You can use Parameter estimation Toolbox  in Simulink

Dear Ahmad,

It is an optimisation problem with multiple local optima since there is a local optimum for any value of n, i.e. ideality factor. Please have a look on my paper entitled "an acurate method for the pv model identification based on a genetic algorithm and the interior point method", Renewable Energy, 72,212-222, December 2014.

Regards, Arash

There are dozens if not hundreds of methods published for this problem.  The challenge is to find one that works for your application and with your data.  A review of methods was published last year by Adelmo Ortiz-Conde:

A review of diode and solar cell equivalent circuit model lumped parameter extraction procedures, Ortiz-Conde Adelmo, García-Sánchez Francisco J., Muci Juan, Sucre-González Andrea, copy at http://www.doiserbia.nb.rs/Article.aspx?id=0353-36701401057O#.Vfnshv7ouJA

My personal ideas are here: https://www.researchgate.net/publication/275961650_Parameter_Estimation_for_Single_Diode_Models_of_Photovoltaic_Modules

In my opinion, formulating the parameter extraction as you propose (optimization over a sum of current residuals), which has been done by many people, is likely to result in biased parameters. The ideality factors are generally overestimated and the dark current term is generally underestimated to compensate. Measurement noise will have a significant effect on these extracted parameters.

My advice is test any method you try using simulated IV curves (calculated from the fitted equation using assumed values) and then see if your parameter extraction can recover the known value.

Technical Report Parameter Estimation for Single Diode Models of Photovoltaic Modules

Dear Arash

Thank you very much for your answer. Actually, I am writing a review article on PV cell parameter estimation methods. As you know, when we are applying metaheuristics to an Engineering optimisation problem, it is very important whether the problem is of uni-modal or multi-modal nature (having only one global optimum or having multiple local optima). If the problem is multi-modal, we should greatly increase the exploration capability of the algorithm, while in the cases of uni-modal problems, high level of exploitation capability is required. Therefore, I must know whether PV cell parameter estimation problem belongs to which category. I had thoroughly read your GA-IP paper. In that paper, you stated that this is a multi-modal problem, but I did not found a solid reason there. Moreover, your objective function in that paper is different from that in my mind (root mean squared error which is the most common in literature. In your answer, I did not understand "It is an optimisation problem with multiple local optima since there is a local optimum for any value of n, i.e. ideality factor". Why it is so? If it is so, since we can have infinite number of ideality factors, we must have infinite number of local optima...

Thank you again for your help

With very warm regards

Sincerely,

Ahmad

Dear Clifford

Thank you very much for your informative answer. I read your recommended materials and they worked well. One more question: Based on your advice for using synthetic data, what will be the objective function? The error between estimate circuit model parameter values and exact circuit model parameters?

Best regards

Sincerely,

Ahmad

- "In that paper, you stated that this is a multi-modal problem, but I did not found a solid reason there"

  Please refer to Fig. 4 of the paper which indicates how there is a local optimum for different values of ideality factor. Actually, it means that there is an optimum value of (Rs, Rsh) for each diode that you are choosing for your model.

 - "we can have infinite number of ideality factors, we must have infinite number of local optima"

   Yes. That is right. It means that you can model your module with infinite different types of diode.

 - "your objective function in that paper is different from that in my mind (root mean squared error which is the most common in literature"

 Regarding the objective function, there are two issues which are addressed in the paper:

    i) Using the power at MPP at STC introduces an algorithmic error as explained as the paragraph just above (10) and therefore a normalized vector norm of the voltage, current and power at MPP have been used;

    ii) It is shown that using only the information available for STC is not enough to extract the optimum values for different types of PV modules (Please refer to the next to the last paragraph of the introduction section). For instance, from Fig. 8, it can be seen that ST40, which is a thin film module, is dominated by NOCT and therefore using the MPP information at STC is not accurate enough.

  As a result, the problem is modelled as a multi-objective problem using the MPP information at both STC and NOCT and is solved using a specific GA designed to solve multi-objective problems with multiple local optima.

Best,

Arash

Ahmad,

One useful reference on the existence (or absence) of multiple optima is

On the Estimability of the PV Single-Diode Model Parameters, Brian R. Zaharatos, Mark Campanelli, Luis Tenorio

I think the objective function should be chosen based on the use of the model you are calibrating. For prediction of power and energy, I'd use a sum of errors in power near maximum power. For other purposes, such as analysis of changes in cell performance over time, it may be more informative to consider different parts of the IV curve, such as the region near Voc. Sorry to answer "it depends" but I think that's the right answer.

Best regards,

Cliff

Dear Cliff

Thank you very much for your help. I tried much to find the PDF of the mentioned paper "On the Estimability of the PV Single-Diode Model Parameters, Brian R. Zaharatos, Mark Campanelli, Luis Tenorio". Is it possible for you to provide me with its PDF source?

Thank you again

Ahmad

Try here:  http://colorado.academia.edu/BrianZaharatos

If you can't download the paper perhaps Brian can send you a copy.

Best, Cliff

 Dear Ahmad

I agree with Cliff that different parameters can be obtained by investigating different portion of I-V curve. I extracted the various parameter by investigatin different portion of the curve. You can find the details of the proof in below paper.

http://scitation.aip.org/content/aip/journal/jap/114/8/10.1063/1.4819961

Dear Cliff and Dear Arash

Thank you again for your help and contribution

One question: IS computational time of the parameter estimation method crucial? I guess the importance depends on the application. Its true? and what is the answer for different applications?

Thank you again

Ahmad

This is an interesting discussion. The large number of publications on this topic is just an indication that the PV community still consider this as a challenge. I have seen cells, which are certified for calibration of instruments for I-V measurement, have declared to deviate from the real value of Voc by up to 5mv. This is a huge error range. In fact, the difference in Voc of a very good and average cell can be around 5 mv! The paper by Kumar and Panchal, which is referred to in the above posts is certainly an interesting contribution and needs some attention. However, I think their contribution should be considered as part of the solution to this challenge and not as the final solution. I think the solution to this problem belongs to probabilistic class of approaches. Here a short list over some of the reasons:

These are just some of the effects that rule out any deterministic approaches as final solution to this challenge. As far as I know, none of the stochastic approaches addresses all the above problems in a proper manner. This does not mean that they are wrong but just incomplete. When it comes to computational challenges, Kumar and Panchal are right in that many of the stochastic approaches are computationally expensive. The multimodality of the solution space is the major reason for it. As far as I known, in general optimisation problems, there are no computational method yet known that can guaranty the optimal solution. The solution by statistician to this kind of problems is to look at the average of many possible solutions. Therefore, they say that they sample and not optimise. There are many reasons, beside the convenience of practicality, for which this might be the correct way of doing it. This would be a paper by itself but I think a quick study of stochastic optimisation and specifically Bayesian optimisation would be advisable. It is difficult to understand that at the time when human are capable of detecting Higgs-Bosons and quarks, still we are struggling to estimate the solar cell parameters. This challenge needs more attention from the PV community.

Dear Ali, Dear Arash and Dear Cliff

Thank you again for you help.

An important question in my mind is that, PV manufacturers give out only three remarkable points (open circuit, short circuit and maximum power point) in their datasheet, however, most of parameter estimation strategies work based on experimental I-V data (not available by datasheet). Why it is so?

Kind Regards

Ahmad

I have not been in the industry for a while so I think others who are more updated can tell you more. However, I know, at least until 2010, some of the PV companies like Q-Cells and REC were developing QR code (1x1 mm) which could be printed on the middle of the cell. With a proper code reader one could access a database where all the information about the cell, including the IV values would have been stored. But as far as I know, this solution is never fully implemented.

Dear Gaurav Kumar, could you provide the PDF file of the article, I could not download it.

Dear Ahmad rezaee jordehi, as you know IV is a curve so it contains a lot of data, Isc and Voc is just 2 numbers.

i wrote an interesting section about parameter identification in this paper you can reference

https://www.researchgate.net/publication/299343083_the_role_of_articial_intelligence_in_photo-voltaic_systems_design_and_control_A_review

Research the role of arti�cial intelligence in photo-voltaic systems ...