Electrochemical characterization tools for lithium-ion batteries

Abstract

Lithium-ion batteries are electrochemical energy storage devices that have enabled the electrification of transportation systems and large-scale grid energy storage. During their operational life cycle, batteries inevitably undergo aging, resulting in a gradual decline in their performance. In this paper, we equip readers with the tools to compute system-level performance metrics across the lifespan of a battery cell. These metrics are extracted from standardized reference performance tests, also known as diagnostic tests, conducted periodically during battery aging experiments. We analyze the diagnostic tests from a publicly available dataset (Pozzato et al. in Data Brief 41:107995, 2022) that consists of the capacity test, high pulse power characterization test, and electrochemical impedance spectroscopy. We provide detailed calculation methodologies and MATLAB^® scripts required to extract capacity, energy, state-of-charge, state-of-energy, open-circuit voltage, internal resistance, power, incremental capacity, and differential voltage. The MATLAB^® scripts developed to generate the plots in this paper have been made accessible to the public (Ha et al. in Mendeley Data, V3, 2023). The primary objective of this paper is to provide an accessible guide for undergraduate and graduate students, educators, and researchers interested in characterizing the performance and health metrics of batteries. Such characterizations are critical to the development of battery aging models that can be used to improve cycle life estimation and advance battery management system algorithms.

Appendices

Appendix 1. C-rate definition

C-rate is the rate at which the battery is discharged or charged relative to its nominal capacity $Q_n$. The equation is given as

$$\begin{aligned} \text {C-rate} = \frac{|I|}{Q_n} \end{aligned}$$

(18)

where $|I|$ is the absolute value of the current applied to the battery in ampere ($\textrm{A}$) and the units of C-rate are in $\frac{\textrm{A}}{\textrm{Ah}}=\frac{1}{\textrm{h}}$. The absolute value of the current is used since C-rate is a positive value regardless of whether the battery is charged or discharged. As an example, the C-rate is calculated and written at different currents for a battery with $Q_n=$ 10 Ah:

$$\begin{aligned} \begin{aligned} \text {C-rate}&= \frac{|I|}{Q_n} = \frac{5[\text {A}]}{10[\text {Ah}]}=\frac{1}{2}\left[ \frac{1}{\text {h}}\right]\\& \rightarrow \text {C/2 (2 h to charge or discharge)} \\ \text {C-rate}&= \frac{|I|}{Q_n} = \frac{10[\text {A}]}{10[\text {Ah}]}=\frac{1}{1}\left[ \frac{1}{\text {h}}\right] \\&\rightarrow 1\text {C (1 h to charge or discharge)} \\ \text {C-rate}&= \frac{|I|}{Q_n} = \frac{20[\text {A}]}{10[\text {Ah}]}=\frac{2}{1}\left[ \frac{1}{\text {h}}\right]\\& \rightarrow 2\text {C (30 min to charge or discharge)} \end{aligned} \end{aligned}$$

(19)

Therefore, the inverse of the C-rate is number of hours it takes to discharge or charge the battery.

Appendix 2. Designing cycling experiments

Battery aging is affected by cell temperature, rate of charge and discharge, and depth-of-discharge (DOD)¹⁸ [57, 58]. In real-world applications, such as in EVs, eVTOL aircrafts, and grid energy storage systems, the battery experiences different discharging profiles that are specific to the application condition. For instance, the urban dynamometer driving schedule (UDDS) profile can be used to replicate the average driving profile in city conditions, characterized by deceleration and acceleration events [59]. In an eVTOL aircraft, the battery experiences constant loads during cruise and high-power loads during takeoff and landing [60]. In grid energy storage systems, batteries are subject to dispatch duty cycles in the form of power profiles [61].

In the dataset used in this paper [1], the aging test campaign was conducted on ten¹⁹ INR21700-M50T cylindrical cells with NMC811 cathode and Si-Gr anode (Table 1). The cells were subjected to repeated instances of the experimental Cycle, a constant current (CC)-constant voltage (CV) charging protocol, and UDDS discharge driving profile used to replicate EV real-driving scenarios. The total number of repeated Cycle instances at every diagnostic test is specified in Table 3, as well as the charging C-rate used for each cell.

Table 2 shows the six steps involved in the Cycle. Step 1 consists of a CC charge at the C-rate of C/4, C/2, 1C, or 3C, which is specified in the second column of Table 3. We vary the charging C-rate to study how charging speed affects battery degradation. Once 4 V is reached, Step 2 begins wherein the battery is under CV charge at 4 V until the current goes below 50 mA. Step 3 performs another CC charge at C/4 until the upper cutoff voltage of 4.2 V is reached. In Step 4, the battery is CV charged until the current goes below 50 mA and then rested for 30 min. Steps 1–4 exemplify a standard CC-CV charging protocol to charge lithium-ion batteries to 100% SOC. In Step 5, the battery is CC discharged from 100 to 80% SOC at C/4. Step 6 discharges the battery from 80 to 20% SOC using a series of concatenated UDDS profiles. The 80 to 20% SOC in Step 6 represents a typical driving SOC range in that most users will not always charge to 100% SOC before driving and will charge the vehicle well before 0% SOC is reached. Once Step 6 is completed, Step 1 will start again to repeat the Cycle until the desired number of cycles is reached. Figure 26 shows a visual representation of the cycling profile described in Table 2.

Table 1 Technical specifications INR21700-M50T cells [23]

Fig. 26

The experimental Cycle used in the aging campaign [1]. Positive current is for discharging, and negative current is for charging. Steps 1–4 correspond to a CC-CV charging protocol, and Steps 5–6 discharge the battery with a CC discharge followed by a series of concatenated UDDS profiles. Table 2 describes the steps in detail. Once Step 6 is completed, the Cycle resumes to Step 1 to repeat the steps. The number of Cycles associated with each diagnostic test is defined in Table 3

Table 2 Description of the experimental Cycle [1]

Table 3 Cells label, test charging condition, temperature, and diagnostic test number. For each diagnostic test, the number of cycles experienced by the cell is reported. All cells are tested at 23 $^\circ \textrm{C}$

Appendix 3. Ampere-hour throughput definition

The ampere-hour throughput ($\textrm{Ah}_{throughput}$) measures the total current passed through the battery in both charging and discharging. It is calculated as

$$\begin{aligned} \textrm{Ah}_{throughput}(t) = \underbrace{\frac{1}{3600} \overbrace{\int _{t_0}^{t}|I(\tau )|\,d\tau }^{\text {A} \cdot \textrm{s}}}_{\textrm{Ah}} \end{aligned}$$

(20)

where $|I|$ is the absolute value of the current applied to the battery in ampere ($\textrm{A}$) and Ah$_{throughput}(t)$ is the ampere-hour throughput in $\textrm{Ah}$ calculated from an initial time instant $t_0$ to a certain point in time $t$. Although cycle number is commonly used to track the number of times the battery has been cycled, a cycle does not contain information on the amount of current passed through the battery for a given cycle. In contrast, $\textrm{Ah}_{throughput}$ allows quantification of the amount of charge passed in and out of the battery and provides a more generalizable metric than cycle number. Figure 27 shows the discharged capacity $Q_{dis}$ as a function of cycle number and Ah$_{throughput}$ for all ten cells. As expected, the $Q_{dis}$ aging trajectory of a cell exhibits similar trends when plotted against cycle number and Ah$_{throughput}$.

Fig. 27

Discharged capacity $Q_{dis}$ as a function of a cycle number and b Ah$_{throughput}$ for all ten cells