## 3 Results and Discussion
### HPES System Charging  
Figure 8 presents a portion of the results obtained specifically from Runs 2 and 7, directly comparing the Alpha and Beta models for the same simulation runs. On observation, the results are highly comparable and follow the same trends, with minimal time differences between the two models. A primary visual difference of the power results between the Alpha and Beta models is the effect of the PID controller and motor inertia within the Beta model, where the controller gain parameters play a crucial role in the pump's power and speed ascent time and overshoot. A finding obtained during simulation runs was that if a full charging cycle were to be performed in the Beta model (from 80 to 200 bar), PID active control would be required. Firstly, due to the large variation in PCS pressure and secondly, owing to the large variation in powers, the system at 120 bar could be charged at powers of between 3.0 and 5.0 MW, thus having a direct influence on the pump's required speed, which is an output of the PID controller, as previously shown in Figure 6 in Section 2.3.1. In Figure 8c,d, the response of the Beta model in the two cases indicates different PID controller gain parameters since the former experiences undershoot and a longer settling time, while the latter is more aggressive, thus experiencing an overshoot, yet obtains a relatively faster settling time. It must be noted that while the PID controller gain parameters are satisfactory for the purposes of this study, further optimisation of the control system's response is not to be excluded. Figure 8: Plots showing (**a**) Accumulator Pressure variation for Run 2, (**b**) Accumulator Pressure variation for Run 7, (**c**) Input Power for Run 2, and (**d**) Input Power for Run 7. Table 6 presents the controller gain parameters implemented for every run. Table 7 presents a comparison between the controller regulation quality indicators for all the charging runs across the two numerical models. While steady state error remains low across all runs, the overshoot for both models towards the upper pressure limit is large. The Alpha model shows a lot less sensitivity to the controller regulation quality across all runs due to the exclusion of inertia and its quasi-steady-state modelling approach. It must be noted that while the PID controller gain parameters are satisfactory for the purposes of this study, further optimisation of the control system's response is not to be excluded. In reality, better-optimised PID control response can lead to even better RMSE results (presented later in Table 8) since the results comparison also considers the pump speed ramp up difference between the two numerical models due to the inclusion of machinery inertia in the Beta model. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Charging Runs** & **Proportional (P)** &
\begin{tabular}{c} **PID Parameter** \\ **Gains Integral (I)** \\ \end{tabular} & **Derivative (D)** \\ \hline Run 1 & 0.004 & 0.0050 & \(5\times 10^{-7}\) \\ Run 2 & 0.008 & 0.0045 & \(5\times 10^{-7}\) \\ Run 3 & 0.005 & 0.0050 & 0.50 \\ Run 4 & 0.005 & 0.0050 & 0.00 \\ Run 5 & 0.006 & 0.0050 & 0.15 \\ Run 6 & 0.003 & 0.0100 & 0.02 \\ Run 7 & 0.200 & 0.0004 & 0.15 \\ Run 8 & 0.003 & 0.0100 & 0.02 \\ Run 9 & 0.009 & 0.0100 & \(1\times 10^{-4}\) \\ Run 10 & 0.003 & 0.0100 & 0.02 \\ Run 11 & 0.0095 & 0.1000 & \(1\times 10^{-4}\) \\ Run 12 & 0.0095 & 0.1000 & \(1\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The controller gain parameters for all charging runs performed in the Beta model.