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9СОЛНЕЧНАЯ ЭНЕРГЕТИКА
SOLAR ENERGY
Статья поступила в редакцию 25.07.11. Ред. рег. № 1094 The article has entered in publishing office 25.07.11. Ed. reg. No. 1094
УДК 621.382:621.383
МОДЕЛИРОВАНИЕ ЛИНЕЙНЫХ ЗЕРКАЛЬНЫХ ОТРАЖАТЕЛЕЙ ДЛЯ СОЛНЕЧНОЙ КОНЦЕНТРАЦИОННОЙ СИСТЕМЫ
1 2 Мохамед Р. Гомаа , Р. Варданян
Инженерный колледж университета Миния, Египет Государственный инженерный институт Армении Армения, 375009, Ереван, ул. Териана, д. 105 Тел. 0037455065258; E-mail: dmoh_elbehary@yahoo.com
Заключение совета рецензентов: 10.08.11 Заключение совета экспертов: 15.08.11 Принято к публикации: 25.08.11
Системы фотогальванических концентраторов позволяют значительно снизить площадь покрытия солнечного элемента, наиболее дорогостоящего элемента в плоской системе. Среди различных систем концентраторов системы френелевского отражения эффективны благодаря простоте и легкости изготовления.
Разработана математическая и имитационная модель и для нового фотогальванического теплового (CPV/T) коллектора с абсорбером линейной конфигурации. Концентратор состоит из плоских стеклянных зеркал, расположенных под разными углами и фокусирующими солнечный свет на солнечные элементы, закрепленные вдоль активной системы охлаждения. Исследуются основные характеристики CPV/T коллектора. Для этого нами была разработана новая компьютерная программа. Данные, полученные с помощью новой программы, сравниваются с данными, полученными ранее в Государственном инженерном институте Армении (SEUA), с помощью программы для концентрационных коллекторов, известной как CPV-CAD. С помощью новой программы анализировалась система CPV/T электрической мощностью 1 кВт. Анализировалось влияние фокусного расстояния на коэффициент концентрации (CR), ширину коллектора, приток тепла к охлаждающей жидкости.
Ключевые слова: френелевское отражение, алгоритм, программное обеспечение, зеркало, фокусное расстояние.
SIMULATION OF LINEAR MIRROR REFLECTOR FOR SOLAR CONCENTRATOR SYSTEM
Mohamed R. Gomaa1, R. Vardanyan2
'College of Engineering, Minia University, Egypt 2State Engineering University of Armenia 105 Teryan str., Yerevan, 375009, Armenia Tel: 0037455065258; E-mail: dmoh_elbehary@yahoo.com
Referred: 10.08.11 Expertise: 15.08.11 Accepted: 25.08.11
A concentrating Photovoltaic (CPV) systems allows to a significant reduction in the area of solar cell coverage, the main cost driver in a flat plate system. Among different concentrating systems the linear Fresnel reflector (LFR) systems are effective due to the simplicity and easy fabrication.
A mathematical model and the simulation for a new concentrating Photovoltaic thermal (CPV/T) collector with a linear configuration absorber is developed. The concentrator system consists of flat glass mirrors, placed under the different angles, and focusing the sun light on to the solar cells mounted along active cooling system. The main properties of CPV/T collector are investigated. For this purpose a new computer program is developed. The data results from computer new program are compared with the result data from formerly developed at State Engineering University of Armenia (SEUA) known as CPV-CAD program for concentrating collectors. With the use new computer program, a CPV/T system with 1 kW electric power is analyzed. The effect of focus distance on concentration ratio (CR), collector width, and gain heat to the coolant fluid are analyzed.
Keywords: Fresnel reflector, Flow chart, software, mirror, Focus distance.
У*
А
Mohamed Ramadan Gomaa Behiri
Education: El-Minia University, Egypt, faculty of Engineering, department of Mechanical Power Engineering & Energy (2003).
Professional Work Experience: Ali Khaliel Company for plastic industries (2003), Kage for center air condition (2004). Teaching assistant at the Mechanical Power Engineering & Energy Department, Faculty of Engineering, El-Minia University (2004-2008). PhD student (Scholarship) State Engineering University of Armenia (since 2008 till now). Publications: 4.
Introduction
The idea of concentrating solar energy to generate electricity has ingeniously made use of the concept in concentrator optics especially for designing a specific geometry of reflectors or lenses to focus sunlight onto a small receiving solar cell [1]. Lenses or mirrors in the concentrator photovoltaic (CPV) system will replace most of the solar cell material and the price of both is taken into account for determining the optimum configuration. The price of solar concentrator is commonly lower than that of solar cells and hence efforts have been put into finding ways for lowering the manufacturing cost using various types of solar concentrators to develop a concentrator photovoltaic system [2].
Chong et al., [3] says that many of the existing concentrator systems produce non-uniform focused illumination. The CPV cells that receive non-uniform illumination will experience a drop in efficiency, as opposed to CPV cells under uniform illumination [4]. With this reason, Mills and Morrison [5] advocated the use of an advanced form of linear Fresnel reflector that can produce a better uniformity of solar irradiation compared to parabolic trough or parabolic dish systems. However, the solar concentration ratio for linear Fresnel reflector is normally lower than 100 suns. To achieve moderate solar concentration ratio (several hundreds of suns), modular Fresnel concentrator has been introduced for the application in CPV system and the results show that the modularly faceted Fresnel lenses can provide a better uniformity of solar irradiance but the transmission efficiency is relatively low, which is less than 80% due to the reflections at the lens surfaces and absorption by the lens material [6]. Chen et al. [7] proposed a non-imaging focusing heliostat in which high solar concentration ratio can be achieved through the superposition of all the mirror images into one at the fixed target. According to them, since the sunlight is not coherent, the resulted solar concentration is the algebra sum of the solar rays without creating a specific optical image.
A typical linear Fresnel reflector consists of long narrow flat mirrors fixed on a horizontal base [8]. Each mirror is tilted at an angle such that all incident solar
rays falling on them are reflected to a common focus. The absorber used are flat horizontal, the absorber is placed on the focus to absorb the concentrated radiation. The absorber is generally a tube or a series of tubes which contains a heat transfer fluid. Considerable attention has been paid of late to develop linear Fresnel reflecting concentrators for thermal and photovoltaic conversion of the solar energy [9]. Fresnel reflecting concentrator has several advantages, (i) it is useful for medium-temperature range (100-250 °C) applications [10]; (ii) it is fabricated with narrow flat mirrors and constituent materials for its fabrication as well as replacement are readily available in the market; (iii) the planar configuration and the air gap between the adjacent mirrors result in very small wind loading on the concentrator. Because of this, it can be mounted on rather simple cost-effective supporting structure.
To achieve a better uniformity of solar irradiance with a low cost the new CPV/T collector is developed. A hybrid PV/T collector is a bi-generating device where solar energy is converted into both electrical and thermal energy. The electrical generation is obtained using a photovoltaic laminate above the absorbent surface. The CPV/T collectors have an inherent advantage over other photovoltaic and thermal technologies with widely used other concentrating systems. The main advantages of the CPV/T are reduced area of solar cell (the main cost driver in a PV system); the thermal energy generated; the efficient use of space inherent in combining electrical and thermal energy generation, which may be advantageous on rooftops or in other applications where space is limited. The overall efficiency thus increases.
This paper presents results of a new computer program for a complete construction and analysis of a CPV/T system structure employing linear Fresnel reflector mirrors with active cooling.
Design Consideration For Linear Fresnel Reflecting Concentrator
The following simplifying assumptions have been made for designing linear Fresnel reflector solar concentrators: (i) the concentrator is tracked so as to follow the diurnal movement of the Sun (the apparent movement of the sun from East to West), (ii) the mirrors
International Scientific Journal for Alternative Energy and Ecology № 10 (102) 2011
© Scientific Technical Centre «TATA», 2011
are specularly reflecting, and (iii) the solar radiation is incident axially. The design of each linear Fresnel reflector solar concentrator is carried out such that the solar radiation reflected from each constituent mirror illuminates the absorber of a specified dimension. A variation in the width of the mirror is allowed for this purpose. An appropriate space, is introduced between two consecutive mirrors so as to avoid the blocking of radiation reflected from any mirror.
Let us consider the concentrator consisting of flat mirrors placed on a flat surface and inclinated on appropriate angles to concentrate the sun rays on to the linear focus (Fresnel linear focus mirror reflecting concentrator). The structure of such a concentrator is shown on Fig. 1. The solar cells are positioned in Focus distance F, on the surface of heat sink with the width a. the additional area C is used for possible occupation of it by heat sink.
Рис. 1. Структура солнечного концентратора на основе линейного отражающего зеркала Френеля Fig. 1. Structure of linear Fresnel mirror reflecting solar concentrator
The main parameters of light reflecting mirrors are the inclination angles a', a2,..., a,, width of mirrors A1D1, A2D2,..., A,D,, the aperture of mirrors (plane area) A'E', A1E1,., AiEi, the distance between two mirrors E^2, E2A3,..., Ei-1Ai, and its location (OiAi) on the aperture plane (XX) of the concentrator. The mathematical expressions for determination of these parameters are given below [11].
For the i-th mirror the indication angle is:
i = m
(a + c) + V A... a, .
1 V ' tf i-1 i 1 (Ai + a/2)
__nr* _-___ _ _ m*A+nn ___
a. = — arctan
' 2
F
= — arctan -2 F
(1)
The width of the first mirror is determined by the intersection point (D1) of a line drawn from the edge B' of the absorber parallel to the line BA1 and the line passing through the point A1. Hence, A1D1 would be the required width of the first mirror element, and the line B'D1 corresponds to the reflected ray associated with the extreme ray (C'1D1) incident on the extreme upper edge of the first mirror. This ensures that all the solar radiation reflected by the first mirror is intercepted by the flat horizontal absorber.
In the same way we can determine the main parameters for the second, third and all other mirrors. Thus we can find the following formulas for aperture A.Ei and width A.Di of each mirror,
note that, O1 At = O1A1 + ^ A_ 1 a, , also for the first
i=1
mirror (A0A1 = 0) as initial values for the iteration and i = 1, 2., m, where, 'm' is the total number of mirrors placed on each half of the reflector.
A¡E¡ = a -and,
a tan a,. tan 2a..
1 + tan a, tan 2a, 1 + tan a, tan 2a,
D¡E¡ = a cos a,
AD =
sin a,. 1 + tan a,. tan 2a,
(2)
(3)
a
or for simplicity,
AiDi = AßJcos a,.
(4)
Now let us define the distance between two neighboring mirrors A1A2. This is an important parameter to constitute the concentrator. It is important also to define the inclination angles by formula (3).
The location of the second mirror and its tilt with the aperture plane are chosen such that the solar radiation reflected from it is not blocked by the first mirror and finally reaches the absorber. This means that ray C2A2 impinging on the lower edge of the second mirror element (Fig. 1), after reflection, just touches the upper edge of the first mirror and finally strikes the edge B of the fiat horizontal absorber. The necessary shift associated with the second mirror (E1A2) is given by taking into consideration the similarity of triangles OBD1 and E1D1A2 and also we can take into consideration the similarity of triangles OBD2 and E2D2A3 we can get (E2A3).
Taking into consideration the similarity calculation above for the i-th mirror we can write for area Ei-1Ai:
E-A =
((a/2 + OxA-1) + A-D-1 cos aM ) A-1 D-i sin a,-
F - A-D-1sin a-1
(5)
The location (OA) on the aperture plane (XX') of the concentrator can be determined from this relation. For the i-th mirror we can write:
O1 At = O1 A,.-1 + A,-D-1 cos a,.-1 + E,_xA,..
(6)
The aperture width (W) of the concentrator achieved in any practical case may be expressed as
W = 2 V (O1A cos a,. + Et-1A ) + 2O1A1.
(7)
The Concentration ratio (CR) at any point on the absorber surface is determined by summing up the contribution of each constituent mirror at that point. This method is called the analytical technique [12]. For this purpose, it is assumed that the radiation reflected from each constituent mirror element is distributed uniformly over the width of the image produced by the mirror element on the surface of the absorber. Since each constituent mirror element illuminates the complete surface of the flat horizontal absorber, the total concentration at any point on the surface of the flat horizontal absorber may be calculated as:
V AE '=m CR = 2 ^^ = 2^CIt.
(8)
Obviously, for the flat horizontal absorber a uniform illumination over the absorber surface can be expected as each constituent mirror illuminates the complete surface of the absorber.
The relation between the cell efficiency and the cell temperature is calculated from the relation below [13].
Пс =ПRef (1 - b (Tc - 25)).
(9)
Where Пс is the calculated cell efficiency at solar cell temperature TC, nRef is the solar cell efficiency at 25 °C, and b is the coefficient for some different type of solar cell presented bellow (Table 1).
Таблица 1
Коэффициент b для различных типов солнечных элементов
Table 1
Coefficient b for some different types of solar cell
Type of Solar cell b (% / °C)
Mono-Si 0.4
Poly-Si 0.4
a-Si 0.11
GaAs 0.25
CdTe 0.24
ClS 0.46
Computer Program For CPV/T Systems Design
With the use of developed mathematical model all parameters of the CPV/T system construction are calculated. For this purpose the computer simulation program based on FORTRAN is developed as well. The algorithm of program presented in Fig. 2, 3
Рис. 2. Алгоритм компьютерной программы Fig. 2. Flowchart for computer program
International Scientific Journal for Alternative Energy and Ecology № 10 (102) 2011
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Входные параметры Input data
Таблица 2 Table 2
Рис. 3. Структура символов, используемых в программе Fig. 3. Structure shown symbols that used in program
With the use of developed simulation program the main parameters of CPV/T collector are calculated for the complete construction of the collector with active cooling. To assess the obtained results by our simulation program, the other existing program developed at SEUA is used also. The input and output parameters for our simulation program and CPV-CAD program are presented in Tables 2, 3.
For the given value of generated electric power 1 kW, ambient temperature, and for some other input parameters (Table 2), the programs calculates the parameters of solar concentrator system.
The results that obtained from the simulation program are compared with the results that obtained from CPV-CAD program. It can be seen from the Table 3 that the construction parameters obtained by our program and CPV-CAD program are almost the same it means that our program is operating in a good way. Not that, the thermal parameters are calculated with the use of our simulation program and CPV-CAD program does not allow us to get the thermal parameters. Thus, this can be considered as advantage of our software.
The cell used in our theoretical simulation work is silicone and to save this cell the operation temperature must not increase than 100 °C. When the temperature increase more than this value the cell will damage, and also the cell efficiency increases as the cell temperature decreases so, the cells must be cooled. The cells can be cooled by passive or active cooling system. In passive cooling system, most of the absorbed energy, from 75% to 80%, is dumped to the surroundings again. When an active cooling system is used the cells are installed over a cooling plate that removes the surplus heat from the cells to a coolant fluid. The coolant is typically water flowing in a circular or a rectangular pipe, sheet and tube design, as in our system. The cell temperature is 68.191 °C and the output coolant water temperature is 40.84 °C are obtained when the mass flow rate (m) of the cooling water is 0.09 kg/sec, as well as the cell temperature is 68.19 °C.
Input parameters for comparison between Fortran simulation and CPV-CAD simulation
Description Symbol Value
Required electric output P req 1 kW
Solar radiation I 1 kW/m2
Efficiency of solar cell "Hcell 25 %
Ambient temperature T a 25 °C
Width of absorber a 0.1 m
Obtained results
Полученные результаты
Table 3 Таблица 3
Output parameters for comparison between Fortran simulation and CPV-CAD simulation Simulation results Obtained results by CPV-CAD
Description Symbol (Units) Value Value
Number of mirror for each side m (#) 5 5
Focus distance F (m) 1.6 1.6
The aperture width W (m) 1.44 1.404
The aperture length L (m) 6.5 6.83
Apparatus area Aap (m sq.) 9.363 9.589
App. actual area Aac (m sq.) 8.282 8.551
Unused aperture area Aun (m sq.) 1.081 1.038
Concentration ratio CR (sun) or (x) 11.584 9.67
Cell temperature Tc CC) 68.191 Inside prog.
Mass flow rate m (Kgs-1) 0.09 Not
No. of pipe No. p (#) 4 Not
Diameter of each p^e Dp (Cm) 1.25 Not
Outlet cooling temperature Tout ( C) 40.84 Not
TC - Tout ac ( " C) 27.351 Not
T - T * out * in Atw ( 'C) 15.84 Not
Electric efficiency 4ELE (%) 12.4 Not
Thermal efficiency 4the (%) 67.1 Not
Combined efficy. ПСТЕ (%) 79.5 Not
Although other fluids may be used in a closed circuit, especially for temperature exceeding 100 °C. The cell temperature and output coolant water temperature can
controlled by controlling the mass flow rate (m) of the cooling water as well as by the inlet temperature. To reach the best performance for the active cooling the maximum temperature difference between the cell and outlet water temperature (AtC) not exceed than 30 °C, and also the minimal temperature difference between outlet and inlet water temperature (Atw), coolant temperature rise, not less than 7 °C. The AtC for our simulation program results (Table 3) is 27.35 °C and coolant temperature rise Atw is 15.4 °C. The hot coolant leaving the CPV/T receiver is directed to a heat exchanger where the heat may be used as an additional energy product, for example to produce hot water for domestic or industrial applications, hot air for space heating, or to drive an absorption cooling machine. It is necessary in any solar radiation collector to reduce the heat losses or to minimize them.
The electric efficiency is obtained by FORTRAN simulation program 12.4% at required power 1kW with a focus distance is 1.6 m and as mentioned above, the cell efficiency is decreased with increasing the cell temperature as well as the electric efficiency is decreased. The thermal energy is available in the cooling process of the photovoltaic cells and the absorber, the thermal efficiency is obtained by FORTRAN simulation program 67.1% for a focus distance is 1.6 m and increased with increasing the cell temperature.
The average cells temperature in a CPV/T collector might be lower than that for a conventional module, thereby increasing its electrical performance. Thus the combined thermal and electrical efficiency from the results obtained is 79.5% and almost constant. Because the combined thermal and electrical performance of a CPV/T device the efficiency is higher than that of the corresponding thermal collector or the photovoltaic module.
о
500
a = 0.1 m —*— L at different (F)
—W at F = 1.0 m —a—W at F = 3.0 m *
А...............
-п
i 5 ?
à
20 DO 2500 Power (W|
Рис. 4. Длина и ширина CPV/T коллектора в зависимости от мощности, необходимой для различных фокусных расстояний Fig. 4. The length and the width of CPV/T collector plotted against the power required with different focus distances
With the use of developed simulation program the parameters of a CPV/T collector with the absorber width of 0.1 m, are investigated. It can be seen from Fig. 4 that
the length of a CPV/T system is increasing with increasing of required power. It can be seen also that the width of a CPV/T collector is increasing with required electric power and it is decreasing with increasing of focus distance (F).
The dependence of a CR from required electric power of a CPV/T collector with different focus distance (F) are presented in Fig. 5. The concentration ratio is increased with increasing the required electric power and focus distance. Thus, the increasing of focus distance of a CPV/T collector structure gives a reduction in the mirrors inclination angles.
Рис. 5. Показатель концентрации CPV/T коллектора в зависимости от мощности, необходимой для различных
фокусных расстояний Fig. 5. Concentration ratio of CPV/T collector plotted against the power required with different focus distances
Рис. 6. Показатель концентрации и ширина CPV/T коллектора в зависимости от фокусного расстояния для различной мощности Fig. 6. Concentration ratio and the width of CPV/T collector plotted against the focus distance with different power required
As shown in Fig. 6, the CR is increasing and the width of the system is decreased with increasing of focus distance for different required electric power. It can be seen that the width is decreasing strongly for small values of F and it is almost constant for higher FS (from 1.5 to 3.0 m ). Then it can be concluded that with the use
International Scientific Journal for Alternative Energy and Ecology № 10 (102) 2011
© Scientific Technical Centre «TATA», 2011
of this dependences the optimal parameters (CR, F, and W) of the system can be defined with the purpose to obtained sufficient CR having small values of focus distance and width.
Conclusion
Developed computer program allows determining all parameter of a CPV/T structure. It can be used for a CPV/T systems design and at universities for education purposes. The developed new FORTRAN simulation program for PV/T solar energy concentrator system has several advantages in comparison with well known systems.
The analyses of parameters of a CPV/T system show that the optimal parameter of the system can be determined with the use of developed simulation program.
References
1. Andreev V.M., Grilikhes V.A., Rumyantsev V.D. Photovoltaic conversion of concentrated sunlight. England: John Wiley & Sons Ltd, 1997. P. 185- 259.
2. Whitfield G.R., Bentley R.W., Weatherby C.K., Hunt A.C., Mohring H.D., Klotz F.H., et al. The development and testing of small concentrating PV systems // Solar Energy 67(1-3), 2000, P. 23-34.
3. Chong K.K., et al. Design and construction of non-imaging planar concentrator for concentrator photovoltaic system // Renewable Energy 34, 2009, P. 1364-1370.
4. Coventry Joe S. Performance of a concentrating photovoltaic/thermal solar collector // Solar Energy 78, 2005, P. 211-222.
5. Mills D.R., Morrison G.L. Compact linear Fresnel reflector solar thermal power plants // Solar Energy 68(3), 2000, P. 263-283.
6. Ryu K., Rhee J.G., Park K.M., Kim J. Concept and design of modular Fresnel lenses for concentration solar PV system // Solar Energy 80, 2006, P. 1580-1587.
7. Chen Y.T., Chong K.K., Lim B.H., Lim C.S. Study of residual aberration for non-imaging focusing heliostat // Solar Energy Materials and Solar Cells 79(1), 2003, P. 1-20.
8. Mathur S.S., Kandpal T.C., Negi B.S. Study of concentration characteristics and performance evaluation of a linear Fresnel reflector. In: Proc. of National Solar Energy Conv., New Delhi: Tata McGraw Hill publishing Co.; 1988. P. 263-70.
9. Mohamed R. Gomaa. Thermal Performance of a Linear Fresnel Reflector Solar Concentrator PV/T Energy Systems. The paper accepted for presenting during 6th International Green Energy Conference - VI (IGEC-VI), which will be held in Eskisehir, Turkey, 5 June (2011).
10. Singh P.L., Ganesan S., Yadava G.C. Performance of a linear Fresnel concentrating solar device // Renew Energy 18, 1999, P. 409-416
11. Mohamed R. Gomaa, Vardanyan R., Dallakyan V. Analysis of properties of linear focus Fresnel reflecting concentrator. Bulletin of State Engineering University of Armenia (Polytechnic), Yerevan 2011, the paper accepted for publication.
12. Royne A., et al. Cooling of photovoltaic cells under concentrated illumination: a critical review // Solar Energy Materials & Solar Cells 86, 2005 P. 451-483
13. Vardanyan R., Dallakyan V. Cost Effective Photovoltaic Solar Energy Concentrating Systems For Terrestrial Applications.
