## 4 Conclusions  
The scope of this research article was to present the design, testing, and comparison of a simplified numerical model, dubbed the Alpha model, to a more comprehensive numerical model, namely the Beta model. Both models simulate the charging and discharging process of a megawatt-scale offshore HPES system's ECU and PCS. While the two numerical models simulate the same system, the degree of complexity of the integrated models differs, thus resulting in significant differences in the computational resources required. The Alpha model is a computationally efficient, quasi-steady-state process which provides modularity and flexibility since numerous centrifugal pump, Pelton turbine, and PCS combinations can be simulated by changing the input parameters. A shortcoming of the Alpha model is that its simplified approach disregards transients due to machinery inertia, control system response, and system pressure losses. Meanwhile, the Beta model, as shown through Figures 4 and 7 in Sections 2.2 and 2.3, is a more complex model which mimics the  
Figure 10: Plots showing (**a**) PCS Pressure variation, (**b**) Pelton turbine wheel rotational speed variation, (**c**) Generator Torque Efficiency variation, (**d**) Nozzle Position variation, (**e**) Flow Rate variation, and (**f**) Overall Efficiency variation. All plots are associated with maintaining a constant power output of 3 MW (Run 3 in Table 5). physical system and aims to implement as many components as possible at the expense of computational efficiency. The Beta model is more suitable for analysing phenomena such as hydraulic machinery ramping, time response over short periods of time due to varying controller parameters, and transient flow analysis through the inclusion of hydraulic piping systems. While experimental data of such a system are not available, a validation step performed within each model was that of setting the pump speed to one of the speeds from the pump curves, setting a fixed head and observing that the power, efficiency, and flow rate values outputted matched the points on the pump curves. Nonetheless, further validation would be beneficial and is, thus, a limitation of the present study. Despite the model differences, the results produced were promising and have demonstrated the reliability of the simplified Alpha model compared to the Beta model by proving that the RMSE results are all consistently exceptionally low across all runs, both for the charging and the discharging simulations. Apart from the aforementioned reason, the runs performed resulted in the following key findings:  
1. The use of a single, variable-speed centrifugal pump under variable head conditions with a pressure ratio of approximately 2.5 means that the operating power (input power) is dependent on the pressure within the PCS. Pump compatibility between input power and pressure must be observed to ensure the pump is operable and further ensure that operation occurs at points as close to the pump's best efficiency point as possible. 2. The aforementioned power and pressure relationship leads to the need for an active PID control system when operating the centrifugal pump. This occurs since the large variations in power and pressure requirements directly impact the centrifugal pump's operating speed as a result of the control system implemented, as depicted in Figures 4 and 6 in Sections 2.2 and 2.3.1, respectively. 3. The mismatch in simulation duration time for the runs performed between the Alpha and Beta models is primarily caused from an amalgamation of the Beta model commencing from a complete stop, as well as the PID controller's overshoot and undershoot. An Undershoot caused the Beta model's results to indicate that charging or discharging of the system took longer. Meanwhile, an overshoot caused the opposite, where the Beta model simulation charged or discharged the system during the respective run quicker. The time described here refers to the time within the simulation, not the computational time required. 4.