProQuest.)




Wasynczuk, Purdue University.

Subject Area

Engineering|Electrical engineering|Mechanical engineering

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