! Abstract-- This paper presents the conceptual model for

pressure amplification in harnessing sea wave energy to

generate electricity. It is named as AH Presto 1 which is the

short form for Air-Hydraulic Pressure Storage Version 1. The

idea of the concept is converting the air pressure generated

from undulating sea water free surface inside the oscillating

wave column (OWC) chamber adopting the concept done

from previous study by few scientists and to amplify the

hydraulic pressure which can be stored in hydraulic

accumulator for consistent pressure distribution source for

electricity generation. The OWC is commonly and widely used

in the existing wave energy converter (WEC) devices to

extract the energy from sea waves. Mathematical model is

used in proving the energy conversion and pressure

amplification. Initially, basic conceptual model is developed to

represent the whole process from the sea wave signal until the

final output. Several sub-modules have been developed to

integrate the complete system. Amongst the sub-modules are;

sea wave energy extraction and air pressure development

using OWC, air pressure to hydraulic pressure amplification,

hydraulic pressure storage; hydraulic pressure distribution,

gearing system and electricity generation. Mathematical

equations have also been derived in this study to represent the

processes involved in each stage.

Index Terms--Electricity generation device, Wave Energy

Converter, Oscillating Wave Column, Pressure amplification,

Pressure storage.

I. INTRODUCTION

Energy plays a big role in driving the economy. The total

worldwide energy consumption was estimated to be 474 x

1018 J in 2008 [1] but decreased by 1.1% for the first time

in 30 years in 2009 [2] due to the slowdown in economic

activities. The slowdown in economic was really affected

United States, European and some of the Asian countries. Most of the energy in the world is generated using the

conventional way, mainly fossil fuel and coal [3] but the

wastes from the processes have affected the environment.

The conventional process which involves the burning of

fossil fuel products, coal and the process of nuclear

contribute to the air, soil and water pollution. The

emmission from the processes’ wastes have damaged the

ozone layer and led to the changing of climate and causing

global warming phenomenon as reported by Folley et. al. in

[4]. Fossil fuel and coal are non-renewable. It was reported

that the amount of fossil fuel and coal are decreasing by 5%

started from year 2005. In 1980’s and after First World

Baharin Abu Bakar at baharin_abubakar@yahoo.com

I. Musirin is with the Faculty of Electrical Engineering, Universiti

Teknologi MARA, Malaysia. (Tel/Fax: +603-55435044. E-mail:

ismailbm@salam.uitm.edu.my)

M.M.Othman can be reached at mamat505my@yahoo.com

M.N.A.Rahim can be reached at beta_ink@yahoo.com

War, the effort in developing wave energy converter

(WEC) has been reduced due to the drop of petroleum price

[5]. Kyoto Protocol, enforced reduction of CO2 emission to

the atmosphere, effect to climate changes, high oil prices,

reduction in fossil fuel quantity, influenced the increase of

research in sourcing alternative techniques inclusive of

WEC in many countries [7-8]. The former Chairman of

Shell, Lord Oxburgh, warned,”Crude oil prices can reach

up to USD 150 per barrel in the next two decades and any

government which does not take immediate measure and

strategies to convert its economy into clean renewable

energy production methods might be slept walking into

unprecedented crises” [8]. One of the most promising

renewable energy which has high power density is the

energy extracted from the sea wave [3, 11]. Wave energy is

more persistent compared to wind energy [7]. The non-

conventional resources are non polluting and has

continuous availability, attract the researchers to develop

new energy extraction system [5]. Ocean covers more than

70% of the earth’s surface and make it the largest power

source on earth. The global wave power was estimated at 1

TW (1 terawatt = 1012W) [7]. There have been many

reports on the efforts to convert the ocean energies into

usable energy such as electricity. Extracting the energy

from sea wave offshore began to be taken seriously since

1970’s [6]. Inventors that are impressed with the energy

produced by the ocean waves, had proposed many different

devices to extract wave power [7]. Not many has been

commercialized and most of them are still under the trial

mode. Existing design of WECs required strong sea waves

with high amplitude to collect the energy. That is why most

of them constructed offshore and north of the hemisphere.

They cannot work efficiently in area with small waves or

during calm sea with low amplitude of wave. The most

popular device of WEC is the OWC which is partly

submerged in the water with open-end at the bottom. The

trapped air on the upper part of the water free surface inside

OWC chamber is directed to the turbine to produce the

electricity. To get high amplitude sea wave, there were few

prototypes that had been built using vertical or horizontal

turbines [8, 10-11]. The nearshore wave energy has been

studied and found to be significantly small compared to the

offshore wave energy, but building the power plant

nearshore is more economical [6]. This paper presents the

conceptual model of sea wave energy in electricity

generation. The study involves the development of

mathematical model of each module for the whole system.

II. DEVELOPED AH PRESTO MODEL

Most of the invented WECs convert the energy from sea

wave to usable energy directly without energy storage.

Those systems totally depends on real time sea wave

conversion result, if the wave is strong enough then the

Mathematical Model of Sea Wave Energy in

Electricity Generation

Baharin Abu Bakar1, Ismail Musirin

2, Muhammad Murtadha Othman

3, M.N.A Rahim

4

The 5th International Power Engineering and Optimization Conference (PEOCO2011), Shah Alam, Selangor, Malaysia : 6-7 June2011

154

978-1-4577-0353-9/11/$26.00 © 2011 IEEE978-1-4577-0354-6/11/$26.00 ©2011 IEEE

energy converted will be high. On the other hand, if the sea

wave is weak then the converted energy will be weak or no

energy will be converted at all. The most promising and

reached commercialized stage and widely used WEC is the

oscillating wave column (OWC). OWC becomes a part of

AH Presto 1 system in extracting the sea wave energy. AH

Presto 1 is a short form of Air-to-Hydraulic Pressure

Storage version 1. The conceptual model is illustrated in

Fig.1.

Fig. 1 Conceptual Model of AH Presto 1

The complete system consists of sea wave energy

extraction and air pressure development using OWC, air

pressure to hydraulic pressure amplification, hydraulic

pressure storage; hydraulic pressure distribution, gearing

system and electricity generation. The sea incident waves

forced the sea water into the column of OWC through the

submerged opening. This will cause the water free surface

inside the column to lift upward. When the incident wave

force is zero, the free water surface will stop raising and

starts to fall down due to gravity. This creates an oscillation

inside the column. The trapped air will be occupied on the

upper part of the free water surface inside the column. The

oscillation of the free water surface inside the column due

to the incident wave action, displaces a volume flow rate of

air and produces an oscillating air pressure. This oscillating

air pressure will be directed to the Air-to-Hydraulic

Pressure Booster. The Air-to-Hydraulic Pressure Booster is

a pressure amplification device. The amplified pressure or

pressure ratio from the Air-to-Hydraulic Pressure Booster is

then stored in hydraulic pressure accumulator and shown

by the following equation:-

pressureair

pressureoil

ratioInput

OutputP

_

_"

pistonhydraulic

pistonair

A

A

_

_" (1)

III. DEVELOPED MATHEMATICAL MODEL

The energy from a single incident wave entering the

OWC is taken as the beginning point. The sea wave

consists of potential energy (PE) and kinetic energy (KE).

Assume a particle on one point of the wave line. This

particle will follow the wave motion up and down results in

vibration. The vibrating particles produce a Simple

Harmonic Motion (SHM) as can be illustrated in Fig. 2.

Referring to a waveform shown in Fig. 2, the equation of an

SHM is given by:

)(2

sin xvty #"$%

& (2)

Where:

!:sea wave amplitude (m)

v: wave propagation velocity (m/s)

": wave length (m)

t: wave cycle time (s)

A. Sea Wave Energy

The particle velocity pv , can be determined by

differentiating equation (2) with respect to time,

dt

dyv p "

Thus, dt

dycan be derived as

)(2

cos2

xvtv

dt

dy#"

$%

$%&

(3)

Work done per unit volume for a displacement of dy is

given by

' ( ))*

+,,-

."""

2

2

dt

ydmddmaFdW

' ( dyxvtv

W /0

123

4#5"

$%

$&%

62

sin4

2

22

(4)

Work done at a distance y, ie:- y70

' (5 /0

123

4#"

y

dyxvtv

W0

2

22 2sin

4

$%

$&%

6

(5)

Potential Energy PE, per unit volume can be determined as,

Therefore,

' (/01

23

4 #" xvtv

PE$%

&$6% 2

sin2 22

2

22

(6)

The kinetic energy per unit volume can be derived as,

2

2

1pvKE 6"

Fig 2 Waveform

155

' (/01

23

4 #" xvtv

KE$%

$&6% 2

cos2 2

2

222

(7)

From equation (6) and (7), we can determine the total

energy, 89!!generated per unit volume as resulted in

equation (8),

KEPEET :"

2

2222

$&6% v

ET " (8)

B. Developed Energy in OWC

The energy developed in the OWC can be represented

from the water flow in Fig. 3. When a volume of sea water

enters the OWC through the submerged opened end, the

upward force generated and caused free water surface to

rise in the opposite direction of the gravity.

Fig.3 Energy developed in OWC

The rising up of the free water surface developed an energy

termed as swowcE # , resulted from the product of the

propagating wave and the volume of the sea water inside

the OWC. The volume of the free water surface is the

volume being displaced.

The energy developed inside the OWC due to the rising

up of free surface sea water can be determined as follows;

VEE Tswowc "# (9)

where, hrV 2%"

V: volume of displaced sea water (m3)

r: internal radius of OWC (m)

h: distance of water free water surface travels from

lowest level to highest level (m)

Assuming that the lowest level of free water surface and the

highest level is equal to sea wave peak to peak, (that is

twice the amplitude), therefore;

&2"h ,

and the displaced sea water is,

&% 22 rV " (10)

By substituting equation (10) into equation (9), we have,

2

23234

$&6% rv

E swowc "# (11)

C. Converted Energy

The law of energy conservation states that energy can be

neither created nor destroyed. If we assume that the air

inside the OWC is incompressible and by ignoring the

energy loss, the energy due the rising water free surface

swowcE # is equal to the energy due to the air motion. That

means the volume displaced by the water free surface is

equal to the volume displaced by the air, airowcE # .

airowcswowc EE ## "

Therefore, from equation (11), we have,

2

23234

$&6% rv

E airowc "# (12)

Where,

#: density of sea water (kg/m3)

r: internal radius of OWC (m)

D. Air to Hydraulic Pressure Amplification

The power generator requires high pressure and rotary

torque in ensuring that the mechanisms to function

accordingly. The characteristics of the sea wave and the

developed air pressure from the trapped air on the upper

side of the water free surface inside the column will be

considered [6]. It is known that the upward force, also

called as the lifting force of the free water surface is greater

as compared to the downward force. Fig. 4 illustrates the

flow of air in the air-to-hydraulic pressure booster. An

object will float if the water lifting force is greater than the

downward force. By differentiating equation (12), the force

generated due to the rising up of the free water surface can

be given by,

2

3238

$&6% rv

dr

dE airowc "# (13)

force" , F

This is the generated force at OWC and is then transferred

to Air-to-Hydraulic Pressure Booster primary section. The

pressure developed at the primary section, Pair can be

written as:

Pair

primaryA

F" (14)

Where,

F: force acting on the primary piston developed

from OWC (N)

156

Aprimary: cross-sectional area of primary piston (m2)

By substituting equation (13) into equation (14), air

pressure is given by;

Pair =

primaryA

rv2

2238

$&6%

(15)

Force acting on primary section; Fprimary is equal to the force

acting on secondary piston Fsecodary.

Fsecondary = Fprimary

Therefore, from equation (13), we have;

2

323

sec

8

$&6% rv

F ondary "

The amplified pressure ampP , can be determined by;

ondary

ondary

ampA

FP

sec

sec"

primary

ampA

rkvP

2

3238

$&6%

" (16)

From equation (16), simplifying the equation;

' (2

3261027.1),,(

$&

$&kv

vPamp

;"

(17)

Where,

#:density of sea water = 1025 kg/m3

v: velocity of propagation wave = (0!2 m/s)

!: wave amplitude = (0!4 m)

r: radius of OWC cross sectional area. Let it be constant at

1

k: amplification factor (>1)

": wavelength = (0!10 m)

Aprimary: Cross sectional area of primary piston = 2 m2

The amplified pressure is shown in equation (17). This

amplified pressure is used to give high torque to rotate the

gearing system where the hydraulic motor is the driver.

This amplified pressure is directed to the hydraulic pressure

accumulator.

IV.RESULTS AND DISCUSSION

The developed model has been reviewed and checked

rigorously. The conceptual and mathematical models

should be able to function accordingly in order generate the

appropriate level of energy, forces and amplified pressure

for the purpose of electricity generation. Each model in

every particular stage has indicated that the mathematical

equations are correctly derived and verified. However, in

this paper no numerical results have been demonstrated

since the idea is to obtain the model which has capability to

generate electricity using the sea wave energy. Derivation

of related mathematical equations in each stage

demonstrated that all the relationships are true and

explainable.

V. CONCLUSION

This paper has presented the conceptual model of

electricity generation harnessing sea wave energy. Several

mathematical models have been developed to represent the

relationship among the sub modules in the system. All the

developed mathematical equations have been validated and

eventually the output will be able to generate electricity.

There are many types of WECs introduced earlier. Each

of WEC has its own capabilities and suitable for some

specific condition of sea wave. The earlier inventions give

some guidance to the future inventions for better design and

this could result in a high standard efficiency sea wave

power plant. Future design of sea wave power plant has to

be suitable for any sea wave condition and location.

VI. ACKNOWEMENT

The authors would like to acknowledge the Ministry of

Higher Education (MOHE) and The Research Management

Institute (RMI) for the financial supports of this research.

This research is jointly financed by MOHE under the

Fundamental Research Grant Scheme (FRGS) with project

code of 600-RMI/ST/FRGS 5/3/Fst (170/2010) and RMI

under the Excellence Research Grant Scheme under the

project code of 600-RMI/ST/DANA 5/3/Dst (278/2009).

REFERENCES [1] Statistical Review of World Energy 2009, BP July 31, 2006.

Retrieved 2009. pp. 10-24

[2] Global Energy Review in 2009, Enerdata Publication.

[3] A.P. McCabe, A. Bradshaw, J.A.C. Meadowcroft, G. Aggidis,

“Developments in the design of the PS Frog Mk 5 wave energy

converter” , Renewable Energy 31 (2006) 141-151.

[4] M. Folley, T.J.T. Whittaker, A. Henry, “The effect of water depth

on the performance of a small surging wave energy converter”,

Ocean Engineering, Vol. 34, 2007, pp 1265-1274

[5] BS Borowy, ZM Salameh, Optimum Photovoltaic Array Size for a

Hybrid Wind/PV System, IEEE Trans Energy Convers 9(3), 1994,

pp 482-488

[6] M. Folley, T.J.T Whittaker,”Analysis of the nearshore wave energy

resource”, Renewable Energy 34 (2009) 1709-1715

[7] Johannes Falnes, “A Review of Wave Energy Extraction”, Marine

Structures, Vol. 20, 2007 pp 185-201.

[8] M. Leijon, O. Danielsson, M. Eriksson, K. Thorburn, H. Bernhoff,

J. Isberg, J, Sundberg, I. Ivanova, E. Sjostedt, O. Agren, K.E.

!

Fig.4 Air-to-Hydraulic Pressure Booster

157

Karlsson, A. Wolfbrandt, “An electrical approach to wave energy

conversion”, Renewable Energy 31 (2006). pp. 1309-1319.

[9] Technology White paper, ‘Wave Energy Potential on the U.S.

Outer Continental Shelf”, Minerals Management Services,

Renewable Energy and Alternate Use Program, U.S. department of

Interior, May 2006.

[10] DV Evans, R. Porter,’Hydrodynamic Characteristics of an

oscillating water column devices’,Applied Ocean Research 17

(1995), pp 155-164

[11] Ruo-Shan Tseng, Rui-Hsian Wu, Chai-Cheng Huang,’Model study

of a shoreline wave power system’, Ocean Engineering 27 (2000),

pp 801-821.

[12] J. Falnes, “Optimum control of oscillation of wave energy

converters”, Main report: Wave Energy Converters: Generic

Technical Evaluation Study, Institutt of fysikk, NTH, Universitetet I

Trondheim, Norway, 1993.

[13] Temel Ozturk, Ayhan Demirbas, “Electricity Generation Using

Water Lifting Force”, Energy Exploration & Exploitation, Vol. 24

No. 4 and 5, 2006, pp 285-296.

[14] A. El Marjani, F. Castro Ruiz, M.A. Rodriguez, M.T. Parra

Santos,’Numerical modelling in wave energy conversion system’,

Energy 33 (2008), pp1246-1253

BIOGRAPHIES Baharin Abu Bakar received Bachelor of

Science in Electrical & Electronics

Engineering from Napier University of

Edinburgh, Scotland, United Kingdom in

1995. He has been working in the industries

for the past 22 years. He was an engineer at

Motorola, Petaling Jaya, Selangor from 1995

to 2001; dealt with equipment maintenance and

machine enhancement. Then he worked at

Bluescope Steel as a reliability engineer from

2001 to July, 2004. In August 2004 until

September 2006, he was attached as a Senior Research Engineer to

Invenqjaya, a research and development company; dealing with water

desalination, hybrid car and self-propelled surf board oil spillage detection

system. He joined Standard Industrial Research Institute of Malaysia

(SIRIM) in November 2006 until June 2010. Then, he set up a research and

development company, HB AGRO Machineries in 2009. He is currently

working towards his MSc Research studies at the Faculty of Electrical

Engineering, Universiti Teknologi Mara, Shah Alam, Selangor, Malaysia.

His research interest includes wave energy conversion to electricity,

machine design and engineering innovation.

Assoc. Prof. Dr. Ismail Musirin obtained

Diploma of Electrical Power Engineering in

1987, Bachelor of Electrical Engineering (Hons)

in 1990; both from Universiti Teknologi

Malaysia, MSc in Pulsed Power Technology in

1992 from University of Strathclyde, United

Kingdom and PhD in Electrical Engineering in

2005 from Universiti Teknologi MARA,

Malaysia. He is currently an Associate Professor

at the Centre for Electrical Power Engineering

Studies (CEPES), Faculty of Electrical Engineering, Universiti Teknologi

MARA, Shah Alam, Malaysia. His research interest includes power system

stability, optimization techniques, distributed generation, biological

computing, computational intelligence and artificial intelligence. He is the

Past Chair, IEEE-PES Malaysia Chapter, member of Computational

Intelligence-IEEE, Senior Member of IACSIT, member of IAENG and

ARTIST.

Dr. Muhammad Murtadha bin Othman

received the B.Eng. (Hons) degree from

Staffordshire University, U.K., in 1998; the

M.Sc. degree from Universiti Putra Malaysia,

Serdang, Malaysia, in 2000 and Ph.D. degree

from Universiti Kebangsaan Malaysia, Bangi,

Malaysia, in 2006. He is currently a senior

lecturer at the Centre for Electrical Power

Engineering Studies (CEPES), Faculty of

Electrical Engineering, Universiti Teknologi MARA, Malaysia. His area of

research interests are artificial intelligence, transfer capability assessment

and reliability studies in a deregulated power system. He is a member of

IEEE.

Muhammad Norazam obtained the B.Eng.

(Hons) degree from Universiti Teknologi

MARA, Shah Alam, Malaysia in 2008. He has

published several technical papers in the

international conferences. He is currently

working towards his MSc Research studies at

the Faculty of Electrical Engineering, Universiti

Teknologi Mara, Shah Alam, Selangor,

Malaysia. His area of research interest is in

optimization techniques such as bee colony

optimization technique, evolutionary programming, particle swarm

optimization and fuzzy logic. He also deals with operational strategy of

hybrid renewable energy system; and distributed generation.

158