## 4 Discussion  
This study presents a dynamic modeling and multi-objective optimization of a compressed natural gas (CNG) refueling station. The system model includes the full refueling cycle: multi-stage compression, cascade storage, vehicle tank filling, and thermodynamic interactions. The model was constructed with a modular structure by using a dynamic simulation environment and was validated against experimental data for pressure and mass flow rate profiles. The effects of varying storage pressures and volume allocations were investigated through a two-stage Taguchi-based optimization framework combined with gray relational analysis (GRA). In the first stage, the optimal storage pressures were determined as 250 bar (P\({}_{\text{high}}\)), 145 bar (P\({}_{\text{medium}}\)), and 70 bar (P\({}_{\text{low}}\)). Compared to the initial configuration, these settings increased the number of vehicles refueled in a 24 h cycle by 5.05%, improved the average charged gas mass by 0.34%, and reduced the compressor specific work by 2.07%. In the second optimization stage, optimal volume ratios were identified as V\({}_{\text{low}}\)/V\({}_{\text{total}}\) = 0.75 and V\({}_{\text{medium}}\)/V\({}_{\text{high}}\) = 2. This configuration led to an additional 5.18% reduction in compressor-specific work compared to equal volume tanks, with no significant change in the number of vehicles filled. However, this stage resulted in a 5.5% reduction in the average mass delivered per vehicle, indicating a trade-off between energy efficiency and refueling completeness. The combined pressure and volume optimization resulted in a total decrease of 12.33% in compressor-specific energy consumption. These findings demonstrate that both pressure levels and volume distributions in cascade storage systems are critical parameters that strongly affect the thermodynamic performance and energy requirements of CNG stations. The applied optimization methodology provides a systematic approach for evaluating such multi-parameter systems under transient operation. In the Taguchi analysis stage, the main effects of each input factor on system response variables were independently examined. For example, increasing the initial pressure in the high pressure section of the cascade storage system resulted in a higher average refueling mass due to the greater pressure differential, but it also increased energy consumption due to the additional compressor workload. In the subsequent GRA stage, where multi-objective optimization was performed, the trade-off between energy savings and filling performance became more apparent. In particular, activating the priority valve earlier in the filling cycle improved energy efficiency while causing a slight decrease in the amount of gas transferred to vehicle tanks. These results can be physically explained by the pressure driven gas flow and the thermodynamic behavior of real gas during rapid compression and expansion. Therefore, the optimization process revealed the engineering balance required between performance objectives and system level physical behavior. These findings are supported by the performance comparison presented in Table 13, and they are consistent with the physical mechanisms described in the literature [24,27]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Performance** & **Initial Configuration** & \
\begin{tabular}{c} **After Pressure** \\ **Optimization** \\ \end{tabular} &
\begin{tabular}{c} **After Volume** \\ **Optimization** \\ \end{tabular} \\ \hline Number of vehicles & 218 & 229 & 229 \\ refueled (n\({}_{\text{vehicle}}\)) & 9.46 & 9.43 & 8.94 \\ Average mass per vehicle (m\({}_{\text{Average}}\), kg) & 0.1938 & 0.1898 & 0.17 \\ Compressor specific work(W\({}_{\text{Comp}}\), kWh/kg) & 0.1938 & 0.1898 & 0.17 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: CNG station performance before optimization, after pressure optimization, and after volume ratio optimization.