Dear Narjes Azizi

Here’s a simple formula for calculating your solar panel’s power output.

Solar panel watts x average hours of sunlight x 75% = daily watt-hours

As an example, let’s say you have 250-watt solar panels and live in a place where you get 5 hours of sunlight per day. What’s that 75 percent for? That’s to account for all those variables we've been going over.

250 watts x 5 hours x .75 = 937.5 daily watt hours

To translate this into the more familiar kilowatt hours you’re used to seeing on your electricity bill, simply divide by 1000.

937.5 / 1000 = 0.937

To round up and make it pretty, that’s 0.94 kilowatt-hours per solar panel.

Dear Narjes Azizi ,

Hope you are well!

This is the 7000 th answer for me on the RG.

After estimating reviewing the your calcualtions I found that the error may come from the calculations of the fill factor.

Your estimated value of the FF may be too large.

The FF under standard conditions is 0.77 and your is = 0.8876

But this may be affordable.

There is a mistake in calculating the open circuit voltage since you operate the cell under much lower INSOLATION of = 267.9426 watt/ m^2 instead of 1000 watt/m^2.

So the open circuit voltage will be lower by N Vt ln (1000/ 267.9426)

with N=no. of cells =60 ,Vt=25 mV one gets 1.975 V

Then the correct value of the your panel = 41.228 (your calculated value) - 1.975=39.253 V.

This will reduce the efficiency to = 21.76 x 39.25/41.228=20.7

You must also recalculate the fill factor.

AS the Voc is reduced it FF will be also reduced.

Yes the solar cell efficiency will increase basically as the environmental temperature decreases. This is a physical behavior.

Best wishes

Abdelhalim abdelnaby Zekry

Dear professor Abdelnaby

I truly appreciate your answer which was a great help to me. Thank you for being so generous as to share your knowledge. There are some other things I would be grateful if you could answer them as well. First, I applied what you said to the open-circuit voltage and the amount of it improved. If possible, give a reference for the formula for me (N*Vt*ln(G/G0)) to understand it better.

The problem with the value of the fill factor still exists and its amount is 0.88 which is still far from 0.77.

In addition, as you said if the ambient temperature decreases the efficiency increases. So, is it ok to conclude “in winter the efficiency of a solar panel is higher than in summer”?

Dear @Narjes,

Hope you are well!

You can find the equation which I used in the book chapter: https://www.researchgate.net/publication/323309527_Solar_cells_and_arrays_Principles_analysis_and_design

Namely equation 1.44

Voc= nVt Ln (Isc/Is),

Isc is proportional to

Accordingly delta Voc= nVt Ln G2/G1,

n is the ideality factor which is equal to 1 for the single crystal silicon solar cells.

G2 is the Insolation at Voc2 and G1 for Voc1.

It is good possible that FF becomes larger due to the decrease in temperature because the series resistance of the solar cells becomes smaller with lower temperature and hence the FF increases.

The single crystal silicon solar cell efficiency increases with reducing the operating temperature.

I see your estimations are now okay.

Best wishes

Abdelhalim abdelnaby Zekry

Dear professor Abdelhalim abdelnaby Zekry,

Thanks a lot for the reference you gave to me. I would be grateful if you could answer this question as well. According to the data I have which was attached to my first question, can I calculate the reverse saturation current on equation 1.44?

Dear Narjes Azizi ,

welocme again!

I would like to tell you that there is a method to calculate directly the new open circuit voltage without knowing Is , the reverse saturation current or Vt the thermal voltage.

It is straight forward from the relation:

Voc= nVt Ln (Isc/Is),

All what we need is to apply the above relation two times at Voc1 at Isc1

and Voc2 at Isc2 as:

Voc1=nVt Ln (Isc1/Is), (1)

Voc2=nVt Ln (Isc/Is), (2)

Dividing (2) by (1) one gets

(Voc2/Voc2) = Ln (Isc2/Isc1)

Since Isc is proportional to G the incident solar radiation,

Then the above equation can be written as:

(Voc2/Voc2) = Ln (Isc2/Isc1)= Ln (G2/G1)

As for estimating the Is the reverse saturation current you can use

the equation directly

Voc= nVt Ln (Isc/Is),

Since you know Voc , Isc , Vt under standard condition and assuming n=1 as it is the case always for the single crystal Si solar cell, one can directly estimate Is.

Bu if you are given the standard illuminated I-V curve you can determine the 5 parameters of the single junction solar cell as given in the book chapter: https://www.researchgate.net/publication/323309527_Solar_cells_and_arrays_Principles_analysis_and_design

Best wishes

Abdelhalim abdelnaby Zekry

Dear professor Abdelhalim abdelnaby Zekry,

you were a great help to me. thank you very much.

hello

Dear Abdelhalim abdelnaby Zekry

I did the calculations again according to your book and came up with the answers in Table 4 in the attached file. The calculated voltage is different. I wonder if you could take a look at calculations and say which solution seems more logical?

Dear Narjes Azizi ,

Ramadan Kareem!

Hope you are well!

Yes there is good agreement in the results of the calculations of Isc and the FF.

The discrepancy in the open circuit voltage. By revising the calculations, it seems me that your first method of the open circuit voltage calcualtions is more accurate than the other method based on calculating Is. It is very probable that there is a mistake in calculating the change of Is with temperature.

Because the value of energy gap must be vert precisely known. Eg also changes with temperature. Namely , it decreases with increasing the temperature.

So such calcualtions of dependence of Is with temperature needs elaboration.

Best wishes