The lithium-ion battery is a new energy storage device widely employed in various fields such as mobile power, electric vehicles, unmanned aerial vehicles, and spacecrafts due to its high energy, high efficiency, lightweight, and environmental friendliness. Understanding the internal mechanism of the battery is of utmost importance. The electrochemical model provides detailed insights into the internal mechanism of lithium batteries and encompasses the single-particle model and the P2D model, as well as enhancements such as thermal coupling, mechanical stress coupling, and electric double-layer capacitive coupling. However, the dispersion effect of capacitors in solid electrolyte interface (SEI) film capacitors and porous electrodes has been basically ignored, which is essential for analyzing the internal mechanism and managing energy conversion in lithium batteries experiencing short-term effects. Furthermore, the determination of the dominant order of the Faraday process and non-Faraday process within a short time period is essential for accurately predicting the lifespan of lithium batteries subjected to high-frequency periodic excitation and assessing performance degradation. While the frequency range of these two processes can be roughly delineated through electrochemical impedance spectroscopy (EIS), the precise transition time of their dominant positions remains uncertain. In a research article recently published in Space: Science & Technology, researchers from National Active Distribution Network Technology Research Center (NANTEC), Beijing Jiaotong University established for the first time a P2D-coupled non-ideal double-layer capacitor (P2D-CNIC) model which can be used for mechanism analysis under high-frequency periodic signal excitation, taken the generally neglected electric double-layer capacitance and its dispersion effects into consideration.
First, the construction of the P2D-CNIC model is presented, which encompasses P2D model, thermal model, and electric double-layer capacitance model.
Figure 1 demonstrates a schematic diagram of the P2D model. The mathematical expression of the P2D model is generally composed of five nonlinear partial differential algebraic equations (PDAEs), which can be divided into three parts: mass conservation, charge conservation, and electrochemical reaction. Mass conservation comprises two processes: dispersion in the solid phase of the electrode’s active material and concentration distribution in the solution phase of the electrolyte. In solid, active material can be described by Fick’s law in r direction. The solution phase concentration in the electrolyte is given by mass balance. Charge balance depicts the potential distribution of solid and solution phases, where the variation of the solid electrode potential can be expressed by Ohm’s law and the spatiotemporal dynamics of the electrolyte potential is defined concerning the molar flux. In electrochemical reaction, the Butler–Volmer kinetics provides the relationship between the intercalation overpotential, η, and the molar flux, jLi(x,t).
In the thermal model, the energy balance equation is written as ρCp∂T/∂t = ∂(k·∂T/∂x)/∂x + Qirr + Qr + q0. The temperature of the battery calculated according to the thermal model mainly affects the electrochemical reaction rate constant, solid-phase dispersion coefficient, and electrolyte parameters, and the higher the temperature, the greater the impact. This relationship is described by the Arrhenius rate law equation.
In the electric double-layer capacitance model, the current density at the solid/liquid interface includes the non-faradaic current in addition to the faradaic current generated by the electrochemical reaction, as shown in Fig. 2. The non-faradaic current comes from the transient change of charging and discharging of the electric double-layer capacitor. In addition, the dispersion effect of capacitance has a great influence, and the capacitance is non-ideal, thus jCap(x,t) = as ∂((Φs – Φe – (jLi + jCap)Rfilm)Cap·ων–1)/∂t where the angular frequency ω = 2πf and f is the frequency of the applied periodic excitation signal.
Then, experiment and model validation are conducted. The subject of this experiment is a pouch cell, with NMC532 and graphite as cathode and anode material, respectively. The electrolyte used is EC:DMC (1:1, w/w), where EC is ethylene carbonate and DMC is dimethyl carbonate. The thickness of the battery is 10.8 mm, the length is 309 mm, and the width is 102 mm. The rate capacity of designed battery at 1 C was 37 Ah. The experimental platform achieves pulse discharge conditions of different frequencies by controlling the on and off time of metal-oxide-semiconductor field-effect transistor (MOSFET). Results are compared among the traditional P2D model, P2D-CIC model, and the proposed P2D-CNIC model. Results (Fig. 3) show that under the influence of the dispersion effect of the electric double-layer capacitance, the voltage response of the electrochemical model exhibits not only variations in value but also important phase changes that should not be overlooked; these differences in both amplitude and phase become more pronounced as the dispersion effect coefficient increases. Capsei also has an undeniable effect on the voltage response of the model in terms of amplitude and phase, and this effect increases with the increase of dispersion effect coefficient. Its impact on battery heat generation cannot be ignored, and this impact will also increase with the increase of dispersion effect coefficient. The traditional P2D model, the P2D-CIC model, and the proposed P2D-CNIC model were compared and analyzed under periodic high-rate pulse discharge conditions (see Fig. 4). It was observed that the voltage response of the traditional P2D model failed to accurately match the actual behavior, lacking a buffering stage during voltage changes. On the other hand, the traditional P2D-CIC model exhibited excessive buffering effect, resulting in higher voltage amplitudes compared to the actual scenario. In contrast, the proposed P2D-CNIC model presented in this paper aligns well with the actual voltage changes. Moreover, three models exhibit important differences in heating. This difference is crucial for analyzing the heating in lithium batteries under the influence of high-frequency periodic signals.
Last, dominant sequence analysis of Faraday processes and non-Faraday processes is presented. Authors applied a half cycle angular frequency of 200π(rad/s) and amplitude of 0.5, 1, 1.5, and 2 C charging and discharging current excitation to the model at 50% SOC, and observed the dominant order of the mid-Faraday process and the non-Faraday process during the charging and discharging processes. Results (in Fig. 5 for cathode and Fig. 6 for anode) show that under short-period signal excitation, the initial dominance is observed by the non-faradaic process of the electrode, which then gradually transitions to the Faraday process. In contrast to the cathode, the anode exhibits a more intricate evolution process divided into three stages. The first stage involves the non-faradaic process of the electric double-layer capacitance of the SEI film. The second stage encompasses the non-faradaic process of the electric double-layer capacitance of the electrode particles, while the third stage entails the faradaic process of the electrode particles.
In conclusion, building upon the verification of the model’s correctness and reliability, this paper focuses on examining the dominant order of the Faraday process and the non-Faraday process of the electrode during high-frequency excitation. The dominant time scales of the behavior of different mechanisms can be clearly observed by the current composition. Such analysis offers valuable insights into the feasibility of studying battery aging and damage under high-frequency periodic excitation, and lays the foundation of long battery life and reliable aerospace batteries.
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