# Parameter Identification Method of a Double-Layer Supercapacitor by Using a Real Voltage Source
## 1 Introduction
This can be very useful in stand-alone systems, uninterruptible power supplies, or emergency lighting. In these cases, the SCs are usually connected directly to the solar panel, which will work, in almost all the range of voltages, as a real constant voltage or current source, both of which can be reduced to the first case [36; 37; 38]. SCs are also used to absorb transient surge voltages of several kV, but of short duration, where the energy involved is low, in an application known as SCASA (Supercapacitor Assistant Surge Absorb). Although SCs have low internal resistance, because their capacitance is very high, their time constant is high enough to withstand the transient surge voltages that occur in the grid, whose durations are usually in the order of milliseconds. To analyze their ability to absorb these surges, SCs are subjected to high-voltage pulses, generated with a constant and very high voltage source, but of short duration [39; 40; 41; 42]. There are industrial applications where SCs work as a power supply for resistive heaters. [PERSON] et al. [43; 44] have proposed a system for heating water in domestic installations, where the SCs discharge their energy on resistors. These are usually made of nichrome, a material whose resistivity varies only slightly with temperature. As the heat generated in them will be transmitted directly to the water, their ohmic value will hardly increase. A similar idea is used by [PERSON] et al. [45] to avoid ice accumulation on wind turbine blades, which can affect their aerodynamic performance. In the manufacturing process, a nichrome coil is embedded along the entire length of the blade, which receives current pulses every minute generated by an SC that discharges its energy on these filaments, which act as heaters. In both cases, it is considered that the SCs are discharged rapidly over practically constant resistances. The main disadvantage of this technique is that it is necessary to charge the SC many times, since its stored energy is low, and in addition, it must be delivered very quickly, so the SC is discharged very fast. However, this system has a very high efficiency since the resistance used as a heater will be quite larger than the internal resistance of the SC, so almost all the energy discharged by the SC will be transformed into heat in the heating resistor. In addition, since the SC withstands a high number of charge and discharge cycles, it will make the set very durable. The main interest in estimating the values of the electrical parameters of a cell is to find out its aging level. According to the manufacturers, when a cell reaches the end of its useful life, it will show a decrease in its capacity (typically 20-30%) compared to what it had at the beginning, while the internal resistance increases by 100%. To know how far a cell is from reaching its end, it is necessary to make periodic monitoring of these parameters. When they reach values close to the limit thresholds, the cells must be replaced with new ones, before an unexpected failure occurs that could affect the entire system where they are installed. This monitoring will be part of the system's predictive maintenance. This study proposes an alternative method for the calculation of the variable capacitance main branch parameters (R, C\({}_{0}\), and k\({}_{\text{c}}\)) by rapidly charging or discharging the SC with a real voltage source or by discharging the cell with a constant resistance, which can be used by taking advantage of any of the industrial applications mentioned previously. Thisnew method makes the necessary test equipment simple and economical, especially when discharging on a constant resistance. The values of the external voltage, \(\mathrm{u_{co}(t)}\), measured during the charging or discharging of the SC, will be taken as the starting data. These will be employed considering the model depicted in Figure 1b.