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+Title: PV Electric Mismatch in Silicon-Cell PV - Part 2
+Date: 2024-08-23 01:10
+Category: Solar
+Tags: solar, modeling, code
+Authors: Mark Mikofski
+Summary: What happens when shade cuts across PV strings?
+
+> Note: This post is part of a joint blog with my colleague Kurt Rhee:
+[Primer on Electrical Mismatch](https://kurt-rhee.github.io/2024/04/15/a-primer-on-electrical-mismatch) 
+
+
+# The many shades of PV electrical mismatch
+Effects from shade are complicated, but can be summarized in two orthogonal categories:
+
+1. [shade parallel to strings](#shade-parallel-to-strings)
+2. [shade perpendicular to strings](#shade-perpendicular-to-strings)
+
+These categories were defined in the Fast Shade Model [[1, 2](#references)]
+developed by Dr. Bennet Meyers after simulating hundreds of different shade
+patterns and grouping them by their electrical mismatch. 
+
+## shade parallel to strings
+One example of shade across all modules that is parallel to strings, is row-to-row
+shade in fixed-tilt systems, typically in winter. When I originally wrote
+about [PV electrical mismatch]({filename}PV-electrical-mismatch.md), I analyzed
+this type of shade using [PVMismatch](https://sunpower.github.io/PVMismatch/)
+to simulate shade across the bottom row of a single string of 10 modules in a
+10 string system. The conclusion of that post was that the string performed as
+well as the most shaded cell, so even though only the bottom cells were shaded,
+the modules in the string lost most of their power. I shaded the bottom cells
+80% to simulate only diffuse light, and the string lost roughly 80% of output.
+The other 9 strings operated at full capacity, so the system only lost 8%. The
+[NIST ground mount array](https://www.nist.gov/el/energy-and-environment-division-73200/heat-transfer-alternative-energy-systems/photovoltaic-1)
+is an example of a system that will have row-to-row shade in winter that will
+cause most of the strings to lose almost all of their output even when only
+the bottom row of cells is shaded.
+
+![NIST Google](./images/nist-ground-array.png)
+
+## shade not parallel to strings
+However, that post also contained a picture of a rooftop with non-uniform shade
+that was not consistent across each module of the string. The shade cast from
+the roofline cut diagonally across the modules in the string, which was wrapped
+in two rows to fit.
+
+![non uniform shade on a roof](./images/20150923_170418.jpg)
+
+I didn't analyze the shade from this system in that post, so it raises the
+question whether the rule of thumb I recommended would still apply?
+
+## shade perpendicular to strings
+To simplify the question, the rest of this post analyzes a PV system with a
+shade obstacle like a wind turbine, a telephone pole, or a chimney, that casts shade
+perpendicular to the strings. My analysis is in this Jupyter notebook on Google Colaboratory:
+[`mismatch_vs_strings.ipynb`](https://colab.research.google.com/drive/1b2Ll7G-4WBKPl57m-FPBhU8MLjLOTfIb)
+
+>TL;DR: When shade cuts perpendicular to strings, cells go into reverse bias,
+bypass diodes activate in the shaded submodules, and the other modules operate
+at higher voltage to match the voltage of unshaded parallel strings.
+
+I simulated perpendicular shade on the first half of the first module in the
+string, while the rest of the strings were unshaded. For example, this shade could be caused by a
+chimney. Then I increased the number of unshaded strings to see if it changed
+the effect. The effect of a shadow perpendicular to the string caused bypass
+diodes to trigger. Adding more strings did not stop the bypass diodes from triggering, even after 20 parallel
+strings. The IV curve of the system had a kink until 4 unshaded parallel strings were added, but after 9 unshaded parallel strings were added, the IV curve
+appeared unaffected. After 19 unshaded parallel strings were added, the total power loss was only 0.85% for the system
+compared to unshaded. However, the power loss in the shaded string was about 15%.
+
+Here is the IV curve of the 20 string PV system with perpendicular shade on the
+1st module of the 1st string from the Jupyter notebook. It looks unaffected!
+
+![20 string PV system with cross-string shade](./images/cross-string-mismatch/pvsystem-20strings.png)
+
+Now check out the IV curve of the string with the shaded module. It should
+be generating about 3200[W], but even though it's lost about 500[W], it
+still operates at 5[A], nearly the same current as the other strings. It
+still has to operate at the same voltage as the other strings, 538.7[V] in
+this example, so how does it do it with 2 bypass diodes activated?
+
+![20 string PV system with cross-string shade](./images/cross-string-mismatch/pvstring-20strings.png)
+
+A look at the module IV curves tells the rest of the story. The shaded module
+still has to carry the 5[A] of the string, but 2 bypass diodes are triggered
+so the voltage is down 75%. Note: these are SunPower/Maxeon 320[W] modules,
+that have 96-cells in 8-columns with 3 bypass diodes in a 24-48-24 cell arrangement.
+
+![20 string PV system with cross-string shade](./images/cross-string-mismatch/pvmod0-20strings.png)
+
+However, the unshaded modules make up for the lost voltage in the shaded
+module by operating just above the max power point. This is why the string
+is operating at 5[A], to increase the voltage in the unshaded strings.
+Very clever! Go team! Luckily for the shaded module, that current is
+also very close to its max power point, which is only down 75% thanks
+to the activated bypass diodes. Recall in the parallel shade scenario,
+the entire string was down.
+
+![20 string PV system with cross-string shade](./images/cross-string-mismatch/pvmod1-20strings.png)
+
+Please check out [`mismatch_vs_strings.ipynb`](https://colab.research.google.com/drive/1b2Ll7G-4WBKPl57m-FPBhU8MLjLOTfIb)
+because the 1-string example isn't limited by the voltage of parallel strings, so it's free to operate at the max power
+point, and the losses are lower. Recall in the 20-string example, the shaded string lost about 15%, but in the 1-string
+example, the loss was only about 8%. Another variation is allowing the shade to cross two or more strings. I covered
+a scattershot of scenarios and found that parallel string voltage began to dominate sowmhere between 5 to 10 strings.
+Of course, that only applies in this contrived example, but it was interesting nonetheless.
+
+## Conclusion
+I wish I could say, that's all there is to it, but as I said in my first blog post,
+electrical mismatch in crystalline silicon is very counter-intuitive.
+That's why I created PVMismatch to begin with. I was tired of guessing and
+being wrong. So don't guess. Simulate with confidence, try PVMismatch, and
+let me know what you learn!
+
+## Epilogue
+So back to that rooftop with the diagonal shade line. It's a bit of both
+categories right? How do you think it will perform? Will it lose nearly
+all of its power or will bypass diodes active and save the day? Or maybe
+something in between or completely different. Try to analyze it using
+PVMismatch. If you need help I analyzed it in this Google Colab notebook:
+[`nonuniform-rooftop-shade.ipynb`](https://colab.research.google.com/drive/1wOSF9aNvxUc2t1iduNKN1Dn-vBW_j92w)
+
+## References
+
+1. Meyers, B., Mikofski, M. A., & Anderson, M. (2016). A Fast Parameterized Model for Predicting PV System Performance under Partial Shade Conditions. In IEEE (Ed.), 2016 IEEE 43rd Photovoltaic Specialists Conference (PVSC) (pp. 3173–3178). IEEE. [https://doi.org/10.1109/PVSC.2016.7750251](https://doi.org/10.1109/PVSC.2016.7750251)
+2. Meyers, B., & Mikofski, M. A. (2017). Accurate Modeling of Partially Shaded PV Arrays. In IEEE (Ed.), 2017 IEEE 44th Photovoltaic Specialist Conference (PVSC) (Vols. 2017-June, pp. 3354–3359). IEEE. [https://doi.org/10.1109/PVSC.2017.8521559](https://doi.org/10.1109/PVSC.2017.8521559)
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