Dear Nallapaneni,

Certainly you can! Just take care to choose a good mathematical function to connect Solar Radiation and Energy produced.

Regards,

M.B.Gavrilov

Not sure I understand what you mean. If E is merely defined to be equal to Area of PV panel*Efficiency of panel*Radiation*Performance Ratio, then there is no need for the regression. Your coefficient on solar radiation would simply be Area*Efficiency*Perform.Ratio. For which variables do you actually have collected data that varies over the course of the year?

There is definitely a correlation between incident radiation and PV system performance.  However, because of the orientation of the panels and the different climates, one must be careful to estimate the irradiance on the panel surface.  Typically on has an estimate of solar radiation on a horizontal surface.  This is referred to as Global Horizontal Irradiance (GHI).  To get the irradiance on the panel surface one must first separate the GHI into the direct and horizontal components.  Then one has to transform the components on the horizontal surface to the components on the tilted surface.  In addition there is a ground reflected component that also has to be taken into account.  Most of these formulas and correlations are discussed in solar radiation text books and there are numerous papers on this subject.  Once one has an estimate of the irradiance in the plane of array (POA), it will correlate well with the PV system performance.

There is considerable uncertainty in the measurement of GHI and other components of solar radiation.  These uncertainties must be kept in mind when analyzing the results.  There is the G.U.M. procedure for evaluating uncertainties. Information on the GUM model can be found at http://www.bipm.org/en/publications/guides/gum.html.

Because of the interplay between latitude, climate, and tilt of the array, a correlation established at one location is unlikely to work as well for the results at another location using monthly average data.  That said, if one is only interested in keeping track of the performance of the system over time, a correlation at one site may be used to follow the change in performance over time.  Unfortunately, on a monthly average basis the uncertainty in the estimated irradiance is often larger than any change in performance seen.

Hi Kumar, 

If you take the log of your formula, you can use least squres method to determine the coefficient of a linear model Y=A.X+B. You must choose the two variables to use in your model.

Dear Nallapaneni,

I believe IEC TC82 WG2 are working on standards for that: IEC 61853-3 and IEC 61853-4. They are both in CD - committee draft stage. Perhaps you can try to get a copy from your national committee.

Regards,

Peter

Here is the list of all TC82 project. You need a password from your NC to have access.

http://www.iec.ch/dyn/www/f?p=103:23:1988422441097::::FSP_ORG_ID,FSP_LANG_ID:1276,25

Dear Milivoj B. Gavrilov,

When I applied regression to identify them... I observed almost a linear relationship with correlation factor as 0.95. But When i tried to calculate theoretically, I am observing a variation in the Area as per the Energy equation. But when considering the practical scenario of a site, Panel area is fixed, the only variable is radiation.

Here I am bit unsatisfied with the results and trying to go for multi-regression models

Thank you for the information sir.

Dear Abdelmajid Ben Hadj Salem,

As per your suggestion, I also tried to co-relate the effective radiation with the help of global radiation and sunshine hours ratio also as per the equation Y=A.x+B and also considered around 17 different models with multiple variables. I have calculated the value of effective radiation and when i tried with energy equation, I am getting a linear relationship. But this linearity is not possible in the practical case. Can you suggest me any other alternative towards this in terms of mathematical expression that merly depend on various factor.

Thank you for your suggestions.

Dear Peter Seidel,

Thank you for giving the information sir.. I will definitely go the IEC documents and will try to get them. Thank you for suggesting.

If i have any doubts after go through that document, i will contact you sir. Please do help me in that case..

Dear Frank Vignola,

I understood the concept about radiation, in-fact i am also working on the radiation analysis using artificial intelligence and other mathematical functions with three to four different variables. I have even gone through the details of PVGIS, NASA data, HOMER data etc. There have given only the old data as per the TMY files. But for effective analysis, I am considering those data for estimating the solar radiation values for the coming years. This estimated data will be more effective for analysing the present and future of the PV system performance.

I will try to implement as per your suggestions. I also gone through ur project on performance on PV modules.

I thank you for the brief explanation as well the document.

Dear Zhaochen He,

Maybe what ur saying might be true. When i did the analysis, i am observing a linear relationship for almost any mathematical expression. But i tried comparing with variation in PR's and Radiation also. Still i am experiencing almost similar results. I would try using CF tool in Matlab or KNIME analytics tool.

Thank you for your suggestion.

Hi Kumar,

If you have numerical values, you must do some graphics between the different parameters, then you can see what type of models to use: quadratics, cubic  or exponential models.

Dear Salem Sir,

I will try to do that sir.. But in similar manner I tried in Matlab CF tool all the existing models.

Dear Nallapaneni,

When there are only two variables, Solar Radiation (y) and Energy produced (x), then it must be used one-dimensional function (fitting curve). This function can be linear (y = ax + b), square (y = ax 2 + bx + c), and higher degrees. Also, the function can be trigonometric, exponential, and so on. Then using the least squares method, you need seeks the best fitting curve. In practice, the most commonly used linear functions. This means that seeking only linear relation of two variables, and the correlation coefficient is a measure of the linear relationship. What is the correlation coefficient is closer to 1, then the points closer to a fitting curve, and vice versa.

If there are connection (dependency) more than two variables, you must use a multi-dimensional functions (multi-regression analysis), and multiple- and partial- correlations.

Regards,

M.B.Gavrilov

What kind of relation between Solar Radiation and Energy produced by PV panels do You use?

Do You consider real cloudness?

Dear Vladimir Kubove...

We can identify the co-relation between any parameters which are affecting the radiation, in the study, we are considering the parameters like cloud cover, temperature, humidity, sunshine hours. Based on the parameters chosen, a mathematical equation has to be developed. 

Yeah we consider real cloud cover also.

I suppose that 12 montly points is too small number for year interval. I prefere to use moving averaging for 7 days inteval (365 points instead of 12 points). Take look on this data.

Data PV-battery Isc averaging

Dear Nallapaneni,

Yes, you can apply least squares estimates on the two sets of data.

I think if it is possible !! The Angstrom model can be adapted, I recommend you the analysis.

Regards

One thing that can make your relationship off a bit is that the efficiency of your panel might vary during the day because of its temperature. When hotter, the efficiency decreases.

I'm assuming that your measurement of solar irradiance and your panel are next to each other. If that's not the case and they are far from each other, then you might also have some spatial differences if clouds are present.

Even though they are monthly values, maybe the mean behavior could be off because of things like these

The best Method for finding the relationship between the two variables is using graphical method. I most cases, the trends are even similar to one another. I am currently working on similar project a comparative study between three states in India.    

If is possible!!

Regards

Thank you, everyone, for the suggestions given... I am really very happy for the excellent support given...