*4.1. Experimental Validation of the HPTO Model*

Figure 4A shows the hardware in the loop (HIL) test rig of the HPTO unit. In general, the HIL test rig was developed based on the design of WECs in Figure 1 and several sensors were installed to monitor the variations of HPTO force, oil pressure, the oil level in the oil tank and as the hydraulic motor shaft speed, as illustrated in Figure 4B. The servo-electric actuator was also installed in the HIL test rig to replicate wave-induced relative pitch motion to drive the HPTO unit to capture the wave energy. A servo motor controller based on Labview/Arduino integration and the data acquisition system for data collection from the sensors were placed in the control system unit. The relative pitch motion generated by the electric actuator is according to the input wave state. To simulate the condition that is close to real-world application, the hydrodynamic parameters from the CFD analysis and the feedback HPTO force were considered to calculate the produced excitation force applied to the floater's arm. The sinusoidal wave input with the amplitude and period of 0.4 m and 2.5 s were considered for the validation of HPTO model. The captured image of maximum upward and downward motions of the HIL test rig during the experimental validation of the HPTO unit is depicted in Figure 4C,D.

**Figure 4.** Experimental evaluation of WEC with hydraulic PTO unit. (**A**) A complete dry-lab test rig, (**B**) Enlarge image of HPTO unit setup, (**C**) Maximum upward, and (**D**) Maximum downward position of the WEC device.

> Figure 5 shows the results of the behaviour of the HPTO unit in a regular wave condition with an amplitude and period of 0.4 m and 2.5 s. From the figure, it can be seen that the simulation results of the developed WEC with the HPTO unit model in

MATLAB/Simulink is in good agreement with the results obtained from the HIL test rig. However, slight differences and some fluctuations in hydraulic motor speed and HPTO force results were obtained during the experiment, as depicted in Figure 5A,B. These differences and fluctuations may be attributed to the errors in the manufacture and assembly of the test rig, the measuring errors of the transducers, the vibration of the hydraulic motor, and the leakage in the hydraulic motor, cylinders and joints. Such a good agreement presented in Figure 5A,B indicates that the developed WEC with HPTO unit model in MATLAB/Simulink presented in the present study would be effective and reliable as a tool for predicting the amount of power that can be generated from the ocean waves.

**Figure 5.** Behaviour of HPTO unit in a regular wave condition. (**A**) Speed of hydraulic motor and (**B**) HPTO force applied to the floater's arm.

#### *4.2. Performance of WEC with HPTO Model in Five Irregular Sea States*

The simulations of the developed WEC with the HPTO unit model using different sea states was first carried out in the present study. This simulation was intended to evaluate the performance of the developed model against the different wave heights and periods. The simulation was started with the nominal sea state (sea state A) and the results from the simulation are presented in Figures 6 and 7. Figure 6A shows the responses of WEC and the hydraulic cylinder piston against the irregular wave input in sea state A. The figure shows that the displacement of the WEC device was slightly lower than the wave elevation, particularly during the upward motion. This is due to influencing factors such as the hydrostatic restoring moment, the moment due to the HPTO unit and the initial moments of floater and arm [36]. Based on the results, the average displacement of the WEC device and hydraulic piston was 70% and 15% of the wave elevation. The figure also depicts that the displacements of the WEC device and piston were slightly delayed from the wave elevation. Figure 6B presents the profile of the HPTO force applied to the WEC device. On average, the HPTO forces applied to the WEC device during upward and downward motion equaled 3.64 kN and 1.99 kN, respectively. The unbalanced HPTO force applied to the WEC device is due to the unsymmetrical effective area of the piston. A larger effective area of piston produced a higher force rather than a smaller effective area piston.

Figure 6C shows the profile of HPA pressure. From the figure, the pressure of HPA reached up to 49 bar several times, which was a 4.5% increased from its pre-charge pressure setting.

**Figure 6.** Performance of WEC with HPTO unit in sea state A, (**A**) Displacement of Wave, WEC and hydraulic cylinder piston, (**B**) HPTO force applied to WEC device, and (**C**) Pressure of high-pressure accumulator.

Meanwhile, Figure 7A,B show the pressure and speed profile of the HM. It can be seen from the figures that the pressure and the speed of the hydraulic motor reached up to 49 bar and 200 rpm. The smoothing effect of the HPA unit on the hydraulic motor pressure can be seen in Figure 7A. The HPA was able to reduce the fluctuation of the hydraulic motor pressure, particularly after 50 s of HPTO operation. Figure 7C illustrates the profile of the generated power from the HPTO unit. The average power generated from the generator was 70.9% of its rated capacity (100 W). The figure also demonstrates that some fluctuations exist in the generated power from the generator, particularly at the early stage of the operation. The comparison simulation results of the WEC with HPTO unit in each sea state are summarized in Table 5. From the table, the simulation result showed that the significant wave height and peak wave period were affected by the overall performance of the WEC with the HPO unit. First, the table reveals that the averaged angular displacement of the WEC device was increased and decreased, relatively, with increases and decreases of the significant wave height and peak wave period. From the table, the angular displacement of the WEC device in sea states B and D were reduced by 38% and 33% (upward) and 24% and 21% (downward) of its angular displacement in the nominal sea state. Meanwhile, the angular displacement in the sea states C and E were increased by 21% and 16% (upward) and 28% and 18% (downward), respectively. The increase and decrease of the angular displacements are due to the increase and decrease HPTO force applied to the WEC device, which can be obtained in Table 5. The increase and decrease of WEC displacement, relatively, also increase and decrease the generated output power from the HPTO unit. As can be seen, the average power generated from the HPTO unit in sea states B and D were decreased by 41% and 34% of power from sea state A, while 15.5% and 10.4% were increased in sea states C and E. Overall, the generated power from the HPTO unit in each sea state is below its rated capacity. Thus, several parameter optimization methods, as suggested in [20], can be further implemented to increase the generated power from the HPTO unit.

**Figure 7.** Performance of WEC with HPTO unit in sea state A (continue), (**A**) Pressure of hydraulic motor, (**B**) Speed of hydraulic motor, and (**C**) Electrical power generated from HPTO unit.


