## 4 Results and Discussion
### Analysis of the Use of the Peukert and Liebenow Equations for Lithium-Ion Cells
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Manufacturer and Model** & \(\mathbf{C_{n}\) **(Ah)1** & \(A\) & \(n\) & \(\delta^{2}\)**(\%)** \\ \hline \multicolumn{6}{c}{Equation (1)} \\ \hline TrustFire IMR16340 & 0.65 & 634.76 & 4.00 & 7.20 \\ Aucooma IMR18650 & 2.8 & 1.07*10\({}^{7}\) & 4.52 & 4.77 \\ Keeppower IMR26650 & 4.2 & 1.56*10\({}^{7}\) & 4.46 & 5.48 \\ Samsung INR18650-13Q & 1.3 & 8.88*10\({}^{6}\) & 5.28 & 6.72 \\ Sony US18650 VT3 & 1.5 & 4.64*10\({}^{8}\) & 5.80 & 5.70 \\ \hline \multicolumn{6}{c}{Equation (2)} \\ \hline TrustFire IMR16340 & 0.65 & 92.42 & 47.81 & 39.4 \\ Aucooma IMR18650 & 2.8 & 791.32 & 28.10 & 30.8 \\ Keeppower IMR26650 & 4.2 & 887.50 & 21.36 & 22.8 \\ Samsung INR18650-13Q & 1.3 & 750.57 & 62.49 & 44.5 \\ Sony US18650 VT3 & 1.5 & 984.76 & 53.06 & 39.6 \\ \hline \hline \end{tabular}  
* Nominal cell capacity. 2 Relative error of experimental data approximation by Equations (1) and (2).  
\end{table} 
Table 3: Optimal parameters of Equations (1) and (2) for lithium-ion cells in the range of discharge currents from inflection point of experimental curve to the highest currents used in experiments. and Liebenow equation complement each other when describing the released capacity of lead-acid batteries at any discharge currents. For lithium-ion cells, the experimental dependence \(C(i)\) of the cell released capacity on the discharge current differs significantly (Figure 2) from \(C(i)\) for lead-acid batteries. For lithium-ion cells, the function C (i) is concave at small discharge currents, convex at medium discharge currents and again concave at high discharge currents. However, both Peukert Equation (1) and Liebenow Equation (2) describe only concave curves. Thus, theoretically, the Peukert Equation (1) and the Liebenow Equation (2) can describe the experimental function \(C(i)\) (Figure 2) only from the discharge currents corresponding to the inflection point of the function \(C(i)\) to infinity, as well as at small discharge currents. In these ranges of the discharge current values (according to our research results given in Figure 3 and Tables 3 and 4), indeed, the Peukert equation corresponds well to the experimental data. The relative error of approximation of the experimental data by Equation (1) is less than 7.2% (Table 3) for high discharge currents and less than 1% (Table 4) for small discharge currents. The range of small discharge currents for some lithium-ion cells is quite large (Table 4), and it sometimes completely covers the usual working discharge currents of these cells. This is why many authors [18] use the Peukert equation to estimate the capacity of lithium-ion cells. Nevertheless, studies have shown that the scope of the Peukert equation for lithium-ion cells is limited. The Liebenow Equation (2) poorly corresponds to the experimental data in the area of high discharge currents, where the function \(C(i)\) is concave (Figure 3 (2) and Table 3). The relative error of approximation of the experimental data by Equation (2) is more than 22% (Table 3). However, in the range of small discharge currents, the Liebenow equation can be used to estimate the capacity of lithium-ion cells (Figure 3 (1) and Table 4). Improvement of the Hausman Analytical Model for Calculating the Remaining Capacity of Lithium-Ion Batteries Based on the Obtained Experimental Data  
In many studies [18; 19; 20; 21; 40], the cell remaining capacity is evaluated based on analytical models relying on the Peukert equation. We believe the most promising method is the analytical model of [PERSON] [18]. This model is specifically designed to evaluate the remaining capacity of batteries in electric vehicles. In electric vehicles, batteries operate in dynamic mode, i.e., discharge currents can change quickly, and the temperature of the batteries must also be taken into account.