*3.2. Step 2: Impact Analysis of Real-World Charge/Discharge Cycles on Battery Model Parameter*

Voltage, current, and temperature are the real-world charge/discharge data types collected from the battery. Data in the time-series comes directly from the BMS. Direct connection with the BMS, plug-and-play devices, or cloud servers are some of the data interaction methods. Although the data interaction method is not standardized, cloud services have been integrated with onboard-BMS in the past (Table 1) for seamless data exchange. Initial investment and time for implementation have made real-work data interactions and control of battery systems challenging.

The simulated experimental inputs used for model parameterization (as described in Section 3.1) in contrast with real-world charge/discharge cycles do not have the same effect on battery model parameters. While driving procedures such as WLTP or USSD are used to validate the accuracy of model parameter identification, after prolonged use of the battery, the battery model parameters do not always mimic the actual state of the battery. Hence, with continued usages, the state estimation results of the battery model go farther and farther away from the actual battery state. The effect of prolonged realworld charge/discharge cycle on the battery behavior and the changes that it causes in the inherent characteristics are experimented and researched by academics [53]. However, these effects are not transparent or readily available.

For the impact analysis, first, the governing equations of both DFN model and ECM model are obtained (Tables A1 and A2). Based on these, the list of parameters of both models is summarized in Table 2. For a battery DT, it is essential to identify the parameters that undergo drastic change due to a long period of usage. Hence, step 2 of the approach is to understand the impact of charge/discharge cycles on battery model parameters. The argumentations provided in this section are based on Uddin et al.'s work [48], which applies non-destructive experimental techniques to quantify the detailed degradation associated with different aging stress factors. Model parameter estimation was done using a non-linear fitting algorithm i.e., minimizing the square of the error between simulated and measured voltage. The authors assert that since model parameters are connected to intrinsic properties of the battery, the evolution of these parameters will highlight physical changes within the battery. Thus, by tracking the evolution of model parameters, it will be possible to deduce the mechanisms by which the battery has degraded over time.

Factors that are known to cause degradation effects on Li-ion batteries are: calendar age (tage), cycle number (N), temperature, SOC, DOD, cycle bandwidth (ΔSOC), charge voltage, C-rate, cycle frequency. Expected parameter changes reviewed in the reference paper and further published literature is depicted in Table 2. Knowing the factors that affect the battery life during cycling is essential to design a DT model that evolves along with the degradation of the actual battery. Hence, the model parameters which are directly and most largely affected by the cycling of the battery system are identified.

For reduced-order modeling of DFN model, no particular consensus exists on which parameter needs to be estimated. Some of the parameters are considered while keeping the others at a nominal value. A systematic approach for selecting which parameters can be reliably estimated is presented in [54] in the form of parameter sensitivity analysis. The parameter sensitivity analysis determines how sensitive is the output of the model with respect to variation in values of parameters. Rather than looking into the sensitivity of the model output with variations in values of the parameters, in the following Table 2, we look into the sensitivity of model parameters with respect to cycling data. Table 2 mainly elaborates the effect of high cycle number and charging current (C-rate) on the parameters of the DFN model and the ECM—based on the referenced literature. High cycle number is a primary factor for cyclic aging, and high C-rate directly impacts the cell temperature, which in turn influences battery degradation. Hence, only these two stress factors are considered and not all the mentioned battery degradation factors because the experimental and quantitative sensitivity analysis for each model parameter will be too large to handle in this paper. With the outlook for battery DTs, understanding the sensitivity of model parameters to the environmental conditions and usage practices is

a requisite. This implies experimental or simulative confirmation of effect of prolonged cycling on model parameters.

**Table 2.** Impact analysis of model parameters vs. battery degradation factors based on [48,54,55]. Legend for the table: **x**—impact identified in the reference article, but the impact level is not specified; **C**—Constants; **Text**—impact level identified by the reference article; **Blank (-)**—No direct information found on the sensitivity or dependency for this parameter.


<sup>1</sup> n = Negative electrode; p = Positive electrode; se = Separator; s = Solid phase; e = liquid phase.

A natural question here is that after continued usage of the battery, shouldn't all the parameters change. Not all the coefficients are majorly altered, and the constants do not change. Also, based on the usage practice, only a particular subset of parameters may undergo significant changes, such as the performance parameters or the structural parameters.

Knowledge of the impact of cyclic aging on model parameters helps in model reduction, intermediate battery state estimation at different stages of battery lifecycle, and control algorithms for the BMS. Additionally, it helps the battery designers evaluate how the cell degrades for various applications in different working conditions because the model is up-to-date with the real system in battery DTs. Thus, supporting product optimization for designers and product state estimation during battery usage and end of life.
