Model construction and dominant mechanism analysis of li-ion batteries under periodic excitation

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, j_Li(x,t).

In the thermal model, the energy balance equation is written as ρC_p∂T/∂t = ∂(k·∂T/∂x)/∂x + Q_irr + Q_r + 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 j_Cap(x,t) = a_s ∂((Φ_s – Φ_e – (j_Li + j_Cap)R_film)Cap·ω^ν–1)/∂t where the angular frequency ω = 2πf and f is the frequency of the applied periodic excitation signal.

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.