station construction by the use of wave energy
Zina Al -Shadidi
Department of Mathematics, College of Education (Radfan), Aden University,
Aden, Yemen
Abstract
Generation energy has been important subject for humans since the beginning of civilization ,and the renewable energy is the most important type of energy because of its wonderful properties where it's the cheapest energy sources and the disappearance of pollution .
The new idea here is very simple , it’s the combination of two renewable source of energy ,(takes from the sea ). Among different types of sea energy we choose the wave energy ,and the sea thermal energy conversion (i.e. the way to differentiate temperature difference into electricity) . Studying and analyzing the new system properties for the new system have been done using Matlab .
Introduction
Renewable energy is the energy derived from natural resources that can be naturally replenished in a short period of time . It includes biofuels (biological materials ,geothermal power ,hydropower ,solar power ,wave power ,wind power ,and sea thermal energy conversion ). It's also considered as a clean energy because It's conversion to useful forms of energy such as electricity without emitting gases (without pollution ).
This kind of energy sources become more attractive especially as the prices of traditional sources of energy become more expensive .Renewable energy sources have been very important for humans since the beginning of civilizations in many ways , for example biomass (such as wood)has been used for heating and then for power generation and hydropower and wind energy for movement and later for electricity production .[1]
This kind of energy can be classified according to Its uses:[2]
• Solar water heater
• Photovoltaic cells
• Concentrated solar power
• Wind energy
• Biofuels
a-Ethanol
b-Biodiesel
• Geothermal power
• hydropower
• sea power
a-wave power
b-Ocean thermal energy conversing (OTEC).
The idea is to join ,two kinds of energy generator (electrical generator ). Theoretically we must do some mathematical calculations using the matrix theory which have been used in circuit analysis to find the set of equations using determinants or mainly for preparing the equations to use it in Matlab.
Now our problem is to built a theoretical mathematical model for a compound electrical generator which use the sea power, (ex. wave energy and OTEC energy ) .So the goal here is by joining any tow kinds of electrical generator one can save a wider range of seas power. On the other hand there is a direct and immediate connection between theoretical concepts in linear circuits and matrices . And the main emphasis is for the solution of a set of equation using determinants to use in Matlab.
The choices were any two types of energy can be collected from the sea ,like: wave energy , OTEC ,or wind energy .
Suppose that the wave generator connected with OTEC generator , where the wave generator can be programmed to works after the sunset till the sun rising and the OTEC generator work after the sun rising till the sun down .
In order to understand the whole idea of the physics concepts related to each type of energy generator it must be explained ,as follows:
Energy from waves:
sea waves are caused when the wind touch the water surface ,or when the wind energy transfers to the sea water when the wind blows across the sea[3] .Because of the ear pressure differences between the upwind and the lee side of a wave crest ,and the friction on a water surface by the wind makes the water goes into the shear stress caused the growth of the waves . Therefore, we can say that waves are generated by wind passing over the surface of the sea ,and as long as the wave propagates slower than the wind speed above the wave the energy transferred from the wind to the waves .
In general ,the wave power depend on the wave speed ,wavelength ,wave high ,and water density .
In deep water where the water depth is larger than half the wavelength of the sea wave ,the energy flux is [4] .
-------------------------(1)
------------------(2)
where ρ represents the water density
g represents the gravity H is the wave high and T is the wave period.
So to get larger p the wave high and (or) wave period must be increase, Therefore the wave energy harness is with an oscillating water column that generates electricity from wave rise and full .The wave rising and falling causes rising and falling water through a long pipe connected with the turbine that generates electricity due to the air movements in the tube ,where the water rising and falling drive air into and out of the shaft ,powering an air driven turbine.
This method in producing energy has several
advantages [5 ].
• By its high power density it is one of the lowest cost renewable energy .
• The wave energy is more predictable than solar and wind energy.
• The conversion of wave energy to electricity is believed to be one of the most environmentally benign ways to generate electricity.
The first known patent to utilize energy from waves dates to 1799 it was field in Paris by Girard and his son [5].An early application of wave power was a device constructed around 1910 by Bochaux praceique to light and power his house at Royan (in France)[6]. It appears that this was the first oscillating water column type of wave energy device[7].From 1855to 1973 there are 340 patents field in the UK alone [5].
Modern scientific pursuit of wave energy was however pioneered by yoshio - Masuda,s experiments in 1940[8].
And there are many attempts for getting the electricity from wave energy until this day
Energy from temperature difference:
During day the surface of the sea water warmed by the sun heat, while the deep water still cold . Sea thermal energy conversion refers to the process that uses the temperature difference between the warm surface of the sea water and cold deep sea water to generate electricity ,and it also called Ocean thermal energy conversion (OTEC). As long as the sufficient temperature difference (20 co) exist between the warm layer of water and the cold deep water ,power can be generated.
There are many types of (OTEC) processes ,some of
them are closed cycle , and the other are open cycle . In the first type (closed cycle system )heat transfers from the warm surface sea water causes a working fluid (like ammonia) which boils at a temperature about 25 co (at atmospheric pressure),to turn to vapor the expanding vapor drives a turbine attached to a generator that produces electricity ,the working fluid passes through a condenser and turns back into a liquid that is then recycled through the system .The second type is (open cycle system ) uses the warm surface water itself as a working fluid . The water vaporizes in a near vacuum at surface water temperatures . The expanding water vapor drives a turbine attached to a generator and produces electricity .The water vapor which has lost its salt is almost pure fresh water ,condensed back into a liquid by exposure to cold temperatures from deep –sea(or deep –ocean) water. If the condenser keeps the vapor from direct contact with sea water ,the condensed water can be used for drinking ,a direct contact produces more electricity , but the vapor is mixed with cold sea water and the discharge water is salty and return to ocean [7] .
in 1930 actually built the first (OTEC) plant in Cuba . The system produced 22kw of electricity with a low pressure turbine .
In 1935 Claude constructed another system in Brazil[9].
In 1956 French scientists designed another 3 megawatt
(OTEC) plant of Abidjan [8]. The united states become involved in
Mathematical and programming tools:
suppose that there are two electrical generator systems ,the first system produces current (I1) and voltage (V1) while the second system produces (I2) and (V2) .
Now if we use Matlab programming language the two systems must be connected horizontally .In order to find the voltage gain for the
resultant system , in language the general form for the horizontal connec on is[10,11]:
------------------------------(7)
Vgain=Vgain1+Vgain2 -------------------------------------(9
Or it could be written as follows :
=Vg1+Vg2 ------------------------------------(10)
But these two systems suppose to work under different conditions
.The first system must work after sun fall to utilize the highest waves , the second system must work after sun rise to reach to the suitable temperature difference of the sea water . Therefore the total Vg /sec will be equal to Vg for any one of these systems . also
(Vgtotal/day=Vg1+Vg2) ,which means that the voltage gain for such system depends upon the period of working time .
Besides the really gain here is the continuous production of electricity without fuel ,without pollution ,without economic losses . Now suppose that each primary circuit is very simple (a system with one generation ) like the following circuit in the fig below:
ZL=the load impedance
RL=the load resistance
XL=the imaginary part for the impedance which represents the impedance of the load connected with the generator. The capacitance is very important in such circuits to save the lower power produced by the generator no.1 while generator no.2 produced a power with a higher voltage .By analyzing the circuit in fig ( 4) the resulting plot of the average power as a function of RL/RS is shown in fig ( 5 ) below .
RL/RS
The above figure shows that when the load resistance around four times the internal resistance for the whole system ,the average power PL will have a maximum value .
Wave power:
Fig ( 6 ) represents the effect of wave high on the wave power(using equation 2) , the figure was plotted for a wave period varies from 0.5 sec to 5 sec . The wave power increases with increasing wave high and wave period (as mentioned in fig (6 ) this kind of generator works during night were the wave high and period having their highest values) .Because the larger force is required to produce highest wave which means that the highest wave has more energy ,so larger power can be collected from a higher wave ,on the other hand the long period means more time to collect energy from the wave .
wave power and wave high
(for different values of wave period )
The total impedance for the resultant system:
The frequency response means the response characteristics of the system when subject to sinusoidal inputs .The input
frequency is varied , and the output characteristics are computed or represented as a function of the frequency . This representation analysis provides useful insights into stability and performance characteristics of the control system . A description of the new system resulting from the horizontal connection between the (wave generator) and the (OTEC generator )was done by scheming the impedance matrix as a function of the frequency for this system using the following equations:
Conclusions :
A wonderful system producing clean energy can be built to produce electrical power during day and night without economic loses (except the cast of the systems building )and without pollution .In addition to that the secondary resultant for such system is a pure fresh water. theoretical studying for this a system leads to the following conclusions:
• larger power can be collected from a highest wave ,on the other hand the long period means more time to collect energy from the wave .
• when the load resistance value is around four times the internal resistance for the whole system ,the average power PL will have a maximum value .
• The horizontal connection between the systems component is useful because of the effect of the secondary currents which reduces with increasing frequency.
References
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