## 4 Results and Discussion
### Dependence of Cell Released Capacity on Discharge Current  
To decrease the temperature changes during cell discharge by high currents, we used a number of methods. Firstly, cells were cycled at the temperature T = 25 \({}^{\circ}\)C inside of the climatic chamber Binder MK240 (BINDER GmbH, Germany). Secondly, modified heat sinks were used (usually applied for refrigeration of processors in computing systems). The heat sinks were fastened to the cells using a specially manufactured clamp and MX-2 heat-conducting paste produced by ARTIC. This arrangement greatly increased the thermal flux from the cells and accelerated their refrigeration. These measures allowed keeping the cell temperature below 55 \({}^{\circ}\)C in all our experiments. It should be noted that all the cells studied by us had no protection; therefore, it was possible to discharge them with high currents. For convenience of comparison between the experimental data and Equations (3)-(5), we rewrite them in the following form  
\[C=\frac{C_{m}}{\left(i/B\right)^{n}}\tanh\left(\left(\frac{i}{B}\right)^{n}\right) \tag{7}\]  
\[C=\frac{C_{m}}{1+\left(\frac{i}{B}\right)^{n}} \tag{8}\]  
\[C=\frac{C_{m}}{\operatorname{erfc}(-B/n)}\operatorname{erfc}\left(\frac{i-B} {n}\right) \tag{9}\]  
For Equations (7)-(9), the condition \(C(0)=C_{m}\) is true, i.e., \(C_{m}\) is the maximum cell capacity. The obtained experimental data are given in Figure 2. In Figure 2, the experimental data are compared with Equation (9), as this equation had the least relative error of approximation of the experimental data in all our experiments (Table 2). Based on the obtained experimental data (Figure 2), the optimal parameters for Equations (7)  
Thus, from the coincidence of the experimental functions \(\mathrm{f}(i)=C(i\mathcal{C}_{m})/\mathcal{C}_{m}\) for the cells TrustFire IMR16340 and Aucooma IMR18650 (Figure 2a), it follows that these cells have the same electrodes and electrolytes, while the difference in the cell capacities is connected only with the different areas of their electrodes. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Manufacturer and Model** & \(\mathbf{C_{n}}\) **(Ah)\({}^{\mathbf{1}}\)** & \(\mathbf{C_{m}}\) **(Ah)** & \(\mathbf{B}\) **(A)** & \(\mathbf{n}\) & \(\mathbf{\delta^{2}(\%)}\) \\ \hline \multicolumn{6}{c}{Equation (7)} \\ \hline TrustFire IMR16340 & 0.65 & 0.610 & 5.385 & 3.242 & 4.000 \\ Aucooma IMR18650 & 2.8 & 2.807 & 25.912 & 3.326 & 2.627 \\ Keeppower IMR26650 & 4.2 & 4.033 & 27.169 & 3.161 & 2.753 \\ Samsung INR18650-13Q & 1.3 & 1.31 & 18.741 & 4.305 & 3.312 \\ Sony US18650 VT3 & 1.5 & 1.49 & 27.208 & 4.41 & 2.776 \\ \hline \multicolumn{6}{c}{Equation (8)} \\ \hline TrustFire IMR16340 & 0.65 & 0.614 & 6.644 & 5.028 & 2.520 \\ Aucooma IMR18650 & 2.8 & 2.807 & 31.866 & 5.513 & 1.837 \\ Keeppower IMR26650 & 4.2 & 4.037 & 33.684 & 5.262 & 1.741 \\ Samsung INR18650-13Q & 1.3 & 1.299 & 22.052 & 6.914 & 2.622 \\ Sony US18650 VT3 & 1.5 & 1.494 & 31.799 & 7.062 & 1.61 \\ \hline \multicolumn{6}{c}{Equation (9)} \\ \hline TrustFire IMR16340 & 0.65 & 0.620 & 6.748 & 3.041 & 0.510 \\ Aucooma IMR18650 & 2.8 & 2.833 & 32.222 & 13.543 & 1.076 \\ Keeppower IMR26650 & 4.2 & 4.073 & 34.027 & 14.864 & 0.542 \\ Samsung INR18650-13Q & 1.3 & 1.319 & 22.123 & 7.854 & 1.886 \\ Sony US18650 VT3 & 1.5 & 1.494 & 32.122 & 10.676 & 0.789 \\ \hline \end{tabular} \({}^{1}\) Nominal cell capacity. \({}^{2}\) Relative error of experimental data approximation by Equations (7)–(9).  
\end{table} 
Table 2: Optimal parameters of generalized Peukert Equations (7)–(9) for lithium-ion cells. Figure 2: Comparison between experimental data for lithium-ion cells of different types and Equation (9): (**a**) cell with cathode LiMn\({}_{2}\)O\({}_{4}\) (IMR); and (**b**) cell with cathode LiNiMnCoO\({}_{2}\) (INR). For each cell, the value of \(C_{m}\) was taken from Table 2. \(\Delta\), \(\Box\), \(\Box\), experimental values.