Villalva's Algorithm for SDM-5P Electric Parameters Extraction Model and OPC Parameters Estimation

[JFrederico2022]

Hello, everyone!

I'd like to propose the implementation of Villalva's Algorithm for extracting the five-parameter Single-Diode Model (SDM-5P) electrical parameters, including a calc_parameters function compatible with Operational Conditions (OPC).

This algorithm was published in 2009 in IEEE Transactions on Power Electronics and provides a robust iterative method for determining an effective combination of SDM-5P parameters for I-V curve modeling, not restricted to Standard Test Conditions (STC), but applicable to arbitrary OPC.

Notably, the paper has accumulated over 6,000 citations in the literature (source: Google Scholar), reflecting its widespread adoption and relevance to the photovoltaic modeling community.

The full paper is attached below for reference:

Comprehensive Approach to Modeling and Simulation of Photovoltaic Arrays (Villalva et al., 2009)

The algorithm that I'm working is attached here:

Villalva Algorithm for Python.ipynb

I'd really appreciate your help. Thanks in advance and let's discuss!

Best regards,
João Frederico

[RDaxini]

Some initial thoughts:

I had a brief review of the paper and I think in principle this would be a valuable addition to pvlib.

I am not sure yet where this would best fit. I think I need some clarification. I thought the paper was proposing a new iterative method to determine diode parameters, as well as new physical representations/equations of the parameters themselves. In the example though, you just use pvsystem.calcparams_desoto, so I am not sure I understood the paper correctly.

In terms of the (new) equations, for context, I am curious of the origin of Equation 7. I understand the paper validates it as part of the analysis, but it seems to pop up out of nowhere as a proposed alternative. I might just be lacking some knowledge of different representations of I0 though and maybe this is a common/well-known equation. Anyway, we'd need to make sure we document these equations clearly in the docs.

One point on notation, we usually try to replicate what a manuscript does, but I think since everywhere else we use I_L for the photocurrent, the use of I_pv might be confusing. I would vote to stick with I_L but make a clear note in the docs that the manuscript uses I_pv.

if you're feeling ambitious, beyond adding new functions to pvlib it would be a bonus if we could get an example gallery addition as well. Since the modules in the manuscript must be pretty old, an example gallery addition fitting a few newer modules (maybe something from here?) could be valuable.

[cwhanse]

I agree with @RDaxini comments.

In pvlib, a calcparams_villalva function would go into pvlib.pvsystem. Code for fitting would go into pvlib.ivtools.sdm in a new module villalva.py

I recall looking at this algorithm some years back and didn't pursue it because we were interested in the commercialized single diode models (PVsyst, CEC). As @RDaxini points out, Eq. 7 creates a new single diode model (single diode equation + all-sky condition equations).

I'd like to see some additional verification of this algorithm. If we 1) assume parameter values for the single diode equation at STC, cells in series and temperature coefficients, 2) use pvlib.pvsystem.singlediode to calculate Vmp, Imp etc., and 3) apply Villalva's algorithm to the calculated Vmp, Imp, etc., do we recover the starting single diode equation parameters? I tried that in the iPython notebook and it looks like the resistances could be quite different from the assumed parameter values, but I may have made mistakes.

[JFrederico2022]

Hello @RDaxini and @cwhanse! Thanks for the comments. I'll gonna work on these topics.

I implemented the pvsystem.calcparams_desoto just to certify the determined parameters by the Villalva's model gives the SDM Parameters under OPC. I'll complete that application to Villalva's equations and show that can reproduce the IV curve key points.

I agree with @RDaxini about we use the standard nominations used by the pvlib community and we can just put a note that in the original paper use different notes for the electric parameters of SDM.

I think that is a great idea to provide an example in the example gallery. We can work on this.

@cwhanse is right! The equation is adapted for different conditions, despite it would be simpler to estimate Io under different temperature levels.

About the algorithm's verification mentioned by @cwhanse, it worked to make the modeling of IV curve and recover the starting SDM equation parameters. I'll organize better the code and bring it here more further to show you step-by-step.

Again, I really appreciate the interest and the comments to help to improve this algorithm.

[markcampanelli]

@JFrederico2022 One question I have about Villalva et al.'s derivation is equation (6). In equation (13) of the online version of Effective Irradiance Ratios to Improve I–V Curve Measurements and Diode Modeling Over a Range of Temperature and Spectral and Total Irradiance, I derived an expression for the reverse saturation current at the reference (aka. nominal) condition, ID0, that uses the non-ideal single-diode model instead of the idealized model, and it is parameterized in terms of Isc0 and Voc0 (both at reference conditions), where the photocurrent is eliminated as well. I am not sure of the effect of using the ideal approximation (might be bad for degraded devices?), but I never saw the value in applying a numerical approximation when it is seemingly not required. Instead of using equation (8) in my paper for ID (not at reference conditions), equation (13) could be altered to adjust Voc and Isc away from their reference conditions by following Villalva et al. I would be happy to help evaluate if this alternative approach provides any benefit. I have lots of code set up in pvfit for evaluating SDM fits against IEC 61853-1 datasets.

[cwhanse]

@markcampanelli I am not disregarding the technical merits of your idea regarding the saturation current. But we need to trace algorithms to references, and I'm a bit concerned about being able to do that if the implementation mixes equations from Villalva's and your papers. What would we call the resulting function?

For this traceability, I think it would be best to first implement Villalva as written, and then consider if a variant (with a different name) is an improvement.

[adriesse]

I think it would be best to first implement Villalva as written, and then consider if a variant (with a different name) is an improvement.

I do agree with @cwhanse, but at the same time want to explicitly encourage constructive collaboration. This github may not be the ideal place for it, but I don't know any other!

[markcampanelli]

@cwhanse @adriesse Fair enough. @JFrederico2022 I can investigate this independently, but please do consider this an open invitation to collaborate. More generally, I am interested in the IEC 61853-1 matrix fit quality of different choices for the so-called "auxiliary equations" that produce the full SDM from the standard 5-parameter SDE. BTW, the AEs I typically use in PVfit are at https://pvfit.app/sdm/info/.

[RDaxini]

Especially since this is João's first contribution, and it's a relatively complex one for a first contribution, let's agree on a clear plan forward for João. If I have understood the discussion correctly, @JFrederico2022, this is what I think needs to be done:

1. Perform some basic additional validation as described here, work with @markcampanelli for assistance
2. Pending validation, implement a calcparams_villalva() function into pvlib.pvsystem, and fitting code into a new module villalva.py in pvlib.ivtools.sdm
3. Generate an example gallery addition demonstrating the use of the Villalva algorithm (we should do this anyway even if the implementation faces any setback e.g. with the additional validation). Functions from here could potentially be refactored into pvlib as described in 2. at a later date anyway.
4. Reach out to @markcampanelli for possible collaboration!

[JFrederico2022]

Hello, everyone.

Thank you all for the warm engagement. I'm happy to take this discussion further.

@markcampanelli I'm glad you're interested in a potential collaboration, let's make it happen! I have some ideas for improving the Villalva model across a range of irradiance levels and PV cell temperatures, which could make the modeling more precise under real operating conditions. The IEC 61853-1 matrix fit is a great direction to explore alongside the Villalva model.

That said, I'd like to prioritize getting the original implementation published in pvlib first, so we have a better foundation to build on for future work.

@RDaxini thank you for the clear guidelines; they've been very helpful in organizing the workflow.

[RDaxini]

Thanks @JFrederico2022, sounds good.
If you require any assistance or have any questions about the GitHub mechanics of contributions (forks, branches, pull requests, commits, etc.) then our contributing guide may provide some guidance, but you can also just ask us directly.

[dgowdaan-cmyk]

Thanks @JFrederico2022 for proposing this. Villalva’s algorithm would be a valuable addition for SDM-5P modeling under OPC.
I’ve reviewed the 2009 paper and the attached notebook, and I agree with @cwhanse that implementing calcparams_villalva in pvlib.pvsystem plus the fitting code in pvlib.ivtools.sdm.villalva.py makes sense.
I’d be happy to help with:
Writing unit tests to verify parameter recovery against singlediode at STC.
Adding an example gallery entry using newer module data.
Drafting the docstrings and equation documentation following pvlib conventions.
Let me know if I can take on the test/example part while the core implementation is developed.

[RDaxini]

Thanks @JFrederico2022 for proposing this. Villalva’s algorithm would be a valuable addition for SDM-5P modeling under OPC. I’ve reviewed the 2009 paper and the attached notebook, and I agree with @cwhanse that implementing calcparams_villalva in pvlib.pvsystem plus the fitting code in pvlib.ivtools.sdm.villalva.py makes sense. I’d be happy to help with: Writing unit tests to verify parameter recovery against singlediode at STC. Adding an example gallery entry using newer module data. Drafting the docstrings and equation documentation following pvlib conventions. Let me know if I can take on the test/example part while the core implementation is developed.

My understanding from recent conversations with JFrederico2022 are that he will handle this in the near future once his grad school schedule permits.