Energy Conversion and Management

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1 Energy Conversion and Management 5 (011) Contents lists available at ScienceDirect Energy Conversion and Management journal homepage: Solar radiation transfer and performance analysis of an optimum photovoltaic/thermal system Jiafei Zhao, Yongchen Song, Wei-Haur Lam, Weiguo Liu, Yu Liu, Yi Zhang, DaYong Wang Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, Dalian 11604, PR China article info abstract Article history: Received 13 December 009 Received in revised form 8 August 010 Accepted 13 September 010 Available online 0 October 010 Keywords: Photovoltaic/thermal Direct absorption collector Inverse method Genetic algorithm Exergy efficiency This paper presents the design optimization of a photovoltaic/thermal (PV/T) system using both non-concentrated and concentrated solar radiation. The system consists of a photovoltaic (PV) module using silicon solar cell and a thermal unit based on the direct absorption collector (DAC) concept. First, the working fluid of the thermal unit absorbs the solar infrared radiation. Then, the remaining visible light is transmitted and converted into electricity by the solar cell. This arrangement prevents excessive heating of the solar cell which would otherwise negatively affects its electrical efficiency. The optical properties of the working fluid were modeled based on the damped oscillator Lorentz Drude model satisfying the Kramers Krönig relations. The coefficients of the model were retrieved by inverse method based on genetic algorithm, in order to (i) maximize transmission of solar radiation between 00 nm and 800 nm and (ii) maximize absorption in the infrared part of the spectrum from 800 nm to 000 nm. The results indicate that the optimum system can effectively and separately use the visible and infrared part of solar radiation. The thermal unit absorbs 89% of the infrared radiation for photothermal conversion and transmits 84% of visible light to the solar cell for photoelectric conversion. When reducing the mass flow rate, the outflow temperature of the working fluid reaches 74 C, the temperature of the PV module remains around 31 C at a constant electrical efficiency about 9.6%. Furthermore, when the incident solar irradiance increases from 800 W/m to 8000 W/m, the system generates 196 C working fluid with constant thermal efficiency around 40%, and the exergetic efficiency increases from 1% to %. Crown Copyright Ó 010 Published by Elsevier Ltd. All rights reserved. 1. Introduction Over the past century fossil fuels have provided most of our energy. However, their extensive utilization leads to shortage, higher cost and environmental pollution. Compared with other forms of energy, solar energy is renewable and environmentally friendly [1,]. Solar hot water is being used for domestic, agricultural and industrial uses. Although it can reduce domestic water heating costs by as much as 70%, it is still mainly used in domestic water heating systems [3]. On the other hand, over 90% of the world s photovoltaic market uses silicon solar cells. The highest efficiencies reported in 009 were 5% ± 0.5% using crystalline silicon and 0.4% ± 0.5% using polycrystalline silicon [4]. Conventional solar cells convert between 5% and 0% of the entire incoming solar radiation into electricity. More than 80% of the incident solar radiation on solar cells is reflected or converted to thermal energy [5,6]. Despite the rapid market growth supported by tax break and other incentives, it remains uncompetitive with fossil fuel based electricity production [7]. In view of this, photovoltaic/thermal (PV/T) Corresponding author. addresses: powere@dlut.edu.cn, jfzhao@dlut.edu.cn (Y. Song). systems have been introduced to simultaneously generate electricity and produce hot water [6]. Photovoltaic/thermal (PV/T) systems consist of a PV module and a thermal unit converting solar radiation into electricity and hot water, respectively [8 10]. The thermal unit cools and extracts heat from the PV module [5,11]. Thus, the working fluid temperature can only be lower than that of the PV module [5]. In order to achieve large thermal exergy, the electrical exergy must be sacrificed [1]. Bergene and Løvvik [13] presented a numerical heat transfer model predicting the performance of PV/T systems. They extended the models for flat plate solar collectors presented by Duffie and Beckman [14]. The overall efficiency of their PV/T system was about from 60% to 80%. Tiwari and coworkers [15 17] presented numerical model predicting the performance of PV/T system, and experimentally validated for various configurations. Tripanagnostopoulos et al. [11] experimentally compared several PV/T systems through outdoor tests. The authors showed that PV cooling could increase the electrical efficiency and the overall efficiency, because of the simultaneous operation of these systems as thermal collectors. Ji et al. [6] constructed a flat-box aluminumalloy photovoltaic and water-heating system. The outdoor performance of their PV/T system demonstrated that a daily thermal /$ - see front matter Crown Copyright Ó 010 Published by Elsevier Ltd. All rights reserved. doi: /j.enconman

2 1344 J. Zhao et al. / Energy Conversion and Management 5 (011) Nomenclature A absorptance c specific heat (J/kg K) G irradiance (W/m ) h convective heat transfer coefficient (W/m K) I electric current (A) k absorption index or thermal conductivity (W/m K) L slab thickness (m) m complex index of refraction, m = n ik _m mass flow rate (kg/s) n refractive index q heat flux (W/m ) r reflection coefficient R reflectance or thermal resistance (K/W) S collector surface area (m ) t transmission coefficient T transmittance or temperature ( C) V voltage (V) Greek symbols d hydraulic diameter (m) e dielectric constant or emissivity g 0 electrical efficiency at 5 C (%) g el electrical efficiency (%) g th thermal efficiency (%) j absorption coefficient (m 1 ) k wavelength (m) m frequency (s 1 ) x angular frequency, pm (s 1 ) c relaxation frequency (s 1 ) q interface reflectivity s optical thickness r Stefan Boltzmann constant (W/m K 4 ) Subscripts abs refers to absorption b refers to bottom air refers to the air cal refers to calculating result conv refers to convection des refers to desired performance f refers to working fluid gl refers to glass i,j refers to indices oc refers to open circuit ov refers to overall pv refers to solar cell sky refers to sky sp refers to support r refers to relative rad refers to radiation t refers to top tu refers to thermal unit vis refers to visible light between 300 nm and 760 nm w refers to wind " refers to upper surface ; refers to lower surface efficiency of about 45% and electrical efficiency of about 10% were achievable. The water temperature rise in the tank was around 8 C. Morita et al. [18] performed a numerical analysis for single and no cover sheet-and-tube PV/T system. Although the optimum hot water temperature reached 83 C, it is clear that the electrical efficiency was sacrificed and was around 6%. To achieve higher energy efficiency and to further reduce the system cost, solar concentrators have been combined with PV/T systems to form concentrating photovoltaic/thermal systems (CPV/T) [7,19]. The use of concentrators is up to now the most viable method to reduce system cost [5]. However, in the concentrating system, active cooling adds 10% to the overall system cost [0]. Additionally, the most basic technique to fabricate a CPV/T system is to glue a commercial PV cell laminate to the absorber of a commercial collector. Then, it is very difficult to prevent delamination caused by excessive heating [1]. Garg and Adhikari [] reported the performance analysis of air type PV/T systems with and without a compound parabolic concentrator (CPC). The studies showed that the system coupled with CPC always performed better in terms of both thermal and electrical efficiencies. Rosell et al. [3] presented a low concentrating PV/T system using high performance silicon cells with a overall efficiency larger than 60% for a concentration ratio larger than six. However, the coolant outflow temperature was less than 60 C. In order to operate at higher temperatures, triple-junction PV cells were used in the PV module of the CPV/T systems. In principle, the operating temperature of the triple-junction PV module can reach up to about 40 C with electrical efficiency of about 30% [19,0]. However, in practice, these triple-junction PV modules are usually operated at temperature below 100 C, and the coolant outflow temperature is typically about 10 C lower than the PV module temperature [0]. Indeed, the concentration system leads to severe thermal stress due to the non-homogeneous temperature distribution in the solar cell [5]. Thus, thermal management remains a major issue of CPV/T systems. First, it requires that the PV module is cooled to ensure satisfactory performance of CPV/T systems and prevent damages to the PV module caused by overheating. On the other hand, the absorbed thermal energy is more valuable if the working fluid reaches higher temperature. Therefore, a compromise must be found to increase the temperature of the coolant without affecting the electrical efficiency [0]. The objective of this study is to optimize the design of a PV/T system using both non-concentrated and concentrated solar radiation. The system considered is based on a direct absorption collector (DAC) [4] using a working fluid directly absorbing the infrared solar flux incident on the collector. The properties of the working fluid are optimized such that the transmission of the visible light and the absorption of the solar infrared radiation are maximum. Moreover, the thermal unit is set above the PV module as the channel PV/T systems. However, by contrast with conventional channel PV/T systems, the thermal unit does not extract heat from the PV module.. Analysis.1. PV/T system considered Fig. 1 shows the schematic of the PV/T system considered in this study. It consists of a thermal unit placed above a PV module and separated by an air gap of arbitrary thickness. Thus, the PV module need not be glued to the thermal unit to avoid delamination concerns. The top and bottom slabs of the thermal unit are made of silicon dioxide with refractive index n 1 = n 3 and absorption index k 1 = k 3. First, the working fluid flows in the back of the PV module to cool the PV cell. Then, it flows through the thermal unit, and ab-

3 J. Zhao et al. / Energy Conversion and Management 5 (011) collimated incident solar radiation (G) Thermal unit PV module top slab bottom slab PV cell support T in T out insulation q f air q air1,conv q f,out1 q f,out q air3,conv q air3,rad G pv q air4,conv q air4,rad T pv q sp q f,in q sky,rad q t,gl q b,gl G f working fluid working fluid q ba L 1 L 3 L L 6 T t,gl T t,gl T mid T b,gl T b,gl T sp q f,m T mid Ta Fig. 1. Schematic of the system considered along with heat fluxes and temperatures used for thermal analysis of the system. sorbs the solar infrared radiation. The working fluid refractive and absorption indices are denoted by n and k, respectively. The thermal unit is surrounded by air (n air and k air ). The infrared portion of the incident solar radiation is directly absorbed and converted into thermal energy (photothermal conversion) by the working fluid in the thermal unit. The photovoltaic solar cell underneath receives the transmitted visible light to perform photoelectric conversion... Assumptions In order to make the problem mathematically trackable, the following assumptions are made: 1. The incident radiation is assumed to be collimated and normal to the system.. The spectral range considered is from 00 nm to 000 nm, where 94% of the solar radiation is concentrated. 3. The sun is assumed to be a blackbody at 576 K [5]. 4. Polarization effects are ignored. 5. Each layer of the system is homogeneous and isotropic. 6. All the surfaces are optically smooth. 7. In the PV/T system, the PV cell produces most of the power in the visible wavelengths, over the spectral range from 00 nm to 800 nm [6,7]. 8. The working fluid is absorbing but non-scattering and nonemitting. 9. In order to calculate the efficiencies of the system, the density, heat capacity, and the thermal conductivity of the working fluid are assumed to be equal to those of water. 10. The working fluid of the system remains liquid, and the properties of the working fluid are independent of temperature. 11. To compare the performance of the water PV/T system and the optimized PV/T system, the consumed electrical power of pumps are ignored in both systems..3. Governing equations.3.1. Optical properties of the working fluid The classical model of a damped oscillator developed by Drude, Lorentz, and Zener [8 30] is adopted to model the refractive index n and absorption index k of the working fluid as a function of wavelength k. The complex dielectric constant ~e r; at frequency x is expressed as [31], ~e r; ¼ e 0 r; ie00 r; ¼ðn ik Þ ¼ e 1 þ X j x pj x 0j x þ ic j x ð1þ where the real and imaginary parts of the complex dielectric constant, respectively denoted by e 0 r; and e00 r;, are given by [31], e 0 r; ¼ n k ¼ e 1 þ X x pj x 0j x ðþ j x 0j x þ c j x e 00 r; ¼ n k ¼ X j x pjc j x x 0j x þ c j x The parameters x pj, x 0j and c j are the plasma frequencies, the oscillator frequencies, and the relaxation frequencies, respectively. The oscillator frequency is the location parameter. It determines the spectral location of the band. Increasing or decreasing the oscillator frequency shifts the band structure to higher or lower frequencies. The plasma frequency is the strength parameter. It determines whether the oscillator is relatively weak or strong. As the plasma frequency increases the value of absorption index increase at all frequencies. Moreover, the damping frequency is the parameter that describes the width of the absorption band for a given strength [31]. The summation is made over all optical excitations contributing to ~e r;. Most studies consider only a limited spectral range and do not comprise the highest oscillator frequencies. The high-frequency dielectric constant e 1 accounts for the collective contribution of such oscillators [31,30]. The corresponding refractive and absorption indices n and k can be computed from the following equations which satisfy the Kramers Krönig relations [31]: n ¼ 4 k ¼ 4 e0 r; þ e0 r; þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3 e 0 r; þ e 00 r; 5 1= qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3 e 0 r; þ e 00 r; 5 1= and In the present study, the thermal unit consists of three slabs as shown in Fig. 1. The spectral reflectance R tu and transmittance T tu of the thermal unit are given by [5], R tu ¼ R 1 þ T 1 R ð1 R R 3 ÞþT 1 T R 3 ð1 R 1 R Þð1 R R 3 Þ R 1 R 3 T T 1 T T 3 T tu ¼ ð1 R 1 R Þð1 R R 3 Þ R 1 R 3 T ð3þ ð4þ ð5þ ð6þ

4 1346 J. Zhao et al. / Energy Conversion and Management 5 (011) where the spectral reflectance R i and transmittance T i of a homogeneous and isotropic slab i with thickness L i sandwiched between slabs i 1 and i + 1 are given by [5], R i ¼ q i 1;i þ q i;iþ1 ð1 q i 1;i Þ e j il i 1 q i 1;i q i;iþ1 e j il i ð7þ T i ¼ ð1 q i 1;i Þð1 q i;iþ1 Þe j il i 1 q i 1;i q i;iþ1 e j il i ð8þ The reflectivity q i,j of the interface between slabs i and j and the absorption coefficient j i of slab i are expressed as, q i;j ¼ ðn i n j Þ þðk i k j Þ and j ðn i þ n j Þ þðk i þ k j Þ i ¼ 4pk i k Note that Eqs. (5) (9) are written on a spectral basis. Over the spectral range, the average transmittance of the thermal unit T tu;ki k j is defined as the ratio of the energy transmitted to the incident solar energy between k i and k j, T tu;ki k j ¼ R kj k i R kj k i T tu I bk dk I bk dk ð9þ ð10þ where I bk is blackbody spectral intensity, and T tu is the spectral transmittance of the thermal unit. Similarly, the average absorptance A tu;ki k j is defined as the ratio of the energy absorbed to the incident solar energy between k i and k j, A tu;ki k j ¼ R kj k i R kj k i A tu I bk dk I bk dk ð11þ where A tu is the spectral absorptance given by A tu =1 R tu T tu, and R tu is the spectral reflectance of the thermal unit. Eqs. (10) and (11) are also valid for the working fluid and the PV cell..3.. Energy balance equation of the PV/T system Energy balance equations are formulated to determine the temperature of the thermal unit and the PV module and the performance of the PV/T system [3]. The system is assumed to operate at steady-state [3], Fig. 1 schematically indicates the heat fluxes and temperatures in the system. The energy conservation equations for the PV module can be written as, G pv A pv g el;pv G pv ¼ q sp þ q air4;conv þ q air4;rad ð1þ where the heat flux between the solar cell and the support is q sp, while the heat fluxes between the PV cell and the surrounding by convection and radiation are denoted by q air4,conv and q air4,rad, respectively. The absorptance of the PV cell on a total basis is denoted by A pv. The irradiance received by the PV module G pv is given by, G pv ¼ T tu;k1 k G ¼ T tu;k1 k Z k k 1 I bk dk ð13þ where G is the total incident solar irradiance on the system while T tu;k1 k is the average transmittance of the thermal unit between k 1 = 00 nm and k = 000 nm. Moreover, the electrical efficiency of the PV module g el,pv and of the PV/T system g el are expressed as [1,33], g el;pv ¼ g 0 ½1 bðt pv T a ÞŠ and g el ¼ g el;pv T tu;k3 k 4 ð14þ where the electrical efficiency g 0 is that of the PV cell working at 5 C. The PV cell temperature and the ambient air temperature are denoted by T pv and T a, respectively. The temperature coefficient b (in %/ C) is the electrical efficiency reduction for every degree centigrade of temperature rise. T tu;k3 k 4 is the average transmittance of the thermal unit between k 3 = 00 nm and k 4 = 800 nm. Note that Eq. (14) has some deficiencies. First, at low solar irradiance, it gives PV module electrical efficiency equals the electrical efficiency of the reference conditions. The equivalence of the solar cell and ambient temperature is the reason of this fact. Second, it cannot estimate the electrical parameters of the PV/T system such as open-circuit voltage, short-circuit current, maximum power point voltage and maximum power point current [9,34]. The PV module considered produces most of the power in the visible wavelengths, thus the electrical efficiency g el,pv is such that, g el;pv G pv ¼ g el;vis G pv;vis ð15þ where the PV module efficiency g el,vis is calculated from the visible light of solar radiation. The irradiance in the visible received by the PV module is G pv,vis. They are expressed as, g el;vis ¼ V MPPI MPP G vis S G ¼ g el;pv and G pv;vis ¼ GT tu;k3 k G 4 ð16þ vis where the visible part of solar irradiance is G vis. The collector surface area is S. The voltage V MPP and the current I MPP correspond to the maximum power, where the product of current and voltage is maximum. Thus, Eq. (1) can be written as, G pv A pv g el;vis G pv;vis ¼ q sp þ q air4;conv þ q air4;rad ð17þ In addition, when the working fluid flows behind the PV cell, the energy conservation equations of the working fluid can be written as, q sp ¼ q f ;in q f ;in ¼ q ba þ q f ;m ð18þ ð19þ where the convective heat fluxes through the PV support to the working fluid is q f,in. The thermal energy collected by the working fluid in the PV module is denoted by q f,m, whereas q ba is the conductive heat flux in the insulation. Moreover, the energy balance of the working fluid in the thermal unit can be written as, G f A f ;k1 k ¼ q f þ q f ;out1 þ q f ;out ð0þ where q f,out1 and q f,out are the convective heat fluxes through the working fluid to the top and bottom glass slabs, respectively. The thermal energy collected by the working fluid in the thermal unit is denoted by q f. A f ;k1 k is the average absorptance of the working fluid between k 1 = 00 nm and k = 000 nm. The irradiance received by the working fluid G f is written as, G f ¼ GT gl;k1 k ð1þ where T gl;k1 k is the average transmittance of the top glass slab between k 1 = 00 nm and k = 000 nm. The energy balances at the top and bottom glass slabs are written as, q f ;out1 ¼ q t;gl q f ;out ¼ q b;gl ðþ ð3þ where the conductive heat flux in the top and bottom glass slabs are q t,gl and q b,gl, respectively. Furthermore, the energy balances of the top and bottom glass slabs can also be expressed as, q t;gl ¼ q air1;conv þ q sky;rad q b;gl ¼ q air3;conv þ q air3;rad ð4þ ð5þ where the heat convection exchanges between the glass slabs and the air are denoted by q air1,conv and q air3,conv. Moreover, q air3,rad and q sky,rad are the net radiation flux exchanged between the glass slab and the air and between the glass slab and the sky, respectively.

5 J. Zhao et al. / Energy Conversion and Management 5 (011) The thermal efficiency of the PV/T is defined as [3], g th ¼ _m c pðt out T in Þ GS ð6þ where _m is the working fluid mass flow rate in the thermal unit, and c q is the heat capacity of the working fluid. The inflow and the outflow working fluid temperatures are denoted by T in and T out, respectively. Expressions for the heat fluxes in Eqs. (17) (5) as a function of the temperatures are provided in Appendix A. Finally, the overall energy efficiency of a PV/T system can be calculated by adding the thermal efficiency and thermal efficiency equivalent of electrical efficiency as follows [9,34,35]: g ov ¼ g th þ g el;th ¼ g th þ g el C f ð7þ where C f is the conversion factor of thermal power plant and its value is taken as 0.36 for many countries Exergy equations of the PV/T system The PV/T system supplies different forms of energy such as electricity and heat. The electrical efficiency g el and thermal efficiency g th of the system are expressed as Eqs. (14) and (6), respectively. However, the electrical and thermal energy produced by combined utilization are not essentially the same in nature. The energy analysis approach has some deficiencies. Fundamentally, the energy concept is not sensitive to the assumed direction of the process. It also does not distinguish the quality of the energy [36]. Therefore, to quantitatively evaluate the usefulness of the energy obtained, the concept of exergy is adopted in this study [37,17]. (1) Electrical exergy is not affected by ambient conditions and therefore is equivalent in work. If the irradiance is denoted by G, then the electrical exergy is given by [38], e e ¼ g el G ¼ n el G and n el ¼ g el ð8þ where e e is the electrical exergy, and n el is the electrical exergetic efficiency. () In order to transform the thermal energy into mechanical work, there must be a temperature difference between a high temperature heat source and a dump of low temperature heat. The magnitude of transformable thermal energy to work is restricted by the Carnot efficiency g c. If the temperature of the system is T 1 (K) and that of the environment is T 0 (K) [39], then g c ¼ T 1 T 0 T 1 ¼ 1 T 0 T 1 ð9þ The thermal exergy is defined as the maximum value of the work, that is, the effective energy, which can be taken out from the system. Moreover, in the considered system, it is assumed that the wording fluid remains liquid, and the properties of the working fluid are independent of temperature. Compered with the PV/T air system, the exergy of fluid pressure is negligible. Therefore, the thermal exergy is written as [38], e t ¼ g c g th G ¼ n th G and n th ¼ g c g th ð30þ where e t is the thermal exergy, and n th is the thermal exergetic efficiency. (3) Therefore, the synthetic exergy of the PV/T system is the total value of the electrical and thermal exergies. The exergetic efficiency of the PV/T system is presented as [38,39], n sys ¼ n el þ n th.4. Inverse method ð31þ The working fluid was designed to have high transmittance in the spectral region from 00 nm to 800 nm, and high absorptance between 800 nm and 000 nm. Its optical properties were retrieved by inverse method based on the Lorentz Drude theory using genetic algorithm [40]. The frequencies e 1, x pj, x 0j and c j are retrieved by minimizing the difference between the model s predictions and the desired transmittance T des,k and reflectance R des,k. The genetic algorithm PIKAIA [41] was adopted to perform the inverse method as it is general and has already been validated [4]. PIKAIA runs following these steps: (1) the desired transmittance and reflectance (T des,k and R des,k ) are prescribed, () PIKAIA starts searching for the values of the parameters e 1, x pj, x 0j and c j to predict the refractive index n cal,k and absorption index k cal,k, based on Eqs. (1) (4), (3) the transmittance and reflectance (T cal,k and R cal,k ) are computed using Eqs. (7) (9), and are optimized to minimize the sum of squared residuals de defined as, de ¼ 1 N X N i¼1 h i ðt cal;ki T des;ki Þ þðr cal;ki R des;ki Þ ð3þ The PIKAIA criterion is to stop calculation after 500 generations. In the present study, considering the wavelength range studied, the magnitudes of the frequencies x pj, x 0j and c j have been set to range between 10 1 s 1 and s Validation of the inverse method Based on the Lorentz Drude model and the radiation transfer equations [31], the frequencies x pj, x 0j, c j and the dielectric constant e 1 are the sensitive parameters on the inverse model. The inverse method was validated with a dense homogeneous slabs of (i) amorphous SiO glass and (ii) water both surrounded by air (n air = 1.0 and k air = 0). During the validation, the spectral transmittance and reflectance are input in the inverse model, and the retrieved parameters are compared with the reference data. First, the frequency parameters and the high-frequency dielectric constant of glass at room temperature (T = 98 K) in the spectral region 0.4 < k <10lm were taken as x p1 = s 1, x 01 = s 1, c 1 = s 1 and e 1 =.13 [31]. The transmittance and reflectance of the glass slab were computed from Eqs. (1) (8). For N = 97 wavelengths with a constant increment of 4k = k i+1 k i = 100 nm, the error de was The retrieved frequencies and the high-frequency dielectric constant were found to be x p1,cal = s 1, x 01,cal = s 1, c 1,cal = s 1 and e 1 =.6, which fall within 1.%, 0.5%,.5% and 6.1% of the reference data [31], respectively. Overall, the retrieved complex index of refraction agrees with the input values confirming the capability of the inverse method. Similarly, the oscillator frequencies of water was retrieved over two wavelength ranges from 00 nm to 1000 nm and from 1000 nm to 000 nm. The theoretical transmittance and reflectance were computed from Eqs. (7) (9) using experimental data for n and k reported in the literature [31]. With a constant increment of 4k = k i+1 k i = 5 nm, for N = 33 from 00 nm to 1000 nm and N = 40 from 00 nm to 1000 nm the error de were both around and Furthermore, the complex index of refraction of water was calculated from the oscillator frequencies. The results and experimental data used are shown in Fig.. Good agreement is found for the index of refraction n for all wavelengths. Between 700 nm and 000 nm, the absorption index retrieved also agrees with the literature value. For wavelengths smaller than 700 nm, the retrieved absorption index was larger than the literature data. In this wavelength region, the absorption index of water was very small and can be neglected. The retrieved values were also less than and can be assumed to be zero. Despite the results for the absorption index did not uniformly match those found in the literature. These retrieved results suggest that the inverse method and the optical model can be used to determine the complex index of refraction of liquids.

6 1348 J. Zhao et al. / Energy Conversion and Management 5 (011) Refractive index, n retrieved Brewster,199 Table 1 The values of coefficients used in the simulations. Variable Symbol Value Unit Ambient temperature T a 5 C Absorption coefficient A pv 0.9 Emissivity of solar cell e pv 0.9 Emissivity of glass e gl 0.9 Heat conduction through glass k gl 0.9 W/m K Heat capacity of working fluid c p 400 J/kg K Nusselt number in PV module Nu pv 5.39 Nusselt number in thermal unit Nu f 6.70 Heat conduction through working fluid k f 0.6 W/m K Hydraulic diameter in PV module d pv 0.04 m Hydraulic diameter in thermal unit d f 0.1 m Coefficient of heat transfer h w 10 W/m K Inflow temperature T in 5 C Mass flow rate in PV module _m pv 76 kg/h Absorption index, k The performance of the system To determine the energy and exergy efficiency of the PV/T system, two models are required. First, the radiation transfer model predicts the amount of incident solar energy absorbed and the spectral and average transmitted by the thermal unit. Second, the thermal model is based on solving the energy conservation equations for all the elements in the system. It is used to determine the PV cell temperature and the working fluid temperature. The thermal model consists of eight energy balances (Eqs. (17) (0) and Eqs. () (5)) solved for eight unknown temperatures (T pv, T out, T t,gl", T t,gl;, T b,gl", T b,gl;, T sp, and T mid ). Once the temperature of the solar cell T pv and that of the working fluid T out are determined, the efficiencies g el and g th of the PV/T system can be calculated from Eqs. (14) and (6). Then, the exergy efficiencies n el, n th and n sys can be determined based on the energy efficiencies and the system temperature..7. Closure laws retrieved Brewster,199 Wavelength, (nm) Wavelength, (nm) Fig.. The refractive and absorption index of water retrieved from the transmittance and reflectance [31] in the wavelength ranges from 00 nm to 1000 nm and 1000 nm to 000 nm. To assess the performance of the system, the values of coefficients used in the simulations are summarized in Table 1. Calculations are performed per unit length and width. The silicon dioxide (glass) top and bottom slabs have thickness L 1 = 0.01 m and L 3 = 0.01 m, refractive indices n 1 = n 3 = 1.45 and absorption indices k 1 = k 3 = 0 over the wavelength range from 00 nm to 000 nm [31]. The thickness of the working fluid layer is L = 0.05 m. The working fluid has an unknown complex index of refraction m = n ik. Furthermore, the desired transmittance and absorptance of the thermal unit are T des,k = 1.0 from 00 nm to 800 nm and A des,k = 1.0 from 800 to 000 nm. The system is surrounded by air (n air = 1 and k air = 0). In order to retrieved the optical properties of the working fluid, two groups of x pj, x 0j and c j are adopted (j = ) in the spectral range studied. Moreover, the support of the PV cell consists of a PE-AL-tedlar layer and an EVA layer. The thermal resistance of the support is R sp = K/W [3]. For the PV cell, the temperature coefficient is b = , and the efficiency g 0 is 0.1 at the ambient temperature T a =5 C [6,43]. In order to maintain the PV cell at low temperature, the coolant mass flow rate _m pv is kept constant and equal to 76 kg/h in the PV module. Furthermore, when the Reynolds number considered is smaller than 300, the value of the Nusselt number Nu f is 6.70 for a rectangular channel at constant heat flux [44]. Thus, the convective heat transfer coefficient between the glass plate and the working fluid is h f = Nu f k f /d f =4W/m K [3,45]. In evaluating collector performance, the sky temperature T sky is not critical and can be simply taken as equivalent to the ambient air temperature [46,47]. Since the temperature of the PV cell T pv is lower than that of the bottom glass plate T b,gl;, the free convection between the PV cell and the glass is neglected. The conductive heat flux in the insulation is also neglected [48]. 3. Results and discussion This section reports the optical properties of the working fluid to achieve maximum absorption in the infrared and maximum transmittance in the visible. It compares the efficiencies of the PV/T systems using the optimized working fluid and water. Moreover, it discusses the effect of the fluid mass flow rate and the irradiance on the performance of the PV/T system Optical properties of the working fluid The inverse method was validated and demonstrated to provide an accurate prediction of the complex index of refraction from the transmittance and the absorptance. In order to maximize both the transmission in the visible light spectrum and the absorption in the infrared spectral range of the working fluid, the optimized working fluid should have T des,k = 1 for 00 nm 6 k nm and

7 J. Zhao et al. / Energy Conversion and Management 5 (011) Optimized reractive index, ncal, optimized working fluid, L =0.05m Absorptance and Transmittance, Ttu Atu A tu, optimized working fluid A tu, water T tu, optimized working fluid T tu, water Optimized absorption index, k cal, Wavelength, (nm) optimized working fluid, L =0.05m Wavelength, (nm) Fig. 3. The retrieved refractive index and absorption index as a function of wavelength for the optimized working fluid with T des,k = 1.0 from 00 nm to 800 nm, A des,k = 1.0 from 800 nm to 000 nm for the thicknesses L = 0.05 m. A des,k = 1 for 800 nm 6 k nm. Based on these properties, the complex index of refraction of the working fluid was retrieved by the inverse method. Fig. 3 shows the retrieved complex index of refraction of the working fluid as a function of wavelength. The sum of squared residuals de between the acquired results and the desired data was about 0.0. To evaluate the optimization, the average transmittance from 00 nm to 800 nm and the average absorptance from 800 nm to 000 nm of the working fluid were computed. The results show that the optimized working fluid is not totally transparent to visible light, but does transmit over 89% of visible light. While the working fluid strongly absorbs the solar infrared radiation, about 9% of the solar infrared radiation is absorbed by it. Therefore, the optimized working fluid prevents the excessive heating of the PV cell by the solar infrared radiation, simultaneously achieves thermal conversion. Since the optical properties of the working fluid were modeled based on the damped oscillator Lorentz Drude model satisfying the Kramers Krönig relations. The optimum optical properties retrieved can serve as a guideline for developing new working fluids such as nanofluids. Obtaining a real fluid satisfying the optimum properties can use by the effective medium models, and it was discussed in reference [49] Wavelength (nm) Fig. 4. The absorptance and transmittance of the thermal unit of the system using the optimized working fluid as a function of wavelength with T des = 1.0 from 00 nm to 800 nm and A des = 1.0 from 800 nm to 000 nm, compared with that of the system using water. 3.. Solar radiation transfer in the thermal unit The thermal unit is positioned over the PV module, and consists of three slabs: the top glass slab, the working fluid and the bottom glass slab. The reflectance of the top and the bottom glass slabs is about 3%, and the transmittance is about 97% calculated from Eqs. (7) and (8). Using these results, before the visible light reached the PV module, the solar radiation transfer in the thermal unit (three slabs) was determined from Eqs. (5) (9). Fig. 4 compares the spectral transmittance and the absorptance of the thermal unit between 00 nm and 000 nm using either the optimized working fluid or water. For the sake of the top glass slab reflectance, the solar energy absorbed by the working fluid is about 3% lower than that of the single working fluid slab. The thermal unit absorbs 89% of the infrared radiation for photothermal conversion, and the PV module accepts 84% of the visible light for photoelectric conversion. Due to the fact that water is almost entirely transparent between 400 nm and 800 nm [50], the average transmittance of water over the visible light is about 6% larger than that of the optimized working fluid. Therefore, the electrical efficiency of the system using the optimized working fluid is slightly lower than the system using water. However, the water average absorptance over the infrared spectral range is about % lower than that of the optimized working fluid. Thus, the relative decrease in the electrical efficiency of the optimized system would be compensated by both the effective thermal conversion of the working fluid and the small increasing temperature of the PV cell. Overall, considering both the thermal efficiency and the electrical efficiency of the PV/T system, the system using the optimized working fluid is the best option, especially with the concentrator, which will be discussed in the following section Performance of the system For the spectral range from k 1 = 00 nm to k = 000 nm, the energy absorbed by the optimized working fluid is G f A f ;k1 k ¼ 0:45G, and the energy absorbed by the solar cell is G pv A pv = 0.47G. Similarly, when water is substituted for the optimized working fluid, G water A water;k1 k ¼ 0:8G and G pv A pv = 0.61G. Note that when using the optimized working fluid, less energy is absorbed by the PV cell, and the overheating of the PV cell is prevented. Additionally, more

8 1350 J. Zhao et al. / Energy Conversion and Management 5 (011) energy is used for the thermal conversion. These values were substituted into the aforementioned energy conservation and exergy equations. The energy and exergy efficiencies of the PV/T system were calculated as a function of the working fluid mass flow rate and the incident solar irradiance with or without concentrator Performance of various working fluid mass flow rates Fig. 5 shows the thermal, electrical and overall efficiencies of the PV/T system using the optimized working fluid and water as a function of the working fluid mass flow rate in the thermal unit with the fixed incident solar irradiance G = 800 W/m. In addition, Fig. 6 shows the working fluid outflow temperature of the PV/T system with respect to the mass flow rate. As intuitively expected, due to water s high transmission in the range of visible light, the electrical efficiency using water is about 0.8% higher than that obtained with the optimized working fluid. However, in the optimized PV/T system, the working fluid directly absorbs most of the infrared radiation and part of the visible light. The solar energy absorbed by the working fluid calculated from Eq. (11) is about 45% of the incident solar radiation. The thermal efficiency achieved, when using the optimized working fluid, is about from % to 11% higher than that achieved with water, and the overall energy efficiency is about from 0.% to 8% higher than that obtained with water. On the other hand, the PV module received only about 6% of the solar infrared radiation, the infrared part of the solar radiation has little effect on the PV module. The PV module and the thermal unit are separated by the slab. The thermal unit and the PV module have little effect on each other. The PV module would work at low temperatures. Therefore, when the mass flow rate decreases, the PV module temperature is always around 3 C, and the electrical efficiency of the optimized system does not decrease as shown in Figs. 6 and 5. Moreover the working fluid outflow temperature of the optimized system is higher than the system using water. The outflow temperature of the optimized working fluid reaches 74 C with the decrease of the mass flow rate. Compared with the conventional PV/T system, the results indicate that the electrical efficiency of the optimized PV/T system is independent of the working fluid mass flow rates. The optimized PV/T system converts solar radiation to higher temperature thermal energy without sacrificing the electrical efficiency. Thermal, electrical and overall efficiency, th el ov optimized working fluid, th optimized working fluid, el optimized working fluid, ov water, th water, el water, ov Mass flow rate, m (kg/s) Fig. 5. The thermal, electrical and overall efficiencies of the systems using the optimized working fluid and water as a function of mass flow rate of the working fluid with the fixed incident solar irradiance G = 800 W/m and working fluid inflow temperature T in =5 C. Temperature, T pv and Tout ( ) optimized working fluid, T pv optimized working fluid, T out water, T pv water, T out Mass flow rate, m (kg/s) Fig. 6. The PV module and the working fluid outflow temperatures of the systems using the optimized working fluid and water as a function of mass flow rate of the working fluid with the fixed incident solar irradiance G = 800 W/m and working fluid inflow temperature T in =5 C. Table The temperature of the PV module and the outflow temperature of the working fluid for the system using optimized working fluid and water at different incident solar irradiance. Irradiance (W/m ) T f,pv ( C) T f,out ( C) T water,pv ( C) T water,out ( C) Performance of various irradiance The temperature of the PV module and the outflow of the working fluid for the CPV/T system using the optimized working fluid and water at different incident solar irradiance are shown in Table. In the system, the thermal unit and the PV module independently achieve photothermal and photoelectric conversion. The thermal unit does not extract heat from the PV module. Contrary to conventional CPV/T systems, the thermal unit has no thermal limitations from the PV module. Thus, the working fluid of the thermal unit can work at high temperatures. When the incident solar energy increases from G = 800 W/m to G = 8000 W/m for the system using the optimized working fluid, the outflow temperature of the working fluid reaches 196 C. However, the PV cell temperature is 65 C with the increment of 36 C. It is also interesting to note that the temperature of the thermal unit is much higher than that of the PV module in the optimized CPV/T system. On the other hand, using the concentrating technology, the thermal unit temperature generated by the optimized system is about 54 C higher than that of the water system, and the PV cell temperature of the optimized system is about 31 C lower than that of the water system. Fig. 7 shows the electrical, thermal and overall efficiencies of the CPV/T system. The result indicates that when the incident irradiance increases, the thermal efficiency of the CPV/T system does

9 J. Zhao et al. / Energy Conversion and Management 5 (011) Thermal, electrical and overall efficiency th el ov optimized working fluid, th optimized working fluid, el optimized working fluid, ov water, th water, el water, ov Irradiance, G (W/m ) Fig. 7. The thermal, electrical and overall efficiencies of the systems using the optimized working fluid and water as a function of incident solar irradiance with the fixed working fluid mass flow rate _m ¼ 16 kg=h and working fluid inflow temperature T in =5 C. Thermal and electrical energy efficiency optimized working fluid, th optimized working fluid, el optimized working fluid, sys water, th water, el water, sys Irradiance, G (W/m ) Fig. 8. The thermal, electrical and total exergetic efficiencies of the systems using the optimized working fluid and water as a function of incident solar irradiance with the fixed working fluid mass flow rate _m ¼ 16 kg=h and working fluid inflow temperature T in =5 C. not decrease. The thermal efficiency of the system using the optimized working fluid is around 40%, and is always 13% higher than that of the system using water. The main reason for the result is that the water does not absorb the solar infrared radiation as much as the optimized working fluid in the thermal unit. Since the optimized working fluid guarantees the small increasing temperature of the PV module. With the increase of the incident solar irradiance, the electrical efficiency of the system using working fluid decreases from 9.8% to 7.3%, and becomes higher than that of the water system. Moreover, the overall efficiency of the optimized system is around 60 67%, and is about 10 13% higher than the water system. Therefore, using concentrated solar radiation, the optimized system has high overall energy efficiency, and generates high grade heat with constant thermal efficiency. Furthermore, the CPV/T system supplies different forms of energy. To quantitatively evaluate the usefulness of the energy obtained, it is necessary to adopt the concept of exergy. Fig. 8 shows the exergy efficiencies of the CPV/T system with respect to the incident solar irradiance. For the system using the optimized working fluid, the electrical exergetic efficiency of the system n el is sacrificed slightly (about.5%) for increasing incident solar irradiance from 800 W/m to 8000 W/m. However, the thermal exergetic efficiency of the system n th quickly goes up from.% to 14.8%, and the exergetic efficiency of the system n sys increases from 1% to %. In addition, it is clear from the figure that the exergetic efficiency of the system using the optimized working fluid becomes higher than that of the system using water from 0.% to 6.4%, as the incident solar irrdiance increases from from 800 W/ m to 8000 W/m. Overall, the study results suggest that using the optimized working fluid is a best option in the concentrating system, and the optimal CPV/T system exergetic efficiency increases along with the solar irradiance. 4. Conclusion This paper presents the design optimization of a photovoltaic/ thermal system using both non-concentrated and concentrated solar radiation. The system separately utilizes the solar visible light and the infrared radiation. The thermal unit absorbs the infrared radiation before it heats the PV module. The optical properties of the working fluid were modeled and optimized to maximize the transmittance and the absorptance of the thermal unit in the visible and infrared part of the spectrum, respectively. The efficiencies of the system were calculated based on the radiation transfer and the energy conservation equations. The following conclusions can be drawn: 1. The optical properties of the working fluid were retrieved based on the inverse method. The optimized working fluid absorbs about 9% of the solar infrared radiation and transmits 89% of the visible light.. Using the optimized working fluid, the thermal unit absorbs 89% of the infrared radiation for photothermal conversion, and the PV module accepts 84% of the visible light for photoelectric conversion. 3. In the optimized PV/T system, when reducing the mass flow rate, the outflow temperature of the working fluid reaches 74 C. However, the PV module temperature remains around 31 C at a constant electrical efficiency about 9.6%. 4. In the optimized CPV/T system, when the incident solar irradiance increases from 800 W/m to 8000 W/m, the electrical efficiency decreases slightly from 9.8% to 7.3%. The thermal efficiency remains constant at 40%. The overall efficiency is around 60 67%. The system generates 196 C working fluid. Moreover, the exergetic efficiency increases from 1% to %. This paper provides an interesting perspective on separately using the solar infrared radiation and the visible light in the PV/T system based on the DAC concept. The retrieved optimum optical properties can be served as a benchmark for developing new working fluids such as nanofluids. The thermal unit can also be used in other system such as greenhouses and in combination with photobioreactors. Acknowledgment Gratefully acknowledges the support of the National Natural Science Foundation of the People s Republic of China under Grant Nos and The author also acknowledges Prof. Laurent Pilon (UCLA) for his guidance and dedication.

10 135 J. Zhao et al. / Energy Conversion and Management 5 (011) Appendix A. Overview of the heat fluxes in the energy conservation equations The heat flux across the PV module can be written as, q sp ¼ T pv T sp R sp S ð33þ where the temperature and the thermal resistance of the support is denoted by T sp and R sp, respectively. Moreover, q f ;m ¼ _m pvc p ðt mid T in Þ S ð34þ where the mass flow rate in the PV module is denoted by _m pv, and the outflow temperature of the coolant is denoted by T mid. e pv e gl q air4;rad ¼ r T e pv þ e gl e pv e 4 pv T4 b;gl# gl ð35þ where the temperature of the lower surface of the bottom glass slab is denoted by T b,gl;. The parameters e pv and e gl are the emissivities of the solar cell and the top and bottom glass slabs, respectively. The thermal energy collected by the working fluid in the thermal unit can be written as, q f ¼ _mc pðt out T mid Þ S ð36þ Furthermore, the temperatures of the lower surface of the top slab and the upper surface of the bottom slab are denoted by T t,gl; and T b,gl". The convective heat transfer coefficient for the working fluid over the glass slabs is denoted by h f. Thus, q f,out1 and q f,out are expressed as, T out þ T mid q f ;out1 ¼ h f T t;gl# ð37þ T out þ T mid q f ;out ¼ h f T b;gl" ð38þ Similarly, the heat fluxes across the top and bottom glass slabs can be expressed as, q t;gl ¼ k gl ðt t;gl# T t;gl" Þ L 1 q b;gl ¼ k gl ðt b;gl" T b;gl# Þ L 3 ð39þ ð40þ where the upper surface of the top glass slab and the lower surface of the bottom glass slab are T t,gl" and T b,gl;. The thermal conductivity of the top and bottom glass slabs are k gl and the thicknesses of the top and bottom glass slabs are L 1 and L 3, respectively. 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