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ANALYSIS OF A CONCENTRATING PHOTOVOLTAIC/THERMAL SOLAR SYSTEMCheng Xuetao, Xu Xianghua, Liang XingangHeat Transfer and Energy Conversion-The Key Laboratory of Beijing MunicipalitySchool of Aerospace, Tsinghua UniversityBeijing 100084, Chinaxtcheng2001@ABSTRACTUses of solar energy both on heat energy and electricity at the same time by concentrating sunlight and tracking the maximum output power of solar cells is an efficient way, which will increase the utility of solar energy and reduce the cost. A reflective concentrator is adopted in the system to increase solar intensity on solar cells while they are cooled underneath by water. In such a way, much less solar cell area is needed to produce the same amount of electricity and hence the cell cost is greatly reduced. And hot water could be supplied at the same time. A mathematical model for a photovoltaic/thermal solar system is set up. The performance of the system is simulated. Some influences are discussed, such as the concentration ratio, flow rate of the cooling water, thermal conductivity, thickness of solar cells, tracking of maximum output power of solar cells, etc. on the thermal efficiency, electrical efficiency and temperature of solar cells. A working cycle is designed and simulated.1. INTRODUCTIONSolar energy is green and reproducible. The situation of the world energy source makes the exploitation and use of solar energy more and more important now. There are three technical ways to use solar energy. It could be turned into heat, electricity, and chemical energy. Because of the high production cost of solar cells at present, using solar energy both on heat energy and electricity at the same time is a good choice for us to get more energy from solar cells and decrease the cost [1].There are also three technical ways to collect more energy from solar cells. First, radiant intensity of solar cells couldbe increased by concentrating sunlight with lens or reflector. Lens has got less attention because it may cause a high temperature partially. Reflector has attracted comprehensive research and application since Rabl invented compound parabolic concentrator (CPC) in 1976 [2]. Second, cooling solar cells to decrease its temperature and improve its electrical efficiency [3, 4]. Compared with air, cooling by water is better because air is limited by its thermal character [5]. The third way is tracking the maximum output power of solar cells to get maximal electrical energy. Many methods such as constant voltage tracking (CVT) were studied [6].A photovoltaic/thermal solar system using all technical ways above was discussed in this paper.2. MATHMATICAL AND PHYSICAL MODELFig. 1 is a sketch map of the system where sunlight is concentrated by a CPC and then irradiates solar cells and cooling water runs beneath the cells. The principle of generating electricity by solar cells is photovoltaic effect. The equivalent electrical circuit of Si solar cell is shown in Fig. 2. The relationship between electrical current I and4 PV TECHNOLOGI ES, SYSTEMS AND APPLI CATI ONS1387output voltage U for the circuit is [7, 8]00()exp 1s sL D sh q U IR U IR I I I n kT R ⎡⎤++=−−−⎢⎥⎣⎦(1)where n 0 is a factor of diode, usually between 1 and 5; k isthe Boltzmann constant; T is the temperature of p-n junction; q is the elementary charge; I L is the photogenerated current which may increase a little when T goes up; I D is the saturation current of diode which may exponentially increase when T is getting higher; R s is the resistance in series which mainly comes from the cell material itself and contact resistance between metal and semiconductor; R sh is the parallel resistance which results from the electricity leakage of p-n junction.Fig. 1: A sketch map of the system.Fig. 2: The equal electric circuit of the solar cell. [7] Equation (1) could be rewritten as:20()exp10s sL D sh q U PR U U PR UI UI P n kT R ⎡⎤++−−−−=⎢⎥⎣⎦(2) Find dP dUand make 0dP dU= from equation (2)0200()exp 1()(1)2exp 0s L D s s D sh q U PR U I I n kT q U PR U q PR U U UI n kT n kT R ⎡⎤+−−⎢⎥⎣⎦⎡⎤+−−×−=⎢⎥⎣⎦(3)where P is the power from cells. The maximum outputpower could be tracked numerically based upon the above equations (2) and (3).The solar cells are composed of a protective glass layer, p-n junction and a substrate. When concentrated sunlight irradiates the protective glass, part of solar energy is reflected (called part 1), part is absorbed (part 2), the rest (part 3) could reaches the p-n junction. At present, the transmission rate is up to 95 percent or larger, so part 2 could be ignored. Some of part 3 turns into electricity as shown in Fig. 2. Some of electricity is output, the rest turns into thermal energy in p-n junction. This thermal energy could be treated as surface heat source because p-n junction is very thin. The rest of part 3 is absorbed by the substrate. For convenience, it could be treated as a uniform heat flux on the top surface of the substrate.As shown in Fig. 1, the section of the p-n junction and below could be treated as a two-dimensional steady heat conduction problem. For convenience, it could be called section 2; the protective glass layer is named section 1. The energy equation of section 1 could be simplified into a one-dimensional heat conduction problem without heat source because its temperature is supposed to change only in X direction there. The thickness of section 1 is d 1, while that of section 2 is d 2. Upper boundary of section 1 is a natural convective and radiant boundary.12441()()a a d a d y d d Th T T T T y λεσ=+∂=−+−∂ (4)where h a is convective heat-transfer coefficient, ε1 is thesurface emissivity, T a is the environment temperature, T d is the temperature of the upper surface of the glass. Lower boundary temperature of section 1 is the upper boundary temperature of section 2.Proceedings of ISES Solar World Congress 2007: Solar Energy and Human Settlement1388The equation of section 2 is expressed like this:22220T Tx y ∂∂+=∂∂ (5) Its left and right boundaries are adiabatic. Considering the energy conducted by glass, the energy equation of its upper boundary should be expressed as below:20(1)q y d T E G UI S E yλρ=∂==−−−∂ (6)where ρ is the surface reflectivity of the glass; S is the area of the cells; E 0 is the heat flux density conducted by the glass; E q is the heat flux density of upper boundary.The temperature of the cooling water and that of lower boundary of section 2 are nearly the same, so radiative heat-exchange could be ignored. Only convection is considered.Assuming that the lower wall of water channel is adiabatic and ignoring heat conduction and thermal radiation of the channel, the equation and boundary condition of the cooling water could be expressed as:000()wxw x wx wxwx x dT c m h a T T dx T T •=⎧=−⎪⎨⎪=⎩ (7) where c is specific heat of water, m •is the mass flow; a is the length of the cells in Z direction; T 0x is the inlet temperature of water; T wx is the local temperature of the water.3. RESULTS AND ANALYSESAssuming that length and width of cells are both 1 m, total thickness is 3 mm (thickness of protective glass is 2 mm). Transmissivity and reflectivity of the glass are 0.9, 0.1, respectively. Its emissivity is 0.94. Thermal conductivity of cells could be treated as constant. Because the material of cells are glass, Si, and some adhesive materials, the conductivity of the glass is given to be 1.4 Wm -1K -1, that of the substrate is between 1 and 2 Wm -1K -1. Solar radiation Gis 1000 Wm -2. Environment temperature T a is 298 K. Inlet temperature of water is 298 K. The width of the cooling water channel is 5 mm.The convective heat-transfer coefficient of the upper boundary of section 1 could be got from the correlation of natural convection with the hot surface upwards. The convective coefficient of water is obtained from the experimental correlation for the forced convection inside a channel.The concentration ratio (CR ) is an important parameter which greatly influences the electrical efficiency and other results. This is shown in Fig. 3 and Fig. 4. When CR goes up, temperature of cells goes up too. A superficial conclusion may conclude that the electrical efficiency should decrease monotonously but the simulated result shows that it increases at first and then decrease. The growth of CR increases the radiation intensity, which is positive for electrical efficiency for small CR and negative for large CR. Further more, the growth of CR increases the temperature of cells, which results in the reduction of cell efficiency. These two adverse effects lead to a maximum electrical efficiency in Fig. 3 and minimum thermal efficiency in Fig. 5.Fig. 3: Relationship between electrical efficiency and CR . A farther explanation could be found by considering Fig. 2. I f radiation intensity becomes N times larger, the photogenerated current roughly increases N times for small4 PV TECHNOLOGI ES, SYSTEMS AND APPLI CATI ONS1389Fig. 4: Relationship between temperature of cells and CR.Fig. 5: Relationship between thermal efficiency and CR. CR. Under the condition that the maximum electrical poweroutput is kept, it is found that the current through diode increase slowly so that the output current increases more than N times. Hence the electrical efficiency increases. When CR is large enough, the increase of temperature of the cells makes the current through diode go up exponentially, which in turn results in a significant loss of electrical power and reduces the electrical efficiency.Thickness of cells is also an important parameter. ts influence is shown in Fig. 6. It is shown that the influence of thickness is getting stronger when CR goes up.The influence of water speed and thermal conductivity of cells is also studied. The variations are similar to those in Fig. 6. When CR is large, there are strong influences from water speed and thermal conductivity of the cells.Fig. 6: Affection to electrical efficiency from thickness ofcells.Fig. 7: Comparison of electrical efficiency between different models.I n the above model, the infrared emission is treated as surface heat source on the top of section 2. Actually, it is not quite reasonable because infrared light may be absorbed by the substrate under Bouguer’s law. To take such case into account another model in which infrared light is absorbed evenly in the substrate is studied to compare with the model above to find out the degree of uncertainty. The comparison of two models is shown in Fig. 7 where Model 1 stands for the first one used in this paper, Model 2 stands for the second. Relative error between them is less than four percent. The uncertainty of the model is acceptable.Total solar energy utility of this system is about 85% and thermal use is dominant. Let us consider an example of thisProceedings of ISES Solar World Congress 2007: Solar Energy and Human Settlement 1390system. Suppose the CR is 6, cell thickness is 3 mm, cooling water speed is 1 m/s and area of solar cells is 1 m2. The simulation shows that this system may give us 8.25 kilowatt-hour electric energy per day (assuming 9 hours a day under sunlight; solar radiation is 1000 Wm-2 ); it also can give us 1012 kilo water whose temperature could be turned from 298 K to 323 K. Considering that the water speed is high, this may increase some cost. We could enhance the heat transfer and design a lower water speed to decrease pressure drop.4. CONCLUSIONSMathematical model is set up for the concentrating photovoltaic/thermal solar system in this paper. Based on the model, the character of this system is analyzed.(1) Total solar energy utility of this system is about 85% and thermal use is dominant.(2) Electrical efficiency of solar cells increases at first and then decreases with the growth of concentration ratio, while thermal efficiency is in an opposite manner. At the same time, temperature of the solar cells goes up linearly. (3) When the water speed goes up, electrical efficiency would increase. When CR gets bigger, this influence turns stronger. The influence which comes from thickness, thermal conductivity acts alike.5. REFERENCES(1) A. Royne, C. J. Dey, D. R. Mill, Cooling ofphotovoltaic cells under concentrated illumination： a critical review，Solar Energy Materals & Solar Cells 86（2005）451-483.(2) L. W. Florschuetz, C. R. Truman, D. E. Metzger，Streamwise flow and heat transfer distributions for jet array impingement with crossflow， J. Heat Transfer 103 (1981) 377-342.(3) A. D. Kraus, A. Bar-Cohen, Design and Analysis ofHeat Sinks, first ed, Wiley, New York,1995.(4) J. B. Lasich, Cooling circuit for receiver of solarradiation, Patent WO02080286, 2002, Australia.(5) Z. M. Zhao, J. Z. Liu, X. Y. Sun, Solar Energy PVGeneration and application, Beijing: Science Press (2005) 109-131(in Chinese).(6) M. Green, Solar cells, Beijing: Publishing House ofElectronics Industry (1987) 60-97 (in Chinese).(7) S. S. Li, Physics of Solar Energy, Beijing: CapitalNormal University Press (1996) 221-290 (in Chinese).。