How much money is your solar roof top saving in different months of the year?

1/6/2015

Do you know that the output of your solar power system is different in every month?
In some months you save more while in other months savings are less. Each month has different average temperature and different solar irradiance values, which makes your solar roof to give different outputs and hence resulting in different savings.

Let us first see how the solar insolation and temperature affects the performance of the solar roof and then finally arrive at the monthly savings by your solar roof.

(1) The output of your solar roof is directly proportional to the solar insolation levels

The solar insolation levels of Delhi/NCR in India are as follows (you can solar insolation values of your region):

Months	Average Solar Insolation in Delhi/NCR
Jan	3.66
Feb	4.86
Mar	6.27
Apr	6.91
May	7.13
Jun	6.54
Jul	5.65
Aug	5.45
Sep	5.47
Oct	5.26
Nov	4.75
Dec	3.49
Average	5.45

Please look at the above chart, the performance of your solar roof will be in correlation with these values. The output of your solar roof will increase with the increase in the solar insolation levels and will decrease accordingly.

(2) Your solar system's performance varies with temperature

Its efficiency is inversely proportional to the temperature. That is the output from your solar panel decreases when temperature rises and efficiency increases when temperature decreases.

Solar roof output \(\alpha\) (1/Temperature)

The temperature coefficient percentage is generally mentioned in the data sheets of the solar panels and also at the back of it. If the temperature coefficient is say 0.5%, it means that the output of the solar panel will decrease by 0.5% with every degree increase in temperature above 25 degree Celsius. Similarly, the output of the solar panel will increase by the same proportion i.e. by 0.5% with every degree drop from 25 degree Celsius.
(With the increase in the humidity levels the output of the solar panels decreases)
Let us see the average temperature of Delhi/NCR in different months of the year.

The average temperature in different months of the year

By looking at the above chart you can see that the average temperature is the maximum in the month of May while it is the lowest in the month of January.
The July and August are the months of monsoon, in which this region receives the rainfall and the humidity levels reaches above 70% (The increase in humidity level decreases the output of the solar panel)

Solar Roof output \(\alpha\) (Solar Insolation / Temperature)

(3) Your solar roof output under standard temperature conditions of \(25^oC\)

Now, in ideal conditions we can say that the 1 KW solar systems produces the same number of units as that of solar insolation levels in that particular month. But in actual conditions, the output is generally lower because of different losses associated with the transfer of energy from one place to another and conversion from one form to another. So, we can assume 85% efficiency of the system and the remaining 15% of the energy is lost.
Let us look into the table for better and clear understanding:

Months	Average Solar Insolation in Delhi/NCR (KWHr/mÂ²/day)	Units generated by 1 KW solar system in ideal conditions (No energy losses)	Daily output units with 85% efficiency (D x 0.85) under standard temperature conditions of 25 Â°C
Jan	3.66	3.66	3.11
Feb	4.86	4.86	4.13
Mar	6.27	6.27	5.33
Apr	6.91	6.91	5.87
May	7.13	7.13	6.06
Jun	6.54	6.54	5.56
Jul	5.55	5.55	4.72
Aug	5.45	5.45	4.63
Sep	5.47	5.47	4.65
Oct	5.26	5.26	4.47
Nov	4.75	4.75	4.04
Dec	3.49	3.49	2.97
Average	5.45	5.45	4.63

Above are the output levels under standard temperature conditions and with 85% efficiency of the solar system.

(4) Your real savings when considering the temperature variations of the different months of the year

Now let us see how the actual output changes when we take into account the temperature variations, please see the table below

A	B	C	D	E	F	G	H
Months	Average temperature	Solar Insolation	Units generated by 1 KW solar system in ideal conditions (No energy losses)	Output units with 85% efficiency (D x 0.85) under standard temperature of 25 degree Celsius	Actual Output units (considering temperature variations)	Actual output increases/ decreases by	Savings (F x Rs. 4.5/ unit)
Jan	15	3.66	3.66	3.11	3.27	5%	â‚¹ 14.72
Feb	21	4.86	4.86	4.13	4.21	2%	â‚¹ 18.95
Mar	28	6.27	6.27	5.33	5.25	-2%	â‚¹ 23.63
Apr	33	6.91	6.91	5.87	5.64	-4%	â‚¹ 25.38
May	39	7.15	7.15	6.08	5.65	-7%	â‚¹ 25.43
Jun	36	6.54	6.54	5.56	5.25	-6%	â‚¹ 23.63
Jul	35	5.65	5.65	4.8	4.56	-5%	â‚¹ 20.52
Aug	34	5.45	5.45	4.63	4.42	-5%	â‚¹ 19.89
Sep	28	5.47	5.47	4.65	4.58	-2%	â‚¹ 20.61
Oct	25	5.26	5.26	4.47	4.47	0%	â‚¹ 20.12
Nov	22	4.75	4.75	4.04	4.1	1%	â‚¹ 18.45
Dec	16	3.49	3.49	2.97	3.1	4%	â‚¹ 13.95
	27.67	5.46	5.46	4.64	4.58	-1%	â‚¹ 20.44

Savings in the different months of the year

You can see in the table above that how with the increase in the temperature (Mar, Apr, May, Jun, Jul, Aug and Sept) above the standard temperature of 25Â°C causes the actual output to decrease.
Also, see that how decrease in temperature below standard temperature of 25Â°C in certain months (Jan, Feb, Nov and Dec) causes the actual output to increase in its value.
See that in the month of October, the average temperature is 25Â°C, which is equal to the standard temperature, therefore there 0% change in the actual output with respect to output under standard conditions.

Conclusion

You are saving the highest in the month of May, Rs. 762.90, although there is major reduction in efficiency of 7% in the actual output of the solar roof. This is due the fact that the average temperature in the month of May is the highest that is \(39^oC\), 14 degrees above the standard temperature, the fall in output is \((39^oC - 25^oC)\)x 0.5% = 7%. But still the actual output is the highest amongst the 12 months of the year, this because of the fact that the solar insolation levels in this month is the highest.
Whereas the output levels in the month of Dec and Jan are the lowest, although their actual output increase by 4% and 5% respectively. The low insolation levels are the main reason of low output of the solar panels.
By looking at the chart above we can say that the 1 KW system saves an average of Rs. 618.30 per month.

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