Modeling and Parameter Extraction of Batteries


Student thesis: Doctoral Thesis

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Award date14 Apr 2022


Electrochemical batteries have been widely used in many applications, for instance, IoT devices and electric vehicles. They play a vital role in smart city development and the fourth industrial revolution for storing energy and buffering difference in local energy generation and demand. Continuous monitoring of battery performance and condition is thus essential. Battery models are often used to mimic battery characteristics and conditions with measured quantities, including battery voltage, battery current, and temperature. Among various approaches, impedance-based electrical models such as parallel resistor-capacitor (RC) models are widely adopted. Various condition monitoring techniques based on sampled battery voltage and current information have been proposed to extract the intrinsic parameters of batteries. Battery condition and performance are predicted by analyzing the variations of the extracted parameters.

This thesis presents the findings of the research on battery modeling and parameter extraction techniques for both lead-acid and lithium batteries. For the sake of implementation, high-order RC model is applied for modeling lead-acid batteries while a new constant phase element (CPE) model is proposed for modeling lithium batteries characteristics.

A battery testing device comprised with a bidirectional dc-dc converter has been built for extracting the intrinsic parameters of eight different types of 12 V lead–acid battery. This battery testing device presents the use of an energy recycling technique by controlling the power flow between battery and a supercapacitor. The sampled battery voltage and current information over the charging and discharging periods are used to estimate the parameters of a high-order electrical battery model. The estimated parameters have been favorably verified with theoretical predictions, results obtained by extended Kalman filter method, and results obtained from a calibrated commercial battery testing system. Results reveal that batteries testing incorporated with both charging and discharging processes give a more accurate battery performance prediction.

A computational model for simulating the time-domain response of lithium batteries under arbitrary charging and discharging profiles will also be presented. The proposed model contains multiple series-connected CPEs with parallel charge transfer resistance to better describe the electrical property of double-layer capacitances between the electrode and electrolyte in lithium batteries. The methodology is based on first formulating a mathematical model that describes the time-domain voltage-current characteristics of a CPE, and then using multiple series-connected CPEs, as well as charge transfer resistances, output resistances, and inductances, to form the computational model. The criteria for ensuring the numerical stability of the proposed model have also been derived. The validity of the computational model has been confirmed by comparing the simulation results of a model consisting of three series-connected CPEs with the measurement results of six SANYO 18650, 3300mAh, 3.7V rechargeable Li-ion batteries under controlled charging and discharging profiles. Experimental results reveal that the accuracy of the computational model is higher than the models using different orders of RC units, which are widely adopted for characterizing lead-acid batteries.

In addition, a new perspective of using electrode charge transfer resistances (e-CTRs) as indicators of the state-of-health (SOH) of lithium batteries has been formulated. Repeated observations show that one of the e-CTRs can increase by more than 900% over hundreds of charge cycles. Such change is more distinctive than the conventional way of observing the variation of the internal ohmic resistance to predict SOH. An alternative definition of the SOH based on e-CTR has been proposed. Accordingly, a parameter extraction algorithm that allows arbitrary battery charging or discharging profiles has been formulated to determine the e-CTRs. It is based on developing an electrical model consisting of an internal ohmic resistance and multiple CPEs, with each one having a parallel CTR. Then, the time-domain battery voltage-current characteristics are obtained by using fractional calculus to solve the Mittag-Leffler functions for characterizing the CPEs. Finally, all parameters in the model are extracted by applying the nonlinear least squares method. The validity of the electrical model and the parameter extraction method is verified by comparing the prediction results with the measurement results, of six 18650 3.7V rechargeable Li-ion batteries with 3300mAh, obtained by electrochemical impedance spectroscopy, which is a widely adopted technique for characterizing electrochemical batteries.

Throughout the research, the effect of current patterns in parameter extraction and a new effective state-of-health (SOH) indicator – Rct have been proven and evaluated. These lay a solid foundation to enable other scientific investigations into the properties of Li-ion batteries and new battery condition testing technologies.