CHAPTER - 4 Improvement in Energy Efficiency of a Solar...
Transcript of CHAPTER - 4 Improvement in Energy Efficiency of a Solar...
Chapter - 4
Hiren D. Raval 52 PhD Thesis
CHAPTER - 4
Improvement in Energy Efficiency of a Solar
Photovoltaic Panel by Thermal Energy Recovery
Summary: As explained in chapter 2, the electrical efficiency of solar photovoltaic (PV)
panel decreases with increase in its temperature because of its negative temperature co-
efficient. The conventional solar PV panel has the conversion efficiency of only 5-17%;
this means, about 83- 95% of incident energy is wasted and the proposition of recovering
energy from solar PV panel can tap more thermal energy than electrical energy generated
by PV panel itself. The heat was transferred by direct contact heat exchange with flowing
water from top of the panel and bottom of the panel. Direct contact heat exchange from top
surface was found more efficient in recovering energy as well improving the performance
of PV panel. The refraction of light as it passes through the water layer straightens the
incident radiation. The straightened radiation along with lower temperature of PV panel
synergistically increases photovoltaic conversion efficiency. The computational fluid
dynamics simulation of PV panel temperature closely resembled the experimental data.
There is a potential to recover energy at larger scale for large scale solar PV installations.
Thus, the present work proposes the win-win scenario of improved panel performance by
controlling its temperature and recovery of thermal energy for alternate applications.
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Published peer-reviewed International Journal paper:
Hiren D. Raval*, Subarna Maiti*, Ashish Mittal (2014) “Computational fluid
dynamics analysis and experimental validation of improvement in overall
energy efficiency of a solar photovoltaic panel by thermal energy recovery”,
Journal of renewable and sustainable energy 6, pp. 033138-1-12, ISSN 1941-
7012.
4.1 Research gap identification
As discussed in literature review (chapter-2), many researchers have attempted
photovoltaic panel cooling. Despite the extensive research on heat transfer from solar PV
panel, modelling and experimental validation of solar panel heat transfer with water
cooling from top surface with overall energy perspective remains the research gap. This
chapter addresses the heat transfer aspects from photovoltaic panel cooling to increase the
panel efficiency and develop understanding on energy recovery aspects to address the
following research questions:
1. Can the temperature of solar photovoltaic panel be validated with theoretical
temperature based on the computational fluid dynamics simulation with and
without cooling of the photovoltaic panel?
2. Can the overall energy efficiency of converting solar radiation to electricity and
captured thermal radiations be calculated with cooling and the same can be
compared without cooling?
3. Is there any other phenomenon apart from cooling that may lead to increase in
energy efficiency?
4.2 Experimental
Heat transfer from solar photovoltaic panels poses the challenge that the panel efficiency
should improve, understandably there should not be any obstruction in incident solar
radiation over the panel.
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The direct contact heat exchanger system was designed with the coolant being water since
radiations are incident from top; the heat exchange from was planned to control the
temperature of PV panel. All the sides and back surface of the panel were properly
insulated with calcium silicate insulation. Rationale was to utilize the maximum thermal
energy and minimize the losses of thermal energy, at the same time achieve higher
photovoltaic conversion efficiency.
4.2.1 Materials
Solar PV panel -70 Wp, frame structure, Rheostat, water tank, Thermocouples,
pyranometer (Kipp & Zonen CM4 pyranometer).
4.2.2 Method
The PV panel was kept at 20o
inclination in southward direction to get the optimal access
to solar radiation with reference to the location Bhavnagar, India, Co-ordinates: 21.7600o
N and 72.1500o E as shown in figure 1. One PV panel was provided cooling from top,
whereas the other panel was kept without cooling. The variable resistance system
(Rheostat) was used to measure the V-I (Voltage- Current) performance of PV panel.
As shown in figure 4.1, the system where, cooling was provided from top comprised of the
perforated pipe over its length at top, perforations being 2 mm in diameter. The flow rate
of cooling water was varied from 1 liter per minute to 2 liter per minute and the V-I
performance of the PV panel was evaluated. The water at outlet was drained out in a tank
open to atmosphere and was then recirculated using a DC (direct current) Kemflo make
pump. The nominal flow rate of the pump was 1 Lmin-1
. Two pumps are operated for
getting flow of 2 Lmin-1
.
FIGURE 4.1: Water flowing from top of the solar photovoltaic panel
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4.3 CFD Simulation
PV panel was exposed to solar radiation out of which a fragment is getting converted into
electricity. The energy balance across the solar PV panel is given by,
Rate of accumulation of heat = Rate of heat input – Rate of heat output + Rate of heat
genera
ρavCpavdT/dt = qsw - qlw - qconv−Pout ...............(4.1)
ρav = Average Density of PV panel and glass
Cpav = Average Specific heat of PV panel and glass
T = Temperature of PV panel (It is assumed that temperature of PV panel and glass above
it are same)
qlw = long wave radiation
qsw = short wave radiation
qconv = Heat loss by convection
Pout = Power output of PV panel
-qlw = A σ [(1+CosƟ)/2*ЄskyTsky4 + (1-CosƟ/2)* ЄgroundTground
4 – ЄpanelTpanel
4]...(4.2)
σ = Stephen Boltzman Constant
Є = Emissivity
Ɵ = Angle between panel and ground
qsw = αΦA.....(4.3)
qconv = A (hcnatural +hcforced)(Tpanel – Tenv)....(4.4)
Substituting (4.2), (4.3) and (4.4) in (4.1)
ρav Cpav dT/dt = A σ [(1+CosƟ)/2*ЄskyTsky4 + (1-CosƟ/2)* ЄgroundTground
4 – ЄpanelTpanel
4] +
αΦA - A (hcnatural +hcforced)(Tpanel – Tenv) – Pout
Єsky = 0.736 +0.00577T
Єground = Emissivity of concrete =0.94
Єpanel = 0.85
Ɵ = 20
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A = Area of panel =0.628 sq. m.
σ = 5.67 X 10-8
W/m2K
4
ρav = 3015 kg/m3
Cpav = 0.7733 J/g oC
hcnatural = 1.31 (Tglass- Tair)1/3
hcforced = 5.82 + 4.07v
The ANSYS Computational fluid dynamics software was used to simulate this model.
Assumptions made in simulating the model using ANSYS CFD tool are depicted below.
A constant water thickness of 2 mm above the panel is considered.
The flow is steady.
The water temperature varies with time (Water absorbs the solar radiation).
Infrared: 50%, Visible radiation: 40% and ultraviolet: 10% of the total incident
radiation.
Absorptivity of opaque material is 80%.
Glass transmissivity: 80%, Absorptivity: 20% and no reflectivity.
Pipe material does not absorb radiation.
Simulations were carried out applying boundary conditions with ANSYS CFD software
until the solution converges.The photovoltaic panel comprised of the following different
layers, physical properties of each layer is given in table 4.1[1, 2].
TABLE 4.1: Physical properties of the constituents of PV panel
Layer Thickness t (m)
Thermal
Conductivity K
(w/m K)
Density
(kg/m3)
Specific heat
Cp (J/kg K)
Tedlar 0.0001 0.2 1200 1250
Rear contact 10X10-6
237 2700 900
EVA 500X10-6
0.35 960 2090
PV Cell 225X10-6
148 2330 677
ARC 100X10-9
32 2400 691
Glass 0.003 1.8 3000 500
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As there are perforations in the feed water pipe, the geometry was created by considering 8
inlets and 4 outlets of water from the panel. Air domain has been considered surrounding
the physical geometry. Thereafter, geometry was also created by considering 1 slit type
inlet and 1 outlet to match the experimental condition.
Figure 4.2 shows the meshed domain of 8 inlets, 4 outlets system and figure 4.3 shows the
sliced domain of this system made using ANSYS CFD software. Skewness of mesh is 0
and orthogonal quality is 1.
FIGURE 4.2: Meshed domain of 8 inlets 4 outlets system
FIGURE 4.3: Sliced domain of 8 inlets 4 outlet system
Figure 4.4A shows the schematic of model and 4.4B shows the schematic of model mesh.
Meshing becomes denser near boundaries as the software will solve equations at the
crossing points. The denser meshing near boundaries will improve the quality of solution.
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4.4 Results and Discussions: Initial part of this section discusses the results with 8
inlets, 4 outlet system; the later part simulates the system with single inlet and single
outlet.
FIGURE 4.4A: Schematic of the model FIGURE 4.4B: Schematic of the model mesh
Figure 4.5 shows the simulation results of temperature on the back side of the panel as well
as on the top of the panel. As there is insulation on the back side, the heat cannot escape
from the back. However, the temperature is within control with the average temperature
near 36oC at the back side except the extreme bottom corner point where the temperature
reached upto 60oC. The temperature is particularly higher at the bottom corners of the
panel where water cannot flow and remain stationary whereas; the temperature is well
under control about 27oC on the top side as visible from the image. The purpose of cooling
from top side is to cool the array surface and insulation at the back side prevents heat loss.
The results show that the cooling is effective as the average temperature does not reach
very high on the back surface.
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FIGURE 4.5: Temperature of photovoltaic panel back surface and top surface
FIGURE 4.6: Velocity of water over photovoltaic panel
Figure 4.6 shows the velocity of water over photovoltaic panel. The velocity is low (less
than 0.05m/s) over the panel, however it is higher at entry and exit points. The central part
is photovoltaic panel over which the velocity profile is shown. The temperature of
photovoltaic panel as shown in Figure 4.5 shows that this velocity was good enough to
control the temperature.
Direct solar
irradiance: 800
w/m2
Inlet cooling
water
temperature:
30oC
Total Inlet flow:
1 Liter/minute
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FIGURE 4.7: Temperature of cross section of photovoltaic panel
Figure 4.7 shows the temperature of photovoltaic panel across the cross-section. It is
explicit that the temperature increases at the bottom because of insulation. When the
thermal energy is transferred from top and it is not allowed to escape from bottom, it is
understandable that the temperature of the back side will increase. The insulation is
efficient to prevent heat loss and heat is transferred from top.
FIGURE 4.8: Temperature of cross section in z axis of photovoltaic panel
Figure 4.8 shows the temperature of cross section in z axis of photovoltaic panel. The
temperature varies because of natural convection of air above the panel.
Direct solar
irradiance: 800
w/m2
Inlet cooling water
temperature: 30oC
Direct solar
irradiance: 800 w/m2
Inlet cooling water
temperature: 30oC
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FIGURE 4.9: Velocity vector above the PV panel surface
Figure 4.9 shows the velocity vectors above photovoltaic panel surface. Velocity is higher
at inlet and outlet. At inlet, it is higher because the flow is coming from the small opening
and at the outlet, the flow converges to a small exit.
There were number of perforations over the length of pipe. Thus, to, simulate the actual
experimental condition with more precision, the meshed domain with single inlet and
single outlet is considered as shown in figure 4.10 with the velocity remaining nearly same
as the actual experimental velocity.
FIGURE 4.10: Meshed domain with single inlet/single outlet
The meshing characteristics: Skewness: 0, Orthogonal quality: 1
The figure 4.11 demonstrates the velocity vectors along the streamline of water. The
velocity of water is low i.e. approximately 0.03 -0.06 m/s for both the cases 1 LPM and 2
Total Inlet flow:
1 Liter/minute
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LPM. However, the increase in velocity is quick for 2 LPM flow when the flow converges
to the exit point.
FIGURE 4.11: Velocity vectors for the flow 1 LPM and 2 LPM at 13:00 Hrs
The snapshot in Figure 4.12A and 4.12B demonstrates the comparison of PV panel
temperature with 1 LPM and 2 LPM flow respectively at 10:00 Hrs and 13:00 Hrs. It can
be seen from the simulation results that larger area of PV panel remains at lower
temperature with increased flow rate, and higher flow rate is particularly required to
maintain the temperature when solar radiation intensity is higher at 13:00 Hrs. When
comparing the panel temperature without cooling as shown in Figure 4.13, it becomes clear
that the panel temperatures are well within control with cooling. The panel temperature
without cooling reaches upto 76oC and the changes at different locations in the panel as a
result of natural convection are indicated in figure 4.14. The panel temperature is
controlled within 40oC by cooling even with lower flow rate of 1 LPM.
Inlet flow: 1 Liter/minute Inlet flow: 2 Liter/minute
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FIGURE 4.12A (Top) and 4.12B (Bottom): PV panel temperature with cooling at 10:00 Hrs 13:00 Hrs
respectively
FIGURE 4.13: Panel temperature without cooling 10:00 Hrs and 13:00 Hrs
Direct solar
irradiance: 813.31
w/m2
Inlet cooling water
temperature: 30oC
Direct solar
Irradiance:
1012.28 W/m2
Inlet cooling
water
temperature:
35oC
Direct solar irradiance at 10:00 Hrs: 813.31
W/m2 at 13:00 Hrs: 1012.28 W/m
2
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FIGURE 4.14: Temperature across the cross section of PV panel at 10:00 Hr and 15:00 Hrs
The figure 4.14 shows the temperature across the cross section of PV panel at 10:00 Hrs
and 15:00 Hrs. It can be seen that the temperature of the bottom layer near insulation
increases despite the panel top surface is maintained at close to 35oC. This is because the
heat is not getting wasted from the bottom on account of insulating layer at bottom. This
also ensures the heat transfer direction from bottom up across the layers of PV panel as the
day progresses.
Direct solar Irradiance: 813.31 W/m2
Inlet cooling water temperature: 30oC
Direct solar Irradiance: 856.31 W/m2
Inlet cooling water temperature: 33.5oC
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FIGURE 4.15: Temperature of panel cross section without cooling at 15:00 Hrs
The figure 4.15 indicates the effect of natural convection. The air adjacent to PV panel gets
heated as the temperature of PV panel increases and the density of air decreases at higher
temperature. The light air climbs up the panel and increases the temperature at the top part
of panel as compared to the bottom as visible in figure 4.15. Thus, natural convection alters
the PV panel temperature at different places.
The ambient conditions on the days of experiment are as shown in table 4.2.
TABLE 4.2: The environmental conditions on the days of experiment
Condition 14 May 1 June
Insolation (7 Hrs- 1030 to 1730) 837.37 W/m2 838.71 W/m
2
Average wind speed 1.4 m/s 1.4 m/s
Average insolation (24 hrs) 488.60 W/m2 343.83 W/m
2
Average ambient temperature 36.51 oC 38.61
oC
The performance of PV panel is assessed by V-I Performance. In figure 4.16, the
performance of PV panel has been demonstrated, where the peak power produced by PV
panel with and without cooling are compared. It is clear that the peak power produced by
PV panel improves with cooling where about 10% improvement in power output is
observed at 13:00 hrs. The pump consumes 5 W power. Therefore, the net power produced
Direct solar irradiance: 856.31 W/m2
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with cooling has to be reduced by 5 W in each case. However, the gravity operated systems
can also be designed where; net power will be the same as power produced.
FIGURE 4.16: Performance comparison of PV panel with and without cooling – Cooling water flow:1
LPM
Total energy generated over the day with cooling was 333 watt-hour, whereas the total
energy generated without cooling was 303 watt-hour.
FIGURE 4.17: Temperature of PV panel with and without cooling
It is explicit from figure 4.17 that there is a significant decline in PV panel temperature as a
result of cooling from top surface at 1 LPM flow. The experimental results are compared
0
10
20
30
40
50
60
1000 1100 1200 1300 1400 1500 1600 1700
Peak Power
produced
by Solar PV
panel
(Watt)
Time (Hours) Peak power
With Cooling
Peak power without cooling
0
10
20
30
40
50
60
70
1000 1200 1400 1600
Temperature
of PV panel
(oC)
Time of the day
Temperature of PV panel with and without cooling -Cooling water flow: 1
LPM
Avg.Temp. without
cooling
(Experimental)
Average temperature of
panel without cooling (by
CFD simulation)
Average temperature of
panel with cooling
(Experimental)
Average temperature of
panel with cooling (by CFD
simulation)
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with CFD simulation results and found in close conformity. When temperature reaches
close to 60o C at 14:00 hrs without cooling the panel, it is controlled well below 40
o C with
cooling.
FIGURE 4.18: Performance comparison of PV panel with cooling water flow-2 LPM and without
cooling
It is evident from the figure 4.18 that the peak power produced by PV panel improves as in
the case of 1 LPM flow, however the improvement is substantial. There is 20%
improvement in peak power produced at 13:00 hrs.
FIGURE 4.19: Temperature of PV panel with and without cooling- Cooling water flow 2 LPM
0
10
20
30
40
50
60
1000 1100 1200 1300 1400 1500 1600 1700
Peak Power
Produced by
PV Panel
(Watt)
Time (Hours)
Peak Power - With cooling Peak power- Without cooling
0
10
20
30
40
50
60
70
1000 1200 1400 1600
Temperature
of PV panel
(oC)
Time of the day
Temperature of PV panel with and without cooling -Cooling water
flow: 2 LPM
Avg.Temp. without cooling(Experimental)
Average temperature of panelwithout cooling (by CFDSimulation)
Average temperature withcooling (Experimental)
Average temperature of panelwith cooling (BY CFDsimulation)
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Fig. 4.19 indicates that the PV panel temperature decreases from 58oC to 37
oC as a result
of cooling with 2 LPM flow at 14:00 Hrs. The experimental results are in close conformity
with the simulation results.
In this way, the experimental results are in close confirmation with simulation results and it
becomes explicit that panel performance improves as a result of cooling from top as the
panel temperature is controlled below 40oC.
It is also important to know V-I performance of photovoltaic panel with and without
cooling. The results below indicate the V-I performance of photovoltaic panel with and
without cooling.
FIGURE 4.20: V-I performance of photovoltaic panel at 12:00 hrs
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 5 10 15 20
Current (Amp.)
Voltage (V)
V-I Performance of Panel at 1200 Hrs
With Cooling
Without Cooling
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FIGURE 4.21: V-I performance of photovoltaic panel at 12:15 hrs
FIGURE 4.22: V-I performance of photovoltaic panel at 12:45 hrs
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 10 20 30
Current
(Amp.)
Voltage (V)
V-I Performance of Panel at 1215 Hrs
With Cooling
Without Cooling
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 10 20 30
V-I Performance of Panel at 1245 Hrs
With Cooling
Without Cooling
Current
(Amp.)
Voltage (V)
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FIGURE 4.23: V-I performance of photovoltaic panel at 13:15 hrs
FIGURE 4.24: V-I performance of photovoltaic panel at 14:45 hrs
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 5 10 15 20 25
Current
(Amp.)
Voltage (V)
V-I Performance of Panel at 1315 Hrs
With Cooling
Without Cooling
0
0.5
1
1.5
2
2.5
3
3.5
4
0 5 10 15 20 25
Current
Amp.
Voltage (V)
V-I Performance of Panel at 1445 Hrs
With Cooling
Without Cooling
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FIGURE 4.25: V-I performance of photovoltaic panel at 15:15 hrs
FIGURE 4.26: V-I performance of photovoltaic panel at 15:45 hrs
Figure 4.20 – 4.26 demonstrates that V-I performance of photovolataic panel improves at
higher resistance. At low resistance, current is slightly lower with the panel cooling, the
relative current performance of panel improves at higher resistance; moreover voltage is
substantially more with cooling. However, the actual applications are generally with higher
resistance and therefore the performance with cooling is better. These data were taken
over several days and average of the data has been reported.
0
0.5
1
1.5
2
2.5
3
3.5
4
0 5 10 15 20 25
Current
(Amp.)
Voltage (V)
V-I Performance of Panel at 1515 Hrs
With Cooling
Without Cooling
0
0.5
1
1.5
2
2.5
3
0 5 10 15 20
Current
(Amp.)
Voltage (V)
V-I Performance of Panel at 1545 Hrs
With Cooling
Without Cooling
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Refraction effect and improvement of panel performance
The influence of refractive index in changing direction of the solar radiation has not been
studied earlier. The reason of improvement in energy efficiency can also be attributed to
the refraction effect because of flow of water above the panel. The angle of incident
radiation in Bhavnagar was obtained by SOLPOS calculator. The angle changes as a result
of refraction by the water layer. The refractive index of air and water and the incident
angle are known. The angle after refraction can be calculated using Snell’s law n1sin1 =
n2sin2. Water has the refractive index 1.333 [3]. Air has refractive index 1.0.
The table 4.3 indicates the effect of refraction over the solar PV panel.
TABLE 4.3: The Angle change as an effect of refraction by solar PV panel
Time Angle Ө1 Angle Ө2
09:00 -61.91 -41.58
10:00 -50.73 -35.63
11:00 -41.78 -30.09
12:00 -36.77 -26.76
13:00 37.27 27.10
14:00 43.11 30.94
15:00 52.54 36.66
16:00 63.98 42.53
17:00 76.49 47.00
From the table 4.3, it is clear that the incident angle varied from -61.91 to 76.49 from
Morning 09:00 hrs to evening 17:00 hrs. The angle changes after refraction and thus, the
angle 2 varied from -41.58 to 47.00. In this way, the span of angle reduced from 138.4 to
88.58. In other words, the incident radiations were straightened as a result of refraction as
shown in the figure 4.27. These straightened radiations helped to improve the performance
of the panel as they strike to panel at relatively larger angle as compared to the one without
water layer on top.
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FIGURE 4.27 Radiation at a given point straightened as a result of refraction
The experiment was performed to justify this finding. Ice was placed on the back side of
the PV panel and water layer on the top of the other identical panel to maintain the
temperature of PV panel at 35oC in both cases. The peak output observed with ice on the
back side was 50.22 Watt, whereas the peak output with water layer on top was 54.04 Watt
at same time 13:00 Hrs (7.6% increase in power output). This made it clear that the
refraction effect played its role to improve the panel performance. Typically, if the increase
in power output is about 20%, 7.6% may be attributed to refraction effect and 12.4% may
be attributed to cooling.
Overall energy efficiency: The energy efficiency with and without cooling was worked
out as a case to understand the effect of cooling on overall energy efficiency. It has been
observed that the efficiency was raised from 6.68% to 40.42% with cooling as shown in
table 4.4.
138.40o
88.58o
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TABLE 4.4: Energy efficiency calculations (For 1 Liter per minute flow)
Time 12:00 Hrs 14:00 Hrs 16:00 Hrs
Inlet water temperature(Twin) 37 36 34
Outlet water temperature(Twout) 39 38 35
Energy contained by water(watt) 139.56 139.56 69.78
Peak power without cooling (watt) 34.51 25.29 14.22
Peak power with cooling (watt) 41.73 28.57 16.3
Difference (watt) 7.22 3.28 2.08
Total power saving (watt) 146.79 142.85 71.86
Watt/m2 1020 732 348
Solar panel area (sq.m) 0.61 0.61 0.61
Power incident on the panel (watt) 624.24 447.98 212.98
Energy efficiency without cooling 5.53 5.64 6.68
Energy efficiency with cooling
(electrical + thermal) 29.0421 37.531 40.417
In this way, there is a significant improvement in overall energy (thermal + electrical)
efficiency with the cooling from top. The heated water can be used for some application
e.g. feed water to reverse osmosis. The higher temperature feed water improves
permeability of membrane and more product water can be generated from given membrane
area.
4.5 Conclusion
The following conclusions can be derived from the experiments to control the photovoltaic
panel temperature and theoretical study by computational fluid dynamics analysis.
Photovoltaic panel demonstrates the poorer performance at higher temperature, thus
cooling of photovoltaic panel is necessary to retain/enhance its efficiency. The
panel temperature could be effectively controlled by transferring heat from top at
low flow rate of 1 and 2 Liters per minute. Insulation at the back surface and sides
ensured that heat is not lost and transfer of heat is bottom-up in the photovoltaic
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panel. CFD analysis is in close confirmation with experimental validation for the
panel temperature.
It is demonstrated that the refraction of incident solar radiation while striking to PV
panel through the water film is beneficial. Refraction narrows the span of incident
radiation over the panel and narrowing the span of angle variation is better from the
point of view of panel performance. This is proven by increased power output in
the panel with water flowing from top.
The rise in water temperature reported indicates that there is a potential to tap the
thermal energy. The higher temperature water can be used for desalination systems
like membrane distillation, reverse osmosis etc. Reverse Osmosis water flux
increases with increase in feed water temperature. It is prudent to utilize the feed
water to Reverse Osmosis as cooling water and utilize the captured thermal energy
as soon as possible. Interdisciplinary approach of tapping thermal energy from
photovoltaic panel and thereby controlling its temperature along with utilizing the
tapped thermal energy for useful application such as Reverse Osmosis can increase
the overall energy efficiency of photovoltaic powered Reverse Osmosis.
In this study, the overall energy efficiency has been increased from about 6% to
40% by direct cooling the array surface of PV panel from top at 1 liter per minute
flow.
References
1. S. Armstrong, W.G. Hurley (2010) A thermal model of photovoltaic panels under varying
atmosphetic conditions, Applied thermal engineering, Volume 30, p. 1488, ISSN 1359-4311.
2. G. Notton, C. Cristofari, M. Mattei, P.Poggi (2005) Modeling of a double glass photovoltaic
module using finite differences, Applied thermal engineering, Volume 25(17-18), p. 2584,
ISSN 1359-4311.
3. X. Han, Y. Wang, L.Zhu (2011) Electrical and thermal performance of silicon solar cells
immersed in dielectric liquids, Applied energy, Volume 88, p. 448, ISSN 0306-2619.