Kurniawan T. Waskito, Juan A.C. Siahaan, Muhamad A.N. Chuzain, Yanuar, Sumit Pal

Corresponding email: yanuar@eng.ui.ac.id

Corresponding email: yanuar@eng.ui.ac.id

**Published at : ** 18 Sep 2024

**Volume :** **IJtech**
Vol 15, No 5 (2024)

**DOI :** https://doi.org/10.14716/ijtech.v15i5.6617

Waskito, K.T., Siahaan, J.A.C., Chuzain, M.A.N., Yanuar, Pal, S., 2024. Design Optimization of a Point Absorber and Hydraulic Power Take-Off Unit for Wave Energy Converter.

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Kurniawan T. Waskito | 1. Department of Mechanical Engineering, Universitas Indonesia, 16424, Depok, Indonesia. 2. Tropical Renewable Energy Center (TREC), Faculty of Engineering, Universitas Indonesia, 16424, Depok, Indon |

Juan A.C. Siahaan | Department of Mechanical Engineering, Universitas Indonesia, 16424, Depok, Indonesia |

Muhamad A.N. Chuzain | Department of Mechanical Engineering, Universitas Indonesia, 16424, Depok, Indonesia |

Yanuar | Department of Mechanical Engineering, Universitas Indonesia, 16424, Depok, Indonesia |

Sumit Pal | TU Delft Wind Energy Institute (DUWIND), Kluyverweg 1, 2629 HS Delft, The Netherland |

Abstract

In recent times, the point absorber Wave Energy
Converter (WEC) has gained popularity due to its practicality. Investigating
the parameters of the Hydraulic Power Take-Off (HPTO) in the WEC, including
hose diameter and check valve variations, is crucial. This study analyzes
optimization using the Sequential Quadratic Programming (SQP) method in
MATLAB/SimScape, leading to a more comprehensive understanding of the
interactions among HPTO components, such as hydraulic cylinders, check valves,
hoses, accumulators, motors, and generators. Key system performance indicators,
including pressure drop, flow rate, and power output, were assessed in both
single and two-point absorber HPTO configurations. The optimization process
yielded a maximum hydraulic power output of 7.33 kW, a mechanical power output
of 6.41 kW, and an electrical power output of 5.4 kW using a 2-inch hose
diameter. Additionally, utilizing a two-point absorber model enhanced power
generation capacity by 47.4%, reaching 9.45 kW. The findings highlight the
significant pressure drop at the check valve, with the 2-inch hose model
experiencing a drop of 31.874 bar. These results demonstrate that optimizing
HPTO parameters can significantly improve the efficiency of converting wave
energy into electricity, providing valuable design recommendations for WEC
technology.

Design optimization; Hydraulic power take-off; Hose diameter; Sequential quadratic programming; Wave energy converter

Introduction

Many
contemporary power plants predominantly rely on conventional energy sources.
However, a notable drawback associated with this approach is the considerable
emissions generated, which inflict detrimental effects on the environment. Consequently, there exists a progressive
trend towards adopting renewable energy sources that manifest a markedly
diminished ecological footprint *et al.,* 2017)*et al.,* 2021; Wahyudie
*et al.,* 2020; Kusuma, 2018; Prasetyo, Kurniawan,
and Komariyah, 2018)

The
literature review highlights the significance of a robust Power-Take Off (PTO)
system in efficiently converting ocean wave energy into electrical power *et al.,*
2022; Jusoh *et al.,* 2019; Gaspar *et al.,* 2018; Hansen, Kramer,
and Vidal, 2013; Marquis, Kramer, and Frigaard, 2010; Drew, Plummer, and Sahinkaya, 2009)*et al.,* 2017; Penalba and Ringwood,
2016; Hansen, Kramer, and Vidal, 2013), Multi-point Absorber *et al.,* 2015; Lin *et
al.,* 2015)*et al.,* 2022). These systems, along with various
parameter configurations (Jusoh *et al.,* 2022; 2021), underscore hydraulic systems'
versatility in WEC.

Furthermore,
the review emphasizes the importance of evaluating the performance of valves
and hoses, pivotal components in the HPTO setup, to understand fluid flow
dynamics and pressure distribution within the system. However, it does not
explicitly compare the performance or effectiveness of different types of
valves and hoses, which could be a potential avenue in this research.

The
necessity for a more efficient and economical approach to optimize HPTO systems
for maximum power generation needs to be investigated. To advance WEC with
HPTO, the stability and energy absorption mechanisms of the HPTO system need
refinement. The optimal design of the kinematics of the floating arm cylinder
plays a pivotal role in the HPTO system. It plays a pivotal role in achieving
optimal power generation. Therefore, it is essential to accurately estimate
each component, as mentioned in the study by * et* *al.,*
2024)

In
this study, we employ the Sequential Quadratic Programming (SQP) numerical
optimization method to estimate parameter values for each component of the
Hydraulic Power Take-Off (HPTO) system, specifically focusing on the check
valve and hose. Unlike traditional experimental methods, SQP offers advantages
such as handling nonlinear relationships, constrained optimization, smooth and
continuous functions, iterative refinement, handling multiple design variables,
global convergence, and incorporation of sensitivity analysis. By leveraging
SQP, the study aims to identify parameter combinations that maximize power
output and consider existing constraints effectively and economically. This
systematic approach represents a novel method for optimizing HPTO systems in
WECs, thereby addressing the research gap and contributing to the advancement
of wave energy conversion technologies.

Experimental Methods

This section describes the methods for
modeling the floating absorbers and HPTO. It begins by modeling the WEC with
the HPTO unit, providing a mechanical overview of the WEC. Next, it describes
the mathematical formulation of the HPTO and the parameter optimization process
using Sequential Quadratic Programming.

*2.1. Modeling the WEC with HPTO Unit: An Overview* The evaluation and presentation of the
HPTO is initiated by outlining its layout and key components. This includes a
description of the HPTO's main features and overall operation. The HPTO with
Double Acting Cylinder (DAC) was selected based on its component efficiency and
power generation capabilities. In this system, the floating absorber is
connected to a fixed body to capture the kinetic energy of ocean waves
effectively. The HPTO
system is coupled with floating absorbers to convert mechanical energy into
usable electrical power. Figure 2 displays the floating absorber system with a Hydraulic Power
Take-Off unit. This
unit comprises a Hydraulic Motor (HM), Check Valve (CV), High-Pressure
Accumulator (HPA), Low-Pressure Accumulator (LPA), and a generator (G). In this
design, the floating absorber's arm experiences reciprocating motion in
response to pitch and heave motions caused by ocean waves at certain
frequencies. This arm motion actuates the cylinder mechanism, generating
pressure in each chamber. This pressure drives hydraulic fluid into the HPA via
hydraulic hoses and check valves (CV1 and CV3). The pressurized fluid is then
directed to the HM. Any excess pressure from the hydraulic motor is stored in
the LPA, subsequently re-entering the flowline input of the double-acting
cylinder through CV2 and CV4.

**Figure 1** Design and Modeling
of the WEC, Single-Point WEC System, Adepted fron *et
al.,* (2024)

*2.2. Mechanical overview of the WEC*

The
geometry of the floaters can be represented as a combination of a sphere and an
upper truncated cone. These floaters are primarily constructed with glass-fiber
material and include a ballast chamber that can be filled through a hole
located at the bottom. This chamber retains water during power generation. The
ballast serves two main purposes: reducing the absorber's natural frequency and
adjusting the draft of the floater as required. Additionally, the PTO cylinders
serve as a mechanism for elevating the floaters during storm protection.

The
oscillating motion of the floater arm generates a moment, as depicted in Figure 3. The arm
position is described by the angle which is defined to be zero when the floater is horizontal. Positive
rotation is defined as the floater moving upwards. The angular velocity of the
arm is denoted The PTO cylinder force is denoted

The cylinder’s moment arm may be expressed as:

The linear potential theory is used for the hydrodynamic model by solving the frequency domain. The formula is given as follows:

where *J*_{WEC}
is the floater and arm moment of inertia of wave energy converter, is the added mass. are the
angular acceleration, angular velocity, and angular position of WEC during the
pitch motion. is the radiation impulse response function, is the time delay, is the hydrostatic restoring coefficient, is the impulse response function, and is the undisturbed wave elevation at the
floater center point. The coefficients can be determined from hydrodynamic
analysis using potential flow computation such as the Constant Panel Method
(CPM), Higher Order Boundary Method (HOBEM), and ANSYS AQWA (ANSYS 2014;
Newman 1986) (11-12). In Equation (4) the non-linear effect of
HPTO is considered, so that the moment on HPTO can use Equation (5).

**Figure 3** Flow chart of the HPTO optimization process

*2.3. Mathematical formulation of the HPTO model*

In the HPTO unit, many parameters are
considered, such as chamber piston area piston friction the pressure of the hydraulic chamber piston acceleration Mass of the piston, rod, and oil and gravitational acceleration All equations are written
in Equation (6-8).

The piston chamber experiences constantly
changing pressure due to the upward and downward motion. By using equations (9)
and (10), it is possible to obtain dynamic values of pressure in the piston
chamber by considering the effective bulk modulus in/out volumetric flow and velocity on piston The chamber area is obtained from Equations (11) and (12). are the piston and rod diameters.

The
fluid flow rectifier uses four check valves in each cylinder. In equation (13), is the flow through the check valve. * *are the pressure on the in and out section of the
valve. is the discharge coefficient. is the area of the valve. is the density of fluid, oil.

High-pressure
accumulators (HPA) and Low-Pressure accumulators (LPA) are essential components
in maintaining pressure stability in the PTO system. Equation (14-17) is used
to find the pressure and volume values of the accumulator. are the pressure and
pre-charge pressure in the HPA and LPA. are the initial and the instantaneous volume
of gas in the HPA and LPA, and ?* *is the adiabatic index accumulators.

Volumetric flow in HPA and LPA can be calculated by
equations (18) and (19):

Equation
(20) below is used to obtain volumetric flow through the hydraulic motor. are displacement, speed, and volumetric flow
losses of the HM. The torque in the HM can
also be determined by Equation (21), where is the difference in pressure in HM.

Hoses
play a crucial role in connecting different components in hydraulic systems.
They facilitate the smooth flow of hydraulic fluid, which helps to convert
fluid energy into mechanical energy. This process ultimately leads to the
generation of electrical power. During simulations conducted in Simulink, hoses
are represented as hydraulic resistive tubes, accounting for the hydraulic
channel's resistance. Additionally, these hoses tend to experience pressure
losses, that is subsequently simulated within Simulink using the Darcy equation
as in the following Equations (22-24):

*P* is Pressure loss along the pipe due to friction, *q* is flowrate
through the pipe. *Re* is a Reynold Number, and are Reynold number at laminar and turbulent flow. *K _{s}* is the
shape factor that characterizes the pipe cross-section. are friction factors at laminar and turbulent flow. are area, diameter, and length of pipe
hydraulic.

*2.4. Parameter Optimization of HPTO using **Sequential
Quadratic Programming*

Figure 3 shows the flow chart of HPTO
optimization process. The initial value for finding the optimal parameters in
the check valve, accumulator, hose, and hydraulic motor is determined by the
predetermined sizing of the hydraulic cylinders and configurations of the
components.

The
Hydraulic Power Take-Off (HPTO) design phase encompasses the establishment of
layout, schematics, and configurations. This design process is executed using
MATLAB/Simscape and Simulink software. An approach based on available
manufacturer specifications is employed to determine initial component
parameters, as outlined in Table 1. Simulations are conducted on the design of
a single absorber to assess its performance, with simulation results compared
against desired performance outputs. This iterative process involves random
component selection until suitable outputs and parameters are
approximatedSubsequently, these parameters are processed using the Sequential
Quadratic Programming (SQP) algorithm through the Response Optimizer feature in
order to optimize the HPTO design. This optimization aims to determine the most
suitable parameter configurations obtained from Equation (25)

**Figure 4** Regular sine wave force input at the hydraulic cylinder 20kN

The Response Optimizer in MATLAB software enables users to determine design parameters based on the system's response to the desired objectives. To achieve this, specific values need to be defined. This optimization aims to ensure that the motor speed does not exceed 4300 RPM or 460 rad/s. Figure 5 illustrates the angular motor speed amplitude in rad/s before optimization.