Performance assessment of a trifunctional system integrating solar PV, solar thermal, and radiative sky cooling

Applied Energy 260 (2020) 114167

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Performance assessment of a trifunctional system integrating solar PV, solar thermal, and radiative sky cooling

T

Mingke Hua,b, Bin Zhaoa, Xianze Aoa, Xiao Rena, Jingyu Caoa, Qiliang Wangc, Yuehong Sub, ⁎ Gang Peia, a

Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei 230027, China Institute of Sustainable Energy Technology, University of Nottingham, University Park, Nottingham NG7 2RD, UK c Department of Building Services Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China b

HIGHLIGHTS

system combining solar photovoltaic, solar thermal and radiative cooling. • AA hybrid verified model was developed to investigate the performance of the system. • Sensitivity analysis was performed to examine the effect of various parameters. • Annual performance assessment of the system was conducted as a reference. • ARTICLE INFO

ABSTRACT

Keywords: Solar energy Solar collector Photovoltaic/thermal PV/T Radiative cooling Sky cooling

Radiative cooling (RC) with the outer space as a natural heat sink has stimulated widespread attention in the research community and has achieved rapid developments in recent years. However, most available radiative coolers exhibit low power density and long payback periods. To overcome such shortcomings, a cost-effective solution that integrates RC into a solar photovoltaic/thermal (PV/T) collector as a secondary function was proposed. In this study, a trifunctional photovoltaic–photothermic–radiative cooling (PV-PT-RC) system was developed. The proposed system could convert solar energy into electricity and/or heat during daytime and offer cooling energy at night through RC. A mathematical model was built to assess the performance of the PV-PT-RC system quantitatively and investigate the key performance indicators of the system numerically. Moreover, a practical-scale PV-PT-RC testing system was built, and experiments were performed to verify the effectiveness of the numerical model. Results revealed that the mean relative errors are less than 5% for the electrical power, aluminum plate temperature, and water temperature in the tank and 6.83% for the cooling power, thereby proving that the mathematical model can accurately assess the performance of the hybrid system. On the basis of the verified model, the overall performance of the system was examined under different insulation thicknesses, initial water temperatures in the tank, packing factors, panel emissivity values, and tank volumes. Furthermore, the results of the annual performance analysis suggested that the annual electrical, heat and cooling gains of the system in Eastern China are 479.67, 2369.07, and 1432.49 MJ, respectively.

1. Introduction

attractive solution for mitigating the thermal effects on PV panels [1]. If dumped heat is collected and sent to the end-user alongside the electricity, then the well-known comprehensive PV/thermal (PV/T) technology is adopted [2]. PV/T utilization has aroused extensive attention for its dual function and overall efficiency [3]. A PV/T collector can provide electricity and heat simultaneously through PV and PT conversions [4]. A flat-plate PV/T collector is commonly integrated into building envelops [5]. In recent decades, several types of flat-plate PV/

Solar energy is considered promising renewable energy for the sustainable development of human society. Among the various solar energy utilization techniques, solar photovoltaic (PV) and photothermic (PT) technologies are two dominant approaches. Given that the crystalline silicon PV cell shows deteriorated efficiency at elevated operating temperatures, extracting waste heat from the PV cell is an

⁎

Corresponding author. E-mail address: [email protected] (G. Pei).

https://doi.org/10.1016/j.apenergy.2019.114167 Received 21 August 2019; Received in revised form 24 October 2019; Accepted 13 November 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature

ε ρ σ λ β θ γ ν ξ η

A area, m2 Br temperature coefficient of PV cells, K−1 c specific heat capacity, J/(kg·K) D diameter, m d distance or thickness, m E radiation or electrical power, W/m2 G solar irradiance, W/m2 g gravitational acceleration, m/s2 H total solar radiant energy, MJ/m2 h heat transfer coefficient, W/(m2·K) I current, A k thermal conductivity, W/(m·K) l length, m m mass of water in the water tank, kg m and M mass flow rate, kg/s MRE mean relative error, – N number, – Nu Nusselt number, – P perimeter, m Q thermal power, W/m2 R thermal resistance, K/W Ra Rayleigh number, – RE relative error, – T temperature, K t time, s Δt time interval, s U voltage or overall heat-transfer coefficient, V or W/(m2·K) u wind velocity, m/s w precipitable water vapor amount or width, cm or m x length (direction), m y width (direction), m z height (direction), m

Abbreviation and subscripts a b c cool conv e exp final i in initial o out p power PV rad ref s sim t tank th TPT w

Greek symbols τ (τα) α

emissivity, – reflectance or density, - or kg/m3 Stefan–Boltzmann constant, – wavelength, µm inclination angle, rad zenith angle, rad thermal diffusion coefficient, m2/s kinetic viscosity, N·s/m2 packing factor, – efficiency, –

transmittance, – transmittance–absorptance product, – absorptivity, –

T collectors have been developed (e.g., water- [6], air- [7], nanofluid[8], heat pipe- [9], and phase change material (PCM)-based PV/T collectors [10]). PV/T is a well-developed technology but restricted to daytime operation. The extension of the application of PV/T to nighttime working must be explored. Radiative cooling (RC) refers to another sustainable and green energy harvesting technology that primarily uses the transparent “atmospheric window” (8–13 μm) as a heat transfer path to dissipate heat from earthbound objects to the cold outer space [11]. RC acts as an effective thermal management and refrigeration solution against the increase in pressure from energy crisis and environmental pollution [12]. Overall, conventional RC devices exhibit a cooling flux of 40–80 W/m2, typically one order of magnitude lower than solar radiation; thus, most of these devices primarily work during nighttime in the absence of sunlight [13]. Most radiative coolers have a flat-plate structure [14], thereby allowing them to be widely integrated into building envelops [15]. The building-integrated RC (BiRC) system can supply cooling energy carriers, such as cold water [16] or cold air [17], to cool the building in a passive and environment-friendly manner. The spectral property of the RC panel acts as a critical factor of the cooling performance of an RC collector. To reach the lowest possible stagnation temperature, the panel should exhibit the maximum possible emissivity in the “atmospheric window” and the minimum possible absorptivity in

ambient air back insulator or blackbody transparent cover cooling energy convection electrical experiment final water temperatures in the tank, K inner inlet initial water temperatures in the tank, K outer outlet panel coal-fired power plant PV module radiation reference sky simulation copper tube water tank thermal Tedlar–polyester–Tedlar water

other bands. By contrast, the panel must exhibit the highest possible spectral absorptivity/emissivity in the entire middle and far-infrared bands to generate the greatest possible RC power [18]. Environmental conditions, except for the spectral characteristic, also affect the RC performance significantly. The transmissivity of the atmosphere determines the RC performance considerably because the thermal radiation from terrestrial structures to the cold universe will inevitably go through the atmosphere. In general, a high atmospheric transmissivity represents high RC power. Accordingly, an RC collector will benefit from clear sky [19], dry climate [20], and high altitude [21]. Recent developments in micro-nano material technologies have allowed daytime RC [22]. Several daytime RC surfaces (e.g., multi-layer photonic structure [23], metamaterial [24], and nanoporous fiber [25]) have been reported. These daytime radiative coolers can reject most (approximately 95%) incident solar radiation while emitting considerable infrared thermal radiation throughout the “atmospheric window.” However, regardless of the availability of continuous 24 h RC, standalone RC systems have limitations in real-world applications for their relatively low cooling intensity and consequent long payback period. Moreover, even a near-perfect emitter with an extremely low solar absorption may fail to achieve continuous daytime RC under local environment conditions (e.g., high relative humidity [20,26]). Considering that nocturnal RC is easy to realize, and solar installations 2

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(e.g., solar PV/T collectors) remain idle at night, it is of significance to integrate nighttime RC into daytime solar energy collectors [27]. Such a hybrid solar energy and RC (SE-RC) collector can extend the operation time of conventional solar installations until nighttime through RC while eliminating the cost disadvantages of stand-alone RC collectors. In contrast to the daytime RC collector that reflects most of the solar energy, the SE-RC collector does not waste the primary renewable energy on earth. Moreover, the SE-RC collector displays superiority to the stand-alone SE or RC collectors in terms of multi-function, overall efficiency, and seasonal adaptability. For example, a stand-alone RC collector may provide undesired cooling energy during winter for buildings, while a hybrid PT-RC collector can offer heat during winter and cooling energy during summer. Eicker and Dalibard [28] modified a commercial PV/T collector by removing the glazing cover of the collector to allow a long wave radiative exchange with the sky. However, without the cover, the heat exchange between the panel and the ambient air sharply increases, thus leading to the poor daytime PT efficiency and nighttime RC performance of the unglazed PV/T collector. In the present study, a combined solar PV, PT, and RC (PV-PT-RC) collector was presented. The hybrid

collector is a trifunctional module that can provide electricity and heat during daytime and gather cooling energy during nighttime. In our previous work, a PV-PT-RC system was developed, built, and tested, and first-hand experimental data on key performance indicators (KPIs; e.g., electrical efficiency, thermal efficiency, and cooling power) were obtained under certain operation conditions [19]. However, extensive and specific KPI data of the PV-PT-RC system under different working conditions and annual energy outputs of the system are also vital in optimizing the key parameters of the hybrid system and providing a general reference for the real-world application of the system in different geographic regions and climates. Given that structural parameters, such as insulation thicknesses, initial water temperatures in the tank, packing factors, panel emissivity, and tank volumes, are fixed once a PV-PT-RC system is set up, using the modeling approach to investigate the sensitive effect of these key parameters on the performance of the system is a good solution. Furthermore, experimentally investigating the annual performance of the PV-PT-RC collector in certain geographic areas is tedious and consumes significant amounts of resources. Thus, a mathematical model was built to assess the performance of the PV-PT-RC system in this study comprehensively. In

Fig. 1. Schematic of the PV-PT-RC collector. (a) Front view of the collector and layout of the copper water tubes. (b) Cross-section view of the collector. (c) Schematic of the PV-PT-RC panel. 3

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contrast to the model of conventional solar installations that only consider the total, hemispherical spectral parameters of the collector and atmosphere, the present model considers the spectral radiant and spatial temperature distributions of the PV-PT-RC system and the atmosphere, thus offering a more objective characterization of the electrical and thermal behaviors of the system. The available experimental data of the previous work can be used to assess the accuracy of the simulation model. Using the verified model, the KPIs of the PV-PT-RC system under different key structural parameters were calculated thoroughly. Moreover, the annual performance of the hybrid system in Hefei, China in the typical meteorological year was also evaluated to investigate its annual electricity, heat, and cooling energy outputs. 2. Description of the PV-PT-RC system 2.1. PV-PT-RC collector The PV-PT-RC collector has a flat-plate structure, with overall dimensions of 2000 mm × 1000 mm × 100 mm. A schematic of the PVPT-RC collector is illustrated in Fig. 1. The major components of the collector include a transparent cover, a PV-PT-RC panel, and some insulation layers and frames. The glazing cover that is commonly applied in PV/T collectors is an unsuitable windshield for RC apparatuses. The polyethylene film acts as the cover of the RC devices for its high transmissivity in most bands [29]. In the present study, a 6 μm-thick polyethylene film served as the cover of the PV-PT-RC collector. The PV-PT-RC panel was a key component in the collector. A 1964 mm × 964 mm × 0.4 mm aluminum plate served as the baseplate, which is fully covered by a 0.3 mm-thick layer of black Tedlar–polyester–Tedlar (TPT). A total of 72 mono-crystalline silicon PV cells, with an area of 1.12 m2, were laminated onto the black TPT

Fig. 3. Photo of the PV-PT-RC experimental rig.

surface. An encapsulation layer of transparent TPT was placed above the PV cells and the black TPT. Two glue layers of ethylene–vinyl–acetate (EVA) were fixed between the aluminum plate and the TPTs. A 40 mm-high air gap was set between the cover and the PV-PT-RC panel. Seven copper water tubes, each with an inner diameter of 8 mm and an external diameter of 10 mm, were welded in parallel at the backside of the aluminum plate. A 30 mm-thick layer of glass fiber was adopted as

Fig. 2. Working principle of the PV-PT-RC system. Red lines represent the water-circulating loop. Green lines refer to electric circuits. Purple lines are signal collection circuits. 4

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the back insulator of the collector, and a 30 mm-high air duct was set between the back insulator and the PV-PT-RC panel. Accordingly, a collector can operate in either water heating/cooling or air heating/ cooling modes under different conditions. In the present study, however, only the water heating/cooling mode was adopted for performance investigation.

3.1.2. Modeling package for the PV module The heat-balance equation of the PV module is expressed as

2.2. Experimental system

where ρPV, cPV, dPV, and kPV are the density, specific heat capacity, thickness, and thermal conductivity of the PV module, kg/m3, J/(kg·K), m, and W/(m·K), respectively; Tp denotes the temperature of the aluminum plate, K; RPV,p is the thermal resistance of the adhesive layer (black TPT and EVA) between the PV layer and the aluminum plate, (m2·K)/W; (τα)PV is the effective transmittance–absorptivity product of the PV layer; QPV_rad,net is the net radiative heat transfer power of the PV layer, W/m2; and EPV is the output electrical power of the PV module, W/m2.

PV c PV dPV

(Tb

QPV,c_rad,net + ( )c G,

PV,c_conv

(Tc

TPV )

TPV ) RPV,p )PV G

QPV_rad,net

(2)

EPV ,

2T p x2

+

Tp )

2T p y2

+ (TPV

Tp) RPV,p +

wp

Nt Dt,o wp

h p,b (3)

Qp,t ,

3.1.4. Modeling package for the copper tube The heat-balance equation of the copper tube is expressed as 2 Dt,o

Dt,i2 Tt 4 t 2 2T Dt,o Dt,i2 k t 2t + Dt,i h w,t (Tw 4 x

t ct

=

(Tb

Tt ) +

Tp

Tt

Rp,t · dx

+ Dt,o ht,b (4)

Tt ),

where ρt, ct, dt, and kt are the density, specific heat capacity, thickness, and thermal conductivity of the copper tube, kg/m3, J/(kg·K), m, and W/(m·K), respectively; Tt and Tw denote the temperatures of the tube and the inner water, K, correspondingly; Dt,i is the inner diameter of the tube, m; hw,t is the convective heat transfer coefficient between the tube and the inner water, W/(m2·K); and ht,b is the heat transfer coefficient between the tube and the back insulation layer, W/(m2·K), of which the formula is equivalent to that of hp,b here.

Tc t

Tc )

)+h

where ρp, cp, dp, and kp are the density, specific heat capacity, thickness, and thermal conductivity of the aluminum plate, kg/m3, J/(kg·K), m, and W/(m·K), correspondingly; wp is the width of the panel, m; Nt is the number of copper tubes; Dt,o is the outer diameter of the tube, m; hp,b is the heat transfer coefficient between the aluminum plate and the back insulation layer, W/(m2·K); Tb is the temperature of the back insulation layer, K; and Qp,t is the heat transfer power between the aluminum plate and the copper tube, W/m2.

3.1.1. Modeling package for the transparent cover The heat-balance equation of the transparent cover is written as

(TPV

2T PV y2

t

= kp dp

• Modeling package for the transparent cover; • Modeling package for the PV module; • Modeling package for the aluminum plate; • Modeling package for the copper tube; • Modeling package for the water in the copper tube; • Modeling package for the back insulation layer; • Modeling package for the water in the circulation water tank.

Tc ) + h s,c (Ts

+

Tp

p cp dp

A dynamic mathematical model was built to express the electrical, heating, and cooling performance of the PV-PT-RC system. The mathematical model primarily covers seven modeling packages as follows:

+ ha,c (Ta

2T PV x2

3.1.3. Modeling package for the aluminum plate The heat-balance equation of the aluminum plate is written as

3.1. Mathematical model

2T c x2

(

+(

3. Mathematical model and performance evaluation

= k c dc

= kPV dPV + (Tp

The PV-PT-RC experimental system was built on the rooftop of a building in the University of Science and Technology of China, Hefei (32° N, 117° E). In Figs. 2 and 3, the system mainly comprises a PV-PTRC collector, a circulating water pump, a water flowmeter, a water tank (120 L), a maximum power point tracking (MPPT) controller, a current sensor, a DC power, two 12-V storage batteries, a pyranometer, a thermometer shelter, several platinum resistances, thermocouples, valves, switches, and a data collecting unit. The PV-PT-RC collector was set up at an inclination angle of 32°, which is equal to the latitude of Hefei. According to the ASHRAE 932010 standards, the water flow rate of the system was set to 0.038 kg/s [30]. One platinum resistance was placed in the thermometer shelter to track the ambient temperature. To monitor the inlet–outlet water temperature difference, two other platinum resistances were fixed at the inlet and outlet of the collector. Ten thermocouples were adhered to the back of the panel to ascertain the panel or copper pipe temperatures. Five other thermocouples were mounted in the circulation water tank to measure the water temperature in the tank. All measured data were monitored by the data logger with a recording interval of 10 s.

c cc d c

TPV t

Tc ) + hPV,c_conv (1)

3.1.5. Modeling package for the water in the copper tube The heat-balance equation of the water in the copper tube is written as

where ρc and cc denote the density and specific heat capacity of the cover, kg/m3 and J/(kg·K), respectively; Tc, Ta, Ts, and TPV represent the temperatures of the cover, ambient air, sky, and PV layer, correspondingly, K; t is the time step, s; ha,c is the convective heat transfer coefficient between the cover and the ambient air, W/(m2·K); hs,c is the radiative heat transfer coefficient between the cover and the sky, W/ (m2·K); hPV,c_conv is the convective heat transfer coefficient between the cover and the PV layer, W/(m2·K); QPV,c_rad,net is the net radiant heat transfer power between the cover and the PV layer, W/m2; (α)c is the equivalent absorptivity of the cover; and G is the solar irradiance per square meter, W/m2. The detailed description of each item is presented in the Appendix A (the same for some of the other modeling packages).

Di2 Tw = 4 t

w cw

mc w

Tw + x

Di2 kw 4

2T w x2

+ Pt h w,t (Tt

Tw ),

(5)

where ρw and cw are the density and the specific heat capacity of water, kg/m3 and J/(kg·K), respectively; m is the mass flow rate of water in each tube, kg/s; and Pt is the inner perimeter of the copper tube, m. 3.1.6. Modeling package for the back insulator The heat-balance equation of the back insulator is expressed as 5

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Tb t

tank during the testing and/or the simulation period, MJ; m denotes the mass of water in the water tank, kg; and Tinitial and Tfinal are the initial and final water temperatures in the water tank, respectively, K. Given that electrical energy has a higher grade than heat, the overall electrical/thermal efficiency of the PV-PT-RC collector in terms of the primary-energy saving is defined as [31]

b c b db

= k b db

2T b x2

(Ta

Tb),

+

wp

Nt Dt,o wp

h p,b (Tp

Tb) +

Nt Dt,o ht,b (Tt wp

Tb) + Ua,b (6)

where ρb, cb, db, and kb are the density, specific heat capacity, thickness, and thermal conductivity of the uppermost layer of the back insulator, kg/m3, J/(kg·K), m, and W/(m·K), correspondingly; and Ua,b represents the overall coefficient of heat transfer between the uppermost layer of the back insulator and ambient air, W/(m2·K).

¯ overall

=

Ttank t Ttank Mc w + Atank k w z

Pcool =

w cw

2T tank z2

+ Ptank Ua,tank (Ta

Ttank ),

as

(7)

Qth mc w (Tfinal Tinitial ) , = HAp HAp

(11)

The nightly cooling energy gain of the PV-PT-RC system is defined

RE =

MRE =

Tfinal ).

(12)

X exp

Xsim

Xexp 1 N

,

(13)

i=N

|REi|, i=1

(14)

where Xexp and Xsim denote the experimental and simulation results, respectively.

(8)

where Δt denotes the time step, s; and H is the total solar radiant energy received per square meter in the testing and/or simulation period, MJ/ m2. The daily average thermal efficiency of the PV-PT-RC system is defined as

¯th =

(10)

To assess the discrepancy between the experimental and simulation results quantitatively, the equations of relative error (RE) and mean relative error (MRE) are used as follows [33]:

3.1.8. Performance evaluation The daily average electrical efficiency of the PV-PT-RC system is defined as

¯e =

mc w (Tin Tout ) . Ap

Qcool = mc w (Tinitial

where Atank denotes the inner cross-sectional area of the water tank, m2; Ttank is the temperature of water in the water tank, K; M is the mass flow rate in the water tank, kg/s; Ptank is the outer perimeter of the tank, m; and Ua,tank is the overall coefficient of heat transfer between the water in the tank and ambient air, W/(m2·K).

UI t UI = 6 , 10 HAPV GAPV

,

power

where ηpower refers to the conversion efficiency of the conventional coal-fired thermal power plant and is considered 0.38 [32]. The instantaneous cooling power of the PV-PT-RC collector is expressed as

3.1.7. Modeling package for the water in the circulation water tank The heat-balance equation of the water in the water tank is written as

Atank

¯e

= ¯th +

4. Results and discussions 4.1. Mathematical model validation The accuracy of the built mathematical model should be verified in accordance with the experimental data before this model is adopted to predict the performance of the PV-PT-RC system under different operation conditions. In this study, the RE and MRE of some critical

(9)

where Qth represents the heat gain of water in the circulating water

Fig. 4. Numerical and experimental electrical powers (daytime operation mode). 6

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parameters (e.g., aluminum plate temperature, inlet and outlet water temperatures, water temperature in the tank, and electrical power) were taken to assess the accuracy rating of the mathematical model.

working modes. Table 1 further demonstrates the electrical output performance of the PV-PT-RC collector by comparing its electrical and thermal efficiency as well as net cooling power with other typical collectors. The thermal efficiencies or cooling powers at zero reduced temperature are chosen to be compared. It is clear from Table 1 that the PV-PT-RC collector shows superiority to the mono-functional PV or PT collector, RC device and dual-functional PV/T collector in terms of multi-function and overall performance.

4.1.1. Validation of the daytime operation mode The correctness of the theoretical model in predicting the daytime operation mode was verified. Experimental data (e.g., temperatures, solar irradiation, and water flow rate) were used in the simulation. The comparisons between the numerical and experimental results are presented in Figs. 4–7. Fig. 4 plots the good consistency between the simulated and experimental electrical powers. Given that the impact of the frame that impeded PV efficiency under a large solar incident angle was ignored in the simulation model, the simulated electrical outputs were slightly greater than the experimental ones in the initial and final stages. Overall, the MRE was only 4.44% for the electrical power. The numerical and experimental results of aluminum plate temperature and water temperature in the tank in the daytime operation mode are demonstrated in Fig. 5. The predicted and measured temperatures are highly consistent. Specifically, the MRE of the aluminum plate temperature and water temperature in the tank (°C) were 2.04% and 3.88%, respectively.

4.2. Simulation study on the PV-PT-RC system Using the verified model, the performance of the PV-PT-RC system can be further investigated under different working parameters. The weather data of two typical days obtained from the typical meteorological year (TMY) data of Hefei, China were used for the parametrical analysis. Specifically, the weather data from 8:00 to 16:00 on February 11 were used to assess the daytime electrical and solar thermal performance of the PV-PT-RC system given that heat is valuable during winter. By contrast, the weather data from 20:00, August 19 to 7:00, August 20 were taken to predict the nighttime cooling performance of the PV-PT-RC system because the demand for cooling energy is high during summer.

4.1.2. Validation of the nighttime operation mode The simulated and measured results of the aluminum plate temperature and water temperature in the tank in the nighttime operation mode are illustrated in Fig. 6. The MREs of the aluminum plate temperature and water temperature in the tank were 2.54% and only 0.66%, thereby implying that the numerical results are consistent with the experimental ones. Fig. 7 exhibits that the numerical and experimental cooling powers in the nighttime operation mode are also highly consistent. For the relatively low response sensitivity of the platinum resistance placed at the inlet and outlet of the PV-PT-RC collector, the predicted cooling power at the beginning was much lower than the measured one. However, the simulated and experimental cooling powers after 18:45 were rather near each other. The MRE of the cooling power during the operation period was 6.83%. Figs. 4–7 display that the built mathematical model can assess the performance of the PV-PT-RC system in the daytime and nighttime

4.2.1. Insulation thickness The effects of insulation thickness on the daytime and nighttime performance of the PV-PT-RC system were investigated. The water flow rate was set to 0.038 kg/s, and the initial water temperature in the tank was set equal to that in the water main at the starting time. The electrical, thermal, and overall electrical/thermal efficiencies at different insulation thicknesses are depicted in Fig. 8. Electrical efficiency decreases with an increase in insulation thickness. By contrast, thermal efficiency improves with an increase in insulation thickness. A thick insulation layer leads to a low heat loss and a high PV module temperature, thus enhancing the solar thermal efficiency while deteriorating the PV efficiency. Furthermore, a high insulation thickness can enhance the overall electrical/thermal efficiency, but the enhancement is unremarkable. The overall electrical/thermal efficiency increased from 48.33% to 50.76% with an increase in insulation thickness from 0.01 m to 0.15 m. Moreover, the rangeability of the electrical, thermal,

Fig. 5. Numerical and experimental temperatures of aluminum plate and water in the tank (daytime operation mode). 7

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Fig. 6. Numerical and experimental temperatures of the aluminum plate and water in the tank (nighttime operation mode).

Fig. 7. Numerical and experimental cooling powers (nighttime operation mode).

and overall electrical/thermal efficiencies weakened with the increase in insulation thickness. The nocturnal final water temperatures in the tank and the cooling energy gain at different insulation thicknesses are shown in Fig. 9. Obviously, the water temperature declined with an increase in insulation thickness. The thick insulation layer suppressed the cooling loss of the PV-PT-RC system. Then, a high cooling energy gain was determined. The cooling energy gain increased from 2.37 MJ to 2.53 MJ with an increase in insulation thickness from 0.01 m to 0.15 m.

Table 1 Output performance of different collectors. Type

Electrical efficiency (%)

Thermal efficiency (%)

Net cooling power (W/m2)

PV panel [34] PT collector [31] RC collector [13] PV/T collector [35] PV-PT-RC collector

around 18.0 – – 6.7–15.0 9.7–11.7

– 72.8–79.0 – 22.0–79.0 55.3

– – 20.0–80.0 – 72.0

Note: The mono-crystalline silicon PV panel, water based PT and PV/T collectors are selected for the comparison; “–” signifies none or very low.

4.2.2. Initial water temperature in the tank Fig. 10 plots the effect of the initial water temperature in the tank

8

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Fig. 8. Effect of the insulation thickness on the diurnal performance of the PV-PT-RC system.

Fig. 9. Effect of the insulation thickness on the nocturnal performance of the PV-PT-RC system.

on the daytime performance of the PV-PT-RC system. The electrical and thermal efficiencies decreased nearly linearly with the increase in the initial water temperature in the tank. A high initial water temperature in the tank indicates a high panel temperature and a high heat loss of the entire system, thus determining the low PV conversion potential and heat gain. With the increase in the initial water temperature in the tank from 1 °C to 30 °C, the electrical efficiency decreased from 12.01% to 11.14%, and the thermal efficiency declined sharply from 37.10% to 18.30%. In accordance with the electrical and thermal efficiencies, the overall electrical/thermal efficiency also decreased nearly linearly from 55.83% to 35.68% with an increase in the initial water temperature in the tank from 1 °C to 30 °C. For the effect of the initial water temperature in the tank on the nighttime performance of the system, Fig. 11 presents that a high initial water temperature in the tank indicates improved cooling capacity. With the increase in the initial water temperature in the tank from 25 °C to 40 °C, the cooling energy gain was

upregulated from 2.38 MJ to 6.69 MJ, and the water temperature decrement in the tank during the night rose from 4.71 °C to 13.24 °C. A high initial water temperature in the tank implies a high panel temperature and a great radiative heat dumped from the panel to the cold outer space. Moreover, a high initial water temperature in the tank signifies high nonradiative heat loss from system components (e.g., PVPT-RC collector, pipelines, and water tank) to the environment. 4.2.3. Packing factor The effect of the packing factor of the PV module on the performance of the PV-PT-RC system was assessed. In Fig. 12, the electrical efficiency increased nearly linearly with the packing factor. Specifically, the electrical efficiency was upregulated relatively by 1.6% from 11.66% to 11.85% with an increase in the packing factor from 0.1 to 0.9. By contrast, the thermal efficiency decreased nearly linearly from 34.23% to 29.16%. The overall electrical/thermal efficiency exhibited 9

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Fig. 10. Effect of the initial water temperature in the tank on the diurnal performance of the PV-PT-RC system.

Fig. 11. Effect of the initial water temperature in the tank on the nocturnal performance of the PV-PT-RC system.

the same variation tendency as electrical efficiency. The overall efficiency was 37.29% when the packing factor is only 0.1 and surged to 57.22% when the packing factor was 0.9. Fig. 13 shows that the packing factor exerted a slight effect on the nighttime cooling performance of the PV-PT-RC system. The final water temperature in the tank and the cooling energy varied by only 0.13% and 0.56% with the increase in the packing factor from 0.1 to 0.9, correspondingly. This result is due to the infrared emissivity of PV cells and the black TPT are near each other, thereby leading to nearly the same cooling capacity at different packing factors.

electrical efficiency was upregulated from 11.50% to 11.80%, and the thermal efficiency was downregulated from 38.95% to 30.29%. Furthermore, the overall electrical/thermal efficiency was primarily determined by the thermal efficiency at changed panel emissivity, with the value decreasing relatively by 14.40% from 56.89% to 48.70%. For the nocturnal performance of the PV-PT-RC system under different panel emissivity values, Fig. 15 illustrates that a high panel emissivity can facilitate the radiant heat dissipation from the panel to the sky and then enhance the cooling performance of the system. With the increase in the panel emissivity from 0.5 to 1, the final water temperature dropped from 21.55 °C to 20.32 °C, and the cooling energy gain was upregulated from 1.83 MJ to 2.45 MJ.

4.2.4. Panel emissivity The effect of the panel emissivity on the performance of the PV-PTRC system also requires examination. A high panel emissivity indicates a high thermal emission and a low panel temperature, thereby resulting in enhanced electrical efficiency and deteriorated thermal efficiency (Fig. 14). With the increase in the panel emissivity from 0.5 to 1, the

4.2.5. Tank volume The effect of the tank volume on the performance of the PV-PT-RC system was investigated. Fig. 16 demonstrates that the electrical, thermal, and overall electrical/thermal efficiencies rose with a gradual 10

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Fig. 12. Effect of the packing factor on the diurnal performance of the PV-PT-RC system.

decrease in increase rates. The three key efficiencies were 11.17%, 19.25%, and 36.67% at a low tank volume of 40 L. However, these values surged to 11.93%, 34.04%, and 52.64% when the tank volume reached 200 L. A large tank volume implies low panel and water-circulating temperatures, thus resulting in improved electrical and thermal performance. For the effect of the tank volume on the nighttime performance of the system, Fig. 17 exhibits that a large tank volume will facilitate the cooling capacity of the system. The cooling energy gain increased relatively by 99.35% from 1.40 MJ to 2.78 MJ with the increase in the tank volume from 40 L to 200 L. A large tank volume denotes high panel and water-circulating temperatures, high radiative heat dissipation, and minimal heat gain from the environment.

system under different working parameters, the annual behavior of the PV-PT-RC system also requires investigation for an improved understanding of its real-world applications. The monthly average ambient temperature and water temperature in the water main and the total solar irradiance received by the PV-PT-RC collector in Hefei, China derived from the TMY weather data are presented in Fig. 18 for reference. The monthly electricity, heat, and cooling energy gained by the PV-PT-RC system can be obtained by accumulating the daily energy gains. In Fig. 19, the maximum electricity and heat gains were achieved in August, with values of 48.97 and 293.90 MJ, respectively, primarily because the greatest total solar irradiance was received in this month. However, the minimum electricity and heat outputs were observed in January (30.40 and 92.07 MJ), during which the total solar irradiance was the poorest. For the nighttime cooling performance, the monthly cooling energy experienced a gradual decrement from January to July and then a successive increment during the other months of the year.

4.2.6. Annual performance With the exception of the performance evaluation of the PV-PT-RC

Fig. 13. Effect of the packing factor on the nocturnal performance of the PV-PT-RC system.

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Fig. 14. Effect of the panel emissivity on the diurnal performance of the PV-PT-RC system.

The system generated the highest monthly cooling energy in December and the lowest in July, reaching 206.90 and 61.12 MJ, respectively. Given that the initial water temperature (water temperature in the water main) is higher than the ambient temperature during winter but lower during summer and the water vapor content is high during summer and low during winter, the cooling performance of the system is confirmed better in winter than n summer. Despite this finding, the system still provides considerable cooling energy during summer to cover a proportion of the cooling load in a passive and environmentfriendly manner. Overall, the annual electrical, thermal, and cooling energy gains of the PV-PT-RC system are 479.67, 2369.07, and 1432.49 MJ, respectively.

Sensitivity analysis was conducted to examine the effect of different key system parameters on the PV, PT, and RC performance of the system. Furthermore, the annual performance of the system in Eastern China in the typical meteorological year was evaluated. On the basis of the results, the following conclusions were drawn: (1) The built mathematical model can predict the operation performance of the PV-PT-RC system precisely in the daytime and nighttime working modes. The MRE for electrical power, aluminum plate temperature, and water temperature in the tank is less than 5%, and that of the cooling power is 6.83%. (2) Different operation parameters have varying influences on the daytime electrical and thermal efficiencies. Thus, the overall electrical/thermal efficiency has a tendency similar to the electrical efficiency in some cases while showing a tendency similar to the thermal efficiency in other cases. (3) Thick insulation and high tank volume are conducive to the

5. Conclusions This study numerically investigated a hybrid PV-PT-RC system using a mathematical model, which was verified using experimental data.

Fig. 15. Effect of the panel emissivity on the nocturnal performance of the PV-PT-RC system. 12

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M. Hu, et al.

Fig. 16. Effect of the tank volume on the diurnal performance of the PV-PT-RC system.

daytime and nighttime performance of the system. The initial water temperature in the tank and the panel emissivity negatively affect the daytime performance but positively impact the nighttime behavior of the system. The packing factor has a remarkable effect on the daytime performance but a negligible effect on the nighttime performance of the system. (4) The results of the annual performance investigation suggest that the maximum and minimum electrical and heat gains of the system are 48.97 and 293.90 MJ in August and 30.40 and 92.07 MJ in January, correspondingly. The peak and lowest cooling gains of the system are expected in December and July, reaching 206.90 and 61.12 MJ, respectively. Furthermore, the annual electrical, heat and cooling gains of the system are 479.67, 2369.07 and 1432.49 MJ, correspondingly.

In summary, the proposed PV-PT-RC collector can serve as a promising cooling-heating-power system and can be applied in fields involving electricity, heat, and cooling energy consumption. Building energy savings is a good application for this trifunctional collector. The building integrated PV-PT-RC system can cover a proportion of energy load in an environment-friendly manner by coupling the collector with the inherent heating, ventilation, and air conditioning system in buildings. 6. Declaration of interest statement The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. The authors report no conflicts of

Fig. 17. Effect of the tank volume on the nocturnal performance of the PV-PT-RC system.

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Fig. 18. Monthly average weather data of TMY in Hefei, China.

Fig. 19. Monthly overall energy gain of the PV-PT-RC system.

interest. The authors alone are responsible for the content and writing of this article.

China (2018YFD0700200), H2020 Marie Skłodowska-Curie Actions Individual Fellowships (842096), National Natural Science Foundation of China (NSFC 51906241, 51761145109, and 51776193), Anhui Provincial Natural Science Foundation (1908085ME138), Fundamental Research Funds for the Central Universities (WK2090130023), and China Postdoctoral Science Foundation (2019M652209).

Acknowledgments This study was sponsored by the National Key R&D Program of Appendix A

This appendix is intended to provide a clear presentation of the mathematical modeling packages described in Section 3.1.

• Modeling package for the transparent cover The convective heat transfer coefficient between the cover and the ambient air is defined as [36] (A1)

ha,c = 2.8 + 3.0ua , 14

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where ua denotes the ambient wind velocity, m/s. The radiative heat transfer coefficient between the cover and the sky is calculated as

hs,c =

(A2)

(Ts2 + Tc2 )(Ts + Tc ),

c

where εc denotes the emissivity of the cover, and σ is the Stefan–Boltzmann constant. The convective heat transfer coefficient between the cover and the PV layer is written as

hPV,c_conv =

Nu· ka , dPV,c

(A3)

where Nu denotes the Nusselt number; ka is the thermal conductivity of air, W/(m·K); and dPV,c is the height of the air gap, m. For collectors with inclination angles ranging from 0° to 75°, if TPV > Tc, then the Nusselt number is expressed as [37]

1708·(sin1.8 )1.6 Ra·cos

Nu = 1 + 1.44 1

+

1708 Ra ·cos

1

+

Ra·cos 5830

+

1 3

1

,

(A4)

where β denotes the inclination angle of the collector, rad; and Ra is the Rayleigh number, –. The + exponent suggests that only positive values are adopted for the terms within the square brackets. In case of negative values, zero is adopted. If TPV < Tc, then the Nusselt number is derived as [38]

Nu = 1 + 0.364

lp dPV,c

Ra1

4

1 sin .

(A5)

where lp denotes the length of the panel, m. If TPV = Tc, then Nu = 0. The Rayleigh number is expressed as

Ra =

3 Tc ) dPV,c

g a (TPV

a va

,

(A6) 2

−1

2

where g denotes the gravitational acceleration, m/s ; δa is the expansion coefficient of air, K ; γa is the thermal diffusion coefficient, m /s; and νa is the kinetic viscosity, N·s/m2. The net radiant heat transfer power between the cover and the PV layer is expressed as [39]

( ) PV

QPV,c_rad,net =

1

c

Tc4

c

c PV

1

c PV

4 ( ) PV TPV ,

(A7)

where αc and (α)PV correspond to the absorptivity of the cover and the PV layer; ρc and ρPV are the reflectivity of the cover and the PV layer, respectively; and (ε)PV is the PV layer. (α)PV and (ε)PV are calculated as

( ) PV =

PV

( ) PV =

PV

+ (1

)

+ (1

)

(A8)

TPT,

(A9)

TPT, 2

where packing factor ξ is calculated as ξ = APV/Ap (APV and Ap represent the area of solar cells and panel, respectively, m ); αPV and αTPT are the absorptivity values of the solar cells and the interstitial black TPT, correspondingly; and εPV and εTPT are the emissivity values of the solar cells and the interstitial black TPT, respectively. (α)c is defined as

( )c =

c

+

c c [1

1

c [1

( )PV ] , ( )PV ]

(A10)

where τc denotes the transmittance of the cover.

• Modeling package for the PV module The thermal resistance of the adhesive layer (black TPT and EVA) is expressed as

RPV,p =

dad , kad

(A11)

where dad and kad are the thickness and the thermal conductivity of the adhesive layer, m and W/(m·K), correspondingly. The effective transmittance–absorptivity product of the PV layer is calculated as

(

)PV =

c(

1

[1

)PV ( )PV ]

.

(A12)

c

The net radiant power of the PV layer is written as

QPV_rad,net = QPV_rad + (1

) QTPT_rad

(A13)

Qs_rad, 2

where QPV_rad and QTPT_rad are the radiant powers of the PV module and the interstitial black TPT, W/m , respectively; and Qs_rad is the sky radiant power absorbed by the PV layer, W/m2. The three physical quantities are written as follows [40]:

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Eb, (TPV )·(1

QPV_rad =

1

0

1

0

c,

((1

TPT,

c,

PV,

Eb, (TPV )·(1

QTPT_rad =

)

c,

((1

PV,

)

)

c,

TPT,

· Eb, (Tc )

PV,

)

)·

· Eb, (Tc ) TPT,

d ,

(A14)

c,

)·

d ,

(A15)

c,

and 2

Qs_rad = 2

0

s,

0

( , )·Eb, ( , Ta )·( ) PV, ( , )·

c,

( , ) sin cos d d ,

(A16)

where Eb, λ denotes the spectral radiant power of the blackbody, W/(m2∙μm); ρc, λ and εc, λ are the spectral reflectance and the emissivity of the cover, respectively; εPV, λ and εTPT, λ are the spectral emissivity values of the solar cells and the interstitial black TPT, correspondingly; (α)PV, λ is the spectral absorptivity of the PV layer; εs, λ and τs, λ are the spectral emissivity and the transmittance of the sky, respectively; and θ is the zenith angle, rad. The output electrical power of the PV module is calculated as [41]

EPV = G

c ref

[1

Br (TPV

(A17)

Tref )],

where ηref denotes the reference efficiency of the solar cells at the reference temperature (i.e., Tref = 298.15 K); and Br is the temperature coefficient of the solar cells (equal to 0.0045 K−1 for crystalline silicon solar cells).

• Modeling package for the aluminum plate The heat transfer coefficient between the aluminum plate and the back insulation layer is calculated as

(Tp2 + Tb2 )(Tp + Tb )

h p,b =

1

p

1 +1

b

1

+

Nu · ka , d p,b

(A18)

where εp and εb are the emissivity values of the aluminum plate and the back insulation layer, respectively; and dp,b is the height of the air channel, m. For the heat transfer power between the aluminum plate and the copper tube, Qp,t = 0 where the plate is disconnected from the tube, and Qp,t = (Tp Tt ) (Rp,t · Aij ) in which the plate is connected to the tube. Aij denotes the area of a control volume, m2; and Rp,t is the thermal contact resistance between the absorber plate and the copper pipe, K/W, and calculated as

Rp,t =

d p,t k p,t Ap,t

,

(A19)

where dp,t, kp,t, and Ap,t are the thickness, the thermal conductivity, and the area of the joint of the aluminum plate and each copper tube, m, W/ (m·K), and m2, respectively.

• Modeling package for the back insulator Ua,b is expressed as

Ua,b =

1 db kb

+

1 ha,b

, (A20)

where ha,b denotes the convective heat transfer coefficient between the back insulator and ambient air, W/(m2·K), whose formula is equal to that of ha,c.

• Modeling package for the water in the circulation water tank Ua,tank is calculated as

Ua,tank =

1 Dtank,o 2ktank

ln

Dtank,o Dtank,i

+

1 ha,tank

, (A21)

where Dtank,i and Dtank,o denote the inner and the outer diameters of the water tank, respectively, m; ktank is the thermal conductivity of the copper tube, W/(m·K); and ha,tank is the convective heat transfer coefficient between the tube and the inner water, W/(m2·K).

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