Applications of Mathematical Models for Lithium-Ion Battery Management Systems

Abstract

Lithium-ion batteries (LIBs) are the most widely used electrochemical storage technology in contemporary electrified vehicles (such as electric vehicles (EVs)), portable consumer products, and renewable energy generation applications. While industries pertaining to LIB manufacturing are now mature, LIB also benefits from enhanced performance in terms of high energy (~300-500 WhrL-1 depending on the battery cell geometry) and power densities, long cycling life (> 1000 cycles), low memory effects, and low discharge rates. The battery cells of LIBs are commercially available in various form factors, including cylindrical, pouch, and prismatic form factors. In the above-mentioned applications, these battery cells are electrically connected in series and parallel combinations to output the desired energy and power requirements. This battery pack in term is connected to the battery management system (BMS) which serves various purposes, including (1) sensing for voltage, current, and temperature, (2) protection against extreme conditions such as excessive currents, under and high voltage limits, etc., (3) interface with the user on useful information such as charge control and range estimation and (4) Battery state estimation for performance management and diagnostics. In this thesis, research works for range estimations, early fault detection, and battery state estimations have been included. Accurate range estimates for EVs are deemed an attractive alternative to conventional internal combustion engines due to their low carbon footprint, low running cost, and higher energy efficiency. However, currently, they suffer from a lower range than conventional vehicles, which induces range anxiety for consumers. First, the EV parameters that strongly impact its range are determined using data-driven techniques. A detailed dataset of commercial EV models manufactured from 2008 to 2021 was collected through web mining. A strong correlation between battery capacity, top speed, curb weight, and acceleration with range was observed. Furthermore, machine learning algorithms were trained and tested on this dataset, with the lowest root-mean-squared error of 19.5 miles. Additionally, a simple linear relationship between the EV range and EV model, battery, and performance parameters was determined to be convenient for EV consumers. Second, the EV system-level vehicle dynamics model and a physics-based battery cell model were utilized to estimate the range for specific vehicles on custom user-specific drive cycles. For this purpose, two types of commercially available battery cells that are utilized in various EV models were selected. While most of the battery cell’s electrochemical parameters from prior literature were used, some of these parameters were estimated using a genetic algorithm (GA). Meanwhile, the vehicle dynamics model was used to determine the battery pack energy and current requirements for various EV models. The drive cycles used in the mentioned model were the highway fuel economy test cycle (HWFET) and urban dynamometer driving schedule (UDDS). These requirements were then inputted into the battery cell models for range estimation. The estimated range was compared to the ranges disclosed by the United States Environmental Protection Agency (EPA). The BMS utilizes the sensor readings from the current, voltage, and temperature readings to estimate the battery diagnostics and ensure user safety. Under extreme conditions, LIBs can undergo thermal runaway leading to battery pack fires and explosions, severely jeopardizing user safety. Hence, early fault detection of an EV battery pack can be a critical asset for EV user safety and battery pack longevity. In this work, an autoencoder was trained and applied to a real-world dataset consisting of 100 EVs. Furthermore, the voltage and temperature time series were compared as input for the fault detection. Temperature-based autoencoder was successfully able to detect a faulty battery pack from normal functioning ones in EVs. Lastly, a process flow of battery pack fault detection, with autoencoder, for large-scale EV applications is discussed. Finally, the last set of research works concerns the state estimations, specifically the state-of-charge (SOC), of LIB. The complex and non-linear electrochemical behavior of the LIBs poses a significant academic and commercial challenge for its state estimations. While cell-level simpler equivalent circuit models (ECM) are commonly used by battery management systems (BMS) hardware, continuum-scale electrochemical models (EM) are attractive due to their higher accuracy, higher fidelity, and ease of integration with thermal and degradation models. However, compared to ECMs, EMs can have higher solution times and their numerical schemes require more extensive mathematical and computational expertise. Various reduced-order EM battery models, specifically the single particle model (SPM), enhanced single particle model (ESPM), reduced order pseudo-two-dimensional (P2D), and their computationally efficient numerical schemes have been proposed in the literature. The computational performance of some of these battery models and solvers has been compared under different programming languages (Python and C++) and computational hardware specifications (hardware specifications representative of embedded, personal computing, and cloud systems). C++ programming language displayed at least a 10-fold reduction in solver and battery model solution times with the exact figure dependent on the cycling steps. Meanwhile, the embedded systems were able to perform the simulations using reduced-order battery solvers and battery models even with the slower-performing Python programming language, making them a reasonable candidate for embedded systems.