## 3 Design Procedure of the HESS  
Based on the profile, Figure 1, and the data from Table 1, the following concept, Figure 2, of the HESS was designed. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Accumulator (unregulated bus) voltage & 20–34 V \\ Accumulator (unregulated bus) delivery current & max. 1 A \\ Accumulator (unregulated bus) charge current & optional \\ Load peak power & 300 W \\ Minimum operating SC module voltage & 6 V \\ Maximum operating SC module voltage & 13 V \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main systems parameters. Figure 1: Power profile. In the laboratory setup, the four-quadrant power supply was used to simulate the SMPM motor drive, which is used in the practical scenario, but it was unavailable at the time of the system verification. The next step in the design is calculating the minimum required SC module capacitance. The calculation of the SC module capacity is based on the energy criterion and power profile from Figure 1. The area under the power profile is the required energy. For the simplicity of the calculation, it can be divided into two triangles and one rectangle. According to the general formula, the energy of the triangle and rectangle is given by Equations (1) and (2):  
\[E_{triangle}=\frac{1}{2\eta}\cdot P_{peak}\cdot t=\frac{1}{2\cdot 0.95}\cdot 300 \cdot 0.2=31\;\mathrm{J} \tag{1}\]  
\[E_{rectangle}=\frac{1}{\eta}\cdot P_{peak}\cdot t=\frac{1}{0.95}\cdot 300 \cdot 0.08=22\;\mathrm{J}. \tag{2}\]  
The total energy of the power profile in one direction is:  
\[E_{profile}=2\cdot E_{triangle}+E_{rectangle}=84\;\mathrm{J}. \tag{3}\]  
Primarily, the SC module was designed for a different profile. This profile had an energy \(E_{rot2}=420\;\mathrm{J}\). This part considered that the capacitor was discharged to 50% of its energy during operation. Therefore, the allowable energy of the SC module was doubled:  
\[E_{SC_{module}}=2\cdot E_{req2}=840\;\mathrm{J}. \tag{4}\]  
The value of the capacity, which allows storing energy of 840 J at a voltage of 13 V, is derived from the equation for calculation energy on the capacitor [14] as follows:  
\[C=\frac{2\cdot E_{SC_{module}}}{V_{SC}^{2}}=\frac{2\cdot 840\;\mathrm{J}}{13^{2} }=10\;\mathrm{F}. \tag{5}\]  
Therefore, the SC module used for the mentioned profile is realized with a 10 F SC module. For the profile from Figure 1, the expected minimum voltage and maximum current are recalculated using Equations (6) and (7):  
\[V_{SC\_min}=\sqrt{\frac{2\cdot(E_{SC_{module}}-E_{profile})}{C}}=\sqrt{\frac{2 \cdot(840-84)}{10}}=12.29\;\mathrm{V} \tag{6}\]  
\[I_{max}=\frac{P_{peak}}{V_{SC\_min}}=\frac{300}{12.29}=24.4\;\mathrm{A}. \tag{7}\]  
Figure 1:0 HESS concept. Based on the calculations of the supercapacitors, the BCAP0010 PZ70X01 was selected [15]. Based on the datasheet rating and calculations, the 656P configuration was selected with the following parameters of the whole SC pack module. This configuration meets the requirements regarding capacity, maximum voltage, and maximum current. The parameters of the designed SC module are shown in Figure 1:1  
The configuration in Figure 3 shows a 3D model of the designed SC module. For rapid development purposes, the commercially available bidirectional interleaved DC/DC converter kit was used because it has all the required parameters for this application. The used evaluation board is Texas Instruments LM5170 EVM-BIDIR (Dallas, TX, USA) [16]. It is a dual interleaved bidirectional DC/DC converter with integrated control IC LM5170 (Dallas, TX, USA), which can be controlled in multiple ways [17]. This controller provides current control of inductor currents. The parameters of the used converter are listed in Figure 1:2