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Energy and Earth Science 
Vol. 1, No. 1, 2018 

www.scholink.org/ojs/index.php/ees 
ISSN 2578-1359 (Print)   ISSN 2578-1367 (Online) 

33 
 

Original Paper 

Systems Design for Energy Demand by Optimal Utilization of 

Renewable Energy in Robust Aquaponic Systems 

Tim Chen1,2, Asim Muḥammad3, Bertrand Chapron4, C.Y.J. Chen5,6 & Alexander Babanin7 
1 School of Geography, Earth and Environmental Sciences, University of Birmingham, Birmingham, 

UK 
2 Department of Surface Water and Maritime Systems, Fraunhofer I0SB-AST, Ilmenau, Germany 
3 Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia 
4 Laboratoire d'Océanographie Physique et Spatiale, Centre de Brest, IFREMER, Plouzané, France 
5 Industrial Technology Research Institute, Hsinchu, Taiwan 
6 BRAC Univ, Department of Computer Science and Engineering, Dhaka, Bangladesh 
7 Department of Infrastructure Engineering, University of Melbourne, Melbourne, Victoria, Australia 

 

Received: October 12, 2018   Accepted: November 8, 2018   Online Published: November 21, 2018 

doi:10.22158/ees.v1n1p33         URL: http://dx.doi.org/10.22158/ees.v1n1p33 

 

Abstract 

In a debate with other reservoirs, ocean waves furnish an ample supply of clean, reliable, and decent 

energy, but this origin requires to be made a cost-effective fount for physical energy return. For this 

mission, the proposed membership functions are adopted and stabilization criterion of the closed-loop 

T-S fuzzy systems are obtained through a new parametrized LMI (linear matrix) inequality which is 

rearranged by machine learning membership functions. 

Keywords 

ocean waves, LMI, membership functions 

 

1. Introduction 

Wave energy can generate large amounts of clean, safe, reliable, and economical renewable energy, 

thus making it an attractive source to meet the rapidly growing demand for energy (Gericke, 1940). 

Although in its infancy, the wave energy industry is expected, similar to the offshore wind power 

industry, to become established in several Nordic countries because of the rapid growth in the past 

decade. Among the various renewable energy sources (such as solar, wind, and tidal power), wave 

energy has the highest power density and provides relatively continuous and reliable output, which is 

advantageous for the operation of the power grids (Klinger & Naylor, 2012). Some large devices are 



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designed as shown in Fig. 1, which indicate the diversity of the practical applications in the ocean. The 

cost of tapping the wave energy has increased from the 1980s but gradually declined and is likely to 

further reduce with advances in the technology industry (Osmundsen, Almklov, & Tveterås, 2017). As 

energy costs from fossil fuels are exorbitant, wave energy could become economically feasible in the 

near future. Thus, policy-makers, the private sector, and the general public are interested in the 

conversion of wave energy into electrical energy. The two important steps in this process are (1) 

assessment of the ability of a site to produce electricity and (2) identification of surrounding 

ecosystems and the potential impacts and activities in support of electricity production (Read & 

Fernandes, 2003). 

 

 

Figure 1. Wave Power Devices 

 

While the waves may provide a source of clean and renewable energy, a wave energy conversion 

project may harm the protection of the marine species and habitats, and create a strategic conflict with 

the existing marine ecosystems. Wave energy conversion facilities and their potential impacts, 

including fishing, planktonic and benthic habitat; recreation; aesthetic point of view changes; 

hydrodynamic and wave environment; and navigational hazards were studied by (Bohl, 1977; Collins 

et al., 1975; Naegel, 1977). Many potential impacts are site specific, and the extent of these impacts on 

coastal and marine ecosystems is unclear, because the studies on the wave energy conversion projects 

are limited; hence, the concept is poorly understood. This knowledge gap hindered the development of 

practical equations to support wave energy projects related to marine spatial planning. An assessment 

of wave energy capacity of a site considers various factors such as wave energy resources, the 

characteristics of wave energy conversion device, the cost-effectiveness of energy conversion facility, 

locational constraints, and uses of the information on ecosystem properties or compatibility with others. 

Marine spatial planning is at a nascent stage in North America, and involves an interaction between the 

planners to consider the cumulative impact of the procedure on the coastal and marine space human 

activities (Sneed, Allen, & Ellis, 1975). Implementing the wave energy projects and efficient marine 



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spatial planning requires a comprehensive framework that considers these various kinds of information. 

It is estimated that the wave power resources can help to identify potential sites of energy-rich areas 

and sustainable resources. Previous studies employed different scales to estimate the potential of wave 

power. For example, the global- and regional-scale studies have shown that the west coast of Europe 

(i.e., Ireland, Portugal, and Scotland), similar to the North American west coast (i.e., British Columbia, 

Washington, Oregon, and California), is the main area of wave energy projects because of its potential 

for abundant wave energy harvest, which can be used to meet the demands of high coastal population 

areas (Lewis, Yopp, & Schramm, 1978; Sutton & Lewis, 1982; Timmons & Ebeling, 2010). Previous 

research focused on a local scale to quantify near-shore wave energy resources and to identify hot spots 

in the field of wave energy (Mollison & Holmgren, 1981; Todd, 1980). 

Different types of wave energy conversion device are used to extract energy from the waves, and 

various technologies are employed to calculate how much energy can be harvested as a function of the 

local wave condition change. For example, using a attenuator-type device (for example, sea snake, the 

Pelamis Wave Power, Edinburgh, Scotland) works more effectively in the Irish and Scottish region 

(Lewis, Yopp, & Schramm, 1978), where the wave height typically under high sea conditions aids in 

the estimation. In contrast, the terminator-type devices (for example, an oscillating water column 

device from Energetech Corporation, Utah, USA) work more efficiently on the west coast of North 

America (Zweig, 1986), where there is disposal of longer period waves (such as swelling). 

In reality, a wave energy conversion efficiency of the device depends not only on the location of the 

potential energy to be harvested, but also on income and decisions related to the construction and 

operating costs of the facility. The economic value of the harvested wave energy facilitates to identify 

the specific location of energy conversion facility and to evaluate the potential tradeoff between the 

cost positioning factors related to the installation location, maintenance, and operation of the facility. 

While the ability to develop the harvest wave energy method is explored in (Lewis, Yopp, & Schramm, 

1978; Sutton & Lewis, 1982; Zweig, 1986; McMurtry, Nelson, & Sanders, 1990), harvest wave energy 

does not provide explicit spatial information to assess the cost of wave site energy generation or the 

other associated estimates. 

This study developed a wave energy conversion device to identify a potential site, which provides 

decision support equations for the policy-makers to respond to the challenges of wave energy projects 

related to integrated coastal and marine spatial planning. First, the study developed a model of wave 

energy as ecosystem services, and the tradeoffs (investment) equation (McMurtry, 1992) is a part of an 

integrated assessment (Rakocy 1984; Watten & Busch, 1984). The wave energy model by using 

ecosystem services is based on the framework of Talese and other researchers (Rakocy, 2012) and 

consists of three parts: (1) the model was based on wave conditions (“supply measures”), (2) the model 

used a wave energy conversion device to quantify the potential of wave power evaluation (“service 

standards”) consisting certain technical information in harvesting energy, and (3) the utility of the 

model was evaluated as capital investment (“value index”) to assess the economic value of wave 



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energy conversion facilities. Second, the study conducted a compatibility analysis to determine the 

optimum compatibility between the wave energy conversion device and the existing uses of the oceans. 

Investment in an ecosystem service model, including wave energy in the model, is described here. This 

equation is used in many other coastal and marine spatial planning processes, and can be used for a 

variety of related marine renewable energy projects to support marine spatial planning (Rakocy, Masser, 

& Losordo, 2006). 

 

2. Evaluation of the Formulas 

The mathematical models of many physical and engineering systems are frequently of high dimension, 

or possessing interacting dynamic phenomena. The information processing and requirements to 

experiment with these models for control purposes are usually excessive. It is therefore natural to seek 

techniques that can reduce the computational effort. The methodologies of large-scale systems provide 

such techniques through the manipulation of system structure in some way. Thus, there has been 

considerable interest in the research area of modeling, analysis, optimization and control of large-scale 

systems (Mahmoud, Hassan, & Darwish, 1985). Recently, many approaches have been used to 

investigate the stability and stabilization of large-scale systems, as proposed in the literature (Routledge, 

2015; Deutsch, Csordas, Sun, & Jarnuczak, 2017). 

During the past several years, fuzzy-rule-based modeling has become an active research field because 

of its unique merits in solving complex nonlinear system identification and control problems. This 

approach can obtain more flexibility and more effective capability of handling and processing 

uncertainties in complicated and ill-defined systems. Unlike conventional modeling, fuzzy rule-based 

modeling is essentially a multimodel approach in which individual rules are combined to describe the 

global behavior of the system (Mei, Grossberg, Ng, Navarro, & Ellmore, 2017).  

In this paper, we consider a fuzzy large-scale system composed of J subsystems with interconnections 

and each subsystem is represented by the so-called Takagi-Sugeno fuzzy model. One critical property 

of control systems is stability and considerable reports have been issued in the literature on the stability 

problem of fuzzy dynamic systems. However, a literature survey indicates that the stability problem of 

fuzzy large-scale systems has not yet been resolved. Hence, a stability criterion in terms of Lyapunov’s 

direct method is proposed to guarantee the asymptotic stability of fuzzy large-scale systems.  

 

3. System Description and Stability Analysis 

Consider a fuzzy large-scale system F which consists of J interconnected fuzzy subsystems 

. ,  2, ,1  , JjFj 
 The jth fuzzy subsystem jF

 is of the following form: 



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






















(1b)                                                                 ),()( 

 )1(                                          )()()()1(

:

1

1

kxCk

akkxAkhkx

F J

jn
n

nnjj

r

i
jjijijj

j

j





 

where ijA
 is a constant matrix with appropriate dimensions, 

)(kx j  is the state vector, 
 C nj  is the 

interconnection between the nth and jth subsystems, jr
 is the number of fuzzy implications and 

)(khij  is the normalized weight. Each isolated subsystem (i.e., 
0njC

) of F is represented by a 

Takagi-Sugeno fuzzy model composed of a set of fuzzy implications and the final output of this fuzzy 

model is described as (Laurens, Batlolona, Batlolona, & Leasa, 2018)  

)1( kx j




jr

i
jijij kxAkh

1

)()(
.                          (2) 

Lemma 1 (Bohl, 1977): The jth isolated subsystem (2) is asymptotically stable if there exists a common 

positive definite matrix jP
 such that 

     
0 jijj

T
ijij PAPAQ

      for jri  ,2, ,1 
.                   (3) 

Based on Lemma 1, a stability criterion is derived below to guarantee the asymptotic stability of the 

fuzzy large-scale system F. 

Theorem 1: The fuzzy large-scale system F is asymptotically stable, if each isolated subsystem of F is 

asymptotically stable and the following inequality is fulfilled (Warsito & Herman, 2018; Wardono, 

Mariani, & Candra, 2016; Yuanita & Zakaria, 2016; Mulbar & Zaki, 2018; Meika, Suryadi, & Darhim, 

2018): 

 )]()()[()()()(
1

2
fjMijMfj

r

fi
ijijM

r

i
ij QQkhkhQkh

jj

 


inj

r

i
in

J

jn
n

r

i
ijnij mkhmkh

jj

)()([
11 1
 



 



])()1( 
2

jnnM CPJ 
< 0  for  

Jjrfi j   ,    2,  , 1     ,   1 
,                      (4) 

where f is a positive integral, 
)( ijM Q

 is the maximal eigenvalue of ijQ
 defined in Eq. (3) and 

 
  ijj

T
njnjj

T
ijijn APCCPAm 

, 
  inn

T
jnjnn

T
ininj APCCPAm 

. 

 

Proof: Let the Lyapunov function for the fuzzy large-scale system F be defined as  



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)()()()(
11

kxPkxkVkV jj

J

j
j

J

j
j 




                                    (5) 

where jP
 is the solution of Eq. (3). Taking the backward difference of V(k), we have 

)()1()( kVkVkV   

=

[ {
1



J

j

)]()()([)]()()(
11

kkxAkhPkkxAkh j

r

f
jfjfjj

T
j

r

i
jijij

jj

 



)}()( kxPkx jj

T
j

 

=
 
 


J

j

r

fi
jjijj

T
ij

T
jij

j

kxPAPAkxkh
1 1

2 )())(()(  
 


J

j
jj

r

fi
fjj

T
ij

T
jfjij kxPAPAkxkhkh

j

1

)())(()()(
 

+

)()()(
1 1

kPAkxkh jj
T
ij

T
j

J

j

r

i
ij

j


  +

)()()(
1 1

kxAPkkh jfjj
T
j

J

j

r

f
fj

j


  +

)()( 
1

kPk jj
T
j

J

j


    

= 54321 mmmmm 
,  where                                        (6) 

1m
 
 


J

j

r

fi
jjijj

T
ij

T
jij

j

kxPAPAkxkh
1 1

2 )())(()( 
 


J

j

r

i
j

T
jijMij

j

kxkxQkh
1 1

2 )()()( )( 
,     (7) 

 2m
 
 


J

j

r

fi
jjfjj

T
ij

T
jfjij

j

kxPAPAkxkhkh
1

 )())(()()(
 

=

 


J

j

r

fi
jjijj

T
fjfjj

T
ij

T
jfjij

j

kxPAPAAPAkxkhkh
1

)()2)(()()(
 

=

 


J

j

r

fi
fjijj

T
fjij

T
jfjij

j

AAPAAkxkhkh
1

)]()[(){()()(

)(]}2[ kxPAPAAPA jjfjj
T
fjijj

T
ij 

 


 


J

j

r

fi
j

T
jfjMijMfjij

j

kxkxQQkhkh
1

)()()]()()[()( 
,                          (8) 

3m
)()()(

1 1

kxCPAkxkh nnjj
T
ij

T
j

J

j

r

i

J

jn
ij

j


  

)()()(
1 1

kxCPAkxkh nnjj
T
ij

J

j

r

i
j

J

jn
ij

j


  


,    (9) 



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4m
)()()(

1 1

kxAPCkxkh jijj
T
nj

T
n

J

j

r

i

J

jn
ij

j


  

)()()(
1 1

kxAPCkxkh jijj
T
njn

J

j

r

i

J

jn
ij

j

 
  


,   (10) 

5m
)()( 

1

kPk jj
T
j

J

j




 ]})()([])()({[ 2211221
1

1  


kxCkxCPkxCkxC jjj
T

j

J

j
j

 

  

])()()1()()()1([
2

22

2

11
1




kxCPJkxCPJ jjMjjM

J

j


 

     

 


J

j

J

jn
nnjjM kxCPJ

1

2
])()()1[( 

 

  

 


J

j

J

jn
jjnnM kxCPJ

1

2
])()()1[(   

 


J

j

J

jn
jjnnM kxCPJ

1

22
)()()1( 

.     (11) 

From Eqs. (9-10), we have  

  43 mm
)( ]  [ )()(

1 1

kxAPCCPAkxkh nijj
T
njnjj

T
ijj

J

j

r

i

J

jn
ij

j


    

       

] )(  )( [ )(
22

1 1

kxkxmkh njijn

J

j

r

i

J

jn
ij

j

 
    

2

1 1

)( )( kxmkh jijn

J

j

r

i

J

jn
ij

j


  


2

1 1

)( )( kxmkh jinj

J

j

r

i

J

jn
in

j


  


.                       (12) 

Substituting Eqs. (7-12) into Eq. (6) yields  

 )( kV
)]()()[()()( )(){(

1 1
M

2
fjMijMfj

r

fi
ij

J

j

r

i
ijij

T
j QQkhkhQkhkx

jj

  
   

      

).(]})()1( )()([
2

1 1

kxCPJmkhmkh jjnnM

J

jn

r

i

r

i
injinijnij

j j

  
    

 

4. Conclusions and Suggestions 

This paper introduced a practical simulation model for renewable energy in aquaponic systems. The 

output current has harmonic component of both high order frequencies and dispersed harmonics. The 

characteristic is more close to the real electric arc furnace property. A flicker testing model is 

established to test the instantaneous flicker visual sensitivity S. Modulating waves of different 

frequencies and the same amplitude is introduced to test the correctness of the model. It can help to 

establish a more practical model to simulate a wide output range of harmonics. It would be more help 

full for harmonic-preventing sets such as active power filter to test their characteristics. The power 

system would be more reliable and Electro-insulating material will have a longer using life. The 

method is proved to be reasonable and realizable to reflect the real electric arc furnace property. 

Developing future politics requires simple goals, which are beyond economic development and 

employment or the protection and environmental protection. The difficulty of the maritime market 



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shows there are many opportunities to increase the pace of sustainable aquatic life and new 

perspectives that can be used through political support. 

 

Funding Acknowledgement 

This research was in part enlightened by the grant 106EFA0101550 of Ministry of Science and 

Technology, Taiwan. 

 

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