Online Spatiotemporal Modeling of Battery Thermal Process


Student thesis: Doctoral Thesis

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Awarding Institution
Award date3 Sep 2019


Various Li-ion batteries have been identified as the power sources of pure electric vehicles (EVs) and hybrid elective vehicles (HEVs), for their high theoretical energy densities and tolerance to cycling. The temperature effect is a key factor which limits the ability of a Li-ion battery. When they are charged or discharged, Li-ion batteries will generate heat. On the contrary, the generated heat will affect the Li-ion batteries from various aspects such as performance, life, capacity, and safety. Thus, accurate modeling of the thermal process will be beneficial to optimizing, monitoring, and controlling a battery system.

The thermal process of a Li-ion battery is described by partial differential equations (PDEs) mathematically. It is difficult to model because of its infinite-dimensional spatiotemporal nature, complex nonlinearities, and parameter uncertainties. During the last decades, numerous methods have been proposed for modeling of PDEs. However, most methods put their emphasis on offline modeling while little effort has been devoted to online prediction. In fact, an online model would be more effective in a practical case, where the process is time-varying. In view of this, we will focus on developing online analytical models for performance prediction of a battery system. The main effort will be devoted to data-driven methods due to the fact that they do not require the exact form of the PDEs to be known and can be used in a more general case. However, it seems not easy to construct an online analytical model of the thermal process. Main difficulties lie in the following aspects:

1. How to sample the data of the temperature efficiently and accurately? For data-driven methods, some sensors are necessary for data sampling. However, it is difficult to allocate too many sensors on the surface of a battery or in a battery management system (BMS).

2. How to adjust the influence of different data and catch the recent dynamics? In practice, a BMS is always working under the boundary cooling. The unknown heat exchange would make the boundary conditions of the PDEs time-varying. In this case, the influence of the data collected at different instants would be different. The out-of-date data could not reflect the current properties of the process. Considering all data equally would have a negative impact on the modeling accuracy.

3. How to further improve the efficiency of updating the nominal model? For online modeling, a nominal model is first constructed offline. Afterward, it is updated online. Traditional methods update the model from scratch when new data is coming. However, it would be extremely time-consuming when the data size increases.

4. How to improve the efficiency of modeling the thermal process with two spatial dimensions? In the real world, the thermal processes of many types of batteries have two spatial dimensions. When modeling these thermal processes, traditional methods consider two spatial dimensions as a whole without separation. However, evaluating the correlation function, which is critical to time/space separation, would be difficult and time-consuming.

It is still an open question for online estimation of the thermal process of a battery. The main objective of this thesis is to develop online modeling methods for the thermal process of Li-ion batteries. The estimated distributions can be used for controlling, health monitoring, and designing purposes.

1. In order to address the first issue, a physical model is calibrated for data sampling. Without the utilization of real sensors, the proposed method could be added to a BMS more easily. The error between the output voltage of the model and that of the battery can be used to evaluate the time-varying parameters. By using a direct search method to minimize the error, we can calibrate these parameters.

2. In order to address the second issue, a sliding window based Karhunen-Loeve (KL) modeling method is proposed. A sliding window is designed to capture the most important information from newly coming data while ignore the old data that is outside of the window. The traditional KL method can be applied inside the window to construct a feasible analytical process model with high efficiency. A forgetting factor is also used to produce a more general window where the influence of all data can be adjusted.

3. In order to address the third issue, a spatial correlation based incremental KL is designed. First, the incremental learning technique is developed to update the dominant spatial basis functions (DSBFs) of the nominal model, which is constructed by KL method. Then, a forgetting factor is incorporated into the incremental learning technique to handle time-varying dynamics. By using the incremental technique, the efficiency of KL can be improved significantly.

4. In order to address the fourth issue, a two-phase separation based KL is proposed. First, one spatial dimension is separated from the process by a set of DSBFs. Then, the other spatial dimension and the time dimension are separated by another set of dominant DSBFs. By separating the spatial dimensions, the proposed method is more effective and efficient than the traditional KL.

Systemic simulations and experiments have been conducted to validate the effectiveness and efficiency of all proposed methods. Additionally, their merits have also been demonstrated in the comparison studies. The proposed models are effective and efficient. Thus, they can be used for online applications easily.