In the field of energy storage, lithium-ion batteries, particularly the LiFePO4 battery, have gained prominence due to their high energy density, power density, and lack of memory effect. These attributes make them ideal for applications in electric vehicles and hybrid electric vehicles. However, a significant challenge associated with the LiFePO4 battery, and indeed most commercial lithium-ion batteries, is aging. Aging manifests as capacity fade and increased internal resistance, which complicates battery management system operations. The aging process in a LiFePO4 battery is predominantly attributed to degradation at the negative electrode, while the positive electrode remains relatively stable. This asymmetry necessitates methods to study negative electrode aging without disassembling the full cell. The core of such methods lies in extracting negative electrode characteristics from the external behavior of the full LiFePO4 battery. The first step is to identify a specific State of Charge (SOC) range where the negative electrode’s signature is most pronounced—a region we term the “negative characteristic SOC region.” This article presents a method to determine this region using a fractional-order model and step-current excitation, analyzes its correlation with aging, and validates the approach through experiments.
The commercial LiFePO4 battery comprises two electrodes: a positive and a negative. Their aging rates are generally inconsistent. For the LiFePO4 battery, aging is primarily contributed by the negative electrode. The formation and growth of the Solid Electrolyte Interphase (SEI) layer, which consumes active lithium and electrolyte, occurs mainly at the graphite negative electrode. During cycling, volume changes in the graphite anode cause SEI layer cracks, leading to continuous reaction and further degradation. Therefore, to monitor the health of a LiFePO4 battery online, it is crucial to distinguish the negative electrode’s behavior from the full cell’s voltage response. This involves obtaining a characteristic curve, such as potential versus SOC, that reflects aging information. Identifying the SOC interval where this curve is most evident is the foundational task addressed here.
To model the dynamic behavior of the LiFePO4 battery, we employ a fractional-order approach that captures solid-phase diffusion processes. The terminal voltage \(U\) of a full cell can be expressed as the difference between the positive electrode potential \(U_p\) and the negative electrode potential \(U_n\), plus the voltage drop due to internal impedance:
$$U = U_p – U_n + IZ$$
Here, \(I\) is the current (discharge is negative), and \(Z\) represents the internal impedance. The impedance spectrum of a LiFePO4 battery under small-signal excitation typically shows a high-frequency inductive part, a mid-frequency semicircle related to charge transfer and interfacial processes, and a low-frequency Warburg-like region associated with solid-phase diffusion. For our analysis, we separate the impedance into an ohmic resistance \(R_{ohm}\) and a mid-frequency impedance \(Z_{mid}\). The solid-phase diffusion effects are embedded in the electrode potentials. Thus, at an initial SOC point \(SOC_0\), the voltage response to a current step can be linearized as:
$$U = U_p(SOC_{0p} + SOC_I + SOC_{diffp}) – U_n(SOC_{0n} + SOC_I + SOC_{diffn}) + IR_{ohm} + IZ_{mid}$$
where \(SOC_I\) is the SOC change due to the current, and \(SOC_{diffp}\) and \(SOC_{diffn}\) are the SOC changes due to solid-phase diffusion in the positive and negative electrodes, respectively. For a LiFePO4 battery, the positive electrode potential curve is relatively flat over a wide SOC range, meaning its variation with SOC is minimal. In contrast, the negative electrode potential curve has a steeper slope in certain regions. This difference is key to isolating the negative electrode’s response.
We linearize the potential change \(\Delta U_n\) of the negative electrode at a given \(SOC_0\) when a step discharge current is applied. Assuming small changes, we have:
$$\Delta U_n \approx k_n (SOC_I + SOC_{diffn})$$
where \(k_n\) is the slope of the negative electrode’s open-circuit potential curve at \(SOC_0\). The term \(SOC_{diffn}\) is governed by fractional-order dynamics representing solid-phase diffusion. Based on the fractional-order model, the relationship between \(SOC_{diffn}\) and the current \(I\) is given by:
$$SOC_{diffn} = \frac{1}{Q_n} \cdot \frac{1}{\tau_n^{1/2} s^{1/2} + \frac{12}{95\tau_n}} I$$
where \(Q_n\) is the negative electrode capacity, \(\tau_n\) is the solid-phase diffusion time constant of the negative electrode, and \(s\) is the Laplace variable. A similar expression holds for the positive electrode, but with parameters \(Q_p\) and \(\tau_p\). For the LiFePO4 battery, \(Q_p\) remains almost constant over aging, while \(Q_n\) degrades. The diffusion time constant \(\tau_n\) may increase with aging due to changes in electrode morphology.
The magnitude of \(\Delta U_n\) thus depends on \(k_n\) and \(\tau_n\). A larger \(k_n\) or a larger \(\tau_n\) results in a more significant potential change. By performing step-current tests at various SOC points on a full LiFePO4 battery and analyzing the voltage response, we can infer which SOC regions exhibit dominant negative electrode characteristics. Specifically, we look for regions where \(\Delta U_n\) is substantial while \(\Delta U_p\) is negligible. Through simulation and experiment, we identify the negative characteristic SOC region.
To obtain the model parameters, we conduct three types of experiments. First, half-cell tests using coin cells with LiFePO4 positive and graphite negative materials against lithium metal are performed to obtain the open-circuit potential curves \(U_p(SOC)\) and \(U_n(SOC)\). From these curves, the slopes \(k_p\) and \(k_n\) at different SOC points are derived. Second, a three-electrode LiFePO4 pouch cell with a reference electrode is assembled to perform Electrochemical Impedance Spectroscopy (EIS) tests. This allows separate identification of the positive and negative electrode impedance spectra. The solid-phase diffusion time constants \(\tau_p\) and \(\tau_n\) are extracted from the low-frequency region of the EIS data, using the relationship between impedance and the potential-SOC derivative. Third, aging experiments are conducted on full LiFePO4 cells by subjecting them to repeated charge-discharge cycles at 1C rate, with periodic reference tests at 0.05C to monitor capacity fade and parameter changes.
The table below summarizes typical parameters obtained from a fresh LiFePO4 battery:
| Parameter | Symbol | Value (Fresh Cell) |
|---|---|---|
| Positive Electrode Capacity | \(Q_p\) | 3.9059 Ah |
| Negative Electrode Capacity | \(Q_n\) | 3.6353 Ah |
| Positive Diffusion Time Constant | \(\tau_p\) | 1616 s |
| Negative Diffusion Time Constant | \(\tau_n\) | 253.3 s |
| Ohmic Resistance | \(R_{ohm}\) | ~0.01 Ω |
Using these parameters in a fractional-order model implemented in simulation software, we simulate the step-current response at various SOC points. For a fresh LiFePO4 battery, the results show that at high SOC (e.g., 100%), the positive electrode potential change \(\Delta U_p\) is significant (about 0.05 V under 1C discharge), while \(\Delta U_n\) is very small (about 0.005 V). This indicates a positive-electrode-dominant region. At mid to low SOC (e.g., 30%), \(\Delta U_p\) becomes negligible (less than 0.001 V), whereas \(\Delta U_n\) is appreciable (about 0.02 V), marking a negative-electrode-dominant region. By sweeping SOC from 0% to 100%, we plot the magnitudes of \(\Delta U_p\) and \(\Delta U_n\). The negative characteristic SOC region is defined as where \(\Delta U_n\) is large and \(\Delta U_p\) is small. For the fresh LiFePO4 battery, this region is approximately SOC 10% to 45%.
The simulation findings are validated through three-electrode EIS experiments on a fresh LiFePO4 battery. At SOC 30%, which lies within the identified negative characteristic region, the solid-phase diffusion time constant \(\tau\) extracted from the full-cell EIS data is 746.11 s, while \(\tau_n\) from the negative electrode EIS data is 710.93 s, yielding a small error of 4.7%. This confirms that the full-cell response at this SOC primarily reflects negative electrode dynamics. Conversely, at SOC 100%, which is outside the negative characteristic region, the full-cell \(\tau\) is 1664.5 s, but the negative electrode’s \(\tau_n\) is 253.3 s (error 84.8%), whereas the positive electrode’s \(\tau_p\) is 1616 s (error 2.96%). This demonstrates that at high SOC, the full-cell behavior is dominated by the positive electrode, reinforcing the validity of the negative characteristic SOC region for the LiFePO4 battery.
Aging impacts the negative characteristic SOC region. As the LiFePO4 battery ages, the negative electrode capacity \(Q_n\) decreases, and the available lithium inventory reduces, causing the negative electrode potential curve to shift and scale. The slope \(k_n\) at a given SOC may change. Additionally, the solid-phase diffusion time constant \(\tau_n\) tends to increase due to microstructural changes in the electrode, leading to larger potential changes under step excitation. We perform aging simulations by adjusting model parameters based on experimental data from aged LiFePO4 cells. For a cell aged to 80% of its initial capacity, the negative characteristic region shifts and expands. The fresh cell’s region (10%-45%) expands to approximately 0%-55% after aging. The intersection of these regions, i.e., 10%-45%, remains consistent and can be considered the robust negative characteristic SOC region that persists throughout the battery’s lifecycle for this LiFePO4 battery type.
Experimental validation on an aged LiFePO4 battery supports this. At SOC 30%, the full-cell EIS gives \(\tau = 1258.23\) s, and the negative electrode EIS gives \(\tau_n = 1184.12\) s (error 5.9%). Compared to the fresh cell, \(\tau_n\) has increased, aligning with the aging effect. At SOC 100%, the error between full-cell and negative electrode \(\tau\) remains large (82.9%), confirming that the negative characteristic region is still identifiable in aged LiFePO4 batteries.
The determination of the negative characteristic SOC region has practical implications for online health monitoring of LiFePO4 batteries. By focusing on this region, battery management systems can extract negative electrode-specific parameters, such as diffusion time constants or capacity estimates, from non-invasive full-cell tests. This enables tracking of negative electrode degradation, which is the primary aging mechanism in LiFePO4 batteries. Future work could explore the precise relationship between parameters like \(\tau_n\) and capacity fade, and develop algorithms for real-time estimation.
In conclusion, we have presented a method to determine the negative electrode characteristic SOC region for LiFePO4 batteries. The approach combines a fractional-order model, linearized potential change analysis, and step-current excitation tests. For the studied LiFePO4 battery, the region is identified as SOC 10% to 45%, where the negative electrode dynamics dominate the full-cell response. This region remains observable even after aging, making it a reliable target for extracting negative electrode aging information. The method is validated through three-electrode experiments, underscoring its potential for enhancing battery management systems for LiFePO4 batteries in electric vehicles and other applications.