## 3 Results and Discussion  
To determine the optimal charge modes from the lithium-ion battery of the supercapacitor and to compare this with similar modes of the equivalent linear capacitor, an analysis of energy characteristics was performed. An analysis of change of a dose of energy arriving in the SC and LC was carried out for energy losses in the circuit, the dose of energy taken from the battery, and the energy transfer coefficient from the battery depending on the voltage to which the SC and LC are charged. Five points were considered: point 1, in which the voltage on the SC and LC \(U_{\rm LC}=U_{\rm SC}=0.25U_{\rm n}\); point 2, in which the voltage on the SC and LC \(U_{\rm LC}=U_{\rm SC}=0.5U_{\rm n}\); point 3, in which the voltage on the SC and LC \(U_{\rm LC}=U_{\rm SC}=0.75U_{\rm n}\); point 4, in which the voltage on the SC and LC \(U_{\rm LC}=U_{\rm SC}=0.9U_{\rm n}\), and point 5, in which the voltage on the SC and LC \(U_{\rm LC}=U_{\rm SC}=0.99U_{\rm n}\) while \((W_{\rm LC}=W_{\rm SC}=2196\) (J). The energy characteristics of SC and LC in the process of charging from AB at different voltage change ranges were considered as \(U_{\rm LC}=U_{\rm SC}=(0.25\ldots 0.5)U_{\rm n}\); \((0.5\ldots 0.75)U_{\rm n}\); \((0.75\ldots 0.9)U_{\rm n}\); \((0.9\ldots 0.99)U_{\rm n}\). Figure 2 shows the functional dependencies. Figure 2: Functional dependences: (**a**) = the dose of energy \(W_{\rm SC}\), which enters the SC at each moment of its charge and the energy dose \(W_{\rm ABI}\), which is selected from the AB; the dose of energy \(W_{\rm LC}\), which enters the LC at each time of its charge and the dose of energy \(W_{\rm AB2}\), which is selected from the AB; (**b**) = energy losses \(W_{\rm loss}\) in the charge circuit LC and SC; (**c**)—energy transfer coefficients from the AB when charging the linear capacitor \(\eta_{\rm LC}\) and supercapacitor \(\eta_{\rm SC}\). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \(R_{\rm 1}\), Ohm & \(C_{\rm 1}\), F & \(k\), F/V & \(R_{\rm 2}\), [PERSON] & \(C_{\rm 2}\), F & \(R_{\rm 3}\), [PERSON] & \(C_{\rm 3}\), F & \(R_{\rm 4}\), [PERSON] & \(E_{\rm 5}\), V & \(R_{\rm AB}\), Ohm \\ \hline
0.0025 & 270 & 190 & 0.9 & 100 & 5.2 & 220 & 9000 & 2.3 & 0.012 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the SC and lithium-ion battery. The dose of energy entering the LC when the voltage changes within \((0.25\) to \(0.5)U_{\mathrm{n}}\) is \(1.39\) times greater than the dose of energy entering the SC, while the energy loss is \(1.43\) times higher in the charge circuit of the LC. With increasing voltage on the LC and SC in the range \((0.5\) to \(0.75)U_{\mathrm{n}}\), they accumulate almost the same energy, but the loss in the charge circuit of the LC is \(5.3\%\) higher. In the ranges of voltage change \((0.75\) to \(0.9)U_{\mathrm{n}}\) and \((0.9\) to \(0.99)U_{\mathrm{n}}\) dose of energy entering the SC in \(1.17\) and \(1.3\) times higher than the dose of energy entering the LC, but losses are \(1.15\) and \(1.27\) times more. The dose of energy taken from the AB when charging the LC in the range \((0.25\) to \(0.5)U_{\mathrm{n}}\) is \(1.4\) times greater than the energy dose for the SC. In the voltage range \((0.75\) to \(0.9)U_{\mathrm{n}}\) and \((0.9\) to \(0.99)U_{\mathrm{n}}\) the dose of energy taken from the AB when the charge of the SC in \(1.17\) and \(1.30\) times higher the energy dose for the charge of the LC. Thus, the most energy-efficient charge occurs in the voltage range \((0.9,\ 0.99)U_{\mathrm{n}}\). At equally high energy transfer coefficients (\(\eta_{\mathrm{SC}}=\eta_{\mathrm{LC}}=0.95\)), the advantage of SC is that it accumulates \(30\%\) more energy than LC. When the LC and SC are charged to a voltage of \(0.99U_{\mathrm{n}}\), the doses of accumulated energies in them are the same (according to the selected initial conditions) \(W_{\mathrm{LC}}=W_{\mathrm{SC}}=2196\) (J), and the energy of losses in the LC charge circuit are \(51\%\) higher than the SC charge circuit losses.