Energy balance model

The energy balance is considered for each component of the CPV receiver:

Tc, Tvb and the fluid, Tf and Tfo. Some geometrical characteristics of the CPV receiver and the silicone oil properties are given in Table 1.

3.1. Solar energy model

The irradiance absorbed by the vessel top, solar cells and vessel bottom are given by:

Ib = CR x I x a

vb g

As input for the model, the optical properties of the materials are used (Table 2).

Table 2. CPV receiver optical parameters









Solar cells



Silicone oil



3.2. Electrical model

A basic and wide spread method is used to estimate the photovoltaic power output [18]:

E = CRX- Ere, [1 + T(T. – Trf)] (9)

1 ref

Where I is the incident irradiance, E is the power output, T is the temperature, subscript ‘ref refers to standard testing conditions, r is the power correction factor for temperature(I = 800^^2 ,

Подпись: / m

Подпись: / m

If = 1000W/ 2 , Ef = 246.8W/ 2 , Tf = 298K, y = -0.65%/K ).

4. Results and discussion

The models above are analyzed to simulate solar cells temperature (Tc), vessel top temperature (Tvt), vessel bottom temperature (Tvb) and fluid average temperature (Tf).

Fig. 3shows the effect of concentration ratio on temperature when wind speed, ambient temperature, fluid inlet temperature and its volume flow rate are constant. The solar cells temperature is increased from 312K to 343K as concentration ratio is increased from 100X to 300X. So, if solar cells are operated in more than 300X, other parameters need be changed. Fig. 4 shows the four component temperature as a function of fluid volume flow rate at fixed wind speed, ambient temperature, fluid inlet temperature and concentration ratio. It is obvious that solar cells temperature and vessel bottom temperature varied with great ranges at beginning, then changed smoothly. A optimal fluid volume flow rate must be existed at a certain condition. Fig. 5 represents the variation of the four component temperature as a function of fluid inlet temperature at fixed wind speed, ambient temperature, fluid volume flow rate and concentration ratio. As an important parameter, the four component temperature is increased with its increased. The effect of environment variables including ambient temperature and wind speed on the four component temperature are shown in Fig. 6 and Fig. 7. The temperature of the four components has little change when ambient temperature and wind speed increased.

5. Conclusion

The main novelties of the HCPV system are the combination of a dish concentrator with solar cells immersed in dielectric liquid. The developed model predicts the effect of concentration ratio, fluid volume flow rate, fluid inlet temperature, ambient temperature and wind speed on solar cells temperature (Tc), vessel top temperature (Tvt), vessel bottom temperature (Tvb) and fluid average temperature (Tf). Results show that this kind of immersion operation of solar cells is an effective

method of cooling solar cells under concentrated light. Based on the experience achieved in the present work about high concentrated photovoltaic system with solar cells immersed in a dielectric liquid, the following topics need to be investigated: (1) construction of HCPV prototype, (2) the material stability, (3) determination the validation of the model and reliability of solar cells immersed in a dielectric liquid under concentrated light through experiments, (4) evaluation on feasibility and cost of the HCPV system.



Fig. 5. Temperature vs. fluid inlet temperature


Concentration Ratio( CR)

Fig. 3. Temperature vs. concentration ratio


w=3m, T =298K, V,=6m, CR=300X

s’ a ’ f h ’



— Tvt – a – Tvb Tf









-A————– A


A————– A————– A-


•——- •——- •——- • ‘…………………………… ‘

275 280 285 290 295 300 30б

Ambient Temperature( K)


Fig. 6. Temperature vs. ambient temperature

Vf =6m , T=293K, w=3m, CR=300X

f h ’ f s’


Fig. 4. Temperature vs. volume flow rate w=3m T =298K, Tf=293K, CR=300X

s a f





[1] Antonio Luque, Gabriel Sala, Ignacio Luque-Heredia. Photovoltaic Concentration at the Onset of its Commercial Deployment. Progress in Photovoltaics: Research and Applications. 2006, 14:413-428

[2] Martin A. Green, Keith Emery, Yoshihiro Hishikawa, et al. Solar cells Efficiency Tables (Version 32). Progress in Photovoltaics: Research and Applications. 2008, 16:435-440

[3] G. Martinelli, M. Stefancich. Chp.7: Solar Cell Cooling, in: Concentrator Photovoltaics. Springer Berlin Heidelberg New York. 2007, 130: 133-149

[4] Pierre J. Verlinden, Allan Lewandowski, Carl Bingham, et al. Performance and Reliability of Multijunction lll-VModules for Concentrator Dish and Central Receiver Applications. 2006 IEEE: 592­597

[5] Anja Royne, Christopher J. Dey, David R. Mills. Cooling of Photovoltaic Cells under Concentrated Illumination: a Critical Review. Solar Energy Materials & Solar Cells. 2005, 86: 451-483

[6] Welford, R. Winston. The Optics of Non-imaging Concentrators, Academic Press, New York, 1978

[7] A. Luque. Solar Cells and Optics for Photovoltaic Concentration, Adam Hilger, Bristol, 1989

[8] Blanco M, Alarcon D, Lopez T, et al. Computing the Solar Vector. Solar Energy. 2001,70(5):431-441

[9] Radziemska Ewa. Thermal Performance of Si and GaAs Based Solar Cells and Modules: a Review. Progress in Energy and Combustion Science. 2003, 29:407-424

[10] Jones A. D. Underwood C. P. A thermal Model for Photovoltaic Systems. Solar Energy.2001, 70(4):349- 359

[11] Davis M. W., Dougherty B. P., Fanney A. H. Prediction of Building Integrated Photovoltaic Cell Temperatures. Journal of Solar Energy Engineering. 2001, 123:200-210

[12] Garg H. P. Adhikari, R. S. Conventional Hybrid Photovoltaic/Thermal (PV/T) Air Heating Collectors

Steady State Simulation. Renewable Energy, 1997,11(3):363-385

[13] Garg H. P. Adhikari R. S. Transient Simulation of Conventional Hybrid Photovoltaic/Thermal (PV/T) air heating collectors. International journal of energy research, 1998,22:547-562

[14] Lee W. M. Infield D. G. Gottschalg R. Thermal Modelling of Building Integrated PV Systems. REMIC 2001.

[15] Duffie JA, Beckman WA. Solar Engineering of Thermal Processes. 2nd ed. New York: Wiley & Sons; 1991

[16] Biehl FA. Test Results and Analysis of a Convective Loop Solar Air Collector. Proc. 6th National Passive Solar Conf., Portland, Oregon, 1981: cited in [17]

[17] Altfeld K, Leiner W, Fiebig M. Second law Optimization of Flat-plate Solar Air Heaters. Part 1: The Concept of Net Exergy Flow and the Modeling of Solar Air Heaters. Solar Energy 1988;41(2):127±32

[18] Menicucci D, Fernandez JP. User’s manual for PVFORM: a Photovoltaic System Simulation Program for Stand-alone and Grid-interactive Applications; 1988. Sandia National Laboratories, SAND85-0376, Albuquerque, USA

Updated: July 15, 2015 — 12:40 pm