# A New Multi-Axial Flux Pm Motor-Generator System for Flywheel Energy Storage
## 2 Materials and Methods
As seen in Table 2, NASA's FESS shows superiority in life cycle, depth of discharge, and cycle efficiency. FESS is a candidate for use and development in many areas. So, a new design using two AFPM machine structures for CML is suggested. In the suggested motor-generator design, the amount of energy obtained by considering the charge and discharge conditions for 1000 rpm is given in Equation (3)[24]. In Equation (3), \(\mathrm{E_{m}}\), j, and \(\mathrm{w}\) are the maximum energy, moment of inertia, and angular velocity, respectively. \[\mathrm{E_{m}}=\frac{1}{2}\mathrm{jw}^{2} \tag{3}\]  
As the speed decreases from the reference value to zero, both the voltage and frequency approach zero. While recovering the energy, it is impossible to recover the maximum energy given in Equation (3). Hence, the energy between the two reference speed values must be recovered. The net amount of energy depending on the difference between the two reference angular velocity values is given in Equation (4)[24]. In Equation (4); Enet, \(\mathrm{w_{max}}\), and \(\mathrm{w_{min}}\) are the net amount of energy, maximum angular velocity, and minimum angular velocity, respectively. \[\mathrm{E_{net}}=\frac{1}{2}\mathrm{j}(\mathrm{w_{max}}^{2}-\mathrm{w_{min}}^ {2}) \tag{4}\]  
In this study, a new FESS design for CML is suggested. The 3D view of the suggested design is given in Figure 2. This design consists of 2-pole and 12-pole AFPM motors, a 12-pole generator winding, and an aluminum flywheel where the kinetic energy is stored. There is an AFPM machine structure on both sides of the flywheel in the proposed design. The 2-pole AFPM motor is designed to drive the flywheel to the high-speed reference point and hold its position. In the 12-pole AFPM motor-generator design, motor and generator windings are designed with different conductor sections and turn numbers to provide high energy capacity in the short time required by the CML. A compact design was obtained, as seen in Figure 2, by using the AFPM machine structure. Figure 3 shows the experimental setup of the FESS design. \(2\mathrm{p}=2\) pole motor design has a toroidal winding structure. The \(2\mathrm{p}=12\) pole motor-generator structure consists of 3 trapezoidal windings. In the experimental setup, current and voltage values were measured using probes connected to the oscilloscope. The data were obtained by calculating the averages of the values recorded between 0 and 0.5 s. Values were also obtained at the desired reference speed point from \(2\mathrm{p}=12\) pole axial flux machine, using the driver shown in Figure 3. Also, this machine's two windings are designed as \begin{table}
\begin{tabular}{l l l} \hline \hline  & **Electrochemical Battery (NiH2)** & **NASA’s FESS** \\ \hline Discharge depth (\%) & 35 & 89 \\ Energy density (Wh/kg) & 10 & 27 \\ Maximum power (kW) & \(\sim\)5.5 & 5.5 \\ Energy capacity (kWh) & 4.6 & 5.5 \\ Cycle efficiency (\%) & 65 & 83 \\ Life Cycle (years) & 5 & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of NiH2 batteries with FESS[25]. at the top is designed as the generator winding. The 2p = 12 pole motor windings are connected in series and parallel for energy storage performances. In addition, the energy storage amounts of the generator and motor windings of the 2p = 12 pole AFPM machine were compared.