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The Simulation of Wave Energy Conversion by Floating Point Absorber Buoy in

Indonesian Sea Waves

Conference Paper · August 2021

DOI: 10.1109/ICA52848.2021.9625671

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 The Simulation of Wave Energy Conversion by
Floating Point Absorber Buoy
in Indonesian Sea Waves
Nurvita Aji Estiyanti Ekawati Irsyad Nashirul Haq
Instrumentation and Control Engineering Physics Research Group Engineering Physics Research Group
Postgraduate Program Faculty of Industrial Engineering Faculty of Industrial Engineering
Faculty of Industrial Engineering Institut Teknologi Bandung Institut Teknologi Bandung
Institut Teknologi Bandung Bandung, Indonesia Bandung, Indonesia
Bandung, Indonesia esti@instrument.itb.ac.id irsyad@tf.itb.ac.id
ajinurvita@alumni.itb.ac.id

Abstract—Referring to National Energy Policy or ocean has the potential to be used as a source of alternative
Government Regulation No. 79/2014, Indonesia has set out energy. The energy stored in the ocean consists of thermal
several plans to increase the New and Renewable Energy (NRE) energy, kinetic energy (waves and current), and chemical and
share in the primary energy mix to 23% by 2025 and 31% by biological products [2]. Waves on the ocean are generated by
2050. Ocean wave energy is one of the potential renewable winds and distributed in all directions over the ocean. The
energy sources. This study presents the simulation of ocean energy density of wave farms is 2-3 kW/m2, higher than solar
wave energy conversion of Indonesian sea waves, specifically parks (0.1-0.2 kW/m2) and wind farms (0.4-0.6 kW/m2).
along the west coast of Sumatra, the southern coasts of Java, and Besides, wave energy is available 90% of the time, whereas
Bali waters. The Wave Energy Converter Simulator (WEC-
solar and wind power availability is hardly 20-30% times [3].
Sim) simulated five hot spots of high wave energy using the
floating-point absorber buoy RM3 model. These five hotspots
Therefore, ocean wave energy is considered a renewable and
are South Pagai Island II (101.25oE-4.25oS), Enggano Island sustainable energy source, especially in Indonesia, based on
(102.25oE-5.5oS), Cilacap (109.06oE-7.94oS), Jember (113.68oE- the fact that its sea area (about 7.9x106 km2, including an
8.56oS), and Bali (115oE-8.75oS). RM3 is the third reference exclusive economic zone) constitutes about 81% of the
model of wave energy converter developed by The U.S. country's total area [4].
Department of Energy (DOE), The National Renewable Energy Ocean wave energy as a renewable energy source was
Laboratory (NREL), and The Sandia National Laboratory
simulated for 25 years, from 1991 to 2015, on the west coast
(SNL). Meanwhile, the WEC-Sim software uses the Cummins
equation in the 6 degrees of freedom (DOF) modeling process.
of Sumatra Island. It shows eight noticeable hotspots in certain
In this simulation, the Pierson-Moskowitz (PM) spectrum was areas with significant wave height values of up to 2.33 m and
used to model irregular waves. The WEC's power take-off wave energy values of up to 67.29 kW/m [5]. Furthermore, 12
(PTO) mechanism was simulated as a hydraulic system where hotspots along the southern coast of Java and Bali have wave
the hydraulic power absorbed depends on the differential energy values of higher than 20 kW/m [6]. These figures
pressure of the hydraulic piston and the piston area. This provide insight into potential locations for ocean-wave energy
simulation used the rotary electrical generator with an energy harvesting. Five hotspots were selected based on the highest
conversion efficiency of 98% in electricity generation. significant wave height and wave energy value in this study to
According to the selected location, the simulation was running simulate wave energy converter. These are South Pagai Island
for 400 seconds of time simulation and 0.01 seconds of time step II (101.25oE-4.25oS), Enggano Island (102.25oE-5.5oS),
with the predefined parameters, such as significant wave height Cilacap (109.06oE-7.94oS), Jember (113.68oE-8.56oS), and
and wave period. The average value of electrical powers Bali (115oE-8.75oS).
generated during the simulation were 15.85, 15.53, 18.13, 14.10,
and 15.69 kilowatts (kW) while the total of accumulated Several Wave Energy Converter (WEC) technologies are
electrical powers were 634, 621, 725, 564, and 627 megawattss developed by institutions and companies, such as oscillating
(MW) for South Pagai Island II, Enggano Island, Cilacap, water column, oscillating wave surge converter, wave dragon,
Jember, and Bali. salter’s duck, and floating-point absorber device [7].
Oscillating water column (OWC) technology is mainly
Keywords—Wave Energy Converter, WEC, WEC-Sim, researched in Indonesia. This type of technology adapted in
renewable energy, wave simulation Aru Island and Arafuru Sea using quantitive analysis based on
The Indonesian Agency for Meteorology, Climatology, and
I. INTRODUCTION Geophysics (BMKG) data could reach out the power of 313
As referred Government Regulation No 79. 2014 on kW [8]. OWC was also implemented in Sungai Suci Beach
National Energy Policy, New and Renewable Energy (NRE) Bengkulu and could generate 1.003 MW of power [9]. This
mix target is at least 23% by 2025 and 31% by 2050. study presents the floating-point absorber-typed wave energy
Meanwhile, in 2018, the installed capacity of power plants converter simulation in the five locations mentioned above
was dominated by fossil fuel power plants, particularly coal using Wave Energy Converter Simulator (WEC-Sim). WEC-
(50%), followed by gas (29%), fuel (7%), and NRE (14%). Sim was chosen because it is free, open-source, and integrated
One of the breakthroughs to achieve the primary energy mix with MATLAB/Simulink, which many engineers are familiar
target as mandated in the National Energy Policy is with this software.
implementing energy efficiency through the massive use of
This study aims to find the output electrical powers in
energy-saving technology and NRE. It is also synchronized
Indonesian sea waves needed for the wave energy converter
with Indonesia’s commitment in Paris Agreement to prevent
implementation in the future. In section 2, the methodology of
earth temperature increase above 2 degrees Celcius [1]. The
WEC-Sim and its code structure are discussed. In section 3, 𝜂𝜂(𝑥𝑥, 𝑦𝑦, 𝑡𝑡) = ∑𝑖𝑖
𝐻𝐻𝑖𝑖
cos(𝜔𝜔𝑖𝑖 𝑡𝑡 − 𝑘𝑘𝑖𝑖 (𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝜃𝜃𝑖𝑖 + 𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝜃𝜃𝑖𝑖 ) + 𝜙𝜙𝑖𝑖 ) (4)
WEC’s geometry and wave specification are described to run 2

the simulation, and the results are presented in section 4. The where 𝜔𝜔 is the wave frequency ( 𝜔𝜔 = ), 𝐻𝐻 is the wave
2π
conclusions of the work are given in section 5. 𝑇𝑇
height, 𝜃𝜃 is the wave direction, 𝑘𝑘 is the wave number (𝑘𝑘 =
2π
II. WAVE ENERGY CONVERTER SIMULATOR (WEC-SIM) ), and 𝜙𝜙 is the wave phase.
𝜆𝜆
WEC-Sim is an open-source code for modeling wave The calculation of wave energy in deep water [16], 𝑃𝑃𝑤𝑤 ,
energy converters. The code is written in Matlab/Simulink and becomes as follows:
uses the multi-body dynamics solver (Simscape Multibody).
WEC-Sim can model devices made up of bodies, joints, power 𝑃𝑃𝑤𝑤 =
𝜌𝜌𝑔𝑔2
𝐻𝐻𝑚𝑚0 2 𝑇𝑇𝑒𝑒 (5)
take-off systems, and mooring systems in the 6 degrees of 64𝜋𝜋
freedom (DOF) modeling process. WEC-Sim is developed by where 𝐻𝐻𝑚𝑚0 is the significant wave height. It is a statistical
the National Renewable Energy Laboratory (NREL) and parameter used to represent the wave in nature and simplify
Sandia National Laboratories (Sandia), funded by the U.S. the calculation of the wave energy, which is defined as four
Department of Energy (DOE) [10]. times the square of variance, and thus 𝐻𝐻𝑚𝑚0 = 4�(𝐻𝐻 2 /8).
WEC-Sim predicts power performance and design Meanwhile, 𝑇𝑇𝑒𝑒 is known as the energy period estimated by 0.9
optimization using a radiation and diffraction method times the peak period.
[11][12]. In general, the hydrodynamic forces are obtained C. Pierson-Moskowitz wave spectrum
via a frequency-domain boundary element method (BEM)
solver that uses linear coefficients to solve the system A wave spectrum is a frequency domain representation of
the linear superposition of regular waves of different
dynamics in the time domain. In this study, AQWA [13]
amplitudes and durations. Specific factors such as significant
BEM solver was used. The BEM solutions are derived by
wave height, peak period, wind speed, and fetch length are
solving the Laplace equation assuming inviscid, used to characterize spectra through statistical analysis. In this
incompressible, and irrotational flow. study, Pierson-Moskowitz (PM) wave spectrum was used to
A. Time-domain numerical method model the irregular sea wave.
WEC system equations of motion [12][14] are used to The peak wave frequency and the significant wave height
compute the system's dynamic response. For a floating body are used to create the PM spectrum. The surface elevation
around its center of gravity, the equation of motion is: spectral density defined by the PM spectrum [17] is defined as
follows:
𝑚𝑚𝑋𝑋̈ = 𝐹𝐹𝑒𝑒𝑒𝑒𝑒𝑒 + 𝐹𝐹𝑟𝑟𝑟𝑟𝑟𝑟 + 𝐹𝐹𝑣𝑣 + 𝐹𝐹𝑃𝑃𝑃𝑃𝑃𝑃 + 𝐹𝐹𝐵𝐵 + 𝐹𝐹𝑚𝑚𝑚𝑚 + 𝐹𝐹𝑚𝑚 (1)
𝐻𝐻𝑚𝑚0 2 5 𝑓𝑓𝑝𝑝
where 𝑚𝑚 is the mass matrix, 𝑋𝑋̈ is the (translational and 𝑆𝑆𝑃𝑃𝑃𝑃 (𝑓𝑓) = (1.057𝑓𝑓𝑝𝑝 )4 𝑓𝑓 −5 𝑒𝑒𝑒𝑒𝑒𝑒 �− � �� (6)
4 4 𝑓𝑓
rotational) acceleration vector of the device, 𝐹𝐹𝑒𝑒𝑒𝑒𝑒𝑒 (𝑡𝑡) is the
wave excitation force and torque vector, 𝐹𝐹𝑟𝑟𝑟𝑟𝑟𝑟 (t) is the force where 𝑓𝑓 is the wave frequency, and 𝑓𝑓𝑝𝑝 is the peak wave
and torque resulting from wave radiation, 𝐹𝐹𝑣𝑣 (𝑡𝑡) is the frequency (𝑓𝑓𝑝𝑝 = 1/𝑇𝑇𝑝𝑝 ).
damping force and torque vector, 𝐹𝐹𝑃𝑃𝑃𝑃𝑃𝑃 (𝑡𝑡) is the power take- D. Hydraulic Power Take-Off (PTO)
off (PTO) force and torque vector, 𝐹𝐹𝐵𝐵 (𝑡𝑡) is the net buoyancy
restoring force and torque vector, 𝐹𝐹𝑚𝑚𝑚𝑚 (𝑡𝑡) is the Morison The reaction force of the hydraulic PTO [18] is given by:
Element force and torque vector, and 𝐹𝐹𝑚𝑚 (𝑡𝑡) is the force and 𝐹𝐹𝑃𝑃𝑃𝑃𝑃𝑃 = Δ𝑃𝑃𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝐴𝐴𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 (7)
torque vector resulting from the mooring connection.
𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 = −𝐹𝐹𝑃𝑃𝑃𝑃𝑃𝑃 𝑋𝑋̇𝑟𝑟𝑟𝑟𝑟𝑟 (8)
Based on the Cummins equation [15], the radiation term
can be calculated as follows: where, Δ𝑃𝑃𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 is the differential pressure of the hydraulic
𝑡𝑡 piston and 𝐴𝐴𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 is the piston area. 𝑋𝑋̇𝑟𝑟𝑟𝑟𝑟𝑟 are the relative
𝐹𝐹𝑟𝑟𝑟𝑟𝑟𝑟 (𝑡𝑡) = −𝐴𝐴∞ 𝑋𝑋̈ − ∫0 𝐾𝐾𝑟𝑟 (𝑡𝑡 − 𝜏𝜏)𝑋𝑋̇ (𝜏𝜏)𝑑𝑑𝑑𝑑 (2)
motion and velocity between two bodies. 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 is the
where 𝐴𝐴∞ is the added mass matrix at an infinite frequency instantaneous hydraulic power absorbed by the PTO.
and 𝐾𝐾𝑟𝑟 is the radiation impulse response function. Meanwhile, E. The Workflow of WEC-Sim
across all wave frequencies, the irregular excitation force can
be calculated as the real part of an integral term as follows: The WEC-Sim workflow is shown in Figure 1 below.
WEC-Sim requires hydrodynamic data (*.h5), geometry file
𝐹𝐹𝑒𝑒𝑒𝑒𝑒𝑒 = (*.stl), Simulink model (*.slx), and input file
𝑖𝑖�𝜔𝜔𝑗𝑗 𝑡𝑡+𝜙𝜙𝑗𝑗 � (wecSimInputFile.m) for running the simulation. The steps to
ℜ �𝑅𝑅𝑓𝑓 (𝑡𝑡) ∑𝑁𝑁
𝑗𝑗=1 𝐹𝐹𝑒𝑒𝑒𝑒𝑒𝑒 �𝜔𝜔𝑗𝑗 , 𝜃𝜃�𝑒𝑒 �2𝑆𝑆�𝜔𝜔𝑗𝑗 �𝑑𝑑𝜔𝜔𝑗𝑗 � (3) run the WEC-Sim code are described referring to the WEC-
Sim workflow diagram [10]:
where ℜ denotes the real part of the formula, 𝑅𝑅𝑓𝑓 is the ramp
function, 𝑁𝑁 is the number of frequency bands selected to a) Step 1: Pre-Processing
discretize the wave spectrum, 𝜙𝜙 is the randomized phase Users input the wave specification (wave height, wave
angle, and 𝑆𝑆(𝜔𝜔) is the irregular wave field. period, wave spectrum) and WEC geometry properties.
b) Step 2: Generate Hydrodata File
B. Irregular waves and wave energy calculation
Users run BEMIO (Boundary Element Method
Irregular waves are modeled as the linear superposition of Input/Output) to convert the hydrodynamic coefficient from
a large number of harmonic waves of various frequencies and
BEM solution into *.h5 format.
incidence angles [10], with the incident wave specified as
𝜂𝜂(𝑥𝑥, 𝑦𝑦, 𝑡𝑡) :
Fig. 1. Wave Energy Converter Simulator (WEC-Sim) workflow diagram [10] based on Matlab/Simulink

c) Step 3: Build Simulink Model displaced water. STL (Standard Tessellation Language or
Users build Simulink model (*.slx) developed in STereoLithography) files represent the surface geometry of a
Simulink/Simscape. 3D object without include any color, texture, or other
d) Step 4: Write wecSimInputFile.m properties. The STL format of the RM3 model, as shown in
Figure 3, can be read and written by 3D design software, such
Users input the settings of simulation, body mass
as Meshlab. The general properties for the full-scale WEC are
properties, wave conditions, and constraints. Users also
shown in Table 1.
specify the location of the WEC-Sim Simulink model,
hydrodynamic data file, and geometry file.
e) Step 5: Run WEC-Sim
Execute the WEC-Sim code by typing “wecSim” into
the Matlab Command Window.
F. Floating-point absorber buoy (RM3)
WEC is modeled in WEC-Sim version 4.2 as a two-body
floating-point absorber buoy (FPAB) developed by U.S.
DOE’s Reference Model Project [19]. FPAB, known as the
third reference model or RM3, consists of a float and a
spar/plate coupled to a central column, and it converts energy Fig. 3. Spar/plate and float geometry of WEC
from the axial motion between these components induced by
ocean waves, as illustrated in Figure 2a. TABLE I. GENERAL PROPERTIES OF RM3 MODEL.

Mass Moment of Inertia (kgm2)

CG (m)
(tonne) 𝐼𝐼𝑥𝑥 𝐼𝐼𝑦𝑦 𝐼𝐼𝑧𝑧
0.00 2.09E+07 0.00E+00 0.00E+00
Float 0.00 727.01 0.00E+00 2.13E+07 0.00E+00
-0.72 0.00E+00 0.00E+00 3.71E+07
0.00 9.44E+07 0.00E+00 0.00E+00
Spar/Plate 0.00 878.30 0.00E+00 9.44E+07 0.00E+00
-21.29 0.00E+00 0.00E+00 2.85E+07

G. Wave specification and simulation

In this study, the 25 years simulated significant wave
height data covering the time interval of 1991-2015 from the
WAVEWATCH-III numerical model was used [5][6]. It was
(a) (b) found that there were eight hotspots along the west coast of
the Sumatra Island and tewlve hotspots along the southern
Fig. 2. A representation of (a) the RM3 model and (b) the WEC-Sim model
coasts of Java, Bali, and Nusa Tenggara waters which were
Figure 2b shows the RM3 model in the WEC-Sim for considered to be high potential wave energy sources. They
were Aceh, Simeuleu Island, Nias Island, Siberut Island,
wave excitation, radiation, net buoyancy restoring, PTO
North Pagai Island, South Pagai Island I, South Pagai Island
force, and viscous damping calculations. The float and
II, Enggano Island, Pandeglang, Sukabumi, Cianjur,
spar/plate masses are in their equilibrium positions (center of Pangandaran, Cilacap, Kebumen, Jogjakarta, Trenggalek,
gravity), in which each body mass equals the mass of
Malang, Jember, Alas Purwo, and Bali with wave energy were needed to run the simulation. These properties are
mean value higher than 20 kW/m. The range of wave period described in the previous subsection. The same RM3
(𝑇𝑇𝑒𝑒 ) between 10 and 16 s and the significant wave height geometry was used for simulation in the five selected
(𝐻𝐻𝑚𝑚0 ) interval between 1.5 and 3 m are found in most sea locations. Figure 5 shows the dynamic responses for float and
states at each selected point. spar/plate body after simulating with the time simulation of
400 seconds and the time step of 0.01 seconds. Spar/plate
The significant wave height is an important parameter that body has more fluctuated total force during the simulation, as
affects the wave energy. Five locations were selected based on shown in the figure below. These total forces are the sum of
the significant wave height value (𝐻𝐻𝑚𝑚0 ) and wave energy excitation force, radiation force, PTO force, viscous damping
mean. The higher significant wave height of the sea wave force, net-buoyancy force, and mooring-connection force.
means the higher generated wave energy. Table II shows the Cilacap is the location that generates the highest total force,
wave specification of the selected location used for the WEC meaning the more energy it can be converted, such as
simulation. The period parameters ( 𝑇𝑇𝑒𝑒 ) were determined mechanical or electrical energy.
based on the higher probability occurrences for 25 years.

TABLE II. GENERAL PROPERTIES OF SEA WAVES

No Location City/Island 𝑇𝑇𝑒𝑒 (s) 𝐻𝐻𝑚𝑚0 (m)
1 109.06oE-7.94oS Cilacap 13 1.91
2 113.68oE-8.56oS Jember 13 1.66
3 115oE-8.75oS Bali 13 1.76
4 101.25oE-4.25oS South Pagai Island II 13 1.77
5 102.25oE-5.5oS Enggano Island 13 1.75

The first step of WEC simulation is modeling the sea

wave of the selected locations. The significant wave height
and wave period parameters with PM wave spectrum were
used to simulate the irregular waves. PM spectrum is created
by peak wave frequency and significant wave height. The
location with the higher significant wave height has the
higher surface elevation spectral density. Cilacap is the
location with the highest wave spectrum, while Jember is the
lowest one. It is shown in Figure 4 that represents the PM
wave spectrum and wave surface location for the five selected
locations.

Fig. 5. Spar/plate and float’s heave force total

H. Hydraulic PTO simulation

The PTO mechanism used in this simulation is modeled as
a hydraulic system. The hydraulic PTO system was used
because of its outstanding qualities, such as low-frequency
and large power density waves [20]. The hydraulic PTO
system, in general, consists of a hydraulic cylinder, a check
(a) valve, a hydraulic motor, hydraulic accumulators, and hoses
to connect the various components. Hydraulic PTO uses a
hydraulic cylinder system to transform wave energy into
mechanical energy and convert it into usable electrical energy
using a generator.

TABLE III. GENERAL PROPERTIES OF HYDRAULIC PTO SYSTEM

Hydraulic
Properties Quantity Unit
PTO element
Top area 0.0378 m2

Piston
Bottom area 0.0378 m2
(b) Total moment
Hydraulic 20 kgm2
of inertia
Fig. 4. The simulation of (a) the wave spectrum and (b) wave elevation motor
Friction 0.05 kgm2/s
The floating-point buoy absorber or RM3 WEC model Efficiency 0.98
Rotary
was simulated after getting the irregular sea wave models. Generator
RM3 geometry files, including float and spar/plate geometry, Speed 150 rad/s
 The reaction force of the hydraulic PTO depends on the Jember. It has the same order for the location which generates
differential pressure of the hydraulic piston and the piston the highest average mechanical power and electrical power.
area. The higher differential pressure will generate higher The generated electrical power is always lower than the
mechanical energy. Therefore, it is crucial to determine the mechanical power because the motor efficiency used during
specification of the hydraulic PTO system. The properties of the simulation is under a hundred percent.
the hydraulic PTO used in this simulation are shown in Table Besides, the WEC device generates the highest average
III above. electrical power in Cilacap with the highest significant wave
III. RESULT AND DISCUSSION height value. On the contrary, Jember, which has the lowest
significant wave height value, generates the lowest average
A. Hydraulic PTO forces electrical power. It means that the significant wave height is
The WEC device is linked to the PTO systems and will a crucial parameter to determine the output power of the wave
actively transfer forces and motions against them. energy.
Meanwhile, a PTO system turns the WEC device's captured
oscillation power into usable electricity. Hydraulic PTO
forces were affected by the total force of WEC bodies (float
and spar/plate). Based on the simulation, Hydraulic PTO
yields the PTO force interval between -0.2 and 0.2 MN, as
shown in Figure 6.

Fig. 6. The simulation of the PTO force for five selected locations

B. WEC Output Power

The absorbed power, mechanical power, and electrical
power exhibited during the simulation are shown in Figure 7.
The average absorbed power by the WEC device is in the
range of 21.13 to 26.19 kW. Meanwhile, the range of average
mechanical power is from 17.02 to 21.53 kW, and the range
of average electrical power is from 14.10 to 18.13 kW. The
location WEC model generates average absorbed power in
which during the simulation from the highest to the lowest
are Cilacap, South Pagai Island II , Bali, Enggano Island, and Fig. 7. WEC absorbed power, mechanical power, and electrical power
C. Accumulated Electrical Power REFERENCES
Figure 8 shows the accumulated electrical energy based [1] N. I. P. Suharyati, S.H. Pambudi, J.L. Wibowo, “Indonesia Energy
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ACKNOWLEDGMENT [19] V. S. Neary et al., “Methodology for Design and Economic Analysis
of Marine Energy Conversion (MEC) Technologies,” Sandia Natl.
This research was funded by P3MI ITB Research 2021 Lab., no. March, p. 261, 2014.
and Indonesia Endowment Fund for Education (LPDP). We [20] J. F. Gaspar, M. Calvário, M. Kamarlouei, and C. Guedes Soares,
gratefully acknowledge the ITB and LPDP supports. The “Power take-off concept for wave energy converters based on oil-
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Postgraduate Program students for their supports and
discussion.

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