# Performance Analysis and Optimization of a Cooling System for Hybrid Solar Panels Based on Climatic Conditions of Islamabad, Pakistan

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## Abstract

**:**

## 1. Introduction

## 2. Problem Description and Methodology

## 3. Mathematical Modeling

#### 3.1. Analytical Model of a PV Panel

_{c}in terms of irradiance and ambient temperature.

#### 3.1.1. Temperature Modeling

_{(next)}and Temp

_{(prev)}are known values of temperatures and t

_{(next)}and t

_{(prev)}is the time at which these temperatures occur. “t” is the time at which temperature is desired.

#### 3.1.2. Irradiance Modeling

_{0}) [43] to find the irradiance near the horizon is given by

_{rbs}model [45] was developed by the US stations for 32° to 42° in latitude. Islamabad has a latitude of 33°. This model is suitable for a subtropical climate which is the same as that of Islamabad. The model is discussed below.

_{t}is clearness index. For this case, M

_{t}is considered constant during the whole day.

_{H}, I

_{b}, and I

_{d}are in turn the horizontal surface, and direct and diffused beam irradiance on the horizontal surface. Solar panels are placed at an angle to the horizontal axis. The Liu and Jordan isentropic model [46] gives satisfactory values of irradiance for the tilted surface in Pakistan.

#### 3.2. Design of Absorber: Hybrid PV Panel

#### 3.2.1. Single-Pass Duct

#### 3.2.2. Multi-Pass Duct

#### 3.2.3. Tube-Type Absorber

## 4. Optimization

- (i)
- Expressions for Duct-Type Absorber

- (ii)
- Expressions for Multi-Pass Duct

- (iii)
- Expressions for Tube-Type Absorber

#### 4.1. Genetic Algorithm

#### 4.2. Comparative Analysis for Different Types of Absorbers

#### 4.3. Energy Produced by Hybrid Multi-Pass PV and Uncooled PV Module

## 5. Validation of Analytical Results through Virtual Experiments

#### 5.1. Simulation Analysis of the PV Module without Cooling

^{−4}; maximum skewness was 0.74. Manual contacts were defined between different layers. The layer with a lower conduction value was placed on the contact side of the pair, and the layer with higher conduction was on the target side. Convection boundary condition with convection coefficient of 6.5 W/(m.K) was placed on glass and back surface. The ambient temperature was varied according to the analytical calculations. The irradiance calculations and the heat flux boundary condition on both Tedlar and solar cells were applied using Equations (53) and (54). The ambient temperature was calculated using the mathematical function for temperature modeling.

#### 5.2. Simulation Analysis of Hybrid PV Panel with a Multi-Pass Duct

## 6. Conclusions

- PV and PV/T modules were analytically modeled using irradiance and ambient air conditions of Islamabad in June. For climate modeling, Erbs, Liu, and Jordan’s model and the sin linking day’s model were used. The optimum angle for solar panel tilt is 23°. Boundary conditions obtained by these models were incorporated in the analytical model, which was then linked with the optimization algorithm. According to analytical calculations, the hybrid system can produce about 0.15 kWh more energy than the ordinary system in June. Results clarify that cooling enhances the net output of the panel by reducing the effect of efficiency loss due to temperature.
- The analytical results were validated using fluent and thermal modules in ANSYS. The fluid flow regime is considered in the transition domain close to turbulent flow. Good agreement between analytical and numerical results for maximum cell temperature of PV panel was observed. The efficiency of the solar panel was directly dependent on the temperature of the cell; thus, the numerical results verified the efficiency of temperature behavior for a multi-pass hybrid solar panel.
- A comparison of PV and hybrid PV panels was carried out considering the power required by a commercial pump that provides the same head and flow rate of the fluid. In a multi-pass absorber, the inlet width was also varied as the number of passes was changed. Due to these facts, the multi-pass absorber can have relatively higher velocities of fluid at lower head losses. The cell temperature is also reduced as higher velocities increase the heat transfer coefficient.
- Absorbers of different types were modeled and compared. The hybrid solar panel with a multi-pass duct system was compared with a PV system without cooling. In March, the output of both the systems is almost equal, but the difference in output increases as ambient temperature increases. The trends and temperature behavior of the PV module and designed Hybrid PV module were verified by ANSYS simulations. However, the optimized result was achieved for the multi-pass duct with 31 passes that delivers a maximum power output of 186.713 W at a mass flow rate of 0.14 kg/s. The maximum cell temperature achieved for this configuration was 37.810 °C at a velocity of 0.092 m/s.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

I | incident radiation |

${\tau}_{g}$ | transmissivity of the glass cover |

$\u0273$ | efficiency |

α_{c} | absorptivity of solar panel |

β | packing factor |

α_{t} | absorptivity of tedlar |

STC | standard test Conditions |

PV | photovoltaic |

T_{a} | ambient temperature |

T_{c} | cell temperature |

U_{t} | Overall heat transfer coefficient from PV to ambient from the top of the panel through glass |

U_{T} | overall heat transfer coefficient from PV to ambient from the bottom of panel trough tedlar |

I_{o} | hourly extraterrestrial radiation |

Γ | day angle |

ω | hour angle |

ST | local solar time |

LT | local standard time |

L_{s} | standard meridian |

L_{L} | longitude of the location |

M_{t} | clearness index |

β | tilt angle |

I_{ββ} | total Irradiance on the tilted surface |

T_{bs} | temperature back surface |

b | breath |

dx | element length |

h_{f} | heat transfer coefficient of fluid |

T_{f-avg} | average temperature of fluid |

C_{p} | specific heat |

U_{b} | an overall heat transfer coefficient from bottom to ambient |

h_{p1} | penalty factor |

h_{p2} | penalty factor |

U_{Tt} | Overall Heat transfer Coefficient from Tedlar to Ambient from the top of the panel across glass |

D_{h} | hydraulic Diameter |

k | conduction coefficient |

U_{b} | overall heat transfer coefficient to ambient from the back side of absorber |

U_{L} | an overall heat transfer coefficient from solar cell to ambient through top and back surface of insulation |

L | length |

m | mass |

T_{f-out} | fluid outlet temperature |

T_{f-in} | fluid inlet temperature |

P | pressure |

U_{tf} | overall heat transfer coefficient from fluid to ambient from the top of the panel through glass |

Subscripts | |

A | Ambient Air |

f | Fluid |

t | Tedlar |

g | Glass |

bs | Back surface |

c | Solar Cell |

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Length (m) | Width (m) | Efficiency at STC | Max Power (W) | Temp Coefficient of P_{max} |
---|---|---|---|---|

1.956 | 0.992 | 16.5 | 320 | 0.45%/°C |

**Table 2.**Predefined variables/parameters for analytical calculations [37].

Variable/Parameter | Value |
---|---|

Fill Factor of PV module | 0.83 |

Coefficient of Convection of Air (W/m^{2}K) | 6.5 |

Thickness of Glass (m) | 0.0032 |

Thickness of Tedlar (m) | 0.0005 |

Thickness of EVA (m) | 0.0005 |

Conductivity of Tedlar (W/(mK)) | 0.033 |

Conductivity of EVA (W/(mK)) | 0.23 |

Conductivity of Glass (W/(mK)) | 1 |

Conductivity of Solar Cell (W/(mK)) | 148 |

Thickness of Cell (m) | 0.00035 |

Duct and tube material | Aluminium |

Aluminium Thickness for Duct Walls (m) | 0.003 |

Aluminium Conductivity (W/(mK)) | 205 |

Tube Dimensions | 15 × 25 (sq.mm) |

Absorptivity of Ted-lar | 0.50 |

Absorptivity of Solar Cell | 0.90 |

Transmissibility of Glass | 0.95 |

Diameter of External Circuit pipe (mm) | 0.0142 |

Fluid Inlet Temperature (°C) | 0.8 times the maximum Ambient temperature of the Month |

**Table 3.**Designed parameters of tube-type heat absorbers. ✓—specify the optimized absorber parameters for analysis.

Tube Type | Passes | Velocity (m/s) | Tc Max (°C) | Mass Flow Rate (kg/s) | PowerInput (W) | Max Power Output (W) |

✓7.00 | 0.28 | 41.94 | 0.11 | 5.18 | 178.97 | |

8.00 | 0.26 | 41.64 | 0.10 | 5.48 | 178.94 | |

12.00 | 0.18 | 41.75 | 0.07 | 5.50 | 178.82 | |

13.00 | 0.16 | 41.91 | 0.06 | 5.40 | 178.78 | |

Single-pass duct | Height(m) | Velocity (m/s) | Tc Max (°C) | Mass Flow Rate (kg/s) | PowerInput (W) | Max Power Output (W) |

✓0.012 | 0.009 | 39.985 | 0.114 | 0.878 | 185.027 | |

0.012 | 0.006 | 40.699 | 0.069 | 0.499 | 184.767 | |

0.016 | 0.007 | 40.835 | 0.110 | 0.843 | 184.301 | |

0.018 | 0.006 | 41.380 | 0.103 | 0.776 | 183.879 |

**Table 4.**Designed parameters of multi-pass duct type heat absorber. ✓—specify the optimized absorber parameters for analysis.

Multi-Pass Duct | Height (m) | Velocity (m/s) | Passes | Tc Max (°C) | Mass Flow Rate (kg/s) | PowerInput (W) | Max Power Output (W) |

0.016 | 0.100 | 32.000 | 38.169 | 0.095 | 0.723 | 186.810 | |

0.029 | 0.107 | 38.000 | 37.638 | 0.149 | 1.241 | 186.768 | |

✓0.025 | 0.092 | 31.000 | 37.810 | 0.140 | 1.141 | 186.713 | |

0.024 | 0.064 | 29.000 | 38.534 | 0.098 | 0.739 | 186.468 |

Month | Monthly Average Temperate (Hi/Low) (°C) | Cooling Water inlet Temperature (°C) | Power Input Commercially Available Pump (W) | Net Energy Produced KWh | |
---|---|---|---|---|---|

PV System without Cooling | PV System with Multi-Pass Duct Cooling | ||||

March | 24/10 | 20 | 10 | 0.99 | 1.01 |

April | 30/15 | 25 | 10 | 1.148 | 1.23 |

May | 35/19 | 28 | 10 | 1.227 | 1.35 |

June | 38/24 | 30 | 10 | 1.2306 | 1.38 |

July | 34/24 | 28 | 10 | 1.234 | 1.369 |

August | 33.4/23.5 | 28 | 10 | 1.193 | 1.30 |

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## Share and Cite

**MDPI and ACS Style**

Sattar, M.; Rehman, A.; Ahmad, N.; Mohammad, A.; Al Ahmadi, A.A.; Ullah, N.
Performance Analysis and Optimization of a Cooling System for Hybrid Solar Panels Based on Climatic Conditions of Islamabad, Pakistan. *Energies* **2022**, *15*, 6278.
https://doi.org/10.3390/en15176278

**AMA Style**

Sattar M, Rehman A, Ahmad N, Mohammad A, Al Ahmadi AA, Ullah N.
Performance Analysis and Optimization of a Cooling System for Hybrid Solar Panels Based on Climatic Conditions of Islamabad, Pakistan. *Energies*. 2022; 15(17):6278.
https://doi.org/10.3390/en15176278

**Chicago/Turabian Style**

Sattar, Mariyam, Abdul Rehman, Naseem Ahmad, AlSharef Mohammad, Ahmad Aziz Al Ahmadi, and Nasim Ullah.
2022. "Performance Analysis and Optimization of a Cooling System for Hybrid Solar Panels Based on Climatic Conditions of Islamabad, Pakistan" *Energies* 15, no. 17: 6278.
https://doi.org/10.3390/en15176278