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Hindawi Publishing CorporationInternational Journal of PhotoenergyVolume 2011, Article ID 201752, 9 pagesdoi:10.1155/2011/201752

Research Article

A Framework for Photovoltaic and Thermosiphon Systems

Gustavo Guidoni, Frederico Papatella, Elizabeth Pereira, and Mark Song

Computer Science Department, Catholic University of Minas Gerais (PUC-Minas), 30535-901 Belo Horizonte, MG, Brazil

Correspondence should be addressed to Mark Song, [email protected]

Received 31 March 2011; Accepted 23 May 2011

Academic Editor: Ugo Mazzucato

Copyright © 2011 Gustavo Guidoni et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

Pessimistic forecasts are growing in the Brazilian energy scenario demanding the use of renewable sources of energy such as thesolar one. As metropolitan regions have become more populous, private and public companies have developed new technologiesbased on renewable energy sources. In order to supply such demand, new computer techniques have to be developed. This paperpresents a framework to assist the developer to model new components and simulate solar energy applications. By applying theframework concepts, such as source code reuse, one can create a complete environment to evaluate solar energy data. The frame-work supports software development and tool implementation to be used in photovoltaic and thermosiphon processes.

1. Introduction

The Brazilian institute (INPE) estimated, in 2005, that theelectric energy demand in Brazil for the next 20 years wouldincrease 4% annually [1]. This fact, and also the concernabout environmental consequences due to the consumptionof nonrenewable fossil fuel, impels the researchers to developalternative technologies to use solar energy generating orreducing the need of electric energy.

There are many tools devoted to solar energy applicationsuch as blast, doe (doeplus and visual doe), ener-win, energyplus, hot2000, passport, and solar5 [2–4].

However, the costs for implantation, management andcontrol are still too expensive [5]. For instance, in orderto accomplish photovoltaic experiments, to report statisticalresults and to evaluate the efficiency of the solar energyconversion into electric energy, new evaluative processesmust be used.

One can use different tools to control or simulatephotovoltaic and thermosiphon systems, such as TRNSYS(http://sel.me.wisc.edu/trnsys/) or RETScreen (http://www.retscreen.net/ang/home.php).

TRNSYS is an energy simulation tool used to describecomplex energy systems based on a process of choosing thesystem components and hooking them together.

Some of the main disadvantages are as follows: it iswritten in Fortran, and it uses standard components to

model a solar application. It is also a commercial tool, andit is not open source software.

The RETScreen is a decision support tool developedto evaluate the energy applications for various types ofrenewable energy. The main disadvantage is the demandof specific software, such as, the Microsoft Excel, MicrosoftWindows 2000 and Microsoft.NET.

The approach presented in this work, which is basedon the framework concept, provides the reuse of softwareproject, analysis, and test for solar energy applications. Onecan manipulate data and formulas related to solar energydomain, especially those ones already tested and validated.It is up to the developer the reuse of the source code, whichcan be specialized according to the solar energy application.

Frameworks are used in very different contexts such asgraphical interfaces (Java Swing, AWT), net services (JavaRMI, Jeeves), and commercial works (IBM’s San Francisco)[6].

In this paper, a framework—for photovoltaic and ther-mosiphon systems—denoted SolarEnergy is presented. Theframework provides many benefits such as the updatingof climatic data, the creation and use of new components,and the incorporation of new functionalities into existingapplications. By applying the idea of code and project reuseit assists the researchers in the generation and simulation ofsolar applications [7].

2 International Journal of Photoenergy

This paper is divided into six sections. The Section 2describes the framework. The Section 3 presents a methodto estimate radiation. The Sections 4 and 5 report modelsfor photovoltaic and thermosiphon systems. In Section 6a case study is presented for each supported application. TheSection 7 concludes this work.

2. The SolarEnergy Framework

The main objective of any framework is to simplify the devel-opment of similar applications [8]. It can be used in orderto encapsulate the business rules involved in the descriptionof any new component, some of which based on detaileddescriptions of the previous ones. In the SolarEnergy frame-work, it has been defined abstractions in order to describeand simulate the following:

(i) thermosiphon systems—a method of passive heatexchange based on natural convection, and

(ii) photovoltaic applications—a radiation process toconvert solar energy into electric energy.

Every solar simulation process, thermal or photovoltaic,is based on the solar radiation. Sensors capture the energy,which is processed and distributed to each component.

To attend such demand, the framework has been dividedinto four basic packages as depicted in Figure 1. The Formspackage is responsible for supplying the interfaces. The Con-troller controls the simulations and the DataBase packageprovides access to data. The Energy package initiates theframework and provides the programmer with all the func-tional operations—its primary responsibility is to coordinatethe internal information flow.

In the SolarEnergy framework, the requirement appliedto the water heating is based on solar data related to a specificregion. However, to estimate the solar radiation, in thephotovoltaic process, it is necessary to process climatic data.

Some design patterns [9] have been used to accomplishsuch task. For example, the factory method pattern has beenused to supply an interface to the environment in order tobuild correlated or independent radiation objects with noneed of specifying their concrete classes.

It is the factory responsibility to select the desirableimplementation. The main advantage is the possibilityto dynamically create environmental objects without anyknowledge on their implementation classes (Figure 2).

The framework is divided into three hierarchical layers(Figure 3). The first one corresponds to the interfacesand classes which are responsible for drawing components(EMCObject, EMCPoint, and EMCPipeVertices classes). Thesecond layer is responsible for guaranteeing that the simu-lation will run correctly. The last one adds the componentsalready developed to the simulation.

The second layer is responsible for guaranteeing thatthe simulation will run correctly. The last one adds thecomponents already developed to the simulation.

Each class has its own functionalities, for example, theEMCPipe class deals with communications between eachconnection point. All components have their connection

Forms Energy

DataBase

Controller

Figure 1: The SolarEnergy packages.

points, and each connection point is defined in terms ofEMCJoinPoint.

The framework organizes the components as a directedgraph where the main node is the solar radiation componentand the others are interfaces such as ICollector, IManipulateor ICapture (Figure 4). All dependency is solved beforerunning the simulation.

The SolarEnergy framework calls the solar radiation com-ponent to calculate the solar radiation data. The solar col-lector supplies information to the heating water and photo-voltaic processes based on the radiation data. For example,the user does not need to be worried if the solar radiationis supplied monthly or hourly. The framework simplysimulates the behavior of each component accordingly.

3. Methods to Estimate Radiation

The equations to be presented describe models to estimateradiation values on the terrestrial surface based on hourly,daily, and monthly climatic variations.

The solar energy conversion process can also be based ona reference year to estimate the radiation once applicationperformance is heavily dependent on climatic aspects.

The reference year represents a set of meteorological vari-ables for a specific region during a year. There are manymethodologies to identify the reference year: the TRY (TestReference Year), TMY (typical meteorological year), DRY(design reference year), and the SRY (short reference year)[10, 11].

Figure 5 shows the method based on historical measureddata and the identification of the presumable reference year.The objective of this phase is to calculate the solar radiationwhich reaches the plan of the solar collector.

The calculation is based on the collector horizontal planand global radiation values (split into two components: thedirect and diffuse radiation).

The global radiation can be described according to

H

Ho= a + b

n

N+ ch, (1)

where H is the daily solar radiation; Ho is the extraterrestrialradiation; n is the total daily radiation; N is the total theoret-ical daily radiation; h is the station altitude; and a, b, c are theEmpirical Bunnett constants [12].

International Journal of Photoenergy 3

EnvironmentFactory

≪interface≫IEnvironment

{energy}

EGYReferenceYear{components}

EGYEnvironment

{components}EGYRadiation

{components}

AttributesOperations

Public void createEnvironment( )Operations

Public boolean calculate( )

Attributes

OperationsPublic void execReferenceYear( )Public boolean calculate( )

AttributesAttributes

OperationsPublic boolean calculate( )

AttributesOperations

Public void execRadiation( )Public boolean calculate( )

Figure 2: The class diagram and the factory pattern implementation.

≪interface≫Object

clone( ): voidpaint(Graphics: g): void

EMCObject

EMCPoint≪interface≫

IPoint

paint(Graphics: g): void

EMCPipeVertice

paint(Graphics: g): void

1◦ layer

2◦ layer

3◦ Layer

≪interface≫IStore

calculate( ): void

≪interface≫IComponent

<< interface>>ICollector

calculate( ): void

≪interface⊃IManipulate

calculate( ): void

EMCTransferPipe

transfer( ): void

≪interface≫IRadiation

calculate( ): void

EMCComponent

EMCJoinPoint

getVar( ): Variable

var: Variable

EMCPipe

from: IPointto: IPoint

≪interface≫IPipe

transfer( ): void

EGYRadiation EGYStoreEGYCollector

addJoinpoint(Point: p): void

setFrom(Variable:f ): void

setTo(Variable: t): void

Figure 3: Main classes of the SolarEnergy framework.

The diffuse radiation can be modeled as described by

Hd

H= 0, 775 + 0, 00606(ωs − 90)

− [0, 505 + 0, 0045(ωs − 90)] cos(

115KT − 103)

,

(2)

where Hd is the diffuse monthly radiation; KT is the monthlyaverage clearness index; and ωs is the sunset angular hour.

Equation (3) calculates the hourly average direct and dif-fuse radiation:

rt = (a + b cosω)cosω − cosωS

sinωS − (πωS/180) cosωS,

rd = π

24cosω − cosωS

sinω − (πωS/180) cosωS,

(3)

where ω is the sunrise angular hour; and a, b are the Empiri-cal Bunnett constants [12].


ICapture ICapture IManipulate

IStore

IPipeIPipe

IPipe

Figure 4: Main classes used in simulations.

Test referenceYear

Global radiationmonthly mean

horizontal place

Direct radiationmonthly mean

horizontal planemonthly mean

horizontal plane

Direct radiationhourly mean

horizontal planehourly mean

horizontal plane

Direct radiationhourly mean

inclined planehourly mean

inclined plane

Global radiationhourly mean

inclined plane

Diffuse radiation

Diffuse radiation

Diffuse radiation

Figure 5: The solar radiation based on the reference year.

Finally, the global radiation (on inclined surface) is cal-culated according to the isotropic diffuse model

IT = IbRb + Id

(1 + cosβ

2

)+ IPr

(1− cosβ

2

), (4)

where Ib is the beam hourly radiation on a horizontal surface;Rb is the beam radiation on sloped surface/beam radiation ona horizontal surface; Id is the hourly diffuse solar radiation; βis the slope angle, the angle between the plane of the surfacein question and the horizontal; I is the global solar radiationon a horizontal surface; and Pr is the reflectance of nearsurfaces reaching the collector.

This section presents a method used in the framework toestimate solar radiation. The next section presents conceptsrelated to photovoltaic systems.

4. Photovoltaic Systems

This section presents the concepts and the mathematicalmodels related to the solar energy conversion into electricenergy. The devices supported by the SolarEnergy frameworkare described as follows.

4.1. The Photovoltaic Panel. The panel is a photovoltaicsystem component responsible to convert the solar energyinto electricity. This process is the result of energy beingabsorbed by the semiconductor components of the solarmodule.

Information about voltage and current for the maximumpower, the open-circuit voltage, the short-circuit current,the temperature coefficient for the short-circuit current, thereferential solar irradiance and the temperature coefficientfor the short-circuit voltage have to be considered.

The solar irradiance of 1,000 W/m2 and the temperatureof 25◦C are the pattern conditions for the photovoltaicarrangement. The maximum value for a fixed solar intensityis found in the inflexion point of the modulus standardcurve.

The luminous intensity and the cells temperature inter-fere in the photovoltaic modulus performance. An increasein the isolation level also alters the cell temperature and,consequently, tends to reduce the modulus efficiency.

For example, crystalline solar cells reach their greatestefficiency at low temperatures—the coefficients depend onthe type of the material. Also, the elevation on temperaturedecreases significantly the voltage value generated by themodulus and increases the current value.

The equation describing the photovoltaic generatorperformance is given by

I = ISC

{1− C1

[exp(V − ΔV

C2VOC

)− 1]}

+ ΔI , (5)

where C1 and C2 are the following coefficients:

C1 =(

1− IMP

ISC

)exp(− VMP

C2VOC

),

C2 = VMP/VOC − 1ln(1− IMP/ISC)

,

(6)

where ISC is the short circuit current; V is the output circuitvoltage; ΔV is the voltage variation; VOC is the open circuitvoltage; ΔI is the current variation; IMP is the maximumpower current; and VMP is the maximum power voltage.

4.2. The Battery. The battery is a convenient device to storeelectric energy generated by photovoltaic modulus. Theinitial charge, the discharge value, and the efficiency arerepresented as follows:

(i) EB: storage energy in the batteries;

(ii) EBmin: minimum discharge level;

(iii) EBmax: maximum charge level;

(iv) ηbat: battery efficiency.


During the first hour, the charging and dischargingbattery process is bounded to EBmin ≤ EB ≤ EBmax. Thisrestriction is enforced by the charge controller component.

4.3. The Charge Controller. This component disconnects thephotovoltaic modulus when the battery reaches its maximumcharge level. Also it activates the supplying component whenthe minimum charge level is reached.

The mathematical model describing its operation is givenbelow. It takes into account two situations: the loading andunloading battery level.

After applying the charge and discharge restriction forthe battery, the controller will charge up to the maximumlimit if the energy generated by the photovoltaic arrangementexceeds the energy demanded (7).

If the energy demanded is higher than the one generatedby the modulus, the batteries will be discharged to supply thedeficit according to (8)

EB(t) = EB(t − 1) +

(EG(t)− EL(t)

ηinv

)ηbat, (7)

EB(t) = EB(t − 1)−(EL(t)ηinv

− EG(t)

), (8)

where EG is the energy generated by the photovoltaic module;EL is the energy wasted in the loading process; t is the time tobe considered (hour); and ηinv is the efficiency of the Inverter.

4.4. The Inverter. Also known as DC-AC converter (directcurrent—alternating current), it establishes a connectionbetween the photovoltaic generator and the DC source.

Its efficiency is given by the input and output power ratiovarying within a band of 50% up to 90% [10].

The efficiency value percentage, commonly specified bythe manufacturer, is the maximum value that can be reachedby this component. It is represented by ηinv (7) and (8).

5. Thermosiphon Systems

The preceding section presented the main photovoltaic com-ponents supported by the framework. This section presentsthe concepts and components related to thermosiphon appli-cations.

All thermosiphon simulations can be modeled accordingto some basic components: the radiation, the collector andthe water container. The solar radiation has been explainedin Section 3.

The following subsections describe the collector andwater tank. All of then are encapsulated in one module ofthe framework as follows.

5.1. The Collector. The collector is a component used in theheating water process to convert solar into thermal energy.

An import aspect modeled by the framework is thecollector efficiency—the ratio between the useful energy

Figure 6: An instance for thermosiphon simulation.

02468

1012141618

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

(MJ/

m2)

The radiation on inclined surface

Figure 7: The solar radiation data for BH city (in MJ/m2).

transferred to the water and the solar energy radiationreaching the collector (9)

η = Qutil

IAG, (9)

where Qutil is the useful energy absorbed by the water; I isthe radiation reaching the collector; and AG is the collectorexternal area.

5.2. The Water Tank. The main purpose of the water tankis to keep the water hot. In the framework, it has beenmodeled as a set of nodes, which represent cold watercoming from outside and hot water kept inside by the device.Equation (10) describes such process. We summarized itsdescription—details can be found in [12]

T+S,i = TS,i +

Δt

mi

[Fci m(Tco − Ts,i

)− FLi

(Ts,i − TL

)

+ m(Ts,i−1 − Ts,i

) i−1∑

j−1

Fcj

− mL(Ts,i − Ts,i+7

) N∑

j=i+1

FLj

−(UA

Cp

)(Ts,i − Ta

)+ Faux

i

(PΔt

Cp

)],

(10)


1000

800

600

400

200

0

−200

−400

−600

−800

−1000

Effi

cien

cy

Solar collector efficiency

Figure 8: The collector efficiency (BH city data).

Figure 9: An instance for photovoltaic simulation.

where Ts,i is the node i temperature; Fci m(Tco − Ts,i) is the

energy absorbed by the collector; FLi (Ts,i − TL) is the energy

lost to the cold outside water; m(Ts,i−1 − Ts,i)∑i−1

j−1 Fcj is

the energy absorbed from a hotter node above i; mL(Ts,i −Ts,i+7)

∑Nj=i+1 F

Lj is the energy lost to the colder node below i;

(UA/Cp)(Ts,i−Ta) is the energy lost to the environment; andFauxi (PΔt/Cp) is the auxiliary heating source.

6. Case Study

In [13], a first version of the SolarEnergy framework has beenpresented. In order to validate the proposed framework, atool called SolBrasil has been developed to simulate ther-mosiphon applications.

The SolBrasil tool is based on three main components:EgyRadiation, EgyColector and EgyStore. The first one is

0

20

40

60

80

100

120

1 2 3 4 5 6 7 8 9 10 11 12

Dem

and

(kW

)

Month

Monthly consumption

Figure 10: Energy consumption graph.

related to the solar radiation. The second one supplies thewater heating data and calculates the efficiency of a collectorgiven its physical data. The last component implements thedynamic of the water-heating process.

The framework has evolved and now both thermosiphonand photovoltaic systems are supported. It is importantto emphasize that hot spots are implemented by both thespecialization of abstract classes and composition of compo-nents, which results, for example, in the following devices:SBFVSolarPanel, BFVController, SBFVBattery and SBFVIn-verter.

We briefly present both simulations using the proposedapproach. Figure 6 depicts an instance of the framework forthermosiphon simulations.

6.1. Simulating Thermosiphon Applications. Initially, all com-ponents are included into the simulation such as the solarcollector and the water tank.

Then, the connections are defined: from the collectoroutput to the tank input, and from the tank output to thecollector input.

The case study presented is based on the data generatedby the solar radiation component. The solar radiation data isrelated to the Belo Horizonte city (Figure 7): an hourly globalradiation on an inclined surface angle of 34◦, azimuth angle= 80◦ and neighborhood reflectivity = 0.22.

Given the collector input data, one can simulate its effi-ciency (Figure 8). The result is obtained after running thesimulation according to the collector location.

One can also define the water tank profile: the waterconsumption in a particular time describing how the watertank behaves, that is, the variation on the water temperature.The data correspond to variations in the water temperaturealong a year.

6.2. Simulating Photovoltaic Applications. Figure 9 shows aninstance of the framework for photovoltaic system. The incli-nation angle of the photovoltaic generator, which maximizes


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0

5

10

15

20

25

30

35

40

45

1 13 25 37 49 61 73 85 97 109 121 133 145 157 169 181 193 205 217 229 241 253 265 277 289 301 313 325 337 349 361

Reference year days

Ligh

tin

dex

(Kt)

Ext

rate

rres

tria

lrad

iati

on(H

o)

and

radi

atio

non

the

surf

ace

(H)

Ho

HDaily kt

Figure 11: Relation of the extraterrestrial and the surface radiation.

Hou

rly

radi

atio

n(W

/m2)

Hours for typical days in each month along the year0 25 50 75 100 125 150 175 200 225 250 275 300

800

600

700

500

400

300

200

100

0

Figure 12: The monthly average hourly radiation based on the ref-erence year.

its own energy production, varies through the year. It meansthat the same photovoltaic generator can be calculated fromone region to another with different estimated values of solarradiation.

The global radiation on the panel surface considered asreference is the azimuth surface angle = 180◦ and the nearbyreflectivity = 0.22 (Belo Horizonte city).

The execution diagram has been designed for a photo-voltaic home system, isolated from the power supply system.

Hours for typical days in each month along the year

150

175

125

100

75

50

25

00 25 50 75 100 125 150 175 200 225 250 275 300

Pow

er(W

)

Figure 13: Monthly mean hourly power generated by the photo-voltaic modulus along the year.

The devices have been specified according to the manufac-turers specifications:

(i) ASE-100-ATF/17 from ASE Americas manufacturer;

(ii) the 12MC36 battery from Moura manufacturer;

(iii) the Sollis controller component from Varixx manu-facturer; and the XantrexGT conversor from Xantrexmanufacturer.


0 25 50 75 100 125 150 175 200 225 250 275 300Hours for typical days in each month along the year

0

250

500

750

1000

1250

Bat

teri

esst

ored

ener

gy(W

h)

Figure 14: Stored energy along a year.

The framework operates based on the registered energyconsumption. It is also possible to inform the demandthrough the component energy consumption (Figure 10).

6.2.1. The Results. Starting from the reference year it is pos-sible to generate a synthetic sequence of light indexes forthe rainy days. The output is related to the solar irradianceand consequently is extremely important to the simulatingprocess.

Figure 11 shows the relation between the light indexalong the reference year and the extraterrestrial radiationreflected on the surface.

It is represented by the Ho curve and it does nothave any influence on the deviation caused by the layers atthe atmosphere. So, its behavior is regular and its intensity isalways high.

The radiation on the earth surface H , is a function of thelight index Kt, which represents the influence of clouds andatmospheric gases in the radiation brightness. That is, ascloudier a day, lower will be the radiance.

Figure 12 shows the monthly average hourly radiationbased on the reference year. It can be notice an increase inthe irradiation showing that the inclination has an influencein the photovoltaic modulus during the months with lowerindexes of irradiation and high indexes of clarity.

Figures 13 and 14 represent the graphics for the powersupplied by one photovoltaic modulus and for the energystored by a cluster of three batteries along a year.

After the computation of the irradiation data, the cal-culus is done to estimate the maximum power point of thephotovoltaic generator. The top line in Figure 14 delimitatesthe maximum storage capacity over which the battery clusterwould be overcharged; the bottom line delimitates theminimum charge depth—below it the batteries would beexposed to a deep discharge that would damage them.

It can be noted that the available capacity is placed bet-ween two limits and the charge controller interferes in sucha way that it does not allow the bank to be overloaded or toreceive a deep discharge.

It also shows that the energy, which is stored along theyear, suffers a directly proportional variation to the mediumhourly power generated by the modulus monthly.

7. Conclusions

In summary, we developed a framework related to the solarenergy domain. The framework approach allows a greatflexibility in the development of new applications due to thefacility in customizing user requirements. It also enables thereuse of the analysis, project and source code. It increasessoftware quality, reduces the effort and time to develop newapplications.

The proposed solution has simplified the procedurestaken by solar energy researchers to develop control systems.For example, one can easily simulate the solar collector effi-ciency. Besides, it allowed the reuse of consolidated andtested solutions.

Using these concepts, the development of new applica-tions to control and simulate thermosiphon and photovoltaicsystems is simplified. Also, the time and cost to develop newcomponents is reduced. The designers do not start a newproject from scratch once they can use existing solutions.

In this work it has been developed the SolBrasil tool,based on an extended version of the framework SolarEnergy,to simulate real systems.

This work can be considered an innovative proposal forthe solar energy area as it has developed a methodologycapable of realizing, for example, a determinant calculationof photovoltaic systems isolated from electric network bymeans of analyzing the solar radiation, the energy balance,the statistical results and the identification of failures.

It is important to emphasize that we indeed checkour work with real data and real applications generatedby GREEN Laboratory (http://bhzgreensrv02.green.pucmi-nas.br/lwp/workplace—the GREEN SOLAR is a group ofstudies in solar energy located at the Pontifical Catholic Uni-versity of Minas Gerais (PUC-Minas)). A great number ofresearches has been developed at GREEN Laboratory formeasuring quality, efficiency and durability of solar compo-nents.

We compared our results with other works, such as theone modeling a photovoltaic generator regarding the featuresprovided by the manufacturer, which simulates it, using, forthat purpose, simulation and curve digitalization programs(Simulink of Matlab)—the work [14] analyzes its behaviorwith regard to the temperature and solar intensity variation,comparing the obtained curves to those provided by themanufacturer.

Also, Brazil’s largest state utility, Energetic Company ofMinas Gerais (CEMIG) has aggressively implemented theuse of decentralized photovoltaic systems to supplement theconventional power grid to satisfy an increasing demand forelectricity to serve rural communities in Brazil [15].

These consumers typically use energy in daytime peakhours of electricity, typically for lighting, television, andcommunication—as well as for a variety of cultural habitssuch as hot water that impose high demands on the utility’spower distribution and generation system.

The work presented in [15] includes examining themethods implemented to ensure system reliability for theconsumers, as well as the standards established under the


Agencia Nacional de Energy Eletrica (ANEEL), the nationalregulator electrical agency that ensures compliance with thefederal regulations—the work also provides an opportunityto compare and contrast their results with ours.

A future work intends to investigate the application of theproposed solution in systems related to other renewableenergy sources such as wind power. The aim is at the useof the proposed solution in order to calculate and simulateapplications that change the wind kinetic energy into rota-tion mechanical energy.

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