## 2 Materials and Methods
Figure 3: Multi-stage compressor stage 1 subsystem. in the \"Priority Valves In\" subsystem sequentially fill the low-pressure, medium-pressure, and high-pressure reservoirs. During the filling of the storage tanks, vehicle refueling through dispensers does not occur. The heat transfer mechanism between the storage tanks and the environment is modeled in the subsystems, and temperature and pressure monitoring is conducted. Thermal mass, conductive heat transfer, and convective heat transfer are modeled using the thermal elements library. Temperature control is modeled using a temperature sensor block, which allows for the analysis of the temperature difference between two desired points without removing heat from the system. The values used in heat transfer and material properties are provided in Table 3.  
On the right side, the \"Priority Valves Out\" subsystem manages the release of gas from the system. During fast refueling, the vehicle tank is initially connected to the low-pressure reservoir. As the pressure in the reservoir drops and the pressure in the vehicle's cylinder increases, the gas flow rate decreases. When the flow rate reaches a predefined threshold, the system switches to the medium-pressure reservoir and finally to the high-pressure reservoir to complete the refueling process. Compared to storing all gas in a single-pressure buffer tank, the cascade system is expected to provide more complete refueling while optimizing the efficiency of both the compressor and the storage tanks. To ensure that vehicle tanks are adequately filled, the high-pressure reservoir must always be maintained at a slightly higher pressure than the target pressure of the vehicle tank. Proper determination of compressor capacity and cascade storage volume is essential to allow the CNG station to manage vehicle frequency efficiently. Additionally, setting the correct maximum and minimum pressure values for the low, medium, and high-pressure tanks and allocating volumes appropriately ensures the effective operation of the station. In the dispenser subsystem, the inlet gas serves as the starting point of the system and is directed through a control mechanism. The control unit regulates the inlet valve using a transfer function, which determines the dynamic response of the gas flow, smoothing sudden changes and ensuring a steady flow. The valve is a fundamental component that regulates both the direction and quantity of flow. When opened, gas moves toward the hose, which provides a flexible conduit for directing the flow. The check valve ensures that the gas moves only in the designated direction, preventing backflow and enhancing system safety. Finally, the outlet gas point is where the gas is delivered to vehicles under appropriate pressure and flow conditions. This system is designed to facilitate the controlled and safe \begin{table}
\begin{tabular}{c c} \hline \hline
**Storage and Environment Properties** & \\ \hline Tank construction material (Type I) & 34 CrMo4 \\ Single storage tank capacity & 150 L \\ Vehicle tank capacity & 70 L \\ Empty storage tank weight & 125 kg \\ Empty vehicle tank weight & 75 kg \\ Storage tank outer diameter & 370 mm \\ Storage tank inner diameter & 350 mm \\ Storage tank height & 1.8 m \\ Vehicle tank height & 0.9 m \\ Tank specific heat capacity & 561 J/kgK \\ Tank thermal conductivity & 50 W/mK \\ Internal heat transfer coefficient & 300 W/m\({}^{2}\)K \\ External heat transfer coefficient & 10 W/m\({}^{2}\)K \\ Total number of storage tanks & 48 \\ Ambient temperature & 20 \({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters for heat transfer at storage and vehicle tanks [55]. distribution of gas. The check valve, hose connection, and control valve are modeled using elements from the gas library. The three-vehicle subsystem models the vehicle tank filling process and its thermodynamic interactions. During gas transfer, parameters such as mass flow, pressure, and temperature are monitored by sensors to ensure efficient and controlled filling.