**1. Introduction**

Ocean waves are considered as one large untapped and predictable renewable energy resource on earth. Ocean waves contain tremendous of usable energy and have the potential to contribute to a significant share of global renewable energy sources. Ocean wave energy has many advantages such as high energy density, high source availability, source predictability and low environmental impact compared to other renewable energy (RE) sources [1]. The energy density of ocean waves is the highest among all renewable energy sources, which is around 50–100 kW/m [2]. Approximately, 8000–80,000 TWh/year ocean wave energy is available globally [2]. Due to its advantages, electrical energy production from the ocean waves has received a great deal of attention over the past several decades. Numerous wave energy converter systems (WECs) with different harnessing methods have been invented to convert the kinetic energy contained in the ocean waves into usable electricity, as reported in [3–6]. The existing WECs can be classified into wave-activatedbody (WAB), oscillating water column (OWC) and overtopping device based on their working principles.

The WAB wave energy converters (WAB-WECs) are also known as oscillating bodies wave energy converters and point absorber wave energy converters. WAB-WECs can be defined as a single body or multiple bodies devices being oscillated by the wave excitation force [7]. WAB-WECs covers a kinds of WEC and recent development of WAB-WECs

**Citation:** Jusoh, M.A.; Yusop, Z.M.; Albani, A.; Daud, M.Z.; Ibrahim, M.Z. Investigations of Hydraulic Power Take-Off Unit Parameters Effects on the Performance of the WAB-WECs in the Different Irregular Sea States. *J. Mar. Sci. Eng.* **2021**, *9*, 897. https:// doi.org/10.3390/jmse9080897

Academic Editor: Eugen Rusu, Kostas Belibassakis and George Lavidas

Received: 13 July 2021 Accepted: 13 August 2021 Published: 20 August 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

around the world has been reported in [4,6,8,9]. In general, these WAB-WECs consist of three main subsystems, namely wave energy converter (WEC), power take-off (PTO) unit, and control system (CS) unit. WEC is a front-end device that absorbs the kinetic energy from the ocean waves. The absorbed energy is then converted to electricity through the PTO unit, whereas the control system unit is used to optimize the electrical energy produced from the WECs during its operation.

PTO is one of the most essential subsystems of WAB-WECs. In recent decades, a wide variety of PTOs have been designed, developed and experimentally tested for numerous types of WEC device, as reported in [10]. The various kinds of PTO concepts can be classified based on their main working principles, such as mechanical–hydraulic, direct mechanical, direct electrical drive, air and hydro turbine. The hydraulic power take-off (HPTO) unit is one of the most reliable and effective PTOs for the WECs [11,12]. The HPTO unit has excellent characteristics, such as high efficiency, wide controllability, well-suited to the low-frequency and large power density of ocean waves, etc. The HPTO unit can also be assembled using standard hydraulic components that are readily available from the hydraulic equipment suppliers. In [11], a review of the most popular HPTO concepts used in WAB-WECs is reported. From the study, the HPTO concepts can be classified into two main groups, i.e., a variable-pressure and a constant-pressure concept. The constantpressure concept has received more attention. Based on the report in [13], the efficiency of the constant-pressure concept is much higher than that of the variable-pressure concept, which can reach up to 90%. According to [14], several crucial parameters may influence the efficiency of the HPTO unit, such as the mounting position and piston size of the hydraulic actuator, volume capacity and pre-charge pressure of the accumulator, displacement of hydraulic motor and damping coefficient of the electric generator.

Recently, several kinds of research into the HPTO in WAB-WECs have been published for various objectives, for example in [15–21]. From the literature, most of the studies have concentrated on the performance of the HPTO unit without investigating the influence of the important parameters of HPTO. Only a few studies have discussed this issue, e.g., [14,16]. In [14], the influence of the HPTO unit parameters on the power capture ability of two-raft-type of WEC was studied. However, the HPTO concept used in [14] is very different from the HPTO concept considered in the present study. The effects of the HPTO unit on the percentage of power reduction were not discussed in this study. Meanwhile, in [16], the sensitivity of the generator damping coefficient on the average generated electrical power was investigated. From the simulation results, the authors concluded that the generator damping coefficient is relatively sensitive to the changes in wave height and period. However, the sensitivity of the other HPTO parameters was not discussed in [16]. Since there is a lack of published articles on this issue, the present study proposes an investigation of the HPTO unit parameters on the performance of the WAB-WECs. The main objective of the study is to investigate the effect of these important parameters on the electrical power generated from the HPTO unit. The findings can be a useful reference to other researchers for improvement of WECs in future.

The remainder of this paper is organized as follows. Section 2 presents the design of the considered WECS and Section 3 describes the simulation study for investigation of the HPTO parameters. Section 4 presents the results and discussion. Finally, the conclusion and future work are discussed in Section 5.

#### **2. Design of WEC with HPTO Unit**

The WEC concept based on [20] is considered in the present study. The simplified concept is shown in Figure 1A. The WECs consist of a single floating body (floater) attached to the fixed body via a hinged arm, which is also known as the WEC device. This WEC device design is almost similar to the concepts used in [13,22–24]. The WEC device is unique due to its ability to convert both wave kinetic energy and wave potential by utilizing the pitch motion of the floater and hinged arm, as presented in Figure 1A. In this system, the WEC is connected to the fixed-body directed to the dominant wave direction to optimally absorb the kinetic energy from the ocean waves. The WEC device is then connected to the HPTO and the CS unit is placed in the HPTO house to convert the mechanical energy from the WEC device into usable electricity.

**Figure 1.** An illustration of WEC with the HPTO unit concept. (**A**) A complete layout design, and (**B**) Enlarge image of the interconnection between HA, floater's arm and fixed structure.

Figure 1A presents the simplified diagram of the HPTO unit which includes a hydraulic actuator (HA), hydraulic hose (HH), check valve rectifier module (CV1, CV2, CV3 & CV4), oil tank (OT), high-pressure and low-pressure accumulators (HPA & LPA), pressure relief valve (RV1 & RV2), hydraulic motor (HM) and electric generator (G). In this concept, double-acting with a single rod type of HA is considered. HA is used as a linear pump to absorb the mechanical energy from the reciprocating motion of the WEC. The piston rod of the HA is attached to the floater's arm using a rod end clevis while the barrel of the HA is attached to the fix-structure. Then, the HA is connected to the check valve rectifier module, an arrangement of four check valves in a bridge circuit configuration, as shown in Figure 1A. The check valve rectifier used in this HPTO unit is similar to the Graetz bridge concept, which is used for conversion of an alternating-current (AC) input into a direct-current (DC) output. For the HPTO, the check valve rectifier module is used to control the fluid flow direction (*QA* & *QB*) from the HA to the HM. Thus, the large chamber (chamber A) of the HA barrel is connected to the inlet and outlet of CV1 and CV4, while the small chamber (chamber B) of the HA barrel is terminated to the inlet and outlet of CV2 and CV3, respectively. The check valve rectifier module is then connected to the HPA and LPA. The HPA is included in the HPTO unit to constrain the pressure of the HM in

the desired ranges. Finally, the generation module which consists of fixed-displacement of HM coupled to G is placed between the HPA and OT. In addition, the pressure relief valves RV1 & RV2 are placed to prevent the HPTO unit from over-pressurized fluid flows.

During the operation of WECs, the passing of ocean waves causes a WEC device to pitch upward and downward simultaneously. Then, the reciprocating motion of the WEC device causes back-and-forth motions of the piston and directly generates the high-pressure fluid flow from the HA chambers. During the upward movement of the WEC device, the high-pressure fluid flows from chamber A to chamber B through CV1, HPA, HM, LPA, and CV2. On the other hand, during the downward movement, the high-pressure fluid flows from chamber B to chamber A through the CV3, HPA, HM, LPA, and CV4 of the WEC device. The high-pressure fluid flowing through the HM causes the HM and G to rotate simultaneously in one direction and thus produces usable electricity. Overall, the speed and torque of the HM depend highly on the characteristics of ocean wave motions such as speed, frequency, wavelength, and amplitude [25]. They also depend on the important parameters of the HPTO unit itself.

#### *2.1. Formulation of Hydrodynamic Pitch Motion of WEC*

The hydrodynamic pitch motion of WEC in real waves can be formulated in the time domain to account for the non-linear effects such as the hydrodynamics of a floater, HPTO force, etc. So, the equation for the pitch motion of the WEC device can be expressed by:

$$M\_D = M\_{\rm cx} - M\_{\rm rad} - M\_{\rm res} - M\_{\rm HPTO} \tag{1}$$

where *MD* is the D'Alembert moment of inertia, and *Mex*, and *Mrad* are the moments due to the diffracted and radiated ocean waves. *Mres* and *MHPTO* are the moments due to hydrostatic restoring and HPTO unit interactions, respectively. The hydrodynamic pitch motion of the WEC equation above can be extended as follows:

$$(f\_{\rm WEC} + f\_{\rm add,\infty})a\_{\rm WEC}(t) + \int\_{0}^{t} k\_{\rm rad}(t - \tau) \cdot \omega\_{\rm WEC}(t) + k\_{\rm res} \cdot \theta\_{\rm WEC}(t) + M\_{\rm HPD}(t) = \int\_{-\infty}^{\infty} h\_{\rm ex}(t - \tau) \eta\_{\rm W}(\tau) d\tau \tag{2}$$

where *JWEC* is the moment of inertia of WEC (includes floater and hinged arm), *Jadd*, <sup>∞</sup> is the added mass at the infinite frequency. *τ* is the time delay. *θWEC*, *ωWEC* and *αWEC* are the angular position, angular velocity and angular acceleration of WEC during the pitch motion, respectively. *θWEC* = 0 corresponds to the WEC device at rest. *krad* and *kres* are the radiation impulse response function and the hydrostatic restoring coefficients. *hex* is the excitation force coefficient and *η<sup>W</sup>* is the undisturbed wave elevation at the center point of the floater. The coefficients of *krad*, *kres* and *hex* can be determined from the dynamic diffraction analysis using computational fluid dynamics (CFD) software, such as ANSYS/AQWA, as previously implemented in [20,26–30]. Alternatively, these coefficients also can be obtained using the boundary element method (BEM) toolbox in WAMIT software, as suggested in several studies [31–35].

Since the non-linear effect of the HPTO unit is considered in Equation (2), the moment due to the HPTO unit *MHPTO* can be described using Equation (3). According to Figure 1B, *FHPTO* is the feedback force of the PTO unit applied to the WEC device. *L*<sup>1</sup> is the perpendicular distance between HA and point *C*, which can be obtained using Equation (4), where *L*<sup>2</sup> and *L*<sup>3</sup> are the distance between points *A-C* and *B-C*, respectively. *L*4,0 is the initial distance between points *A-B*. *θWEC*,0 and *θWEC* are the initial and instantaneous angle of the WEC device. *xp* is the linear displacement of the piston. Based on Equation (4), *L*<sup>1</sup> is always relatively changes according to the change of the arm angle, as illustrated in Figure 1B.

$$M\_{\rm HPTO} = F\_{\rm HPTO} L\_1 \tag{3}$$

$$L\_1 = \frac{L\_2 L\_3 \sin(\theta\_{WEC,0} - \theta\_{WEC})}{L\_{4,0} + x\_{HA}}\tag{4}$$

$$\mathbf{x}\_p = L\_{4,0} - \sqrt{L\mathbf{z}^2 + L\mathbf{z}^2 - 2L\_2L\_3\cos(\theta\_{WEC,0} - \theta\_{WEC})}\tag{5}$$

#### *2.2. Formulation of HPTO Unit*

Technically, the force generated by the HPTO unit, *FHPTO* is represented by the feedback force applied by the HA to the WEC device. The nonlinear *FHPTO* is generated due to the dynamic pressure in chambers A and B (*PA* & *PB*) and the piston friction force (*Ff ric*) of the HA. The *FHPTO* can be expressed using Equation (6), where *Ap*,*<sup>A</sup>* and *Ap*,*<sup>B</sup>* are the sectional areas of the piston in chambers A and B, respectively. *Ap*,*<sup>A</sup>* and *Ap*,*<sup>B</sup>* can be obtained using Equations (7) and (8), where *dp* and *dr* are the piston and rod diameter of the HA. Meanwhile, the dynamics of *PA* and *PB* can be calculated according to the fluid continuity function, as described in Equations (9) and (10), where *βeff* is the bulk modulus of the hydraulic fluid. *QCV*<sup>1</sup> to *QCV*<sup>4</sup> are the flow rates across the check valves CV1 to CV4. *Ls*, *xp* and . *xp* are the stroke length, linear displacement and linear velocity of the piston, respectively.

$$F\_{\rm HPTO} = P\_A A\_{p,A} - P\_B A\_{p,B} + F\_{fric} \tag{6}$$

$$A\_{p,A} = \pi d\_p^{-2}/4\tag{7}$$

$$A\_{p,B} = \pi \left(d\_p^{\ 2} - d\_r^{\ 2}\right) / 4 \tag{8}$$

$$\frac{d}{dt}P\_A = \frac{\beta\_{eff}}{A\_{p,A}(L\_s - \chi\_p)} \left(\dot{\mathbf{x}}\_p A\_{p,A} + Q\_{CV4} - Q\_{CV1}\right) \tag{9}$$

$$\frac{d}{dt}P\_B = \frac{\beta\_{eff}}{A\_{p,B}\left(L\_s - \chi\_p\right)} \left(\dot{\chi}\_p A\_{p,B} + Q\_{CV2} - Q\_{CV3}\right) \tag{10}$$

The flow rates *QCV*<sup>1</sup> to *QCV*<sup>4</sup> can be generally calculated using Equation (11), where *Cd* and *ACV* are the discharge coefficient and the working area of each check valve. *PCVin* and *PCVout* are the inlet and outlet pressure of each check valve. *ρoil* is the hydraulic oil density.

$$Q\_{CV} = \begin{cases} \mathbb{C}\_d A\_{CV} \sqrt{\frac{2}{\rho\_{\rm oil}} |P\_{CVin} - P\_{CVout}|} & \text{, if } P\_{CVin} > P\_{CVout} \\ 0 & \text{, if } P\_{CVin} < P\_{CVout} \end{cases} \tag{11}$$

On the other hand, the fluid volume (*VHPA*) and flow rate (*QHPA*) which enters the accumulator can be calculated using Equations (12) and (13), where *VHPA*,*cap* is a capacity, *PHPA*,0 is the initial pressure and *PHPA*,*in* is the inlet gauge pressure of HPA, and *n* is the specific heat ratio, respectively. The initial pressure in the accumulators depends on the pre-charge pressure of the nitrogen gas in the HPA bladder.

$$V\_{HPA} = \begin{cases} V\_{HPA, \text{cap}} \left[ 1 - \left( \frac{P\_{HPA,0}}{P\_{HPA,in}} \right)^{\frac{1}{n}} \right] & \text{, if } P\_{HPA,in} > P\_{HPA,0} \\ & 0 & \text{, if } P\_{HPA,in} \le P\_{HPA,0} \end{cases} \tag{12}$$

$$Q\_{\rm HPA} = \dot{V}\_{\rm HPA} = \begin{cases} \frac{1}{n} V\_{\rm HPA,cap} \left( 1 - \frac{P\_{\rm HPA,0}}{P\_{\rm HPA,in}} \right)^{\frac{1-n}{n}} \frac{P\_{\rm HPA,0} \dot{P}\_{\rm HPA,in}}{P\_{\rm HPA,in}^2} & \text{, if } P\_{\rm HPA,in} > P\_{\rm HPA,0} \\ 0 & \text{, if } P\_{\rm HPA,in} \le P\_{\rm HPA,0} \end{cases} \tag{13}$$

Meanwhile, the flow rate across the HM (*QHM*) and the actual torque of HM (*τHM*) can be obtained using Equations (14) and (15), where *DHM*, *ωHM* and Δ*PHM* are the displacement, angular speed and the internal pressure difference of HM. *ηHM*, *<sup>V</sup>* and *ηHM*, *<sup>M</sup>* are the volumetric and mechanical efficiency of HM.

$$Q\_{HM} = D\_{HM} \omega\_{HM} / \eta\_{HM,V} \tag{14}$$

$$
\pi\_{HM} = \Delta P\_{HM} D\_{HM} \eta\_{HM,M} / 2\,\pi \tag{15}
$$

Finally, the electric power generated by the electric generator (*PG*) can be expressed using Equation (16), where *ωG*, *τ<sup>G</sup>* and *η<sup>G</sup>* are angular speed, the torque and overall efficiency of the electrical generator. Since the electrical generator and HM are rotating simultaneously, the *ω<sup>G</sup>* and *τ<sup>G</sup>* are equal to *ωHM* and *τHM*, respectively.

$$P\_{\mathbb{G}} = 2\pi\omega\omega\_{\mathbb{G}}\tau\_{\mathbb{G}}\eta\_{\mathbb{G}} = 2\pi\omega\_{HM}\tau\_{HM}\eta\_{\mathbb{G}} \tag{16}$$
