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Solar energy is directly converted into electrical energy by using photovoltaic (PV) panels. The efficiency of PV panel varies with its orientation and tilt angle with the horizontal plane. In this paper, we investigate the optimum tilt angle of solar panels installed at Sukkur IBA University. The optimum angle for tilted surfaces varying from 0° to 90° in steps of 1° was calculated for the values of which the daily total solar radiation was maximum for a specific period. It was found that the optimum tilt angle changed between 0° and 61.1° throughout the year in Sukkur IBA University, Sindh Pakistan (

There are two main resources of power, namely, conventional and nonconventional. Nonconventional resources have become popular due to various advantages such as being nonpollutant, fuel free, and nonexhausted [

A key requirement to achieve maximum power from solar is to avoid the shading effects on solar modules and usage of solar tracking systems. Solar tracking system is the best solution for tracking sunrays to approach the tilt angle continuously, but these trackers are expensive and are not always applicable [

Selection of tilt angle has become a hot area research to improve system efficiency. Numerous studies have been carried out to check the performance of PV systems by using different observations, proper diagrams, design, and relationships between different parameters and characteristics related to choosing proper installation site [

Optimum tilt angle for solar PV system is different due to geographical locations and seasonal variations. The geographical factors include declination angle and data related to solar resources which are important to decide the optimal tilt angle for solar PV system [

For determining the optimal tilt angle of solar PV module, it is important to calculate declination angle of the sun and estimation of solar radiation on the tilted surface [

Moreover, researchers have also suggested different theoretical models for calculating the optimum tilt angles of several solar collectors and consider a collector with given structural parameters that the latitude of installation site, climate conditions, tilt, and azimuth angles are related to collectible radiations in a year [

Sukkur region, located in northern Pakistan, has great solar radiation potential since the number of sunshine is large. Its rural areas face acute power cut off usually 14 to 16 hours per day. So the farmers are resorting to PV systems to cultivate small areas by using drip irrigation method and for other purposes. But due to unavailability of proper data, PV systems are installed in random orientations so they do not get optimal power. Therefore, by employing the analytical and numerical methods, we have found out the optimal angle for PV systems for the given region. This research work will provide local community a way to achieve maximum power output which is bound to give numerous economic benefits.

In this paper, we have calculated and compared irradiance on fixed and variable optimal tilt angle by using MATLAB/Simulink. The fixed angles are 15 degrees and 29.5 degrees. A 15-degree tilt angle is currently used at Sukkur IBA University for PV solar system.

Initially, constant values

Tilt angle is varying from 0 to 90 degrees with one degree step size for accurate results. For finding irradiances, we have gone through the steps to first calculate the

The equation used to calculate the total solar radiation on the tilted surface is given as [

where

where

Now, the tilt coefficient diffuse solar radiation on the tilted surface can be calculated as:

where

Here,

The data related to global solar radiations on horizontal surface is taken from NASA database.

where

The clearness index is a measure of the clearness of the atmosphere. It is the fraction of the solar radiation that is transmitted through the atmosphere to strike the surface of the earth. And it can be calculated from equation (

^{2}/day) and can be calculated by:

^{2} [

Using equations from (

Flowchart for finding optimal tilt angle.

Through mathematical modeling as discussed in Section

The input data for finding maximum irradiance on solar panel are global solar radiations on horizontal surface (^{2}/day and W/m^{2}/day carried from NASA database as shown in Table

Monthly specific daily global irradiance (

^{2}/day | ^{2}/day | Year day | Month day | Tilt angle (deg) | Irradiance level after tilt | Declination angle of earth |
---|---|---|---|---|---|---|

7490 | 913 | 21 | 21 Jan | 15 | 1222 | -20.14 |

7560 | 921 | 52 | 21 Feb | 15 | 1125 | -11.23 |

8770 | 1069 | 80 | 21 Mar | 15 | 1186 | -0.403 |

9420 | 1148 | 111 | 21 Apr | 15 | 1161 | 11.58 |

10610 | 1293 | 141 | 21 May | 15 | 1227.6 | 20.14 |

11210 | 1367 | 172 | 21 Jun | 15 | 1265.5 | 23.45 |

11420 | 1392 | 202 | 21 Jul | 15 | 1319 | 20.44 |

10250 | 1250 | 233 | 21 Aug | 15 | 1261.5 | 11.75 |

10390 | 1267 | 264 | 21 Sep | 15 | 1403 | -0.2 |

8830 | 1076 | 294 | 21 Oct | 15 | 1320 | -11.75 |

9000 | 1097 | 325 | 21 Nov | 15 | 1474 | -20.44 |

6990 | 852 | 355 | 21 Dec | 15 | 1187.5 | -23.45 |

After putting this input data in equations, we have calculated declination angle and irradiance at fixed optimal tilt angle using MATLAB/Simulink model. The value of irradiance is maximum 1474 W/m^{2}/day in November and minimum 1125 W/m^{2}/day in February. The average value of irradiance throughout the year will be 1262.675 W/m^{2}/day. The irradiance is not constant in every month throughout the year, but it is varying as shown in Figure

Specific monthly irradiance on fixed tilt angle (15 deg) and declination angle vs. months.

The graph shows that solar PV module is fixed at tilt angle of 15° where it has received irradiance between 1300 w/m^{2}/day and 1474 w/m^{2}/day in 4 months, between 1200 w/m^{2}/day and 1300 w/m^{2}/day for 3 months, and 1100 w/m^{2}/day and 1200 w/m^{2}/day for 5 months in year 2019. 15° tilt angle is optimal for months (Oct–Feb) referring to Table

The input data is used to find the irradiance and declination angle at different variable angles. The results achieved from calculations are shown in Table

Monthly specific daily global irradiance (

^{2}/day | ^{2}/day | Year day | Month day | Optimum tilt angle (deg) | Irradiance level after tilt | Declination angle of earth |
---|---|---|---|---|---|---|

7490 | 913 | 21 | 21 Jan | 57.73 | 1630 | -20.14 |

7560 | 921 | 52 | 21 Feb | 47 | 1310 | -11.23 |

8770 | 1069 | 80 | 21 Mar | 30.95 | 1229 | -0.403 |

9420 | 1148 | 111 | 21 Apr | 10.16 | 1164 | 11.58 |

10610 | 1293 | 141 | 21 May | 0 | 1294 | 20.14 |

11210 | 1367 | 172 | 21 Jun | 0 | 1367 | 23.45 |

11420 | 1392 | 202 | 21 Jul | 0 | 1392.7 | 20.44 |

10250 | 1250 | 233 | 21 Aug | 9.834 | 1265.8 | 11.75 |

10390 | 1267 | 264 | 21 Sep | 30.62 | 1452 | -0.2 |

8830 | 1076 | 294 | 21 Oct | 47.74 | 1549 | -11.75 |

9000 | 1097 | 325 | 21 Nov | 58.06 | 1977 | -20.44 |

6990 | 852 | 355 | 21 Dec | 61.19 | 1677.6 | -23.45 |

Table

Specific monthly irradiance on variable optimal tilt angle and declination angle versus months.

Solar panel with small input global solar irradiance on horizontal surface between 7000 and 9000 Wh/m^{2}/day received maximum amount of irradiance between 1200 w/m^{2}/day and 1977 W/m^{2}/day on tilt angle of 30° or above in the month from September to March. It is actually getting maximum irradiance for seven months at an angle 30° or above. The value of irradiance is found to decrease from April to August at an angle of 0 to 11 degrees, and the average value of irradiance is 1442.342 W/m^{2}/day. This value of irradiance is greater than the value at 15 degrees optimal tilt angle.

We have taken a fixed optimal tilt angle of 29.5 degrees to check the irradiance. The value is actually taken as the average value of all variable angles to see the irradiance level. The results of irradiance and declination angle are shown in Table

Monthly specific daily global irradiance (

^{2}/day | ^{2}/day | Year day | Month day | Tilt angle (deg) | Irradiance level after tilt | Declination angle of earth |
---|---|---|---|---|---|---|

7490 | 913 | 21 | 21 Jan | 29.5 | 1447.27 | -20.14 |

7560 | 921 | 52 | 21 Feb | 29.5 | 1253.4 | -11.23 |

8770 | 1069 | 80 | 21 Mar | 29.5 | 1229 | -0.403 |

9420 | 1148 | 111 | 21 Apr | 29.5 | 1108 | 11.58 |

10610 | 1293 | 141 | 21 May | 29.5 | 1102.8 | 20.14 |

11210 | 1367 | 172 | 21 Jun | 29.5 | 1109.5 | 23.45 |

11420 | 1392 | 202 | 21 Jul | 29.5 | 1182 | 20.44 |

10250 | 1250 | 233 | 21 Aug | 29.5 | 1202.5 | 11.75 |

10390 | 1267 | 264 | 21 Sep | 29.5 | 1451.6 | -0.2 |

8830 | 1076 | 294 | 21 Oct | 29.5 | 1476.6 | -11.75 |

9000 | 1097 | 325 | 21 Nov | 29.5 | 1749.5 | -20.44 |

6990 | 852 | 355 | 21 Dec | 29.5 | 1440.2 | -23.45 |

From Table ^{2}/day. The data of Table

Specific monthly irradiance on optimal fixed tilt angle (29.5 deg) and declination angle versus months.

Figure ^{2}/day received maximum amount of irradiance between 1250 w/m^{2}/day and 1451 w/m^{2}/day which are greater than irradiance received on solar panel at 15° tilt angle. This value is receiving from September to March. Means solar panel received 7 months out of 12 months maximum irradiance at an angle 29.5°.

After receiving irradiance at fixed and variable angles, we have get our results. The results at all conditions are compared as shown in Figure ^{2}/day in the month of November. Although this value is greater than 15 degree and 29.5 degree values, yet it is impossible to practically use variable optimal tilt angle.

Comparison of irradiance on different tilt angles.

After comparison from all results, we are suggesting to use optimal tilt angle of 29.5 degrees to get the maximum irradiance value.

In this paper, an analytical and numerical analysis has been carried out on different tilt angles to check the irradiance by using MATLAB/Simulink. A 15-degree tilt angle is used at Sukkur IBA University for solar system of 1 MW. For finding optimum tilt angle, the PV module is tilted from 0 to 90 degrees, where the value of

The results are taken at both fixed and variable tilt angles which shows that maximum irradiance can be achieved at 29.5 degrees as compared to 15 degrees used at Sukkur IBA University.

The method employed in this paper can also be used for installing the PV systems in other locations so as to obtain maximum power from system.

Total solar radiations received on tilted surface

Solar beam radiations on horizontal surface

Tilt coefficient to calculate direct solar direct radiations

Solar diffused radiations on horizontal surface

Tilt coefficient to calculate solar diffused radiations

Global solar radiations on horizontal surface

Ground reflectivity coefficient

Tilt angle of surface

Sunrise hour angle on tilted surface

Sunrise hour angle on horizontal surface

Latitude of the place

Declination angle of the earth

Counted number of days

Clearness index

Monthly average daily extraterrestrial radiation.

Data is available on request.

The authors declare that they have no conflicts of interest.