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Optimization and practical verification of system configuration parameter design for a photovoltaic thermal system combined with a reflector

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Abstract

This study designed and optimized the system parameters for a photovoltaic thermal system (PV/thermal system) combined with reflectors. Moreover, it discussed the gain of electrical efficiency and thermal efficiency on the system after adding two reflectors on each of the south and north sides, and adjusting the water circulation system. As the rising angle and position of the sun varies each season, in order to make this study more rigorous, experiments were conducted in four seasons of a year. The Taguchi orthogonal array was used for experimental planning, and the optimal parameters were analyzed for electrical efficiency and thermal efficiency. The analysis of variance was conducted to examine the influential parameters, and principal component analysis was used to calculate the principal component point of each experiment. The results were employed to construct a response surface methodology model. Finally, the steepest descent method was applied to obtain the optimal parameters. The reflector theory was applied to calculate the gain of solar radiation amount after installing the reflector. Moreover, the gain was inputted into the simulation software TRNSYS to simulate the electrical power output and the water temperature in the water storage tank. The confirmatory experiments of the four seasons found that the electrical energy after installing the reflector increased by 0.117–0.183 kWh, and the thermal energy increased by 1.7–2.6 \(^{\circ }\hbox {C}\). The experiment confirmed that the prediction error was \(<\)4 %.

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Abbreviations

P:

Total generated electrical energy during the day (kWh)

G:

Total solar radiation energy during the day \((\hbox {J/m}^{2})\)

A:

Module dimension \((\hbox {m}^{2})\)

\(\hbox {V}_{\mathrm{m}}\) :

PV voltage at maximum power point (V)

\(\hbox {I}_{\mathrm{m}}\) :

PV current at maximum power point (A)

Q:

Total generated thermal energy during the day (J)

V:

Water mass flow rate (kg/s)

\(\hbox {C}_{\mathrm{p}}\) :

Water specific heat (4.18 kJ/kg \(^\circ \hbox {C}\))

\(\hbox {T}_{\mathrm{f}}\) :

Water final temperature \(({^\circ }\hbox {C})\)

\(\hbox {T}_{\mathrm{i}}\) :

Water initial temperature \(({^\circ }\hbox {C})\)

\(\hbox {A}_{\mathrm{r1\_a}}\) :

Actual receivable area of upper reflector \((\hbox {m}^{2})\)

\(\hbox {W}_{1}\) :

Upper plate width (m)

\(\hbox {W}_{1^{\prime }}\) :

Upper plate reflect to module width (m)

\(\hbox {L}_{1^{\prime }}\) :

Upper plate reflect to module height (m)

\(\hbox {L}_{1}\) :

Upper plate height (m)

\(\hbox {A}_{\mathrm{r1}}\) :

Reflection area of upper reflector \((\hbox {m}^{2})\)

\(\uptheta \) :

Included angle between reflector and azimuth \(({^\circ }\hbox {C})\)

\(\hbox {A}_{\mathrm{r2\_a}}\) :

Actual receivable area of lower reflector \((\hbox {m}^{2})\)

\(\hbox {W}_{2}\) :

Lower plate width (m)

\(\hbox {W}_{2^{\prime }}\) :

Lower plate reflect to module width (m)

\(\hbox {L}_{2}\) :

Lower plate height (m)

\(\hbox {L}_{2^{\prime }}\) :

Lower plate reflect to module height (m)

\(A_{r2}\) :

Reflection area of lower reflector \((\hbox {m}^{2})\)

\(\hbox {G}_{\mathrm{r1\_c}}\) :

Reflection solar radiation of upper plate \((\hbox {J/m}^{2})\)

\(\hbox {G}_{\mathrm{r1}}\) :

Receiving solar radiation of upper reflector \((\hbox {J/m}^{2})\)

\(\hbox {L}_{1}^{{\prime }{\prime }}\) :

Upper plate reflect to module lengthen width (m)

\(\hbox {G}_{\mathrm{r2\_c}}\) :

Reflection solar radiation of lower plate \((\hbox {J/m}^{2})\)

\(\hbox {G}_{\mathrm{r2}}\) :

Receiving solar radiation of lower reflector \((\hbox {J/m}^{2})\)

\(\hbox {L}_{2}^{{\prime }{\prime }}\) :

Lower plate reflect to module lengthen width (m)

C:

Concentration ratio (–)

S/N:

Signal to noise ratios

n:

Experimental numbers

y:

Experimental results

Y:

Principal components

\(\hbox {Y}_{\mathrm{k}}\) :

Matrix of k row vectors

\(\hbox {C}_{\mathrm{k}}\) :

covariance matrix

x:

Factor level

\(\uprho \) :

Reflection coefficient of reflector (–)

\(\upalpha \) :

Elevation angle of sun \(({^\circ })\)

\(\upbeta \) :

Collector inclination \(({^\circ })\)

\(\upalpha _{1}\) :

Inclination of upper reflector \(({^\circ })\)

\(\uptau \) :

Included angle between upper reflected light and collector \(({^\circ })\)

\(\upalpha _{2}\) :

Inclination of lower reflector \(({^\circ })\)

\(\upchi \) :

Included angle between lower reflected light and collector \(({^\circ })\)

\(\upbeta _{0}\) :

Regression coefficient

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Acknowledgments

The research was supported by the Bureau of Energy, Ministry of Economic Affairs, Republic of China, under the Grant No. 102-E0608.

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Authors and Affiliations

  1. Department of Materials Science and Engineering, National Taiwan University of Science and Technology, Taipei, 106, Taiwan

    Chung-Feng Jeffrey Kuo, Sheng-Siang Syu & Wei-Lun Lan

  2. Department of Materials Engineering, Kun Shan University, Tainan City, 710, Taiwan

    Chung-Yang Shih

  3. Green Energy and Environment Research Laboratories, Industrial Technology Research Institute, Chutung, Hsinchu, 31040, Taiwan

    Chao-Yang Huang

  4. Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, 300, Taiwan

    Chao-Yang Huang

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  1. Chung-Feng Jeffrey Kuo
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  2. Sheng-Siang Syu
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Correspondence to Chung-Feng Jeffrey Kuo.

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Kuo, CF.J., Syu, SS., Shih, CY. et al. Optimization and practical verification of system configuration parameter design for a photovoltaic thermal system combined with a reflector. J Intell Manuf 28, 1017–1029 (2017). https://doi.org/10.1007/s10845-015-1043-7

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