# Supercapacitor-Based Energy Storage in Elevators to Improve Energy Efficiency of Buildings
## 4 Energy Storage System
### Supercapacitor Bank  
The nominal voltage of the SC bank is typically in the range of 100 V to 300 V [14; 18]. Considering that the nominal operating voltage of the VFD DC bus is 565 V and the non-isolated topology of the DC/DC converter is best suited for a transform ratio of 4 or less [32], the nominal voltage of the SC bank of 300 V was selected. The operating voltage range for the SC bank is usually selected in the range of \(U_{\mathrm{n}}/2\) to \(U_{\mathrm{n}}\), where \(U_{\mathrm{n}}\) is the nominal voltage. In this way, 75 % of the total energy stored in the supercapacitors is used [14]. The selected operating voltage range for the SC bank is thus between 150 V and 300 V DC. Since the typical nominal voltage of a supercapacitor cell is in the range of 1.2 V to 3.5 V [33], several supercapacitor cells must be connected in series to form an SC bank. The capacitance tolerance of each supercapacitor cell can vary between \(\pm 20\%\) of nominal [34], which can result in uneven voltage distribution across the series-connected supercapacitor cells and higher than expected voltages across the supercapacitor cells. Higher than nominal voltages can lead to higher leakage currents, increased gassing, and overall destruction of the supercapacitor cells [35]. To solve the problem of uneven voltage distribution on supercapacitors, balancing circuits are used. Considering the complexity of the overall model and the complexity of the balancing circuits of supercapacitors, supercapacitor cells with the same characteristics are used to model the supercapacitor bank. Their series representation can be modeled as a supercapacitor with higher nominal voltage. Supercapacitors are non-linear elements because their capacitance changes with voltage and frequency [34]. Several models of supercapacitors can be found in the literature [34; 36; 37]. The most accurate model of a supercapacitor is the transmission line model [36], which is very complex. In this paper, the supercapacitor bank was modeled as an ideal capacitor with ESR due to the high demands on the execution of the entire simulation model. The SC bank was sized to store energy for a maximum of two regenerative energy cycles. For the studied elevator, the maximum continuous regenerative power was 5.5 kW. The maximum regenerative energy was determined from field measurements and was 86 kJ, so the SC bank would be able to store at least 172 kJ. The energy stored in the supercapacitor bank that can be further used can be calculated as follows:  
\[E_{\mathrm{us}}=\frac{U_{\mathrm{n}}^{2}\cdot C}{2}\cdot 0.75 \tag{2}\]  
where \(U_{\mathrm{n}}\) is the nominal voltage of the charged supercapacitor bank and \(C\) is the capacitance of the supercapacitor bank. The energy is multiplied by 0.75 since 75 % of the energy stored in the supercapacitor is used. Using the Equation (2) and the known maximum voltage of the supercapacitor bank, the required minimum capacitance of the supercapacitor bank was calculated to be 5.1 F.  
Figure 7: Schematic of supercapacitor-based EESS. Commercially available supercapacitor cells that could be used to form the supercapacitor bank have a nominal voltage of 2.7 V to 3 V. In [38], it is reported that charging a supercapacitor cell with 200 mV above the nominal voltage can shorten the lifetime of the supercapacitor by 64 times. It was also shown that it is possible to extend the lifetime of the supercapacitor cell if the operating voltage of the supercapacitor cell is kept below the nominal voltage. Thus, with a nominal voltage of 300 V selected for the supercapacitor bank in this paper, 120 supercapacitor cells with a nominal voltage of 2.7 V are required, and each cell should be charged to a maximum of 2.5 V. The minimum required capacitance of a cell can be calculated as follows:  
\[C_{\text{cell\_min}}=N\cdot C_{\text{SC\_bank}} \tag{3}\]  
where \(N\) is the number of supercapacitor cells connected in series and \(C_{\text{SC\_bank}}\) is the minimum required capacitance of the supercapacitor bank.