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Dynamic modeling, practical verification and energy benefit analysis of a photovoltaic and thermal composite module system
Energy Conversion and Management 154 (2017) 470–481
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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Dynamic modeling, practical verification and energy benefit analysis of a photovoltaic and thermal composite module system
T
⁎
Chung-Feng Jeffrey Kuo , Yu-Wei Lee, Mega Lazuardi Umar, Pei-Chung Yang Department of Materials Science and Engineering, National Taiwan University of Science and Technology, Taipei 10607, Taiwan, ROC
A R T I C L E I N F O
A B S T R A C T
Keywords: Solar energy Photovoltaic and thermal module Dynamic modeling Solar energy saving efficiency Heat transfer
This study aims to derive the dynamic modeling of a photovoltaic and thermal composite (PV/T) module. The environmental factors including ambient temperature, wind speed and solar radiation are used as the input parameters, and the dynamic temperature of various layers inside the module can be simulated. Depending on the solar cell temperature, the dynamic electric power, electrical efficiency and daily average thermal storage efficiency can be obtained. The PV/T modeling accuracy is verified by a practical real module. The errors in electric power and electric efficiency are less than 2.5%, and the daily average thermal storage efficiency is less than 1.3%. At the same time, this study uses the built dynamic model to improve the output performance of the PV/T module. After the water flow rate is improved, the electric efficiency and electric power, and the daily average thermal storage efficiency are increased. The output performance of the PV/T module is ameliorated effectively. Finally, the comparison of the energy benefit analysis between photovoltaic (PV) and PV/T modules is discussed. The electric efficiency and daily average thermal storage efficiency are converted into energy saving efficiency. PV/T is more efficient than PV by 14.127%, its investment recovery period is lower than the PV by 4.5 years, and its profit recovery is higher than PV by 187.18%. Installing a PV/T can increase solar energy effectiveness effectively.
1. Introduction Solar power generation has been driven by cost reduction, economic incentives and the need for meeting growth in electricity demand while reducing reliance on fossil fuels [1]. As a renewable energy, solar energy is environmentally friendly, sustainable and inexhaustible. It has become more and more popular and important for both industrial and residential applications [2]. It is obvious that efficiently utilizing solar energy is an effective measure to solve energy and environmental issues [3]. PV technology has been recognized as an important way to realize sustainable development and carbon emission reduction. To facilitate the development of PV technology, raising the electrical efficiency and cutting down the manufacturing cost are essential for technological innovation. As the conversion efficiency of a PV cell descends with the rising operational temperature, removing excess heat from PV cells is the key for performance improvement [4]. The PV/T system combines both solar energy conversion processes: solar thermal conversion and solar photovoltaic conversion [5]. It enhances the energy performance of the PV, the thermal energy is removed and subsequently decreases the operating temperature of the solar cell. An effective means of
⁎
improving system performance has been proposed using a combination of PV devices and thermal collectors to produce both heat and electricity [6,7]. The possibility of the utilization of heat for climatization makes them attractive for building integration [8]. In these studies, the PV/T system, which can supply electricity and thermal energy simultaneously, has attracted much attention. The solar cell converting incident sunlight into electrical output, the range of photoelectric conversion efficiency in Standard Test Condition (STC) is 7 ∼ 40% according to the module type, and the rest of the incident light energy is converted into heat energy. The temperature increase of a solar cell caused by the accumulation of heat energy is the factor that influences the PV performance most severely. It not only reduces the electric power from the solar cell but also shortens the life cycle of the electric power [9]. According to STC and the Nominal Operating Cell Test (NOCT), the temperature coefficient of the electric efficiency of a crystalline silicon solar cell is −0.38%/°C, indicating that the electric efficiency decreases by 0.38% when the solar cell’s operating temperature rises by 1 °C [10,11]. Spontaneously, the solar cell temperature rise reduces the solar cell’s module outputs of electrical energy. However, research scholars regard heat energy as an auxiliary capacity other than solar cell module
Corresponding author. E-mail address: jeff[email protected] (C.-F. Jeffrey Kuo).
https://doi.org/10.1016/j.enconman.2017.11.036 Received 29 July 2017; Received in revised form 11 November 2017; Accepted 13 November 2017 0196-8904/ © 2017 Elsevier Ltd. All rights reserved.
Energy Conversion and Management 154 (2017) 470–481
C.-F. Jeffrey Kuo et al.
σ θ η
Nomenclature Symbols
A C G I L P q R T W c n ṁ k h
area (m2) thermal capacitance (J/K) solar radiation (W/m2) current (A) thickness (m) electric power (W) heat flow resistance (Ω) temperature change (K) wind speed (m/s) specific thermal capacitance (J/kg K) no. of heat collecting pipe mass flow rate (kg/s) thermal conductivity coefficient (W/m K) thermal convection coefficient (W/m K)
Subscripts
a s t w m + co g fg in mw pv ra cov con out act sim f i
Greek letters
α β ε ρ τ
Stefan-Boltzmann constant thermal resistance (K/W) efficiency
radiation absorption rate inclination angle (23°) radiation emission rate density (kg/m3) radiation transmittance
ambient atmosphere layer TPT water maximum top of glass layer heat collecting pipe short wavelength radiation glass layer heat collecting pipe inlet average water temperature solar cell heat radiation heat convection heat conduction heat collecting pipe outlet actual simulated final initial
MATLAB and TRNSYS. Two identical PV/T panels were tested alongside two PV panels to gather an electrical baseline for comparison. Aste and Fabrizio [19] provided the design of a covered PV/T collector made with thin film PV technology and a roll-bond flat plate absorber along with a simulation model developed through the elaboration of several mathematical equations, to evaluate the performance of covered PV/T water collectors. Rejeb et al. [20] proposed an experimental and numerical study to evaluate the performance of a PV/T nanofluid-based collector. The model was applied to predict the annual electrical and thermal output of the PV/T for three different countries: France, Iran and Tunisia. It was also found that the thermal and electrical energy output for Tunisia was higher than the others. Calise [21] presented the performance of PV/T from both energetic and economic points-of-view by means of a zero-dimensional transient simulation using TRNSYS. The economic results show that the system under investigation could be profitable. Gholami et al. [22] utilized an optimal sizing of a PV/T system for supplying the electricity and heat consumption of a household load for one year including the PV/T installation angle, electrical battery and thermal storage tank for supplying electrical and thermal loads. Gholami et al. [23] presented the design and optimization of a concentrated photovoltaic thermal system considering electrical, mechanical, and economic aspects. An active ventilation was used for absorbing the thermal power of radiation. From the above-mentioned literature reviews, models have been prepared that are able to reproduce the dynamic behavior of the PV/T panels representing a flexible tool for developing innovative and useradapted system control criteria in a global system optimization perspective. First, this study derives the dynamic modeling of PV/T. The heat transfer architecture resulting from each layer of PV/T is analyzed, and a thermal model is implemented according to the heat energy conservation law and lumped capacitance method. Afterwards, the thermal model is equivalently converted into a current circuit to get the thermal equivalent equation for each layer’s structure. Then, the simultaneous differential equation is computed by using the Simulink software tool. The dynamic temperature of each layer of PV/T is acquired by inputting
electrical energy [12] and have begun to study PV/T actively [13]. The PV/T development planning is combined with a solar energy heater and PV. A tube bank with cold water flowing inside is placed on the back side of the solar cell layer. The flowing cold water takes away the heat energy of the solar cell reducing the temperature of the solar cell to increase the output electrical energy, and the heat energy heats up the cold water to obtain a heat energy output. In comparison to two standalone systems, the PV/T has a higher overall output performance [14]. Some scholars in the previous studies have derived PV/T models to predict the output performance of a PV/T. Koech and Ondieki [15] built a steady state thermal model for a PV/T system under various conditions. A steady state thermal model of a PV/T air solar collector was developed, validated from experimental data and used to evaluate the effects of various parameters on the performance of the system. The results indicated that increasing the air mass flow rate when the design parameters are optimum will result in a significant increase in the overall performance of the system. Aste and Giancarlo [7] presented the experimental and theoretical results of research and development on the design, development and performance monitoring of a PV/T air collector. The simulation model predicted the thermal and electrical performance of a PV/T collector quite well. Maifi and Chari [16] illustrated the modeling of a photovoltaic thermal hybrid solar collector with a cylindro-parabolic concentrator. The influence of inlet parameters on the electrical and thermal performances of the collector, the parameters affecting the PV/T performance, such as the glazing, mass flow rate and temperature of the collector element and absorber impedance, and also the ratio of the compound parabolic concentrator’s design types were discussed. Mattia and Giorgio [17] derived a dynamic thermal model for hybrid photovoltaic panels. This model was used to describe a simplified numerical model to reproduce the shorttime dynamic behavior of the PV/T panel. The model has been validated using experimental data which were collected during outdoor tests conducted at the University of Genoa using a prototype realized by retrofitting a commercial PV collector. Annis [18] dealt with the performance analysis and modeling of hybrid photovoltaic-thermal solar panels. A PV/T panel was constructed, tested and modeled using both 471
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Power (W)
local environmental factors, and the dynamic electric efficiency, electric power and daily average storage efficiency are obtained. Second, this study implements a real PV/T to verify the PV/T dynamic modeling results to warranty the accuracy of the dynamic model. Finally, the structural parameters of PV are modified according to local environmental factors using the dynamic model to reach the optimal parameter design and output of PV/T. The advantages of PV/T compared with PV and a solar energy water heater will be analyzed as well. 2. PV/T description & related methodology 2.1. PV/T module and performance representation
Voltage (V) The PV/T generates electrical energy and heat energy at the same time. The structure is shown in Fig. 1 [24]. It is comprised of the PV, collecting plate, heat collecting pipe, isolation layer and shell [25]. The top down PV structure includes a cover plate, ethylene vinyl acetate (EVA), a solar cell, EVA and a tedlar/polyester/tedlar (TPT) backsheet. When the sun irradiates the PV, electrical energy output is generated but only some of incident sunlight is converted into current during irradiation. The other energy is converted into heat energy, accumulated in the PV so that the electrical efficiency of the solar cell decreases. In order to maintain the electrical efficiency of a PV, the PV/T uses the collecting plate on the back of the PV. The PV heat is conducted to the cold water in the heat collecting pipe rack for heat exchange, the operating temperature of the PV is reduced and the cold water absorbs the heat energy, becoming hot water. The hot water is stored. The performance index of PV/T is electric efficiency, electric power and storage thermal efficiency [26]. Electric efficiency [27]:
ηe =
P=
P GApv
∫ Vm Im dt
Fig. 2. The power drop of PV module at various solar cell temperatures [27].
ηe = ηstc [1−ϑ(Tpv−25)]
(3)
where ηstc is the measured efficiency under STC. This condition includes: solar radiation intensity (1000 W/m2), environmental temperature (25 °C) and mass of atmosphere (1.5). ϑ is the temperature coefficient of the solar cell (single crystal silicon cell used in this study), ηstc is 20.3% and Tpv is the temperature of the solar cell (°C). Thermal storage efficiency:The thermal storage efficiency ηth is the ratio of the total generated thermal energy to total solar radiation energy between the water outlet and inlet during the day.
̇ p (Tf −Ti ) mC
ηth =
(4)
GA
where ṁ is the water mass flow rate, Cp is the water specific thermal capacitance (4.18 kJ/kg K), Tf and Ti are the final temperature and initial temperature.
(1)
2.2. Heat transfer mechanism description Three fundamental forms of heat can flow from one substance to another: conduction, convection and radiation [29]. Heat flow is expressed as Eq. (5):
(2)
where P is the total output electric power within test time, Vm is the voltage at the maximum power point, Im is the current at the maximum power point, G is the solar radiation received by PV, and A is the area of PV/T. One of the important factors is the solar cell’s operating temperature. The reason for the temperature increase includes an increase in thermal lattice vibration, a decrease in the charge carrier’s mobility and the reduction of the p-n junction ability of the solar cell [28]. The relation between the solar cell temperature and electric power is shown in Fig. 2. The vertical axis represents the maximum power output, and the horizontal axis represents the maximum output voltage. The electric power of the solar cell declines obviously as the solar cell’s operating temperature rises [8]. The relationship between solar cell efficiency and the temperature of the solar cell is expressed as Eq. (3):
qx =
ΔT θ
(5)
where qx related to heat flow of conduction, convection, or radiation, ΔT is temperature different between two layer, and θ is thermal resistance. 2.2.1. Conduction and convection heat transfer For conduction and convection heat transfer [10], the thermal resistance for conduction is expressed as Eq. (6):
θcon =
L kA
(6)
where L is the thickness, k is thermal conductivity coefficient, and A is Fig. 1. PV/T structure [24].
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the area. While the thermal resistance for convection it is expressed as Eq. (7):
θcov = 1/(hforced + hfree ) A
Table 1 The equivalence system between thermal-electrical.
(7)
where hforced and hfree are the coefficients of forced and free convection [10]. In this study, convection in a windward condition is expressed as Eq. (8):
θcov = 1/(11.4 + 5.7W ) A
(8)
Thermal system
Electrical system
Change in temperature ΔT (K) Heat flow q (W) Thermal resistance θ (K/W) Thermal capacitance C (J/K) q*θ = ΔT
Voltage V (V) Current I (A) Resistant R (Ω) Capacitance C (F) I *R = V
q = Ct
where W is the wind speed from the ambient.
dT dt
I=C
dV dt
2.2.2. Heat radiation The heat radiation wavelength range is between 0.00001 nm and 1 mm. The heat radiation can be divided into short wavelength and long wavelength heat radiation [30,31]. 2.2.2.1. Short wavelength heat radiation. The sunlight’s wavelength range belongs to the short wavelength heat radiation classification which is less than 2500 nm. The short wavelength radiation heat flow can be obtained as shown in Eq. (9) [32].
Ig = αGA
(9)
where G is solar radiation, A is area, and the radiation absorption rate used in this study αfg is 0.5 and αpv is 0.9. 2.2.2.2. Long wavelength heat radiation. The long wavelength heat radiation heat flow is emitted between two body surfaces when the wavelength is longer than 2500 nm. This heat flow is expressed as Eq. (10):
q = (AεσTs4 )−(AεσT14 ) = Aεσ (Ts4−T14 )
(10)
where Ts and T1 are the surface temperature values of two bodies respectively, σ is Stevan-Bolztmann constant, β is the inclination angle of the PV/T, and the radiation emission rate ε of glass used in this study is 0.85. The heat radiation thermal resistance is expressed as Eq. (11):
1 θra = 1/ Aεσ (Ts2 + T12)(Ts + T1) (1 + cosβ ) 2
Fig. 3. The sectional view of PV/T.
between the thermal parameter and electrical parameter is shown in Table 1 [33].
(11)
3. Dynamic modeling of PV/T
Based on the heat flow as expressed in Eq. (5), the dynamic temperature can be obtained according to the thermal resistance and the temperature difference.
The structure configuration in the real PV/T is shown in Fig. 1. The sectional view is drawn as shown in Fig. 3. The heat transfer mechanism analysis is implemented for each layer’s structure to establish the thermal model. This thermal model is converted into the correspondingly equivalent electrical system. After that, the thermal equilibrium equation of each layer structure is used to obtain the simultaneous differential equation for PV/T dynamic model, simulated by Simulink. The ambient temperature, solar radiation and wind speed are the input parameters. Then, the dynamic temperature of each layer can be obtained. The electric power and daily average thermal storage efficiency are obtained according to the relationship between the temperatures of the water and solar cell.
2.3. Lumped thermal capacitance method The lumped thermal capacitance method applies the thermal energy conservation law to move the heat flows caused by different heat transfer mechanisms into heat capacity. The change per second or rate of change of the stored heat is equal to the net heat flow [31,19]. The thermal system is described by the differential equation:
C=
dT = qcon + qra + qcov + Ig dt
(12)
where C is the thermal capacitance, qcon is the heat flow of conduction, qra is the heat flow of radiation, qcov is heat flow of convection, and Ig is the heat flow of short wavelength heat radiation. Thermal capacitance is expressed as Eq. (13).
C = ρALc
3.1. Assumptions of the dynamic modeling The assumptions of the modeling are as follows: (1) The aluminum frame is mounted in the lateral region of the PV/T module whose area is very small compared with the top surface area. Therefore, the heat flow of the aluminum frame is neglected. (2) The module is exposed to the same environmental factors and each layer has uniform temperature distribution. Therefore, the temperature of each layer can be simulated accurately by one-dimensional analysis. (3) The heat conduction in the EVA layer can be neglected because its heat conduction coefficient is very low in comparison to the adhered structures in the module.
(13)
where ρ is the mass density, A is the area, L is the thickness, and c is the specific thermal capacitance. 2.4. Equivalence system between thermal model and electric loop The thermal model analysis was simplified according to heat transfer. The thermal model was converted into a current loop displayed in the circuit and computed. The equivalent transformation 473
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ρfg Afg Lfg cfg
dTfg dt
=
1 1 (T+−Tfg ) + (Tpv−Tfg ) R con,fg R con,pv
(16)
The solar cell layer (Tpv ):
ρpv Apv Lpv cpv
dTpv dt
= (Ipv−Epv )
1 1 (Tfg−Tpv ) + (Tt −Tpv ) R con,pv R con,t
(17)
where Ipv is the short wavelength radiation heat flow of the solar cell, Epv is the electric energy production when the solar cell receives short wavelength radiation as expressed in Eq. (18):
(Ipv−Epv ) = αpv τfg GApv
(18)
where the value of radiation absorption rate αpv used in this study is 0.9, and radiation transmittance τfg is 0.95.The TPT layer (Tt ):
ρt At Lt ct
dTt 1 1 = (Tpv−Tt ) + (Tco−Tt ) dt R con,t R con,co
(19)
The heat collecting pipe (Tco):
ρco Aco Lco cco
dTco 1 1 = (Tt −Tco) + (Tmw−Tco) dt R con,co R con,w
(20)
The water inside the heat collecting pipe (Tmw)
nρw Aw L w c w
Fig. 4. Heat transfer mechanism of PV/T.
R cov,w = m w ρw Aw L w c w
The heat transfer mechanism analysis diagram for PV/T after considering the assumptions is shown in Fig. 4. The heat transfer mechanism received by the external module is the heat convection resulting from the ambient temperature, wind speed and heat radiation including long wavelength and short wavelength radiation. The glass transmits the short wavelength radiation to the solar cell, so the solar cell layer has a heat radiation mechanism. The contact between the layer structures inside the module belongs to the heat conduction mechanism, while the heat flow generated by the heat transfer mechanism results from the thermal resistance and temperature difference in each layer.
(22)
The mass flow rate ṁ used in this study is 0.07 (kg/s), Tin−Tout is 6 °C, and the number of pipe n is 10. After the thermal balance equation of each layer of PV/T is established, the simultaneous differential equation can be established using the Simulink. The numerical values of thermal model input parameters for each layer are shown in Table 2, and the flowchart of PV/T simulation is shown in Fig. 5. 4. Experimental planning & simulation This study implements the PV/T dynamic model in order to predict the electric efficiency, electric power and daily thermal storage efficiency. A true PV/T is set up to identify its dynamic model. For the sake of getting the optimum structural and corresponding output performances for a PV/T design, the structural parameters of PV/T are modified according to its dynamic model. The advantages of installing PV/T will be analyzed as well.
3.3. Set up of the differential equations for each layer The thermal model of PV/T is decomposed for analysis according to each layer’s structure. The thermal model is then converted into the electrical system, layer by layer. From Fig. 4, using the Kirchhoff circuit law, the thermal balance equation for each layer can be obtained as:At the top of the glass layer (T+):
4.1. The PV/T real entity implementation
dT+ 1 1 1 = Ig + (Ta−T+) + (Ts−T+) + (Ts−T+) dt R cov, + Rra ,+ R con,fg
The real PV/T is located in the National Taiwan University of Science and Technology, Taipei, Taiwan. This PV/T model comes from BenQ Corporation: Sun Forte-Mono 203, PM-096B00, 330 W and 200 liter water tank. The real entity is shown in Fig. 6. The test is from 05:00 AM to 06:00 PM every day. The ambient temperature, wind speed, solar radiation, water pipe outlet and inlet temperature are measured by a heliograph, weather station and thermal couple. The electric power is extracted by DC electric loading.
(14) where Ts is the temperature of the sky [20] as expressed in Eq. (15):
Ts = 0.0552Ta1.5
(21)
where R cov,w is expressed in Eq. (22):
3.2. Heat transfer mechanism and thermal model implementation
ρfg Afg Lfg cfg
dTmw 1 1 = (Tco−Tmw ) + (Tout −Tin−Tmw ) dt R con,w R cov,w
(15)
The glass layer (Tfg ): Table 2 Numerical value parameters for each layer. Parameter 3
ρ density (kg/m ) A area (m2) L thickness (m) c specific thermal capacitance (J/kg K) k thermal conductivity coefficient (W/m K)
Glass (fg)
Solar cell (pv)
TPT (t)
Heat collecting pipe (co)
Water (w)
3000 1.6307 0.003 500 1.1
2330 1.6307 0.0003 677 130
1200 1.6307 0.0005 1250 0.033
8920 1.6307 0.003 (heat collecting plate) +0.0127 (rad = 1/2″) 385 401
1000 0.1328 pipe length * (rad = 1/2″) 0.0127 (rad = 1/2″) 4200 0.6
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Fig. 5. Flowchart of PV/T simulation.
These environmental factors are the inputs for the PV/T dynamic model to get the temperature of each layer as shown in Fig. 8. When the sunshine amount and ambient temperature increase hourly in the daytime, the PV cell temperature will be risen distinctly. The water flowing in the heat collecting pipes will take the PV cell heat energy away, and the rise of the PV cell temperature is suppressed effectively. The higher electrical efficiency and thermal storage efficiency will be provided. There is no incident sunlight at night. The rise in PV cell temperature does not influence the electrical efficiency but the thermal storage efficiency will be increased. When the dynamic temperature of the solar cell is obtained by PV/T dynamic model, the dynamic electric power can be obtained from Eq. (2). In order to verify the accuracy of the PV/T dynamic model, the comparison of the electric power between the dynamic model and real entity is shown in Fig. 9. The hourly electrical efficiency can be obtained from the solar radiation and module area. Its comparison between the dynamic model
4.2. Simulation results and verification This study selected three days in spring, summer, autumn and winter respectively, for simulation and real experimentation on the performance of the dynamic model for a PV/T. First, the dynamic temperature of each layer is acquired from the dynamic model. Then, the electric efficiency, electric power and daily average thermal storage efficiency are obtained. This information is compared with the real PV/ T to verify the prediction accuracy of the dynamic model.
4.2.1. Day based experiment For the day based experiment, the model simulation and practical validation were implemented on summer, 2016/06/15. Fig. 7 was the line chart of environmental factors on the day. It was a sunny day, a few black clouds. The sunshine amount changed steadily from 0.116 W/m2 at 05:00 AM to 935.416 W/m2 at 12:00 noon hourly, and then decreased to 73.151 W/m2 at 06:00 PM hourly. 475
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applicable to predict the electric efficiency, thermal storage energy, and electric power of a PV/T accurately. 4.2.2. Season-based experiment This study selected three days in spring, summer, autumn and winter respectively, for theoretical simulation and real experimentation on the dynamic model performance of a PV/T. The comparison is shown in Table 4. From Tables 3 and 4, the accuracy of the dynamic model could be verified. It can be seen that the dynamic model can simulate the temperature of a solar cell effectively when the environmental factors change slowly. The experiment shows that this dynamic model is useful to any place under any weather conditions, predicting the electrical efficiency, thermal storage efficiency and output electric power of a PV/ T accurately. 4.3. PV/T dynamic modeling innovation In order to simulate the output performance of PV/T, some references have been derived PV/T dynamic modeling. However, the previous studies did not take into account all the factors which could cause PV/T temperature change. The nominal operating cell temperature (NOCT) will be applied in this study to compare the accuracy of the solar cell temperature with that in the previous studies as shown in Table 5. The temperature of a solar cell is tested under NOCT conditions (solar radiation 800 W/m2, wind speed 1 m/s and ambient temperature 20 °C). Koech [15] built the dynamic modeling of PV/T, but different thermal inertias of various structures were not considered, so the error between the entity and dynamic modeling was 6.81 °C in NOCT verification. Hasan et al. [34] did not consider the difference between the heat convection transfer mechanisms received by the front and back sides of the PV/T. The same heat convection empirical value was used to calculate the heat convection coefficient on the front and back sides of the PV/T, so that the error between the entity and dynamic modeling was 6.24 °C in NOCT verification. Maifi and Chari [16] did not consider the concept of the heat flow heat energy conservation law. The heat flow could not flow completely in the heat capacity, so the heat flow was lost. The error result between the entity and dynamic modeling was 4.87 °C in NOCT verification. Mattia [17] calculated the heat convection coefficient and indicated that the intermediate current of heat
Fig. 6. PV/T real entity.
and real entity is shown in Fig. 10. The electric power absolute error percentage is 2.272% as calculated by Eq. (23):
|Psim−Pact | ∗100% Pact
(23)
In order to calculate thermal storage efficiency, the thermocouple is placed at the water outlet and inlet of the real PV/T to measure the water outlet and inlet temperatures. The daily average thermal storage efficiency can be obtained from Eq. (4) as shown in Fig. 11. The simulated and actual daily average thermal storage efficiency are 1.699% and 2.003%, respectively. The difference is 0.304%. This study also select 2016/06/14 and 2016/07/01 for summer dynamic model validation, the absolute error percentages of electric power and entity validation are 3.334% and 1.845%, respectively. For daily average thermal storage efficiency, the difference between simulated and actual value is shown in Table 3. The increase of the mean absolute error for electric power is due to high sunshine amount in the summer. The prediction accuracy of the PV cell temperature is better when the environmental factors change slowly. According to practical validation, the dynamic model is
Temperature ( C) Wind Speed (m/s) 2 Radiation/10 (W/m )
100
80
60
40
20
0
04:0 0
08:0 0
12:0 0
16:0 0
20:0 0
Time (hours) 476
24:00
Fig. 7. 2016/06/15 environmental factors.
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80 T+ Tfg Tpv Tt Tco Tmw
70
Fig. 8. The temperature simulation results from the dynamic modeling.
Temperature ( C)
60
50
40
30
20
04:00
08:00
12:00
16:00
20:00
300
24:00
Fig. 9. Hourly electrical power of PV/T.
Simulated Actual
250
Power (W)
200
150
100
50
0 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00
Time (hours)
is 1.57 °C in NOCT verification. This dynamic modeling can simulate effectively and make theoretical simulation precise.
convection had a slight effect on the PV/T temperature variation. It could be neglected, so the error between the entity and dynamic modeling was 4.43 °C in NOCT verification. Annis [18] indicated that the arrangement mode and quantity of heat collecting pipes in the PV/T did not influence the temperature of each layer’s structure in the PV/T. Therefore, in the analysis of the heat transfer mechanism, the influence of quantity and arrangement mode of the heat collecting pipes was neglected. The error between the entity and dynamic modeling was 4.07 °C in NOCT verification. Aste [19] neglected the least influential thermal radiation mechanism in the heat transfer mechanism, so that the heat transfer mechanism analysis was incomplete. The error between the entity and dynamic modeling was 3.29 °C in NOCT verification. In order to build the PV/T dynamic modeling effectively and make the theoretical simulation precise, this study considers all heat transfer mechanisms which includes heat conduction, convection and radiation. The experience value of the thermal convection coefficient is adopted from literature and theoretical discussion. The solar cell temperature error between the real entity and dynamic modeling built in this study
4.4. PV/T optimal structural design The dynamic model implemented in this study can not only predict the performance of PV/T, but also improve the output performance by modifying the internal structural parameters. The performance simulation in the four seasons from the dynamic model are shown in Table 6. It can be seen that when the ambient temperature and solar radiation are high and the wind speed is low in summer, the solar cell temperature rise. The corresponding electrical power and the thermal storage efficiency are lower than for other seasons. Therefore, the summer will be selected to design new structural parameters in order to get higher electrical power and thermal storage efficiency. Tiwari and Sodha [35] presented the numerical model of PV/T and found that the water flow rate was the first factor influencing the output performance of the PV/T. In this paper, 0.07 kg/s m2 was taken as the maximum value reduced by 0.02 kg/s m2. The optimum water flow rate 477
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Simulated Actual
24
Fig. 10. Hourly electrical efficiency of PV/T.
Electrical Efficiency (%)
22 20 18 16 14 12 10
5:00
6:00
7:00
8:00
9:00 10 :00 11 :00 12 :00 13 :00 14 :00 15:00 16:00 17 :00 18:00
Time (hours)
is obtained by dynamic model, as shown in Table 7. It is observed that the water flows fast when the water flow rate is high. The heat energy cannot be absorbed effectively, so the electric efficiency and thermal storage efficiency decrease. When the water flow rate is low, the water transfers the heat energy to the solar cell again. The temperature rises, the electric efficiency decreases and the thermal storage efficiency rises. The optimal water flow rate is 0.05 kg/s m2 in summer, not only increasing thermal storage efficiency but also increasing electrical efficiency. In other words, the performance is predicted by the dynamic model. The optimum parameter design for PV/T can be obtained to perform the maximum advantage for solar energy.
Table 3 Comparison of daily average thermal storage between dynamic model and real entity. Date
Dynamic model (%)
Real entity (%)
Difference (%)
2016/06/14 2016/07/01
0.167 5.691
0.774 6.183
−0.607 −0.492
Table 4 The dynamic model identification from four seasons.
5. Benefit analysis The output performance index of PV/T is electric efficiency and thermal storage efficiency. They cannot be compared directly for different output energy forms. The electrical energy performance evaluation will be applied in this study to compare the electrical energy performance of PV and PV/T. The energy-saving efficiency is applied to justify what kind of solar cell module can perform the maximum
Daily average error
Spring
Summer
Autumn
Winter
Daily average power absolute error (%) Daily average thermal storage efficiency difference (%)
1.429 −0.382
2.483 −1.201
2.32 −0.672
0.399 −0.467
advantage in solar energy technology. Finally, the cost recovered years, return on investment and floor area of PV and PV/T are analyzed to evaluate the performance of the PV and PV/T at the location.
Simulated Actual
4
Heat storage efficiency (%)
3
2
1
0
-1
-2 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00
Time (hours) 478
Fig. 11. Hourly thermal storage efficiency of PV/T.
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Table 5 Dynamic modeling accuracy comparison. Previous study
Electric power efficiency absolute error (%)
Daily average storage efficiency absolute error (%)
Actual NOTC (°C)
Simulated NOTC (°C)
Difference (°C)
Koech and Ondieki [15] Hasan et al. [34] Maifi [16] Mattia [17] Annis [18] Aste [19] This study
6.143 5.876 4.981 4.546 3.286 3.511 1.657
3.964 3.619 2.764 2.173 1.696 1.727 0.68
42 40 37 37 34 37 37
35.19 33.76 32.13 32.57 29.93 33.71 35.43
6.81 6.24 4.87 4.43 4.07 3.29 1.57
5.1. Electrical energy performance evaluation
Table 6 Four seasons simulation from PV/T dynamic model. Season
Daily average electrical efficiency (%)
Daily average thermal storage efficiency (%)
Autumn Winter Spring Summer
18.85 20.80 19.58 18.38
3.161 1.003 6.874 1.669
The electrical energy performance evaluation is used to compare the output electrical energy performance of PV and PV/T in the four seasons. The electrical energy performance evaluation is the ratio of the solar cell module output electric power (P) divided by the product of the electrical rating power (Pn ) and solar radiation (G) called the electric power performance ratio (PR) and expressed as Eq. (24).
PR = Table 7 The performance improvement of the PV/T. Water flow rate (kg/s m2)
Daily average electrical efficiency (%)
Daily average thermal storage efficiency (%)
0.03 0.05 0.07
17.97 18.64 18.38
4.543 2.765 1.699
PR of PV (%)
PR of PV/T (%)
Autumn Winter Spring Summer
92.39 102.28 93.6 83.55
91.91 102.44 95.04 88.16
(24)
This study implemented electrical energy performance for PV and PV/T on the same location, day and environmental factors in four seasons. The evaluations of electrical energy performance for the PV and PV/T are obtained and the performance ratios are averaged, as shown in Table 8. The statistical results show that the environmental factors in autumn cause heat exchange between the water in the PV/T and the solar cell. High water temperatures transfer the heat energy to the solar cell again, so that the PV/T’s electrical power is a little lower than that of the PV. For the low ambient temperatures and high wind speeds in winter, the solar cell module performance can be performed effectively. In spring and summer, the ambient temperature is high, the wind speed is low and the amount of sunshine is great. The water flow in the PV/T can take the solar cell heat energy away effectively, so as to reduce the PV temperature to increase the electrical power, so the PV/T is better than the PV.
Table 8 Comparison of electric power performance ratio (PR) for four seasons. Season
P G ∗Pn 1000
5.2. Energy-saving efficiency evaluation Table 9 Comparison of energy-saving efficiency between PV and PV/T. Season
PV energy-saving efficiency (%)
PV/T energy-saving efficiency (%)
Autumn Winter Spring Summer
50.394 54.786 51.178 46.263
52.832 55.739 58.408 50.088
The overall efficiency of PV/T is the sum of the electric efficiency and thermal storage efficiency. The two types of solar cell modules cannot be compared by the different energy forms of the output performance index [26]. Therefore, the energy-saving efficiency evaluation is used for comparison [17]. As the electric energy is a high-level energy converted from heat energy, the electric efficiency must be divided by the electric efficiency of fossil fuel (38%) plus the thermal storage efficiency to obtain the energy-saving efficiency Ef (%), expressed in Eq. (25), as shown in Table 9.
Table 10 PV and PV/T specifications.
Ef = ηth + Parameter
PV
Test time Location PV type PV efficiency Module size Material of heat collecting plate Size of heat collecting pipe No. of heat collecting pipe Capacity of water storage tank Mass flow rate Cycling temperature Angle of inclination Azimuth
05:00 ∼ 18:00 Da An District, Taipei Monocrystalline silicon 20.3% 1.559 m * 1.046 m / / / / / / 23° South
PV/T
ηe 38%
(25)
Whatever the environmental factors are, the PV/T can perform energy-saving efficiency better than PV, so the dynamic model can judge PV/T to be suitable for the site according to local environmental factors and the prediction of output performance. Copper 1/2 in. 10 Pieces 200 L 0.07 kg/s 6 °C 23° South
5.3. Cost recovered years, return on investment and floor area analysis The cost recovered years, return on investment and floor area will be analyzed to evaluate the performance of PV and PV/T. For the analysis of cost recovered years, the difference between PV and PV/T specifications in electricity generation and thermal storage capacity shall be given, as shown in Table 10. 479
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12000
(1) This study considers all heat transfer mechanisms which include heat conduction, convection and radiation. The heat energy balance law of the heat transfer and heat capacity method are combined to derive the dynamic model of a PV/T. The accuracy of this dynamic modeling has been proven by the real entity showing that the electrical efficiency and electric power error is less than 2.5%, and the daily thermal storage efficiency error is less than 1.3%. The solar cell temperature error in NOCT verification is 1.57 °C. (2) The dynamic model of PV/T is applied to enhance the output performance. After the water flow rate is improved, the electrical efficiency and thermal storage efficiency are increased by 1.397% and 62.742%, respectively. The PV/T output performance is improved effectively. (3) The PV/T can perform energy-saving efficiency better than the PV. The cost recovered years of a PV is 6.857, and that of a PV/T is only 2.302. Based on the warranty period of PV of 20 years, the return on PV/T is higher than that of PV by 187.182%. In addition, a PV/T only needs a floor area 50% smaller than that of a PV and solar energy water heater. The installation of a PV/T can create the greatest investment benefit among the solar energy modules.
10000
PV/T
8000
USD
6000 4000
PV
2000 0 -2000 -4000
0
5
10
15
20
Duration (Years) Fig. 12. Investment profit analysis.
Table 11 Comparison of total energy production per unit area.
Acknowledgment
Energy
Floor area (m2/ 1 kW)
Electric energy per unit area (MJ/m2/year)
Heat energy per unit area (MJ/m2/ year)
Total energy production per unit area (MJ/m2/year)
PV Water heater PV/T
11.26 11.26 11.26
399.61 / 421.59
/ 695.89 737.37
399.61 695.89 1158.96
The research was supported by the Ministry of Science and Technology of the Republic of China under Grant No. 105-1221-E-011156. References [1] Belhaouas N, Ait Cheikh MS, Agathoklis P, Oularbi MR, Amrouche B, Sedraoui K, et al. PV array power output maximization under partial shading using new shifted PV array arrangements. Appl Energy 2017;187:326–37. [2] Zubi G, Dufo-López R, Pasaoglu G, Pardon N. Techno-economic assessment of an off-grid PV system for developing regions to provide electricity for basic domestic needs: a 2020–2040 scenario. Appl Energy 2016;176:309–19. [3] Su D, Jia Y, Huang X, Alva G, Tang Y, Fang G. Dynamic performance analysis of photovoltaic–thermal solar collector with dual channels for different fluids. Energy Convers Manage 2016;120:13–24. [4] Cai J, Ji J, Wang Y, Zhou F, Yu B. A novel PV/T-air dual source heat pump water heater system: dynamic simulation and performance characterization. Energy Convers Manage 2017;148:635–45. [5] Slimani M, Amirat M, Kurucz I, Bahria S, Hamidat A, Chaouch W. A Detailed thermal-electrical model of three photovoltaic/thermal (PV/T) hybrid air collectors and photovoltaic (PV) module: comparative study under Algiers climatic conditions. Energy Convers Manage 2017;133:458–76. [6] Abdelhamid M, Widyolar BK, Jiang L, Winston R, Yablonovitch E, Scranton G, et al. Novel double-stage high-concentrated solar hybrid photovoltaic/thermal (PV/T) collector with nonimaging optics and GaAs solar cells reflector. Appl Energy 2016;182:68–79. [7] Aste N, Giancarlo C. Design, development and performance monitoring of a photovoltaic-thermal (PVT) air collector. Renew Energy 2008;33:914–27. [8] Makki A, Omer S. Advancements in hybrid photovoltaic systems for enhanced solar cells performance. Renew Sustain Energy Rev 2015;41:658–84. [9] Browne MC, Norton B, McCormack. Phase change materials for photovoltaic thermal management. Renew Sustain Energy Rev 2015;47:762–82. [10] Notton G, Cristofari C, Mattei M, Poggi P. Modelling of a double-glass photovoltaic module using finite differences. Appl Therm Eng 2005;25:2854–77. [11] Hasanuzzaman M, Islam M. Global advancement of cooling technologies for PV systems: a review. Sol Energy 2016;137:25–45. [12] Tiwari S, Tiwari GN. Performance analysis of photovoltaic-thermal (PV/T) mixed mode greenhouse solar dryer. Sol Energy 2016;133:421–8. [13] Sahota L, Tiwari GN. Review on series connected photovoltaic thermal (PVT) systems: analytical and experimental studies. Sol Energy 2017;115:96–127. [14] Reddy SR, Ebadian MA. A review of PV/T systems: thermal management and efficiency with single phase cooling. Int J Heat Mass Transf 2015;91:861–71. [15] Koech RK, Ondieki HO, Tonui JK, Rotich SK. A steady state thermal model for photovoltaic/thermal (PV/T) system under various conditions. Int J Sci Technol Res 2012;1:1–5. [16] Maifi L, Chari A. Study and modelling of a photovoltaic thermal hybrid solar collector with cylindro-parabolic concentrator. Conference International des Energies Renouvelables Sousse 2013;2:2356–5608. [17] Mattia DR, Giorgio R. Dynamic thermal model for hybrid photovoltaic panels. Energy Proc 2015;81:345–53. [18] Annis NC. Performance analysis and modelling of hybrid photovoltaic-thermal solar panels. Doctoral Dissertations (2015). [19] Aste N, Fabrizio F. Design, modeling and performance monitoring of a photovoltaicthermal (PVT) water collector. Sol Energy 2015;112:85–99.
This study analyze the cost recovered years of a 1 kW PV and PV/T. The PV data are the statistical data of annual electricity generation provided by Bureau of Energy, Ministry of Economic Affairs, Taiwan. The PV system generates about 4499.64 MJ of electric energy in Taipei, Taiwan in a year. The experiment shows that the PV/T output electric power increase by about 5.5% as the module temperature decrease. The annual electricity generation is 4747.12 MJ and the heat energy generation is 8302.86 MJ, in comparison to the PV. There is no electric power output but there is heat energy generated. Afterwards, the productive capacity is converted to the cost of electricity and gas to analyze the cost recovered years of PV and PV/T systems. The cost recovered years for a PV is 6.857 and for a PV/T is only 2.302. The corresponding implementation cost for a PV and PV/T are 2000 and 2830 US dollars, respectively. At present, the warranty period of PV is 20 years, based on this study’s analysis of the PV and PV/T investment profit. As shown in Fig. 12, the PV/T construction cost is higher than PV by 41.67%, but the return on PV/T is faster than that on PV by 66.42%. When the warranty period is expired, the return on PV/T is higher than that on PV by 187.182%, so the PV/T has a better investment profit than PV. PV/T is the aggregate of the PV and solar energy water heater. The floor area of the PV and solar energy water heater modules is reduced, and the output efficiency is increased. In terms of a 1 kW PV/T, PV and solar energy water heater, the PV/T only needs a floor area 50% of the size required for the PV and solar energy water heater. The total energy production per unit area is higher than the two modules, as shown in Table 11. The PV/T has a better land use rate and energy conversion efficiency.
6. Conclusions This paper is devoted to dealing with the dynamic modeling, practical verification and energy benefit analysis of a photovoltaic and thermal composite module system. The conclusions are as follows: 480
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thermal systems. Sol Energy 2001;70(5):443–8. [28] Radziemska E. The effect of temperature on the power drop in crystalline silicon solar cells. Renew Energy 2013;28:1–12. [29] Pierrick H, Christophe M. Dynamic numerical model of a high efficiency PV/T collector integrated into a domestic hot water system. Sol Energy 2015;111:68–81. [30] Douglas T. Dynamic modeling and simulation of a solar-PV hybrid battery and hydrogen energy storage system. J Storage Mater 2016;7:104–14. [31] Yanqiu W, Jie J, Wei S. Experiment and simulation study on the optimization of the PV direct-coupled solar water heating system. Energy 2016;100:154–66. [32] Elarga H, Goia F. Thermal and electrical performance of an integrated PV-PCM system in double skin facades: a numerical study. Sol Energy 2016;136:112–24. [33] Burke TG, Schiller DR. Using pspice for electrical heat analysis. IEEE Potentials 2003;22:35–8. [34] Hasan H, Rashid M, Keerio J, Asad B. Simulation of combined photovoltaic, thermal & biogas hybrid system. Int J Electr Comput Sci IJECS-IJENS 2012;12(5):84–9. [35] Tiwari A, Sodha MS, Chandra A, Joshi JC. Performance evaluation of photovoltaic thermal solar air collector for composite climate of India. Sol Energy Mat Sol C 2006;90(2):175–89.
[20] Rejeb O, Sardarabadi M, Ménézo C, Passandideh-Fard M, Dhaou MH, Jemni A. Numerical and model validation of uncovered nanofluid sheet and tube type photovoltaic thermal solar system. Energy Convers Manage 2016;110:367–77. [21] Calise F, d’Accadia MD, Vanoli L. Design and dynamic simulation of a novel solar trigeneration system based on hybrid photovoltaic/thermal collectors (PVT). Energy Convers Manage 2012;60:214–55. [22] Gholami H, Khalilnejad A, Gharehpetian GB. Electrothermal performance and environmental effects of optimal photovoltaic-thermal system. Energy Convers Manage 2015;95:326–33. [23] Gholami H, Sarwat AI, Hosseinian H, Khalilnejad A. Evaluation of optimal dual axis concentrated photovoltaic thermal system with active ventilation using Frog Leap algorithm. Energy Convers Manage 2015;105:782–90. [24] www.newformenergy.com. Last access: September 23; 2017. [25] Lee YW, Kuo CFJ, Weng WH, Huang CY, Peng CY. Dynamic modeling and entity validation of a photovoltaic system. Appl Energy 2017;200:370–82. [26] Coventry JS, Lovegrove K. Development of an approach to compare the value of electrical and thermal output from a domestic PV/thermal system. Sol Energy 2003;75:63–72. [27] Huang BJ, Lin TH, Hung WC, Sun FS. Performance evaluation of solar photovoltaic/
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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Dynamic modeling, practical verification and energy benefit analysis of a photovoltaic and thermal composite module system
T
⁎
Chung-Feng Jeffrey Kuo , Yu-Wei Lee, Mega Lazuardi Umar, Pei-Chung Yang Department of Materials Science and Engineering, National Taiwan University of Science and Technology, Taipei 10607, Taiwan, ROC
A R T I C L E I N F O
A B S T R A C T
Keywords: Solar energy Photovoltaic and thermal module Dynamic modeling Solar energy saving efficiency Heat transfer
This study aims to derive the dynamic modeling of a photovoltaic and thermal composite (PV/T) module. The environmental factors including ambient temperature, wind speed and solar radiation are used as the input parameters, and the dynamic temperature of various layers inside the module can be simulated. Depending on the solar cell temperature, the dynamic electric power, electrical efficiency and daily average thermal storage efficiency can be obtained. The PV/T modeling accuracy is verified by a practical real module. The errors in electric power and electric efficiency are less than 2.5%, and the daily average thermal storage efficiency is less than 1.3%. At the same time, this study uses the built dynamic model to improve the output performance of the PV/T module. After the water flow rate is improved, the electric efficiency and electric power, and the daily average thermal storage efficiency are increased. The output performance of the PV/T module is ameliorated effectively. Finally, the comparison of the energy benefit analysis between photovoltaic (PV) and PV/T modules is discussed. The electric efficiency and daily average thermal storage efficiency are converted into energy saving efficiency. PV/T is more efficient than PV by 14.127%, its investment recovery period is lower than the PV by 4.5 years, and its profit recovery is higher than PV by 187.18%. Installing a PV/T can increase solar energy effectiveness effectively.
1. Introduction Solar power generation has been driven by cost reduction, economic incentives and the need for meeting growth in electricity demand while reducing reliance on fossil fuels [1]. As a renewable energy, solar energy is environmentally friendly, sustainable and inexhaustible. It has become more and more popular and important for both industrial and residential applications [2]. It is obvious that efficiently utilizing solar energy is an effective measure to solve energy and environmental issues [3]. PV technology has been recognized as an important way to realize sustainable development and carbon emission reduction. To facilitate the development of PV technology, raising the electrical efficiency and cutting down the manufacturing cost are essential for technological innovation. As the conversion efficiency of a PV cell descends with the rising operational temperature, removing excess heat from PV cells is the key for performance improvement [4]. The PV/T system combines both solar energy conversion processes: solar thermal conversion and solar photovoltaic conversion [5]. It enhances the energy performance of the PV, the thermal energy is removed and subsequently decreases the operating temperature of the solar cell. An effective means of
⁎
improving system performance has been proposed using a combination of PV devices and thermal collectors to produce both heat and electricity [6,7]. The possibility of the utilization of heat for climatization makes them attractive for building integration [8]. In these studies, the PV/T system, which can supply electricity and thermal energy simultaneously, has attracted much attention. The solar cell converting incident sunlight into electrical output, the range of photoelectric conversion efficiency in Standard Test Condition (STC) is 7 ∼ 40% according to the module type, and the rest of the incident light energy is converted into heat energy. The temperature increase of a solar cell caused by the accumulation of heat energy is the factor that influences the PV performance most severely. It not only reduces the electric power from the solar cell but also shortens the life cycle of the electric power [9]. According to STC and the Nominal Operating Cell Test (NOCT), the temperature coefficient of the electric efficiency of a crystalline silicon solar cell is −0.38%/°C, indicating that the electric efficiency decreases by 0.38% when the solar cell’s operating temperature rises by 1 °C [10,11]. Spontaneously, the solar cell temperature rise reduces the solar cell’s module outputs of electrical energy. However, research scholars regard heat energy as an auxiliary capacity other than solar cell module
Corresponding author. E-mail address: jeff[email protected] (C.-F. Jeffrey Kuo).
https://doi.org/10.1016/j.enconman.2017.11.036 Received 29 July 2017; Received in revised form 11 November 2017; Accepted 13 November 2017 0196-8904/ © 2017 Elsevier Ltd. All rights reserved.
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σ θ η
Nomenclature Symbols
A C G I L P q R T W c n ṁ k h
area (m2) thermal capacitance (J/K) solar radiation (W/m2) current (A) thickness (m) electric power (W) heat flow resistance (Ω) temperature change (K) wind speed (m/s) specific thermal capacitance (J/kg K) no. of heat collecting pipe mass flow rate (kg/s) thermal conductivity coefficient (W/m K) thermal convection coefficient (W/m K)
Subscripts
a s t w m + co g fg in mw pv ra cov con out act sim f i
Greek letters
α β ε ρ τ
Stefan-Boltzmann constant thermal resistance (K/W) efficiency
radiation absorption rate inclination angle (23°) radiation emission rate density (kg/m3) radiation transmittance
ambient atmosphere layer TPT water maximum top of glass layer heat collecting pipe short wavelength radiation glass layer heat collecting pipe inlet average water temperature solar cell heat radiation heat convection heat conduction heat collecting pipe outlet actual simulated final initial
MATLAB and TRNSYS. Two identical PV/T panels were tested alongside two PV panels to gather an electrical baseline for comparison. Aste and Fabrizio [19] provided the design of a covered PV/T collector made with thin film PV technology and a roll-bond flat plate absorber along with a simulation model developed through the elaboration of several mathematical equations, to evaluate the performance of covered PV/T water collectors. Rejeb et al. [20] proposed an experimental and numerical study to evaluate the performance of a PV/T nanofluid-based collector. The model was applied to predict the annual electrical and thermal output of the PV/T for three different countries: France, Iran and Tunisia. It was also found that the thermal and electrical energy output for Tunisia was higher than the others. Calise [21] presented the performance of PV/T from both energetic and economic points-of-view by means of a zero-dimensional transient simulation using TRNSYS. The economic results show that the system under investigation could be profitable. Gholami et al. [22] utilized an optimal sizing of a PV/T system for supplying the electricity and heat consumption of a household load for one year including the PV/T installation angle, electrical battery and thermal storage tank for supplying electrical and thermal loads. Gholami et al. [23] presented the design and optimization of a concentrated photovoltaic thermal system considering electrical, mechanical, and economic aspects. An active ventilation was used for absorbing the thermal power of radiation. From the above-mentioned literature reviews, models have been prepared that are able to reproduce the dynamic behavior of the PV/T panels representing a flexible tool for developing innovative and useradapted system control criteria in a global system optimization perspective. First, this study derives the dynamic modeling of PV/T. The heat transfer architecture resulting from each layer of PV/T is analyzed, and a thermal model is implemented according to the heat energy conservation law and lumped capacitance method. Afterwards, the thermal model is equivalently converted into a current circuit to get the thermal equivalent equation for each layer’s structure. Then, the simultaneous differential equation is computed by using the Simulink software tool. The dynamic temperature of each layer of PV/T is acquired by inputting
electrical energy [12] and have begun to study PV/T actively [13]. The PV/T development planning is combined with a solar energy heater and PV. A tube bank with cold water flowing inside is placed on the back side of the solar cell layer. The flowing cold water takes away the heat energy of the solar cell reducing the temperature of the solar cell to increase the output electrical energy, and the heat energy heats up the cold water to obtain a heat energy output. In comparison to two standalone systems, the PV/T has a higher overall output performance [14]. Some scholars in the previous studies have derived PV/T models to predict the output performance of a PV/T. Koech and Ondieki [15] built a steady state thermal model for a PV/T system under various conditions. A steady state thermal model of a PV/T air solar collector was developed, validated from experimental data and used to evaluate the effects of various parameters on the performance of the system. The results indicated that increasing the air mass flow rate when the design parameters are optimum will result in a significant increase in the overall performance of the system. Aste and Giancarlo [7] presented the experimental and theoretical results of research and development on the design, development and performance monitoring of a PV/T air collector. The simulation model predicted the thermal and electrical performance of a PV/T collector quite well. Maifi and Chari [16] illustrated the modeling of a photovoltaic thermal hybrid solar collector with a cylindro-parabolic concentrator. The influence of inlet parameters on the electrical and thermal performances of the collector, the parameters affecting the PV/T performance, such as the glazing, mass flow rate and temperature of the collector element and absorber impedance, and also the ratio of the compound parabolic concentrator’s design types were discussed. Mattia and Giorgio [17] derived a dynamic thermal model for hybrid photovoltaic panels. This model was used to describe a simplified numerical model to reproduce the shorttime dynamic behavior of the PV/T panel. The model has been validated using experimental data which were collected during outdoor tests conducted at the University of Genoa using a prototype realized by retrofitting a commercial PV collector. Annis [18] dealt with the performance analysis and modeling of hybrid photovoltaic-thermal solar panels. A PV/T panel was constructed, tested and modeled using both 471
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Power (W)
local environmental factors, and the dynamic electric efficiency, electric power and daily average storage efficiency are obtained. Second, this study implements a real PV/T to verify the PV/T dynamic modeling results to warranty the accuracy of the dynamic model. Finally, the structural parameters of PV are modified according to local environmental factors using the dynamic model to reach the optimal parameter design and output of PV/T. The advantages of PV/T compared with PV and a solar energy water heater will be analyzed as well. 2. PV/T description & related methodology 2.1. PV/T module and performance representation
Voltage (V) The PV/T generates electrical energy and heat energy at the same time. The structure is shown in Fig. 1 [24]. It is comprised of the PV, collecting plate, heat collecting pipe, isolation layer and shell [25]. The top down PV structure includes a cover plate, ethylene vinyl acetate (EVA), a solar cell, EVA and a tedlar/polyester/tedlar (TPT) backsheet. When the sun irradiates the PV, electrical energy output is generated but only some of incident sunlight is converted into current during irradiation. The other energy is converted into heat energy, accumulated in the PV so that the electrical efficiency of the solar cell decreases. In order to maintain the electrical efficiency of a PV, the PV/T uses the collecting plate on the back of the PV. The PV heat is conducted to the cold water in the heat collecting pipe rack for heat exchange, the operating temperature of the PV is reduced and the cold water absorbs the heat energy, becoming hot water. The hot water is stored. The performance index of PV/T is electric efficiency, electric power and storage thermal efficiency [26]. Electric efficiency [27]:
ηe =
P=
P GApv
∫ Vm Im dt
Fig. 2. The power drop of PV module at various solar cell temperatures [27].
ηe = ηstc [1−ϑ(Tpv−25)]
(3)
where ηstc is the measured efficiency under STC. This condition includes: solar radiation intensity (1000 W/m2), environmental temperature (25 °C) and mass of atmosphere (1.5). ϑ is the temperature coefficient of the solar cell (single crystal silicon cell used in this study), ηstc is 20.3% and Tpv is the temperature of the solar cell (°C). Thermal storage efficiency:The thermal storage efficiency ηth is the ratio of the total generated thermal energy to total solar radiation energy between the water outlet and inlet during the day.
̇ p (Tf −Ti ) mC
ηth =
(4)
GA
where ṁ is the water mass flow rate, Cp is the water specific thermal capacitance (4.18 kJ/kg K), Tf and Ti are the final temperature and initial temperature.
(1)
2.2. Heat transfer mechanism description Three fundamental forms of heat can flow from one substance to another: conduction, convection and radiation [29]. Heat flow is expressed as Eq. (5):
(2)
where P is the total output electric power within test time, Vm is the voltage at the maximum power point, Im is the current at the maximum power point, G is the solar radiation received by PV, and A is the area of PV/T. One of the important factors is the solar cell’s operating temperature. The reason for the temperature increase includes an increase in thermal lattice vibration, a decrease in the charge carrier’s mobility and the reduction of the p-n junction ability of the solar cell [28]. The relation between the solar cell temperature and electric power is shown in Fig. 2. The vertical axis represents the maximum power output, and the horizontal axis represents the maximum output voltage. The electric power of the solar cell declines obviously as the solar cell’s operating temperature rises [8]. The relationship between solar cell efficiency and the temperature of the solar cell is expressed as Eq. (3):
qx =
ΔT θ
(5)
where qx related to heat flow of conduction, convection, or radiation, ΔT is temperature different between two layer, and θ is thermal resistance. 2.2.1. Conduction and convection heat transfer For conduction and convection heat transfer [10], the thermal resistance for conduction is expressed as Eq. (6):
θcon =
L kA
(6)
where L is the thickness, k is thermal conductivity coefficient, and A is Fig. 1. PV/T structure [24].
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the area. While the thermal resistance for convection it is expressed as Eq. (7):
θcov = 1/(hforced + hfree ) A
Table 1 The equivalence system between thermal-electrical.
(7)
where hforced and hfree are the coefficients of forced and free convection [10]. In this study, convection in a windward condition is expressed as Eq. (8):
θcov = 1/(11.4 + 5.7W ) A
(8)
Thermal system
Electrical system
Change in temperature ΔT (K) Heat flow q (W) Thermal resistance θ (K/W) Thermal capacitance C (J/K) q*θ = ΔT
Voltage V (V) Current I (A) Resistant R (Ω) Capacitance C (F) I *R = V
q = Ct
where W is the wind speed from the ambient.
dT dt
I=C
dV dt
2.2.2. Heat radiation The heat radiation wavelength range is between 0.00001 nm and 1 mm. The heat radiation can be divided into short wavelength and long wavelength heat radiation [30,31]. 2.2.2.1. Short wavelength heat radiation. The sunlight’s wavelength range belongs to the short wavelength heat radiation classification which is less than 2500 nm. The short wavelength radiation heat flow can be obtained as shown in Eq. (9) [32].
Ig = αGA
(9)
where G is solar radiation, A is area, and the radiation absorption rate used in this study αfg is 0.5 and αpv is 0.9. 2.2.2.2. Long wavelength heat radiation. The long wavelength heat radiation heat flow is emitted between two body surfaces when the wavelength is longer than 2500 nm. This heat flow is expressed as Eq. (10):
q = (AεσTs4 )−(AεσT14 ) = Aεσ (Ts4−T14 )
(10)
where Ts and T1 are the surface temperature values of two bodies respectively, σ is Stevan-Bolztmann constant, β is the inclination angle of the PV/T, and the radiation emission rate ε of glass used in this study is 0.85. The heat radiation thermal resistance is expressed as Eq. (11):
1 θra = 1/ Aεσ (Ts2 + T12)(Ts + T1) (1 + cosβ ) 2
Fig. 3. The sectional view of PV/T.
between the thermal parameter and electrical parameter is shown in Table 1 [33].
(11)
3. Dynamic modeling of PV/T
Based on the heat flow as expressed in Eq. (5), the dynamic temperature can be obtained according to the thermal resistance and the temperature difference.
The structure configuration in the real PV/T is shown in Fig. 1. The sectional view is drawn as shown in Fig. 3. The heat transfer mechanism analysis is implemented for each layer’s structure to establish the thermal model. This thermal model is converted into the correspondingly equivalent electrical system. After that, the thermal equilibrium equation of each layer structure is used to obtain the simultaneous differential equation for PV/T dynamic model, simulated by Simulink. The ambient temperature, solar radiation and wind speed are the input parameters. Then, the dynamic temperature of each layer can be obtained. The electric power and daily average thermal storage efficiency are obtained according to the relationship between the temperatures of the water and solar cell.
2.3. Lumped thermal capacitance method The lumped thermal capacitance method applies the thermal energy conservation law to move the heat flows caused by different heat transfer mechanisms into heat capacity. The change per second or rate of change of the stored heat is equal to the net heat flow [31,19]. The thermal system is described by the differential equation:
C=
dT = qcon + qra + qcov + Ig dt
(12)
where C is the thermal capacitance, qcon is the heat flow of conduction, qra is the heat flow of radiation, qcov is heat flow of convection, and Ig is the heat flow of short wavelength heat radiation. Thermal capacitance is expressed as Eq. (13).
C = ρALc
3.1. Assumptions of the dynamic modeling The assumptions of the modeling are as follows: (1) The aluminum frame is mounted in the lateral region of the PV/T module whose area is very small compared with the top surface area. Therefore, the heat flow of the aluminum frame is neglected. (2) The module is exposed to the same environmental factors and each layer has uniform temperature distribution. Therefore, the temperature of each layer can be simulated accurately by one-dimensional analysis. (3) The heat conduction in the EVA layer can be neglected because its heat conduction coefficient is very low in comparison to the adhered structures in the module.
(13)
where ρ is the mass density, A is the area, L is the thickness, and c is the specific thermal capacitance. 2.4. Equivalence system between thermal model and electric loop The thermal model analysis was simplified according to heat transfer. The thermal model was converted into a current loop displayed in the circuit and computed. The equivalent transformation 473
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ρfg Afg Lfg cfg
dTfg dt
=
1 1 (T+−Tfg ) + (Tpv−Tfg ) R con,fg R con,pv
(16)
The solar cell layer (Tpv ):
ρpv Apv Lpv cpv
dTpv dt
= (Ipv−Epv )
1 1 (Tfg−Tpv ) + (Tt −Tpv ) R con,pv R con,t
(17)
where Ipv is the short wavelength radiation heat flow of the solar cell, Epv is the electric energy production when the solar cell receives short wavelength radiation as expressed in Eq. (18):
(Ipv−Epv ) = αpv τfg GApv
(18)
where the value of radiation absorption rate αpv used in this study is 0.9, and radiation transmittance τfg is 0.95.The TPT layer (Tt ):
ρt At Lt ct
dTt 1 1 = (Tpv−Tt ) + (Tco−Tt ) dt R con,t R con,co
(19)
The heat collecting pipe (Tco):
ρco Aco Lco cco
dTco 1 1 = (Tt −Tco) + (Tmw−Tco) dt R con,co R con,w
(20)
The water inside the heat collecting pipe (Tmw)
nρw Aw L w c w
Fig. 4. Heat transfer mechanism of PV/T.
R cov,w = m w ρw Aw L w c w
The heat transfer mechanism analysis diagram for PV/T after considering the assumptions is shown in Fig. 4. The heat transfer mechanism received by the external module is the heat convection resulting from the ambient temperature, wind speed and heat radiation including long wavelength and short wavelength radiation. The glass transmits the short wavelength radiation to the solar cell, so the solar cell layer has a heat radiation mechanism. The contact between the layer structures inside the module belongs to the heat conduction mechanism, while the heat flow generated by the heat transfer mechanism results from the thermal resistance and temperature difference in each layer.
(22)
The mass flow rate ṁ used in this study is 0.07 (kg/s), Tin−Tout is 6 °C, and the number of pipe n is 10. After the thermal balance equation of each layer of PV/T is established, the simultaneous differential equation can be established using the Simulink. The numerical values of thermal model input parameters for each layer are shown in Table 2, and the flowchart of PV/T simulation is shown in Fig. 5. 4. Experimental planning & simulation This study implements the PV/T dynamic model in order to predict the electric efficiency, electric power and daily thermal storage efficiency. A true PV/T is set up to identify its dynamic model. For the sake of getting the optimum structural and corresponding output performances for a PV/T design, the structural parameters of PV/T are modified according to its dynamic model. The advantages of installing PV/T will be analyzed as well.
3.3. Set up of the differential equations for each layer The thermal model of PV/T is decomposed for analysis according to each layer’s structure. The thermal model is then converted into the electrical system, layer by layer. From Fig. 4, using the Kirchhoff circuit law, the thermal balance equation for each layer can be obtained as:At the top of the glass layer (T+):
4.1. The PV/T real entity implementation
dT+ 1 1 1 = Ig + (Ta−T+) + (Ts−T+) + (Ts−T+) dt R cov, + Rra ,+ R con,fg
The real PV/T is located in the National Taiwan University of Science and Technology, Taipei, Taiwan. This PV/T model comes from BenQ Corporation: Sun Forte-Mono 203, PM-096B00, 330 W and 200 liter water tank. The real entity is shown in Fig. 6. The test is from 05:00 AM to 06:00 PM every day. The ambient temperature, wind speed, solar radiation, water pipe outlet and inlet temperature are measured by a heliograph, weather station and thermal couple. The electric power is extracted by DC electric loading.
(14) where Ts is the temperature of the sky [20] as expressed in Eq. (15):
Ts = 0.0552Ta1.5
(21)
where R cov,w is expressed in Eq. (22):
3.2. Heat transfer mechanism and thermal model implementation
ρfg Afg Lfg cfg
dTmw 1 1 = (Tco−Tmw ) + (Tout −Tin−Tmw ) dt R con,w R cov,w
(15)
The glass layer (Tfg ): Table 2 Numerical value parameters for each layer. Parameter 3
ρ density (kg/m ) A area (m2) L thickness (m) c specific thermal capacitance (J/kg K) k thermal conductivity coefficient (W/m K)
Glass (fg)
Solar cell (pv)
TPT (t)
Heat collecting pipe (co)
Water (w)
3000 1.6307 0.003 500 1.1
2330 1.6307 0.0003 677 130
1200 1.6307 0.0005 1250 0.033
8920 1.6307 0.003 (heat collecting plate) +0.0127 (rad = 1/2″) 385 401
1000 0.1328 pipe length * (rad = 1/2″) 0.0127 (rad = 1/2″) 4200 0.6
474
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Fig. 5. Flowchart of PV/T simulation.
These environmental factors are the inputs for the PV/T dynamic model to get the temperature of each layer as shown in Fig. 8. When the sunshine amount and ambient temperature increase hourly in the daytime, the PV cell temperature will be risen distinctly. The water flowing in the heat collecting pipes will take the PV cell heat energy away, and the rise of the PV cell temperature is suppressed effectively. The higher electrical efficiency and thermal storage efficiency will be provided. There is no incident sunlight at night. The rise in PV cell temperature does not influence the electrical efficiency but the thermal storage efficiency will be increased. When the dynamic temperature of the solar cell is obtained by PV/T dynamic model, the dynamic electric power can be obtained from Eq. (2). In order to verify the accuracy of the PV/T dynamic model, the comparison of the electric power between the dynamic model and real entity is shown in Fig. 9. The hourly electrical efficiency can be obtained from the solar radiation and module area. Its comparison between the dynamic model
4.2. Simulation results and verification This study selected three days in spring, summer, autumn and winter respectively, for simulation and real experimentation on the performance of the dynamic model for a PV/T. First, the dynamic temperature of each layer is acquired from the dynamic model. Then, the electric efficiency, electric power and daily average thermal storage efficiency are obtained. This information is compared with the real PV/ T to verify the prediction accuracy of the dynamic model.
4.2.1. Day based experiment For the day based experiment, the model simulation and practical validation were implemented on summer, 2016/06/15. Fig. 7 was the line chart of environmental factors on the day. It was a sunny day, a few black clouds. The sunshine amount changed steadily from 0.116 W/m2 at 05:00 AM to 935.416 W/m2 at 12:00 noon hourly, and then decreased to 73.151 W/m2 at 06:00 PM hourly. 475
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applicable to predict the electric efficiency, thermal storage energy, and electric power of a PV/T accurately. 4.2.2. Season-based experiment This study selected three days in spring, summer, autumn and winter respectively, for theoretical simulation and real experimentation on the dynamic model performance of a PV/T. The comparison is shown in Table 4. From Tables 3 and 4, the accuracy of the dynamic model could be verified. It can be seen that the dynamic model can simulate the temperature of a solar cell effectively when the environmental factors change slowly. The experiment shows that this dynamic model is useful to any place under any weather conditions, predicting the electrical efficiency, thermal storage efficiency and output electric power of a PV/ T accurately. 4.3. PV/T dynamic modeling innovation In order to simulate the output performance of PV/T, some references have been derived PV/T dynamic modeling. However, the previous studies did not take into account all the factors which could cause PV/T temperature change. The nominal operating cell temperature (NOCT) will be applied in this study to compare the accuracy of the solar cell temperature with that in the previous studies as shown in Table 5. The temperature of a solar cell is tested under NOCT conditions (solar radiation 800 W/m2, wind speed 1 m/s and ambient temperature 20 °C). Koech [15] built the dynamic modeling of PV/T, but different thermal inertias of various structures were not considered, so the error between the entity and dynamic modeling was 6.81 °C in NOCT verification. Hasan et al. [34] did not consider the difference between the heat convection transfer mechanisms received by the front and back sides of the PV/T. The same heat convection empirical value was used to calculate the heat convection coefficient on the front and back sides of the PV/T, so that the error between the entity and dynamic modeling was 6.24 °C in NOCT verification. Maifi and Chari [16] did not consider the concept of the heat flow heat energy conservation law. The heat flow could not flow completely in the heat capacity, so the heat flow was lost. The error result between the entity and dynamic modeling was 4.87 °C in NOCT verification. Mattia [17] calculated the heat convection coefficient and indicated that the intermediate current of heat
Fig. 6. PV/T real entity.
and real entity is shown in Fig. 10. The electric power absolute error percentage is 2.272% as calculated by Eq. (23):
|Psim−Pact | ∗100% Pact
(23)
In order to calculate thermal storage efficiency, the thermocouple is placed at the water outlet and inlet of the real PV/T to measure the water outlet and inlet temperatures. The daily average thermal storage efficiency can be obtained from Eq. (4) as shown in Fig. 11. The simulated and actual daily average thermal storage efficiency are 1.699% and 2.003%, respectively. The difference is 0.304%. This study also select 2016/06/14 and 2016/07/01 for summer dynamic model validation, the absolute error percentages of electric power and entity validation are 3.334% and 1.845%, respectively. For daily average thermal storage efficiency, the difference between simulated and actual value is shown in Table 3. The increase of the mean absolute error for electric power is due to high sunshine amount in the summer. The prediction accuracy of the PV cell temperature is better when the environmental factors change slowly. According to practical validation, the dynamic model is
Temperature ( C) Wind Speed (m/s) 2 Radiation/10 (W/m )
100
80
60
40
20
0
04:0 0
08:0 0
12:0 0
16:0 0
20:0 0
Time (hours) 476
24:00
Fig. 7. 2016/06/15 environmental factors.
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80 T+ Tfg Tpv Tt Tco Tmw
70
Fig. 8. The temperature simulation results from the dynamic modeling.
Temperature ( C)
60
50
40
30
20
04:00
08:00
12:00
16:00
20:00
300
24:00
Fig. 9. Hourly electrical power of PV/T.
Simulated Actual
250
Power (W)
200
150
100
50
0 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00
Time (hours)
is 1.57 °C in NOCT verification. This dynamic modeling can simulate effectively and make theoretical simulation precise.
convection had a slight effect on the PV/T temperature variation. It could be neglected, so the error between the entity and dynamic modeling was 4.43 °C in NOCT verification. Annis [18] indicated that the arrangement mode and quantity of heat collecting pipes in the PV/T did not influence the temperature of each layer’s structure in the PV/T. Therefore, in the analysis of the heat transfer mechanism, the influence of quantity and arrangement mode of the heat collecting pipes was neglected. The error between the entity and dynamic modeling was 4.07 °C in NOCT verification. Aste [19] neglected the least influential thermal radiation mechanism in the heat transfer mechanism, so that the heat transfer mechanism analysis was incomplete. The error between the entity and dynamic modeling was 3.29 °C in NOCT verification. In order to build the PV/T dynamic modeling effectively and make the theoretical simulation precise, this study considers all heat transfer mechanisms which includes heat conduction, convection and radiation. The experience value of the thermal convection coefficient is adopted from literature and theoretical discussion. The solar cell temperature error between the real entity and dynamic modeling built in this study
4.4. PV/T optimal structural design The dynamic model implemented in this study can not only predict the performance of PV/T, but also improve the output performance by modifying the internal structural parameters. The performance simulation in the four seasons from the dynamic model are shown in Table 6. It can be seen that when the ambient temperature and solar radiation are high and the wind speed is low in summer, the solar cell temperature rise. The corresponding electrical power and the thermal storage efficiency are lower than for other seasons. Therefore, the summer will be selected to design new structural parameters in order to get higher electrical power and thermal storage efficiency. Tiwari and Sodha [35] presented the numerical model of PV/T and found that the water flow rate was the first factor influencing the output performance of the PV/T. In this paper, 0.07 kg/s m2 was taken as the maximum value reduced by 0.02 kg/s m2. The optimum water flow rate 477
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Simulated Actual
24
Fig. 10. Hourly electrical efficiency of PV/T.
Electrical Efficiency (%)
22 20 18 16 14 12 10
5:00
6:00
7:00
8:00
9:00 10 :00 11 :00 12 :00 13 :00 14 :00 15:00 16:00 17 :00 18:00
Time (hours)
is obtained by dynamic model, as shown in Table 7. It is observed that the water flows fast when the water flow rate is high. The heat energy cannot be absorbed effectively, so the electric efficiency and thermal storage efficiency decrease. When the water flow rate is low, the water transfers the heat energy to the solar cell again. The temperature rises, the electric efficiency decreases and the thermal storage efficiency rises. The optimal water flow rate is 0.05 kg/s m2 in summer, not only increasing thermal storage efficiency but also increasing electrical efficiency. In other words, the performance is predicted by the dynamic model. The optimum parameter design for PV/T can be obtained to perform the maximum advantage for solar energy.
Table 3 Comparison of daily average thermal storage between dynamic model and real entity. Date
Dynamic model (%)
Real entity (%)
Difference (%)
2016/06/14 2016/07/01
0.167 5.691
0.774 6.183
−0.607 −0.492
Table 4 The dynamic model identification from four seasons.
5. Benefit analysis The output performance index of PV/T is electric efficiency and thermal storage efficiency. They cannot be compared directly for different output energy forms. The electrical energy performance evaluation will be applied in this study to compare the electrical energy performance of PV and PV/T. The energy-saving efficiency is applied to justify what kind of solar cell module can perform the maximum
Daily average error
Spring
Summer
Autumn
Winter
Daily average power absolute error (%) Daily average thermal storage efficiency difference (%)
1.429 −0.382
2.483 −1.201
2.32 −0.672
0.399 −0.467
advantage in solar energy technology. Finally, the cost recovered years, return on investment and floor area of PV and PV/T are analyzed to evaluate the performance of the PV and PV/T at the location.
Simulated Actual
4
Heat storage efficiency (%)
3
2
1
0
-1
-2 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00
Time (hours) 478
Fig. 11. Hourly thermal storage efficiency of PV/T.
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Table 5 Dynamic modeling accuracy comparison. Previous study
Electric power efficiency absolute error (%)
Daily average storage efficiency absolute error (%)
Actual NOTC (°C)
Simulated NOTC (°C)
Difference (°C)
Koech and Ondieki [15] Hasan et al. [34] Maifi [16] Mattia [17] Annis [18] Aste [19] This study
6.143 5.876 4.981 4.546 3.286 3.511 1.657
3.964 3.619 2.764 2.173 1.696 1.727 0.68
42 40 37 37 34 37 37
35.19 33.76 32.13 32.57 29.93 33.71 35.43
6.81 6.24 4.87 4.43 4.07 3.29 1.57
5.1. Electrical energy performance evaluation
Table 6 Four seasons simulation from PV/T dynamic model. Season
Daily average electrical efficiency (%)
Daily average thermal storage efficiency (%)
Autumn Winter Spring Summer
18.85 20.80 19.58 18.38
3.161 1.003 6.874 1.669
The electrical energy performance evaluation is used to compare the output electrical energy performance of PV and PV/T in the four seasons. The electrical energy performance evaluation is the ratio of the solar cell module output electric power (P) divided by the product of the electrical rating power (Pn ) and solar radiation (G) called the electric power performance ratio (PR) and expressed as Eq. (24).
PR = Table 7 The performance improvement of the PV/T. Water flow rate (kg/s m2)
Daily average electrical efficiency (%)
Daily average thermal storage efficiency (%)
0.03 0.05 0.07
17.97 18.64 18.38
4.543 2.765 1.699
PR of PV (%)
PR of PV/T (%)
Autumn Winter Spring Summer
92.39 102.28 93.6 83.55
91.91 102.44 95.04 88.16
(24)
This study implemented electrical energy performance for PV and PV/T on the same location, day and environmental factors in four seasons. The evaluations of electrical energy performance for the PV and PV/T are obtained and the performance ratios are averaged, as shown in Table 8. The statistical results show that the environmental factors in autumn cause heat exchange between the water in the PV/T and the solar cell. High water temperatures transfer the heat energy to the solar cell again, so that the PV/T’s electrical power is a little lower than that of the PV. For the low ambient temperatures and high wind speeds in winter, the solar cell module performance can be performed effectively. In spring and summer, the ambient temperature is high, the wind speed is low and the amount of sunshine is great. The water flow in the PV/T can take the solar cell heat energy away effectively, so as to reduce the PV temperature to increase the electrical power, so the PV/T is better than the PV.
Table 8 Comparison of electric power performance ratio (PR) for four seasons. Season
P G ∗Pn 1000
5.2. Energy-saving efficiency evaluation Table 9 Comparison of energy-saving efficiency between PV and PV/T. Season
PV energy-saving efficiency (%)
PV/T energy-saving efficiency (%)
Autumn Winter Spring Summer
50.394 54.786 51.178 46.263
52.832 55.739 58.408 50.088
The overall efficiency of PV/T is the sum of the electric efficiency and thermal storage efficiency. The two types of solar cell modules cannot be compared by the different energy forms of the output performance index [26]. Therefore, the energy-saving efficiency evaluation is used for comparison [17]. As the electric energy is a high-level energy converted from heat energy, the electric efficiency must be divided by the electric efficiency of fossil fuel (38%) plus the thermal storage efficiency to obtain the energy-saving efficiency Ef (%), expressed in Eq. (25), as shown in Table 9.
Table 10 PV and PV/T specifications.
Ef = ηth + Parameter
PV
Test time Location PV type PV efficiency Module size Material of heat collecting plate Size of heat collecting pipe No. of heat collecting pipe Capacity of water storage tank Mass flow rate Cycling temperature Angle of inclination Azimuth
05:00 ∼ 18:00 Da An District, Taipei Monocrystalline silicon 20.3% 1.559 m * 1.046 m / / / / / / 23° South
PV/T
ηe 38%
(25)
Whatever the environmental factors are, the PV/T can perform energy-saving efficiency better than PV, so the dynamic model can judge PV/T to be suitable for the site according to local environmental factors and the prediction of output performance. Copper 1/2 in. 10 Pieces 200 L 0.07 kg/s 6 °C 23° South
5.3. Cost recovered years, return on investment and floor area analysis The cost recovered years, return on investment and floor area will be analyzed to evaluate the performance of PV and PV/T. For the analysis of cost recovered years, the difference between PV and PV/T specifications in electricity generation and thermal storage capacity shall be given, as shown in Table 10. 479
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12000
(1) This study considers all heat transfer mechanisms which include heat conduction, convection and radiation. The heat energy balance law of the heat transfer and heat capacity method are combined to derive the dynamic model of a PV/T. The accuracy of this dynamic modeling has been proven by the real entity showing that the electrical efficiency and electric power error is less than 2.5%, and the daily thermal storage efficiency error is less than 1.3%. The solar cell temperature error in NOCT verification is 1.57 °C. (2) The dynamic model of PV/T is applied to enhance the output performance. After the water flow rate is improved, the electrical efficiency and thermal storage efficiency are increased by 1.397% and 62.742%, respectively. The PV/T output performance is improved effectively. (3) The PV/T can perform energy-saving efficiency better than the PV. The cost recovered years of a PV is 6.857, and that of a PV/T is only 2.302. Based on the warranty period of PV of 20 years, the return on PV/T is higher than that of PV by 187.182%. In addition, a PV/T only needs a floor area 50% smaller than that of a PV and solar energy water heater. The installation of a PV/T can create the greatest investment benefit among the solar energy modules.
10000
PV/T
8000
USD
6000 4000
PV
2000 0 -2000 -4000
0
5
10
15
20
Duration (Years) Fig. 12. Investment profit analysis.
Table 11 Comparison of total energy production per unit area.
Acknowledgment
Energy
Floor area (m2/ 1 kW)
Electric energy per unit area (MJ/m2/year)
Heat energy per unit area (MJ/m2/ year)
Total energy production per unit area (MJ/m2/year)
PV Water heater PV/T
11.26 11.26 11.26
399.61 / 421.59
/ 695.89 737.37
399.61 695.89 1158.96
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This study analyze the cost recovered years of a 1 kW PV and PV/T. The PV data are the statistical data of annual electricity generation provided by Bureau of Energy, Ministry of Economic Affairs, Taiwan. The PV system generates about 4499.64 MJ of electric energy in Taipei, Taiwan in a year. The experiment shows that the PV/T output electric power increase by about 5.5% as the module temperature decrease. The annual electricity generation is 4747.12 MJ and the heat energy generation is 8302.86 MJ, in comparison to the PV. There is no electric power output but there is heat energy generated. Afterwards, the productive capacity is converted to the cost of electricity and gas to analyze the cost recovered years of PV and PV/T systems. The cost recovered years for a PV is 6.857 and for a PV/T is only 2.302. The corresponding implementation cost for a PV and PV/T are 2000 and 2830 US dollars, respectively. At present, the warranty period of PV is 20 years, based on this study’s analysis of the PV and PV/T investment profit. As shown in Fig. 12, the PV/T construction cost is higher than PV by 41.67%, but the return on PV/T is faster than that on PV by 66.42%. When the warranty period is expired, the return on PV/T is higher than that on PV by 187.182%, so the PV/T has a better investment profit than PV. PV/T is the aggregate of the PV and solar energy water heater. The floor area of the PV and solar energy water heater modules is reduced, and the output efficiency is increased. In terms of a 1 kW PV/T, PV and solar energy water heater, the PV/T only needs a floor area 50% of the size required for the PV and solar energy water heater. The total energy production per unit area is higher than the two modules, as shown in Table 11. The PV/T has a better land use rate and energy conversion efficiency.
6. Conclusions This paper is devoted to dealing with the dynamic modeling, practical verification and energy benefit analysis of a photovoltaic and thermal composite module system. The conclusions are as follows: 480
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