Preliminary report results

1. Daylight Duration and Time Period

• Full daylight duration: 11.11 hours (from sunrise to sunset).
• Experiment duration: 6 hours (12:00 PM to 18:00 PM), which is about 54% of the full daylight period.

Since the calculator gives results for the entire day, we need to adjust the theoretical values to only cover the second half of the day.

2. Effective Irradiance During Experiment

The effective irradiance changes throughout the day because of the sun's position and weather. To refine the calculation:

• Clear sky irradiance: Assume an average of 876 W/m² during peak sunlight hours.
• Cloud cover impact:
  • From 12:00 PM to 15:00 PM: Clear skies (no reduction in irradiance).
  • From 15:00 PM to 18:00 PM: 70% cloud cover, reducing irradiance by 70%.

Step 1: Irradiance from 12:00 PM to 15:00 PM

For the first 3 hours (clear skies): Effective irradiance = 876 W/m².

Step 2: Irradiance from 15:00 PM to 18:00 PM

For the last 3 hours (70% cloud cover): Effective irradiance = 876 * (1 - 0.7) = 876 * 0.3 = 262.8 W/m².

Step 3: Average Irradiance During Experiment

The average irradiance over the 6-hour period is: Average irradiance = [(Clear irradiance * Clear time) + (Cloudy irradiance * Cloudy time)] / Total time.

Substitute the values: Average irradiance = [(876 * 3) + (262.8 * 3)] / 6
= (2628 + 788.4) / 6
= 3416.4 / 6
= 569.4 W/m².

So, the average effective irradiance during the experiment is 569.4 W/m² .

3. Theoretical Power Output During Experiment

Using the formula for power output: Power = Average irradiance * Panel area * Efficiency.

Substitute the values: Power = 569.4 * 0.2709 * 0.0605
= 9.28 W.

The theoretical average power output during the experiment is 9.28 W .

4. Total Energy Generated During Experiment

The total energy generated is: Energy = Power * Time.

Substitute the values: Energy = 9.28 * 6
= 55.68 Wh.

The theoretical total energy generated during the experiment is 55.68 Wh .

Comparison with Experimental Results

Key Observations

1. Close Alignment : The theoretical values are now much closer to the experimental results after adjusting for cloud cover and timing.

2. Remaining Discrepancy :

   • The experimental average power output (10.34 W) is slightly higher than the theoretical value (9.28 W). This could be due to:
     • Temporary peaks in irradiance caused by light scattering under partial cloud cover.
     • Cooler temperatures improving panel efficiency.
     • System dynamics allowing the system to operate closer to the panel's maximum power point (MPP).

3. Energy Storage Efficiency : The experimental energy stored (62.043 Wh) exceeds the theoretical prediction (55.68 Wh) by about 11.4%. This suggests that the system efficiency was higher than assumed in the theoretical model.

Conclusion

By refining the theoretical calculations to account for the specific timing (12:00 PM to 18:00 PM) and visibility conditions (70% cloud cover after 15:00 PM), we achieve a much closer alignment between theory and experiment:

• Theoretical Average Power Output: 9.28 W
• Experimental Average Power Output: 10.34 W
• Theoretical Total Energy Generated: 55.68 Wh
• Experimental Total Energy Generated: 62.043 Wh

The remaining discrepancies can be attributed to localized weather effects, temperature variations, and system efficiency.

Final Answer

The refined theoretical calculations predict an average power output of 9.28 W and total energy generation of 55.68 Wh , closely matching the experimental results.