*2.3. Main Parameters of HPTO Unit*

As previously mentioned in [14], there are several important parameters affecting the performance of the HPTO unit such as piston diameter, the volume capacity of HPA, displacement of HM, etc. Table 1 provides the important parameters of the HPTO unit that are summarized from Equations (3)–(16). For some parameters, the higher and lower values can reduce the performance of the HPTO unit. To investigate this problem, a detailed study regarding the influence of these parameters on the overall performance of WECs is performed in the present study.


**Table 1.** Important parameters of the HPTO unit.

In the present study, the complete simulation investigation of HPTO unit parameters was implemented in the MATLAB/Simulink software (Version: 2018b). The detailed methodology of the present study is described in the following subsections.

#### **3. Simulation Investigation of HPTO Unit Parameters**

#### *3.1. Simulation Set-up of WEC with HPTO Unit*

The MATLAB/Simulink software was used in this study to model a complete WEC system shown in Figure 1. The WECs consists of two main parts, the WEC model and the HPTO model. The WEC model was developed using a mathematical function block based on Equations (1)–(5). The wave elevation data, *η<sup>W</sup>* and *FHPTO* are the inputs, while the *xp* is the output of the WEC model. According to Equations (1) and (2), the hydrodynamics parameters of the WEC device such as *krad*, *kres*, *hex*, added mass coefficient (*kadd*) and impulse response function (*kimp*) are required to develop the considered WEC model. The hydrodynamic parameters of the WEC model from the previous study in [20] were used, since a similar WEC concept was considered in this study. In [20], these hydrodynamic parameters were obtained from the frequency domain analysis study that was carried out using ANSYS/AQWA software. The obtained hydrodynamic parameters are presented in Figure 2.

**Figure 2.** Hydrodynamic parameters of WEC device. (**A**) Excitation force coefficient, (**B**) Added mass coefficient, (**C**) Radiation damping coefficient, and (**D**) Impulse response function.

Meanwhile, the Simscape SimHydraulic toolbox in MATLAB/Simulink was used to develop the HPTO unit model. The snapshot of the developed model in MATLAB/Simulink is depicted in Figure 3. As illustrated in the figure, *xp* is the input of the HPTO unit. Using *xp* signal, the linear velocity of the piston, . *xp* is obtained using a first-order lag-based linear displacement to linear velocity converter. The double-acting hydraulic cylinder (DAC) component was used as HA. In the Simscape SimHydraulic toolbox, the DAC component is constructed based on the translational hydro-mechanical converter and translational hard stop blocks. The rod motion is limited with the mechanical translational hard stop block. The ideal force sensor block was connected to the HA rod to measure the *FHPTO*. The pressure and flow rate sensor blocks were also connected to the HA to measure the dynamic pressure and flow rate of HA. To account for the friction loss along the pipe length and the fluid compressibility, the hydraulic pipeline blocks were used to connect some of the components, as illustrated in Figure 3. The thermodynamic transformation in the HPA was assumed to be isentropic, which is reasonable considering the cycle time in the device. Furthermore, for ease of control, a simple rotational damper with varying damping coefficients was used to represent the electric generator unit. In this way, the resistive torque imposed by the electric generator can be manipulated by varying the value of the damping coefficient (*dG*). The generated electric power from the electric generator can be calculated using Equation (16). In this study, the initial parameters of the HPTO unit were manual tuned. However, these parameters are not optimal yet. The detailed specifications of each component in the developed HPTO model are provided in Table 2. Finally, the developed HPTO unit model in MATLAB/Simulink was then experimentally validated using an actual HPTO test rig in the dry lab environment.

**Figure 3.** A complete model of WEC with HPTO unit in MATLAB/Simulink. (**A**) WEC device model, and (**B**) HPTO unit model.


