*2.2. Hydraulic Power Take-off (HPTO) Mechanism*

Figure 2A illustrates the considered HPTO unit, which includes a hydraulic actuator, set of control check valves (CV), high-pressure and low-pressure accumulator (HPA and LPA), hydraulic motor (HM) and electrical generator (G). In the HPTO unit, the large chamber of the hydraulic cylinder (chamber A) is connected to the *CV*<sup>4</sup> (outlet) and *CV*<sup>1</sup> (inlet), while the small chamber of DAC (chamber B) is connected to the *CV*<sup>2</sup> (outlet) and *CV*<sup>3</sup> (inlet), respectively. Meanwhile, HPA and LPA are placed at the inlet and outlet of the hydraulic motor. During the operation, the wave force generated from the passing ocean wave causes a floater to swing upward and downward repeatedly, as illustrated in Figure 2B. The mechanical force produced by the WEC device forces the rod and piston of the hydraulic cylinder at the specified velocity (x˙ *<sup>p</sup>*) relatively subjected to the PTO load force. During the upward motion, the high-pressurised fluid in chamber A flows to the chamber B through *CV*1, HPA, HM, LPA and *CV*2. On the other hand, the process is vice-versa during downward motion, where high-pressure fluid in chamber B flows to chamber A through *CV*3, HPA, HM, LPA and *CV*4. The high-pressure fluid flows through HM lead to the HM, and G rotates simultaneously at the specified rotation speed *(ωG*) subjected to the load torque of the G (*τG*). As a result, the usable electricity can be generated by the continuous motion of this mechanism.

In general, the behaviour of the HPTO unit is strongly nonlinear. Equations (6)–(21) theoretically explain the operation of the considered HPTO unit illustrated in Figure 2. According to Equation (6), the *FPTO* from the HPTO unit applied to the WEC device depends on the pressure in both hydraulic chambers (*pA* and *pB*) and the effective piston area (*AP*). Further, the effects of piston friction (*Ff ric*) and initial force of rod, piston and oil (*Fin*) are also considered. These effects can be expressed using Equations (7) and (8), where *<sup>η</sup>f ric* is a friction coefficient, .. *xp* is the piston acceleration, *g* is a gravitational acceleration, *Mp*, *Mr* and *Moil* are the mass of the piston, rod, and oil, respectively [12,36].

$$F\_{\rm PTO} = A\_p(|p\_A - p\_B|) + F\_{fric} + F\_{in} \tag{6}$$

$$F\_{fric} = |A\_p(p\_B - p\_A)| \left(1 - \eta\_{fric}\right) \tag{7}$$

$$F\_{\rm in} = \ddot{x}\_p \left( M\_p + M\_r + M\_{\rm oil} \right) + \left( M\_p + M\_r \right) \text{g} \tag{8}$$

Since a double-acting-cylinder with a single rod piston is considered a hydraulic actuator, the *FPTO* is unbalanced during the upward and downward motion of the WEC device due to the unbalanced pressure in both chambers of the hydraulic cylinder. Based on the configuration of the HPTO unit in Figure 2, the *FPTO* during the upward movement is greater than the *FPTO* during the downward movement. The dynamics of *pA* and *pB* can be described using a fluid continuity equation as in Equations (9) and (10) [12,37]. *βeff* , *qA* and *qB* are the effective bulk modulus and the in/out volumetric flows in the hydraulic cylinder actuator. *xp*, . *xp* and *L* are position, velocity and stroke length of the piston. *Ap*,*<sup>A</sup>* and *Ap*,*<sup>B</sup>* are the effective piston area in the hydraulic chamber A and B, that can be expressed by Equations (11) and (12), where the *dp* and *dr* are the diameter of the piston and rod, respectively.

$$\frac{d}{dt}p\_A = \frac{\beta\_{eff}}{A\_{p,A}(L-x\_p)}(q\_A - \dot{x}\_p A\_{p,A})\tag{9}$$

$$\frac{d}{dt}p\_B = \frac{\beta\_{eff}}{A\_{p,B}\left(L - x\_p\right)} \left(\dot{x}\_p A\_{p,B} - q\_B\right) \tag{10}$$

$$A\_{p,A} = |\pi d\_p|^2 / 4 \tag{11}$$

$$A\_{p,B} = \pi \left(d\_p^{\;2} - d\_r^{\;2}\right) / 4 \tag{12}$$

For the check valve, the spring-loaded non-return valves are used in this HPTO model. The flow across the valve (*qCV*) can be described by the orifice equation, as expressed in Equation (13), where *Cd* is the discharge coefficient, *ACV* is the check valve opening area and *ρoil* is the fluid density. The *pCVin* and *pCVout* are the pressure at the inlet and outlet of the check valve [12,38].

$$q\_{CV} = \begin{cases} \ \ \ \mathbb{C}\_d A\_{CV} \sqrt{2|p\_{\mathbb{C}V\_{in}} - p\_{\mathbb{C}V\_{out}}|/\rho\_{\text{oil}}} \ \ \text{if} \ p\_{\mathbb{C}V\_{in}} > p\_{\mathbb{C}V\_{out}} \\ \ \ \text{0, else} \end{cases} \tag{13}$$

Besides that, the gas compression and expansion in the HPA and LPA, which are based on the isentropic process, can be described according to Equations (14) and (15), respectively. Where *pHPA*, *pLPA*, *p*0,*HPA* and *p*0,*LPA* are the pressure and pre-charge pressure in the HPA and LPA. *γ* is the adiabatic index of the compressed gas in the HPA and LPA, while, *VHPA*., *VLPA*, *V*0,*HPA* and *V*0,*LPA* are the initial and the instantaneous volume of gas in the HPA and LPA, respectively. The instantaneous volume of gas can be expressed by Equations (16) and (17), where *qHPA* and *qLPA* are the volumetric flow in the HPA and LPA.

$$p\_{HPA} \cdot V\_{HPA}{}^{\gamma} = \ p\_{0,HPA} \cdot V\_{0,HPA}{}^{\gamma} \tag{14}$$

$$p\_{\rm LPA} \cdot V\_{\rm LPA}{}^{\gamma} = \ p\_{0, \rm LPA} \cdot V\_{0, \rm LPA}{}^{\gamma} \tag{15}$$

$$V\_{HPA}(t) = V\_{0,HPA} - \int\_0^t q\_{HPA} dt\tag{16}$$

$$V\_{LPA}(t) = V\_{0,LPA} - \int\_0^t q\_{LPA} dt\tag{17}$$

Meanwhile, the fluid continuity in the HPTO model should satisfy the following equations:

$$q\_{HPA} = q\_{CV\_1} + q\_{CV\_2} - q\_{HM} \tag{18}$$

$$q\_{LPA} = q\_{\bar{C}V\_3} + q\_{\bar{C}V\_4} - q\_{HM} \tag{19}$$

where *qHM* is the volumetric flow through the hydraulic motor. Here, *qHM* is given by Equation (20), where *DHM*, *ωHM*, and *qHM,loss* are displacement, speed and volumetric flow losses of the hydraulic motor, respectively. The output torque of the hydraulic motor, *τHM* can be expressed by Equation (21), where Δ*pHM* is the pressure difference in the hydraulic motor.

$$q\_{HM} = D\_{HM} \omega\_{HM} - q\_{HM,loss} \tag{20}$$

$$
\pi\_{HM} = D\_{HM} \Delta p\_{HM} \tag{21}
$$

Based on the theoretical descriptions provided in Equations (6)–(21), the most important component parameters, which influence the operation of the HPTO model can be defined as summarised in Table 1. The inaccuracy of the selected component parameters will reduce the HPTO unit's capability in converting the absorbed wave energy to electrical energy. Thus, the optimisation of these important component parameters using mathematical algorithms is considered in this study.

**Table 1.** Important component parameters of the HPTO system.


#### **3. Simulation Studies of WECs**

#### *3.1. Ocean Wave Input Data*

A previous study reported that the ranges of the wave height (*HW*) and wave period (*TW*) at several locations in Terengganu, Malaysia, were equal to the range of 0.2–1.2 m and 2–8 s, respectively [39]. In addition, a further forecast analysis found that the most annual occurrences sea-state at the considered installed location were equal to 0.8 m and 2.5 s. From these statistical results, the regular and irregular wave inputs data were generated based on Airy's wave theory and Joint North Sea Wave Observation Project (JONSWAP) spectrum, as illustrated in Figure 3A,B, respectively. For the irregular wave data profile generation, the peak enhancement factor (γ) of JONSWAP was set to 2. Regular wave input profile data were used in determining the optimal parameters of the HPTO unit process. While the irregular wave input profile data were used to evaluate the effectiveness of the optimal HPTO unit in generating the electricity in inconsistent wave circumstances.

**Figure 3.** Ocean wave elevation inputs, (**A**) regular wave and (**B**) irregular wave.

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

In the present study, the main specifications of the computer device that was used for the simulation studies are given in Table 2. As can be seen from Equations (1) and (2), the frequency domain analysis was required to determine the hydrodynamic parameters of the WEC device. Thus, hydrodynamic simulation of the WEC model was preliminarily performed using ANSYS/AQWA software. The hydrodynamic simulation method presented in [40,41] was considered. The results from the preliminary hydrodynamic simulation are presented in Figure 4. The parameters obtained from the hydrodynamic simulation were used to build the complete simulation model of WEC with the HPTO unit in *MATLAB*®®/Simulink software, as illustrated in Figure 5. A WEC model based on the linear wave motion, as mentioned in Equations (1)–(5), was developed using the function blocks.

**Table 2.** Main specifications of the computer device.


**Figure 4.** Hydrodynamic analysis parameters. (**A**) Excitation force coefficient, (**B**) added mass coefficient, (**C**) radiation damping coefficient, and (**D**) impulse response function.

**Figure 5.** Illustration of simulation model set-up in MATLAB software.

Meanwhile, the HPTO model was developed using the hydraulic components in the Simscape Fluid toolbox, such as double hydraulic chamber single rod jack, hydraulic motor, hydraulic accumulator, hydraulic check valve with saturation, et cetera. The actual parameters of the hydraulic components from manufacturers were used to configure the HPTO model. Since the selection of the HPTO components was incredibly complex due to the variety of hydraulic products from the manufacturers and suppliers, the specification data of hydraulic components from a well-known manufacturer such as Parker Hannifin was considered, as summarised in Appendix A. The data in Appendix A were used as a guideline in determining the optimal configuration parameters of each element in the HPTO model simulation.

Furthermore, a simple dynamic sub-model of a rotary load was utilised to represent the permanent magnet synchronous generator (PMSG) unit. The generated electrical power output from the HPTO model was calculated based on the speed-power curve of PMSG, which was obtained from the manufacturer. In addition, the PTO force, hydraulic motor torque, hydraulic motor speed and electrical power were the acquired outputs from the HPTO model. The detailed specifications of each component that were used in the HPTO model are presented in Table 3.


**Table 3.** Technical specifications of the developed HPTO model.

\* Initial value by manual estimation.

Simulation results of the WEC with non-optimal HPTO unit using the regular waves input profile data are shown in Figure 6. Figure 6A shows that the displacement of WEC was relatively lower than the wave displacement due to the PTO force applied to the WEC device. The PTO force profile applied to the WEC device is shown in Figure 6B. The figure shows that the PTO forces applied to the WEC device during the upward and downward motion were equal to 1.5 kN and 0.7 kN, respectively. Meanwhile, Figure 6C shows the electrical power generated from the non-optimal HPTO unit only can be reached up to an average of 71 W, which was 71% of its rated capacity.

**Figure 6.** Preliminary simulation results of WEC with non-optimal power take-off (PTO) unit (*HW* = 0.8, *TW* = 2.5 s). (**A**) Wave, WEC and piston displacements, (**B**) PTO force, and (**C**) PTO power.

#### *3.3. Optimisation of Configuration Parameter*

As the sea state was relatively unstable throughout the year, a suitable HPTO unit was compulsory for a WEC device to ensure that the ocean wave energy can be maximally absorbed and converted to electrical energy. Conventionally, the optimal parameters of the HPTO unit were obtained by iteratively simulating the HPTO model using any sophisticated analysis software. In this process, the designer was required to manually specify a set of configuration parameters value, evaluate the HPTO unit model and analyse the PTO model output. Normally, this process may be repeated many times due to unsatisfactory results from the HPTO performance. Consequently, the designer again proposed a new set of HPTO parameters value based on experience and intuition, which probably will result in a better output of the HPTO model. This optimisation process will end when the time runs out. Unfortunately, sophisticated analysis software and highspeed computer technology were unable to help the designer in determining the optimal parameters of the HPTO unit using this technique.

Alternatively, the optimisation technique HPTO unit parameters using a computer algorithm was presented in this study. By using this technique, the designer was taken out from the trial-and-error loop process. The sophisticated computer was now utilised to conduct a complete determination process of the optimal configuration parameters. Through this technique, the designer workload can be reduced, in which the designer only focused on the interpretation of the optimisation results. Moreover, the determination of the optimal configuration parameters can be found in a shorter and more accurate time compared to the case using a conventional technique. In the algorithm-based optimisation technique, many kinds of algorithms can be applied to solve the optimisation problem.

In the present study, the simulation–optimisation using two major types of optimisation algorithms was explored in this present study. A specific objective function (OF) was designed to maximise the electrical energy generation of the HPTO unit, as described

in Equation (22). Here, *PPTO,ref* and *PPTO* represented the desired and the actual electrical power output of the HPTO unit. The optimisation problem in Equation (22) was solved by two kinds of optimisation algorithms, i.e., NLPQL and GA. In order to provide a fairground for comparison between two optimisation algorithms, the same constraints, design parameters, and objective function were considered for both cases under study. The details of the considered algorithms are described in the following subsections.

$$OF(\mathbf{x}) = \min \left[ \frac{\int\_0^T \left( \left| P\_{\rm PTO}(t) - P\_{\rm ref}(t) \right| \right) dt}{\int\_0^T P\_{\rm PTO, ref}(t) \, dt} \right] \tag{22}$$
