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Effects of mounting geometries on photovoltaic module performance using CFD and single-diode model
Available online at www.sciencedirect.com
ScienceDirect Solar Energy 103 (2014) 541–549 www.elsevier.com/locate/solener
Effects of mounting geometries on photovoltaic module performance using CFD and single-diode model Wei Xing a,c, Jianqiu Zhou a,b,⇑, Zhiqiang Feng d a
Department of Mechanical Engineering, Nanjing University of Technology, Nanjing, Jiangsu Province 210009, China b Department of Mechanical Engineering, Wuhan Institute of Technology, Wuhan, Hubei Province 430070, China c Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA d State Key Laboratory of PV Science and Technology, Trina Solar Limited Company, Changzhou, Jiangsu Province 213031, China Received 29 September 2013; received in revised form 20 February 2014; accepted 22 February 2014
Communicated by: Associate Editor G.N. Tiwari
Abstract The performance of a photovoltaic module under operating conditions mainly depends on two factors: solar irradiation and cell temperature. These two factors are strongly influenced by mounting geometrical parameters. This paper studies the effects of mounting parameters on photovoltaic (PV) module performance by using CFD and single diode model. The results show that maximum power output happens at the tilt angle where the incoming solar irradiation reaches the peak value. The relationship between efficiency and tilt angle acts differently based on wind velocity inside the gap. The air gap height, the distance between the module and roof, determines the heat transfer mechanism inside the air gap and then greatly affects the module performance. When the flow inside the air gap becomes fully developed, both the module power output and efficiency reach the greatest value. The result of this study provides theoretical basis to design mounting parameter for PV module installation and helps maximize energy efficiency in practical operating condition. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: Solar energy; PV module; CFD; Single diode model
1. Introduction Photovoltaic (PV) technology, which directly transfers solar irradiation to electrical energy, has been widely used in residential and commercial applications with an increasing rate about 25% in market growth over the last decade (Parida et al., 2011; Hoffmann, 2006). PV systems are generally used in buildings (known as building integrated PV systems), transport and agriculture applications (Tiwari, 2002). Beside electrical power generation, PV systems are ⇑ Corresponding author at: Department of Mechanical Engineering, Nanjing University of Technology, Nanjing, Jiangsu Province 210009, China. Tel.: +86 25 83588706; fax: +86 25 83374190. E-mail address: [email protected] (J. Zhou).
http://dx.doi.org/10.1016/j.solener.2014.02.032 0038-092X/Ó 2014 Elsevier Ltd. All rights reserved.
always coupled with thermal application, such as air/water heating. These applications and their energy/cost analysis are comprehensively summarized and reviewed. (Tiwari et al., 2011) The actual performance of a PV module under operating condition is primarily influenced by two factors: the solar irradiation on the module and the cell temperature (Nakamura et al., 2001). Thermodynamically, the solar irradiation acts as the availability, while the cell temperature affects the module efficiency. Specifically, the incoming solar energy is the maximum amount of energy that could be transferred into electrical energy and the cell temperature determines the percentage of energy transferred. As the cell temperature rises, the module efficiency drops considerably. This is due to the characteristic
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Nomenclature A – Cp h G g I Ki Kv k – Ns P q – Rs Rp T u V v – a b
area (m2) ideality factor for solar cell specific heat (J/kg K) air gap height (mm) solar irradiation (W/m2) gravitational acceleration (m/s2) current (A) temperature coefficient of short circuit current (%/°C) temperature coefficient of open circuit voltage (%/°C) thermal conductivity (W/m K) Boltzmann’s constant (J/K) number of cells linked in series power (W) heat flux (W/m2) charge of electron (C) equivalent series resistance (X) equivalent parallel resistance (X) temperature (K) fluid velocity on x direction (m/s) voltage (V) wind velocity inside the air gap (m/s) fluid velocity on y direction (m/s) thermal diffusivity (m2/s) expansion coefficient
of the cell material. The efficiency of a commercial PV module is usually between 10% and 15%, depending on the operating condition (Kumar and Rosen, 2011). Thus, even 1% of efficiency drop could lay great influence on the overall performance. It has to be noted that for PV/ thermal system, the overall energy efficiency (electrical and thermal efficiency) could be much higher. Due to the advancement in heat transfer, some PV/T system could reach 26.7% efficiency (Agrawal and Tiwari, 2011). Mounting parameters, such as tilt angle and the distance between the module and roof, the air gap height, determine solar irradiance, heat transfer mechanism and solar cell temperature. By changing the tilt angle, the angle between the PV panel and incoming solar radiation changes, in turn, the energy received by the panel changes. It is obviously that the maximum amount of incoming solar energy occurs when the PV module is normal to the sun radiation. The air gap height and tilt angle form the flow passage for air to flow between the module and rooftop. The geometry of this flow pattern determines the heat transfer mechanism between the PV module and rooftop and the module temperature. As described earlier, the mounting parameters could determine the module performance. To study the role of mounting parameters on the PV module performance,
h q l k e g
PV module tilt angle (degree) density (kg/m3) viscosity (kg/m s) absorption coefficient (lm) emissivity efficiency (%)
Subscripts a ambient rad radiation mpp maximum power point n nominal (value under standard testing condition) ph photo-generated sat saturation OC open circuit SC short circuit v voltage i current Abbreviations PV photovoltaic STC standard testing condition CFD computational fluid dynamics DO discrete coordinates
knowledge of both heat transfer and electrics is required. Previous researches focusing on the thermal characteristics and electrical modeling have been carried separately (Skoplaki and Palyvos, 2009; Sahina et al., 2007; Walker, 2001; Gow and Manning, 1999; Sahin et al., 2007). Several studies considered both thermal and electrical factors and used numerical and/or experimental approaches to determine the module performance. Skoplaki et al. proposed a simple correlation for PV temperature under arbitrary mounting conditions and introduced a dimensionless mounting parameter to deliver the correlation for more applications (Skoplaki et al., 2008). Hiraoka et al. conducted a one-year experiment studied the tilt angle dependence of PV modules comprising of different types of solar cells (Hiraoka et al., 2003). Experimental data from various testing sites were also analyzed statistically (Koehl et al., 2011). Research concerning the metrology and PV module performance relationship was conducted by Katsumata et al. (2011). Kim et al. (2011) studied the role of ambient temperature on the performance of a PV module with the ranging of ambient temperature from 25 °C to 50 °C. They also simulated the situation when fins are attached to a PV module. Wilson and Paul (Wilson and Paul, 2011) studied the role of the
W. Xing et al. / Solar Energy 103 (2014) 541–549
mounting parameters on cell temperature and efficiency using CFD. The CFD model shows great accuracy and reasonable computation time. However, they did not take the variation of solar irradiation into account and actual power output is beyond their research scale. Usama Siddiqui et al. (2012) developed a three dimensional thermal model to predict the thermal performance of PV module under varying conditions i.e. different ambient temperature and irradiation. Their study was coupled with the single diode, five-parameter model. They also studied the influence of module performance with and without cooling system. However, few studies combined CFD approach and PV electric modeling to investigate the role of mounting parameters on electric output, considering both the incoming solar irradiance and the efficiency variation due to temperature rise. The goal of this study is to evaluate the PV module performance under different mounting geometries which are similar to practical operating condition. To do this, CFD method is first invoked to get the temperature of the solar cell, incorporating different mounting conditions, and then an equivalent circuit model, the single diode, five-parameter model, is then applied to evaluate the module performance. The PV module evaluated in this paper is TSM-270DC05A/ 05A.08 (monocrystalline silicon cells).
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Fig. 1. Ways of radiation on a PV module.
2. Methodology and models 2.1. Methodology In order to investigate the role of mounting parameters on the PV module performance, tools of heat transfer and equivalent circuits are required. The methodology used in this study is the coupling of solar irradiation model, CFD model and equivalent circuit model. The solar irradiation model establishes the relationship between the incoming solar energy and the tilt angle. The CFD model evaluates the effects of mounting parameters on the cell temperature from a heat transfer prospective. The CFD model is executed by FLUENT. The last step is to input the cell temperature and solar irradiation data to the equivalent circuit model to evaluate the PV module performance. The circuit model is run by MATLAB. Following are the descriptions of the three models. 2.2. Simplified solar irradiation model To reach the PV module, sunlight has to travel through the atmosphere, where direct radiation, ground-reflected radiation and sky diffuse radiation caused by air molecules, dust, drops and ice crystals might happen (Fig. 1) Rekioua and Matagne, 2012. In this study, we ignore the groundreflected radiation and sky diffuse radiation and assume the direct radiation is the only source of input energy and only depends on the tilt angle (Fig. 2). The input solar irradiation reaches the maximum value, 1000 W/m2, when the tilt reaches 30°. The solar irradiation at other tilt angles can be found using Eq. (1) based on the geometrical parameters
Fig. 2. Simplified direct radiation model.
shown in Fig. 2. Corresponding results are shown in Table 1. Gnormal ¼ Gincident cosð30 aÞ
ð1Þ
As shown in Table 1, the input solar energy increases from 0° to 30° tilt angle, then decreases with the tilt angle increase. 2.3. Description of CFD modeling 2.3.1. Basic theories and fundamental equations The idealized energy balance of a PV module is shown in Fig. 3. In this case, the input source is the solar irradiation and the output is the generated electrical power, meanwhile, heat can be lost from both the front and rear side of the panel. In this study, we assume that 30% of the total input solar energy has been lost from the back side of the panel. In the air gap, conduction, radiation, natural and forced convection take place. We also assume the heat
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Table 1 Radiation value at different tilt angles. Tilt angle (degree)
Solar irradiation (W/m2)
Heat diffuse in the air gap (W/m2)
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90
866 906 940 966 985 996 1000 996 985 966 940 906 866 819 766 707 643 574 500
259.8 271.8 282 289.8 295.5 298.8 300 298.8 295.5 289.8 282 271.8 259.8 245.7 229.8 212.1 192.9 172.2 150
observations (Kurnik et al., 2011). Operational parameters, such as wind speed and temperature difference between PV cell and ambient, were controlled as inputs. Wilson and Paul (2011) studied the role of the mounting parameters on cell temperature and corresponding efficiency using CFD. In this study, mounting parameters, such as tilting angle and air gap size and wind velocity inside the air gap, were controlled (Fig. 4). The CFD model was then verified by the experimental data from Trinuruk (Trinuruk et al., 2006). However, the study did not take into consideration the variation of solar irradiance induced by tilt angle change. In this study, we will generally follow their model and include the solar irradiation variation resulted from change of tilt angle. In this study, we use the TSM270DC05A PV module, the specification is shown in Table 2 (http://www.trinasolar.com/cn/product/Mo_Honey.html.). In the modeling process, mesh size is chosen to be 350 70 with successive ratio of 1.02 and 1.2, respectively. The mesh interval number of the short side changes proportionally with the air gap height. The ambient temperature is set to be 298 K. We also assume the wind velocity to be 0.5 m/s at the air gap inlet and the rooftop is insulated. Since radiation heat transfer inside the gap plays an important role in the overall heat transfer (Moshfegh and Sandberg, 1998), the Discrete Ordinates (DO) model is invoked. The solver is set to be 2D, steady state, pressured based (PRESTO!). The momentum and energy
Fig. 3. Idealized energy balance for a PV module.
transfer is based on a two dimensional scenario. The fundamental equations of continuity, momentum and energy are listed below @u @v þ ¼0 @x @y
ð2Þ Fig. 4. Sketch for CFD modeling.
u
2
2
@u @u 1 @p @ u @ u þv ¼ þ þ þ gbðT TaÞ cos h @x @y q @x @x2 @y 2 ð3Þ
u
2
2
@v @v 1 @p @ v @ v þv ¼ þ þ þ gbðT TaÞ sin h @x @y q @y @x2 @y 2 ð4Þ
2 @T @T @ T @2T u þv ¼a þ r qrad @x @y @x2 @y 2
ð5Þ
2.3.2. CFD modeling Kurnik et al. studied the effects of different mounting conditions (open rack and roof integrated) using well-established energy balance model, based on their experimental
Table 2 TSM-270DC05A/0.5A.08 Specification datasheet (Incropera and DeWitt, 1996). Characteristics
Specifications
Cell type Dimensions (mm) Maximum power, Pmpp (W) Maximum power voltage, Vmpp (V) Maximum power current, Impp (A) Open circuit voltage, VOC (V) Short circuit current, ISC (A) Number of cells, Ns Module efficiency, g (%) Temperature coefficient of VOC, Kv (%/°C) Temperature coefficient of ISC, Ki (%/°C) Nominal operating cell temperature
Monocrystalline silicon 1650 992 35 270 30.8 8.77 38.6 9.23 60 16.5 0.32 0.053 44 °C (±2 °C)
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Table 3 Material properties (Trinuruk et al., 2006). Material
Density, q (kg/m3)
Specific heat, Cp (J/kg K)
Thermal conductivity, k (W/m K)
Radiation emissivity, e
Tedlar Concrete
1475 1444
1130 1229
0.14 0.5868
0.893 0.6
Table 4 Properties of air. Parameters 3
Density, q (kg/m ) Specific heat, Cp (J/kg K) Viscosity, l (kg/m s) Thermal conductivity, k (W/m K) Thermal expansion, b (1/K) Absorption coefficient k, (lm)
Model
Value
Boussinesq Constant Constant Constant Constant Constant
1.1806 1005 1.858e5 0.02568 3.47e3 10.6
equation are set to be 2nd order upwind, Discrete Ordinates 1st order upwind. Other parameters remain default. The corresponding material and air properties can be found in Tables 3 and 4.
Fig. 5. Single diode equivalent circuit model.
2.4. Solar cell model Various equivalent electrical models for solar cell have been developed, such as the single-diode and double-diode model. These models have been simplified and improved over years (Brano et al., 2012; Ishaque et al., 2011). Generally, the more accurate the model is the more unknown parameters. Among these models, the five-parameter model shows good accuracy and reasonable computation time. The model consists of a photovoltaic current source, a diode, a series resistance and a parallel (shunt) resistance, as shown in Fig. 5. The model is described as follows: V þIRs V þ IR s I ¼ I ph I sat eN s AV T 1 ð6Þ Rp V T ¼ kT =q gmpp ¼
Fig. 6(a). I–V curves under different solar irradiation at T = 25 °C.
ð7Þ
P mpp AG
ð8Þ
The five unknown parameters are: Iph, the photo-generated current at Standard Testing Condition (STC, 25 °C 1000 W/m2 AM1.5), Isat, dark saturation current in STC, Rs, panel series resistance, Rp, panel parallel resistance and A, the diode ideality factor. To obtain these unknown parameters, we first test the module under different solar radiation and temperature (Fig. 6(a) and 6(b)), and then solve the parameters numerically. Table 5 shows all the parameters and values. Since the model is for STC, when the temperature and solar irradiation deviates from STC, the following equations are used to establish the connection. I ph ¼ I ph;n ð1 þ K i DT Þ
I sat
T ¼ I sat;n Tn
A3
qEg
G Gn
e½ AK ðT n T Þ 1
1
ð9Þ ð10Þ
Fig. 6(b). I–V curves under different temperature at G = 1000 W/m2.
Using Eqs. (6)–(10), the PV module performance under arbitrary solar irritations and temperature can be
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Table 5 Parameters used in single diode model. Parameter
Value
Photovoltaic current, IPV (A) Diode saturation current, Isat (A) Equivalent series resistance, Rs (X) Equivalent parallel resistance, Rp(X) Diode ideality factor, A Boltzmann’s constant,k (J/K) Charge of electron, q (C)
9.36727 5.89184E9 0.34527 917.69651 1.2 1.38E23 1.60E19
calculated. This is done by Newton–Raphson method in MATLAB. 3. Results and discussion
Fig. 7. Comparison of cell temperatures at different wind velocities at h = 100 mm.
3.1. Tilt angle Having set up all the three models, effects of mounting parameters on cell temperature and I–V curve are studied. We first change the tilt angle from 0° to 90° with an increment of 5°. Fig. 7 shows the cell temperature and tilt angle relation. The black curve in Fig. 7 can be divided into two parts: 0–30° tilt angle region and 30–60° region. It can be easily seen that from 0–30° the cell temperature falls slowly than that of 30–90°. Two reasons account for this. First, in the 0–30° region, the input solar irradiation increases with the escalation of tilt angle. After the 30°, the energy input decreases with the increase of tilt angle. Second, the wind velocity in the air gap is low and natural convection plays an important role in the overall heat transfer. As a result, the change in air gap geometry, which allows buoyance force to intensify natural convection, enhances the heat transfer and lowers the cell temperature. As we further increase the wind velocity inside of the air gap, the impact of natural convection on the total heat transfer is getting weaker, and thus, the cell temperature generally depends on the input solar radiation. This could be observed in Fig. 7 (red1 curve) in which the wind velocity inside the air gap reaches 3 m/s. The cell temperature first increases with the growth of input energy and then decreases with the drop in solar irradiation. It is obviously that cell temperature is lowered due to enhanced heat transfer brought by stronger forced convection. With the data on solar irradiance and cell temperature, it is feasible to calculate the I–V curve, maximum power output and cell efficiency at each mounting angle. Fig. 8 shows the I–V curves at mounting angles of 0°, 15°, 30°, 45°, 60° and 75°. From the curve, two patterns are easily observed. First, the starting point of the I–V curve is significantly determined by G, the solar irradiation on the panel. As a result, curve of 30°, where the panel receives the most solar energy, has the highest starting point on the graph. 1 For interpretation of color in Figs. 9, 10 and 13, the reader is referred to the web version of this article.
Fig. 8. I–V curves at different tilt angles, h = 100 mm, v = 0.5 m/s.
For the same reason, 90° curve lies at the lowest position. Second, the turning point of I–V curve mostly depends on T, the cell temperature. As the incoming solar irradiance values on both 15° and 30° angle are the same, the starting points remain at almost the same position. However, since the cell temperature is lower at 45°, the curve drops at a greater voltage. The maximum power output and efficiency of all investigated angles are plotted in Fig. 9 (red curves), noting that the wind velocity inside the gap is 0.5 m/s. The power output first rises up and then falls down as the same behavior of the incoming solar energy. The efficiency gradually increases as the temperature drops. It is worth noting that similar behavior happens between the cell temperature and module efficiency: a less rate before 30° and a greater rate after 30°. The efficiency difference can be up to 2 percent. As we increase the wind velocity to 3 m/s, the efficiency curve displays different pattern than that of 0.5 m/s (Fig. 9 blue curves). This is because the temperature in this case appears to be monotonically decreasing.
W. Xing et al. / Solar Energy 103 (2014) 541–549
Fig. 9. Module performance at h = 100 mm, v = 0.5 m/s and 3 m/s.
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Fig. 11(a). Velocity magnitude vs. air gap height at exit, 30° angle, h = 10 mm, v = 3 m/s.
Fig. 11(b). Temperature distribution at the exit, 30° tilt angle, h = 10 mm, v = 3 m/s. Fig. 10. Comparison of wind velocity effects on cell temperature, 30° tilt angle.
3.2. Air gap height Air gap sizes of 10 mm, 20 mm, 30 mm, 40 mm, 50 mm, 100 mm, 150 mm, 200 m, 250 mm and 300 mm are studied. As the wind velocity set to be 0.5 m/s, the cell temperature and air gap height is plotted in Fig. 10 (black). The sudden drop in temperature marks the transition of heat transfer mechanism from conduction to convection. As we further increase wind velocity to 1 m/s and 3 m/s, the temperature-gap height curve appears to be different than the curve of 0.5 m/s, as shown in Fig. 10 (red and blue). The reason for this is that the heat transfer mechanism inside the air gap switched from conduction to forced convection. Another important pattern of the curves at 1 m/s and 3 m/s is that the temperature first rises and then slowly decreases as the enlargement of the air gap height. This is because the flow reached fully developed, namely parabolic velocity profile, at the air gap height of 10 mm. Fig. 11(a) depicts the outlet velocity profile which demonstrates this fact. Fig. 11(b) shows temperature profile of the gap exit. It can be observed the thermal boundary layers merge into
each other. Greater distance between the PV module and the roof requires more length on the X-direction for the flow to be fully developed. As a result, the flow exits the air gap without reaching the fully developed region. The presence of the flat plain in Fig. 11(c) clearly demonstrates this. Accompanying the underdeveloped velocity profile is the weakening in heat transfer and rise in the cell temperature. As the air gap height further increases, the heat transfer between the PV panel and the roof falls into the infinitely separated plates model and the cell temperature begins to fall down. Fig. 12 shows the I–V curves for different air gap heights. It can be clearly seen that the curves except 10 mm height almost overlap each other. This is because the solar energy input the same for all heights and the only difference is the cell temperature. Moreover, since the incoming solar energy is the same for each air gap size, the power output is proportional to the cell efficiency. For the 0.5 m/s wind velocity, the efficiency increases drastically in the beginning then increases with a lower rate. The maximum efficiency difference is less than 1 percent (Fig. 13 red curves). For the case of 1 m/s and 3 m/s wind velocity, as the opposite of their temperature profiles, the efficiency drops then rises (Fig. 13 blue curves and black
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4. Conclusion
Fig. 11(c). Velocity magnitude vs. air gap height at exit, 30° angle, h = 30 mm, v = 3 m/s.
The effects of mounting parameters i.e. tilt angle and air gap size, on PV module temperature and power output were studied. The results have shown that at the maximum power output comes at the angle where the solar irradiation reaches the highest. Meanwhile, the efficiency and tilt angle relationship shows different behaviors at different wind velocities. When the tilt angle reaches 90°, the module efficiency maximizes. However, at this angle, the power output reaches the lowest value. Since the income solar irradiation is the same at different air gap sizes, the PV performance depends only on the air gap height, which determines the heat transfer mechanism inside the gap. At low wind velocity (0.5 m/s), heat conduction dominates the heat transfer process and greater efficiency can be achieved by increasing the gap size. At high wind velocity (>1 m/s), the cell temperature depends on whether the flow inside the gap reaches fully developed or not. At the fully developed scenario, both the module power output and cell efficiency can reach the maximum point. Acknowledgement The authors would like to acknowledge the funding of High Technology project of Jiangsu Province (No: BE2013129) and the Program for Chinese New Century Excellent Talents in university (NCET-12-0712). References
Fig. 12. I–V curve for different air gap heights, 30° tilt angle, v = 0.5 m/s.
Fig. 13. Module performance at 30° tilt angle with various air gap height and flow velocity.
curves). Noting that the lowest cell temperature, which gives the greatest power output and efficiency, happens at the time when the flow inside the gap reaches fully developed.
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ScienceDirect Solar Energy 103 (2014) 541–549 www.elsevier.com/locate/solener
Effects of mounting geometries on photovoltaic module performance using CFD and single-diode model Wei Xing a,c, Jianqiu Zhou a,b,⇑, Zhiqiang Feng d a
Department of Mechanical Engineering, Nanjing University of Technology, Nanjing, Jiangsu Province 210009, China b Department of Mechanical Engineering, Wuhan Institute of Technology, Wuhan, Hubei Province 430070, China c Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA d State Key Laboratory of PV Science and Technology, Trina Solar Limited Company, Changzhou, Jiangsu Province 213031, China Received 29 September 2013; received in revised form 20 February 2014; accepted 22 February 2014
Communicated by: Associate Editor G.N. Tiwari
Abstract The performance of a photovoltaic module under operating conditions mainly depends on two factors: solar irradiation and cell temperature. These two factors are strongly influenced by mounting geometrical parameters. This paper studies the effects of mounting parameters on photovoltaic (PV) module performance by using CFD and single diode model. The results show that maximum power output happens at the tilt angle where the incoming solar irradiation reaches the peak value. The relationship between efficiency and tilt angle acts differently based on wind velocity inside the gap. The air gap height, the distance between the module and roof, determines the heat transfer mechanism inside the air gap and then greatly affects the module performance. When the flow inside the air gap becomes fully developed, both the module power output and efficiency reach the greatest value. The result of this study provides theoretical basis to design mounting parameter for PV module installation and helps maximize energy efficiency in practical operating condition. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: Solar energy; PV module; CFD; Single diode model
1. Introduction Photovoltaic (PV) technology, which directly transfers solar irradiation to electrical energy, has been widely used in residential and commercial applications with an increasing rate about 25% in market growth over the last decade (Parida et al., 2011; Hoffmann, 2006). PV systems are generally used in buildings (known as building integrated PV systems), transport and agriculture applications (Tiwari, 2002). Beside electrical power generation, PV systems are ⇑ Corresponding author at: Department of Mechanical Engineering, Nanjing University of Technology, Nanjing, Jiangsu Province 210009, China. Tel.: +86 25 83588706; fax: +86 25 83374190. E-mail address: [email protected] (J. Zhou).
http://dx.doi.org/10.1016/j.solener.2014.02.032 0038-092X/Ó 2014 Elsevier Ltd. All rights reserved.
always coupled with thermal application, such as air/water heating. These applications and their energy/cost analysis are comprehensively summarized and reviewed. (Tiwari et al., 2011) The actual performance of a PV module under operating condition is primarily influenced by two factors: the solar irradiation on the module and the cell temperature (Nakamura et al., 2001). Thermodynamically, the solar irradiation acts as the availability, while the cell temperature affects the module efficiency. Specifically, the incoming solar energy is the maximum amount of energy that could be transferred into electrical energy and the cell temperature determines the percentage of energy transferred. As the cell temperature rises, the module efficiency drops considerably. This is due to the characteristic
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Nomenclature A – Cp h G g I Ki Kv k – Ns P q – Rs Rp T u V v – a b
area (m2) ideality factor for solar cell specific heat (J/kg K) air gap height (mm) solar irradiation (W/m2) gravitational acceleration (m/s2) current (A) temperature coefficient of short circuit current (%/°C) temperature coefficient of open circuit voltage (%/°C) thermal conductivity (W/m K) Boltzmann’s constant (J/K) number of cells linked in series power (W) heat flux (W/m2) charge of electron (C) equivalent series resistance (X) equivalent parallel resistance (X) temperature (K) fluid velocity on x direction (m/s) voltage (V) wind velocity inside the air gap (m/s) fluid velocity on y direction (m/s) thermal diffusivity (m2/s) expansion coefficient
of the cell material. The efficiency of a commercial PV module is usually between 10% and 15%, depending on the operating condition (Kumar and Rosen, 2011). Thus, even 1% of efficiency drop could lay great influence on the overall performance. It has to be noted that for PV/ thermal system, the overall energy efficiency (electrical and thermal efficiency) could be much higher. Due to the advancement in heat transfer, some PV/T system could reach 26.7% efficiency (Agrawal and Tiwari, 2011). Mounting parameters, such as tilt angle and the distance between the module and roof, the air gap height, determine solar irradiance, heat transfer mechanism and solar cell temperature. By changing the tilt angle, the angle between the PV panel and incoming solar radiation changes, in turn, the energy received by the panel changes. It is obviously that the maximum amount of incoming solar energy occurs when the PV module is normal to the sun radiation. The air gap height and tilt angle form the flow passage for air to flow between the module and rooftop. The geometry of this flow pattern determines the heat transfer mechanism between the PV module and rooftop and the module temperature. As described earlier, the mounting parameters could determine the module performance. To study the role of mounting parameters on the PV module performance,
h q l k e g
PV module tilt angle (degree) density (kg/m3) viscosity (kg/m s) absorption coefficient (lm) emissivity efficiency (%)
Subscripts a ambient rad radiation mpp maximum power point n nominal (value under standard testing condition) ph photo-generated sat saturation OC open circuit SC short circuit v voltage i current Abbreviations PV photovoltaic STC standard testing condition CFD computational fluid dynamics DO discrete coordinates
knowledge of both heat transfer and electrics is required. Previous researches focusing on the thermal characteristics and electrical modeling have been carried separately (Skoplaki and Palyvos, 2009; Sahina et al., 2007; Walker, 2001; Gow and Manning, 1999; Sahin et al., 2007). Several studies considered both thermal and electrical factors and used numerical and/or experimental approaches to determine the module performance. Skoplaki et al. proposed a simple correlation for PV temperature under arbitrary mounting conditions and introduced a dimensionless mounting parameter to deliver the correlation for more applications (Skoplaki et al., 2008). Hiraoka et al. conducted a one-year experiment studied the tilt angle dependence of PV modules comprising of different types of solar cells (Hiraoka et al., 2003). Experimental data from various testing sites were also analyzed statistically (Koehl et al., 2011). Research concerning the metrology and PV module performance relationship was conducted by Katsumata et al. (2011). Kim et al. (2011) studied the role of ambient temperature on the performance of a PV module with the ranging of ambient temperature from 25 °C to 50 °C. They also simulated the situation when fins are attached to a PV module. Wilson and Paul (Wilson and Paul, 2011) studied the role of the
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mounting parameters on cell temperature and efficiency using CFD. The CFD model shows great accuracy and reasonable computation time. However, they did not take the variation of solar irradiation into account and actual power output is beyond their research scale. Usama Siddiqui et al. (2012) developed a three dimensional thermal model to predict the thermal performance of PV module under varying conditions i.e. different ambient temperature and irradiation. Their study was coupled with the single diode, five-parameter model. They also studied the influence of module performance with and without cooling system. However, few studies combined CFD approach and PV electric modeling to investigate the role of mounting parameters on electric output, considering both the incoming solar irradiance and the efficiency variation due to temperature rise. The goal of this study is to evaluate the PV module performance under different mounting geometries which are similar to practical operating condition. To do this, CFD method is first invoked to get the temperature of the solar cell, incorporating different mounting conditions, and then an equivalent circuit model, the single diode, five-parameter model, is then applied to evaluate the module performance. The PV module evaluated in this paper is TSM-270DC05A/ 05A.08 (monocrystalline silicon cells).
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Fig. 1. Ways of radiation on a PV module.
2. Methodology and models 2.1. Methodology In order to investigate the role of mounting parameters on the PV module performance, tools of heat transfer and equivalent circuits are required. The methodology used in this study is the coupling of solar irradiation model, CFD model and equivalent circuit model. The solar irradiation model establishes the relationship between the incoming solar energy and the tilt angle. The CFD model evaluates the effects of mounting parameters on the cell temperature from a heat transfer prospective. The CFD model is executed by FLUENT. The last step is to input the cell temperature and solar irradiation data to the equivalent circuit model to evaluate the PV module performance. The circuit model is run by MATLAB. Following are the descriptions of the three models. 2.2. Simplified solar irradiation model To reach the PV module, sunlight has to travel through the atmosphere, where direct radiation, ground-reflected radiation and sky diffuse radiation caused by air molecules, dust, drops and ice crystals might happen (Fig. 1) Rekioua and Matagne, 2012. In this study, we ignore the groundreflected radiation and sky diffuse radiation and assume the direct radiation is the only source of input energy and only depends on the tilt angle (Fig. 2). The input solar irradiation reaches the maximum value, 1000 W/m2, when the tilt reaches 30°. The solar irradiation at other tilt angles can be found using Eq. (1) based on the geometrical parameters
Fig. 2. Simplified direct radiation model.
shown in Fig. 2. Corresponding results are shown in Table 1. Gnormal ¼ Gincident cosð30 aÞ
ð1Þ
As shown in Table 1, the input solar energy increases from 0° to 30° tilt angle, then decreases with the tilt angle increase. 2.3. Description of CFD modeling 2.3.1. Basic theories and fundamental equations The idealized energy balance of a PV module is shown in Fig. 3. In this case, the input source is the solar irradiation and the output is the generated electrical power, meanwhile, heat can be lost from both the front and rear side of the panel. In this study, we assume that 30% of the total input solar energy has been lost from the back side of the panel. In the air gap, conduction, radiation, natural and forced convection take place. We also assume the heat
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Table 1 Radiation value at different tilt angles. Tilt angle (degree)
Solar irradiation (W/m2)
Heat diffuse in the air gap (W/m2)
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90
866 906 940 966 985 996 1000 996 985 966 940 906 866 819 766 707 643 574 500
259.8 271.8 282 289.8 295.5 298.8 300 298.8 295.5 289.8 282 271.8 259.8 245.7 229.8 212.1 192.9 172.2 150
observations (Kurnik et al., 2011). Operational parameters, such as wind speed and temperature difference between PV cell and ambient, were controlled as inputs. Wilson and Paul (2011) studied the role of the mounting parameters on cell temperature and corresponding efficiency using CFD. In this study, mounting parameters, such as tilting angle and air gap size and wind velocity inside the air gap, were controlled (Fig. 4). The CFD model was then verified by the experimental data from Trinuruk (Trinuruk et al., 2006). However, the study did not take into consideration the variation of solar irradiance induced by tilt angle change. In this study, we will generally follow their model and include the solar irradiation variation resulted from change of tilt angle. In this study, we use the TSM270DC05A PV module, the specification is shown in Table 2 (http://www.trinasolar.com/cn/product/Mo_Honey.html.). In the modeling process, mesh size is chosen to be 350 70 with successive ratio of 1.02 and 1.2, respectively. The mesh interval number of the short side changes proportionally with the air gap height. The ambient temperature is set to be 298 K. We also assume the wind velocity to be 0.5 m/s at the air gap inlet and the rooftop is insulated. Since radiation heat transfer inside the gap plays an important role in the overall heat transfer (Moshfegh and Sandberg, 1998), the Discrete Ordinates (DO) model is invoked. The solver is set to be 2D, steady state, pressured based (PRESTO!). The momentum and energy
Fig. 3. Idealized energy balance for a PV module.
transfer is based on a two dimensional scenario. The fundamental equations of continuity, momentum and energy are listed below @u @v þ ¼0 @x @y
ð2Þ Fig. 4. Sketch for CFD modeling.
u
2
2
@u @u 1 @p @ u @ u þv ¼ þ þ þ gbðT TaÞ cos h @x @y q @x @x2 @y 2 ð3Þ
u
2
2
@v @v 1 @p @ v @ v þv ¼ þ þ þ gbðT TaÞ sin h @x @y q @y @x2 @y 2 ð4Þ
2 @T @T @ T @2T u þv ¼a þ r qrad @x @y @x2 @y 2
ð5Þ
2.3.2. CFD modeling Kurnik et al. studied the effects of different mounting conditions (open rack and roof integrated) using well-established energy balance model, based on their experimental
Table 2 TSM-270DC05A/0.5A.08 Specification datasheet (Incropera and DeWitt, 1996). Characteristics
Specifications
Cell type Dimensions (mm) Maximum power, Pmpp (W) Maximum power voltage, Vmpp (V) Maximum power current, Impp (A) Open circuit voltage, VOC (V) Short circuit current, ISC (A) Number of cells, Ns Module efficiency, g (%) Temperature coefficient of VOC, Kv (%/°C) Temperature coefficient of ISC, Ki (%/°C) Nominal operating cell temperature
Monocrystalline silicon 1650 992 35 270 30.8 8.77 38.6 9.23 60 16.5 0.32 0.053 44 °C (±2 °C)
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Table 3 Material properties (Trinuruk et al., 2006). Material
Density, q (kg/m3)
Specific heat, Cp (J/kg K)
Thermal conductivity, k (W/m K)
Radiation emissivity, e
Tedlar Concrete
1475 1444
1130 1229
0.14 0.5868
0.893 0.6
Table 4 Properties of air. Parameters 3
Density, q (kg/m ) Specific heat, Cp (J/kg K) Viscosity, l (kg/m s) Thermal conductivity, k (W/m K) Thermal expansion, b (1/K) Absorption coefficient k, (lm)
Model
Value
Boussinesq Constant Constant Constant Constant Constant
1.1806 1005 1.858e5 0.02568 3.47e3 10.6
equation are set to be 2nd order upwind, Discrete Ordinates 1st order upwind. Other parameters remain default. The corresponding material and air properties can be found in Tables 3 and 4.
Fig. 5. Single diode equivalent circuit model.
2.4. Solar cell model Various equivalent electrical models for solar cell have been developed, such as the single-diode and double-diode model. These models have been simplified and improved over years (Brano et al., 2012; Ishaque et al., 2011). Generally, the more accurate the model is the more unknown parameters. Among these models, the five-parameter model shows good accuracy and reasonable computation time. The model consists of a photovoltaic current source, a diode, a series resistance and a parallel (shunt) resistance, as shown in Fig. 5. The model is described as follows: V þIRs V þ IR s I ¼ I ph I sat eN s AV T 1 ð6Þ Rp V T ¼ kT =q gmpp ¼
Fig. 6(a). I–V curves under different solar irradiation at T = 25 °C.
ð7Þ
P mpp AG
ð8Þ
The five unknown parameters are: Iph, the photo-generated current at Standard Testing Condition (STC, 25 °C 1000 W/m2 AM1.5), Isat, dark saturation current in STC, Rs, panel series resistance, Rp, panel parallel resistance and A, the diode ideality factor. To obtain these unknown parameters, we first test the module under different solar radiation and temperature (Fig. 6(a) and 6(b)), and then solve the parameters numerically. Table 5 shows all the parameters and values. Since the model is for STC, when the temperature and solar irradiation deviates from STC, the following equations are used to establish the connection. I ph ¼ I ph;n ð1 þ K i DT Þ
I sat
T ¼ I sat;n Tn
A3
qEg
G Gn
e½ AK ðT n T Þ 1
1
ð9Þ ð10Þ
Fig. 6(b). I–V curves under different temperature at G = 1000 W/m2.
Using Eqs. (6)–(10), the PV module performance under arbitrary solar irritations and temperature can be
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Table 5 Parameters used in single diode model. Parameter
Value
Photovoltaic current, IPV (A) Diode saturation current, Isat (A) Equivalent series resistance, Rs (X) Equivalent parallel resistance, Rp(X) Diode ideality factor, A Boltzmann’s constant,k (J/K) Charge of electron, q (C)
9.36727 5.89184E9 0.34527 917.69651 1.2 1.38E23 1.60E19
calculated. This is done by Newton–Raphson method in MATLAB. 3. Results and discussion
Fig. 7. Comparison of cell temperatures at different wind velocities at h = 100 mm.
3.1. Tilt angle Having set up all the three models, effects of mounting parameters on cell temperature and I–V curve are studied. We first change the tilt angle from 0° to 90° with an increment of 5°. Fig. 7 shows the cell temperature and tilt angle relation. The black curve in Fig. 7 can be divided into two parts: 0–30° tilt angle region and 30–60° region. It can be easily seen that from 0–30° the cell temperature falls slowly than that of 30–90°. Two reasons account for this. First, in the 0–30° region, the input solar irradiation increases with the escalation of tilt angle. After the 30°, the energy input decreases with the increase of tilt angle. Second, the wind velocity in the air gap is low and natural convection plays an important role in the overall heat transfer. As a result, the change in air gap geometry, which allows buoyance force to intensify natural convection, enhances the heat transfer and lowers the cell temperature. As we further increase the wind velocity inside of the air gap, the impact of natural convection on the total heat transfer is getting weaker, and thus, the cell temperature generally depends on the input solar radiation. This could be observed in Fig. 7 (red1 curve) in which the wind velocity inside the air gap reaches 3 m/s. The cell temperature first increases with the growth of input energy and then decreases with the drop in solar irradiation. It is obviously that cell temperature is lowered due to enhanced heat transfer brought by stronger forced convection. With the data on solar irradiance and cell temperature, it is feasible to calculate the I–V curve, maximum power output and cell efficiency at each mounting angle. Fig. 8 shows the I–V curves at mounting angles of 0°, 15°, 30°, 45°, 60° and 75°. From the curve, two patterns are easily observed. First, the starting point of the I–V curve is significantly determined by G, the solar irradiation on the panel. As a result, curve of 30°, where the panel receives the most solar energy, has the highest starting point on the graph. 1 For interpretation of color in Figs. 9, 10 and 13, the reader is referred to the web version of this article.
Fig. 8. I–V curves at different tilt angles, h = 100 mm, v = 0.5 m/s.
For the same reason, 90° curve lies at the lowest position. Second, the turning point of I–V curve mostly depends on T, the cell temperature. As the incoming solar irradiance values on both 15° and 30° angle are the same, the starting points remain at almost the same position. However, since the cell temperature is lower at 45°, the curve drops at a greater voltage. The maximum power output and efficiency of all investigated angles are plotted in Fig. 9 (red curves), noting that the wind velocity inside the gap is 0.5 m/s. The power output first rises up and then falls down as the same behavior of the incoming solar energy. The efficiency gradually increases as the temperature drops. It is worth noting that similar behavior happens between the cell temperature and module efficiency: a less rate before 30° and a greater rate after 30°. The efficiency difference can be up to 2 percent. As we increase the wind velocity to 3 m/s, the efficiency curve displays different pattern than that of 0.5 m/s (Fig. 9 blue curves). This is because the temperature in this case appears to be monotonically decreasing.
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Fig. 9. Module performance at h = 100 mm, v = 0.5 m/s and 3 m/s.
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Fig. 11(a). Velocity magnitude vs. air gap height at exit, 30° angle, h = 10 mm, v = 3 m/s.
Fig. 11(b). Temperature distribution at the exit, 30° tilt angle, h = 10 mm, v = 3 m/s. Fig. 10. Comparison of wind velocity effects on cell temperature, 30° tilt angle.
3.2. Air gap height Air gap sizes of 10 mm, 20 mm, 30 mm, 40 mm, 50 mm, 100 mm, 150 mm, 200 m, 250 mm and 300 mm are studied. As the wind velocity set to be 0.5 m/s, the cell temperature and air gap height is plotted in Fig. 10 (black). The sudden drop in temperature marks the transition of heat transfer mechanism from conduction to convection. As we further increase wind velocity to 1 m/s and 3 m/s, the temperature-gap height curve appears to be different than the curve of 0.5 m/s, as shown in Fig. 10 (red and blue). The reason for this is that the heat transfer mechanism inside the air gap switched from conduction to forced convection. Another important pattern of the curves at 1 m/s and 3 m/s is that the temperature first rises and then slowly decreases as the enlargement of the air gap height. This is because the flow reached fully developed, namely parabolic velocity profile, at the air gap height of 10 mm. Fig. 11(a) depicts the outlet velocity profile which demonstrates this fact. Fig. 11(b) shows temperature profile of the gap exit. It can be observed the thermal boundary layers merge into
each other. Greater distance between the PV module and the roof requires more length on the X-direction for the flow to be fully developed. As a result, the flow exits the air gap without reaching the fully developed region. The presence of the flat plain in Fig. 11(c) clearly demonstrates this. Accompanying the underdeveloped velocity profile is the weakening in heat transfer and rise in the cell temperature. As the air gap height further increases, the heat transfer between the PV panel and the roof falls into the infinitely separated plates model and the cell temperature begins to fall down. Fig. 12 shows the I–V curves for different air gap heights. It can be clearly seen that the curves except 10 mm height almost overlap each other. This is because the solar energy input the same for all heights and the only difference is the cell temperature. Moreover, since the incoming solar energy is the same for each air gap size, the power output is proportional to the cell efficiency. For the 0.5 m/s wind velocity, the efficiency increases drastically in the beginning then increases with a lower rate. The maximum efficiency difference is less than 1 percent (Fig. 13 red curves). For the case of 1 m/s and 3 m/s wind velocity, as the opposite of their temperature profiles, the efficiency drops then rises (Fig. 13 blue curves and black
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4. Conclusion
Fig. 11(c). Velocity magnitude vs. air gap height at exit, 30° angle, h = 30 mm, v = 3 m/s.
The effects of mounting parameters i.e. tilt angle and air gap size, on PV module temperature and power output were studied. The results have shown that at the maximum power output comes at the angle where the solar irradiation reaches the highest. Meanwhile, the efficiency and tilt angle relationship shows different behaviors at different wind velocities. When the tilt angle reaches 90°, the module efficiency maximizes. However, at this angle, the power output reaches the lowest value. Since the income solar irradiation is the same at different air gap sizes, the PV performance depends only on the air gap height, which determines the heat transfer mechanism inside the gap. At low wind velocity (0.5 m/s), heat conduction dominates the heat transfer process and greater efficiency can be achieved by increasing the gap size. At high wind velocity (>1 m/s), the cell temperature depends on whether the flow inside the gap reaches fully developed or not. At the fully developed scenario, both the module power output and cell efficiency can reach the maximum point. Acknowledgement The authors would like to acknowledge the funding of High Technology project of Jiangsu Province (No: BE2013129) and the Program for Chinese New Century Excellent Talents in university (NCET-12-0712). References
Fig. 12. I–V curve for different air gap heights, 30° tilt angle, v = 0.5 m/s.
Fig. 13. Module performance at 30° tilt angle with various air gap height and flow velocity.
curves). Noting that the lowest cell temperature, which gives the greatest power output and efficiency, happens at the time when the flow inside the gap reaches fully developed.
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