Spreadsheet to calculate PV output with shading

[ovonrein]

the 6.3A comes from the datasheet.

Penny's just dropped.  You are now reasoning V=f(I), I=f(sun).  Only problem is that at 6.3A the reverse biased cell cannot run at -9V so the sunny cells need to push past their Vmp a little to meet V(string), which they can do happily.  So your cell will likely run hotter than mine.

PS:  Incidentally, a single shaded cell isn't so unlikely at all, assuming you have birds passing over your array (doing unmentionable things) once in a blue moon, no?

[ovonrein]

Slowly the pieces of the diode-puzzle are falling into place for me.  I am beginning to get the feeling that Eric was right when he wrote

As the V-I curve shows, solar cells are illumination dependent current sources (with a soft voltage compliance) so you need to analyse them in terms of current not voltage.

So when a shade travels over one (previously sunny) cell, then its Q4 IV curve will shift down from 7A, say, to 0.5A.  Still following Eric

It a property of current sources that when you try and force more current though any current source than it is generating, it goes reverse biased.

the shaded cell immediately switches bias (as 7A > 0.5A) and will seek out in (the unpublished) Q3 of its IV curve some -V that is consistent with 7A.  Let's assume (against all odds) that the -V is in fact sufficient to turn the Vstring on the affected string negative.  The diode wants to switch to bypass BUT as it does so, Vpanel collapses by 33%.  But the inverter circuit target has not changed.  So all remaining sunny cells on the string must jump up in Vcell to sum up to that target.  In doing so, Istring must collapse.  Whether the diode remains in bypass then depends whether the new Istring settles > 0.5A.  If not, the shaded cell switches back into forward bias at very low +V and the entire string finds itself in a very sub-optimal place.

The same logic extends to multiple shaded cells on one string.  It becomes virtually impossible for short strings to have a diode in bypass.  There simply aren't enough sunny cells left on the string to sum up to Vstring without dropping Istring so low, that the shaded cells will join the party again (and the diode blocks).

The only way that a short string can ever operate with shaded diode-strings forced into bypass is when the MPPT algorithm is willing to start its search at very low Vstring.

[ericw]

ovorein
Try this
Forget about the inverter for the moment.
Run the spreadsheet with all substrings at 1000w/m^2
It will give you a graph of the panel power output v voltage. This is obtained by taking the V-I curve and multiplying the voltage by current. The operating point for the combined panel plus inverter must lie on the curve.

The MPP algorithm will adjust the load presented by the inverter so that the operating point is at the peak of the curve.

Now set one of the substrings to 200 w/m^2 - the shape of the curve changes (it's not totally correct but good enough for the purpose of this illustration)
Now the new operating point must lie on this new curve.
So the inverter MPPT algorithm should now adjust the load presented to the panel so the operating point moves to the peak of the new graph, which gives a new lower power output.

[StBarnabas]

Eric
my MPPT does not work well and gets trapped in a local minimum early morning. The followin plots might illustrate, though I would like at some stage to make an animation. Early morning the entire array is shaded and the shading gradually reduces. With shading one can get muptiple peaks and my MPPT tends to get stuck at the one nearest Voc. Here is an "illustrative" plot.
    

[ovonrein]

The new operating point must lie on this new curve.  So the inverter MPPT algorithm should now adjust the load presented to the panel so the operating point moves to the peak of the new graph, which gives a new lower power output.

I understand, Eric.  However, I know that you realize that a partially shaded string always presents two PP.  The argument that I am making is principally this:  If a string shifts from all sunny to partially shaded (and it performs this recalibration instantaneously), then on short strings (eg a single panel), the Vstring which previously constituted the MPP(sunny) now forces the partially shaded string into a highly sub-optimal low Istring configuration.  In this situation, the MPPT will always find that dW/dV is positive for small dVs  until the shaded cells have arrived at their MPP (the sunny cells are trapped way past their MPP all along).  No diode bypasses and Wstring is terrible, your point.  This would not need to be that way if the MPPT ventured to sample dV=-25V, say.  At such reduced Vstring, the shaded sub-string would switch to bypass and the sunny MPP on the remaining diode-strings will reveal itself.

Either that, or you have to have a REALLY long string so that the multitude of sunny cells can compensate for the sudden loss in V of a diode-string that switches to bypass without Istring collapsing down to a level where the shaded cells go back into forward bias.  On a long string, dW/dV will out itself as negative (as all the sunny cells are running at V > Vmp)

I guess the "ideal" IV curve (or solar cell) is one that is quite flat throughout Q3 and decays slowly for V > Vmp.

[ovonrein]

my MPPT does not work well and gets trapped in a local minimum early morning.

My plot would be considerably more dramatic than that.  More like MPP(255V)=120W, MPP(170V)=700W.

[ericw]

Sean,

A double maxima was the shape of curve I was expecting the spreadsheet to produce and I was rather surprised when it didn't. I assume that when I add a more realistic reverse characteristic it will appear.
I would just like to get a handle on how bad its likely to be - not that there is much you can do about it.
Presumably the enhanced algorithm on Sunny boys from time to time resets things and starts from a low voltage point so it will pick up that maxima.

[ovonrein]

A double maxima was the shape of curve I was expecting the spreadsheet to produce and I was rather surprised when it didn't.

What voltage range did you try? At 60% of Vmp, it must jump even with only one shaded cell.

[StBarnabas]

Eric
with some shading configurations I get a double peak, some of which as Ovonrein says are a lot more dramatic. But a lot of the time I get a fairly continuous curve, particularly if I add shading gradually (put solid Gaussian shading patterns on the array).  I can produce loads of plots similar to the last two and would like to characterise shading patterns which are bad and ones that are less troublesome. As you say some of the newer SMA inverters have global MPPT trackers. Mine just uses I think the classic P&O (hill climb) algorithm.
Sean

[ericw]

A double maxima was the shape of curve I was expecting the spreadsheet to produce and I was rather surprised when it didn't.

What voltage range did you try? At 60% of Vmp, it must jump even with only one shaded cell.

I've got a 'conventional' system with 60 sub-strings in series so I'm not expecting anything like that sort of voltage shift, at least not rapidly.

Sean,
If there is no double hump then I would expect the standard MPPT algorithm to be able to cope.
I really want to probe whether things should go downhill as quickly as claimed or its another urban myth.
 

[StBarnabas]

Eric,
indeed. I am gradually trying to build up to a model I believe in. I'm tempted to get another panel YL110 (156) before they disappear altogether. My observation of my system is that I do get a sudden change in power and a simultaneous drop in voltage at c 10:30. I think I am definitely getting a double peak in power, which disappears mid morning. The other thing is that you might  consider avalanching. Outta (currently in Japan in Fukushima  Provence) thinks that this might happen as low as -5V, though I'm not sure that Excel is up to the task.

[ericw]

Sean,

This http://www.intusoft.com/nlhtm/nl78.htm may be of interest - but its all low power stuff with rsh very large.

[ovonrein]

I've got a 'conventional' system with 60 sub-strings in series so I'm not expecting anything like that sort of voltage shift, at least not rapidly.

Sorry, I did not see this comment.  Last I looked at your xls, I understood it to be a model for a single panel - hence my comment.  A string with 20 panels is a different proposition.  I assume that your diode-strings have Vmp=10V and 20 cells.  It now depends on your IV curves:  If flat-ish for V<0 and precipitously falling off for V>Vmp (typical), then it is unlikely that one shaded cell can force its string diode into bypass when Vstring is held at Vmp(string)=600V.

That said, if you set Vstring to 590V (or less), that should do the trick I had thought.  Generally, Vbypass will be found around Vmp(string) - Vmp(sub-string) or below.

[StBarnabas]

Sean,

This http://www.intusoft.com/nlhtm/nl78.htm may be of interest - but its all low power stuff with rsh very large.

Eric
I have used similar tools such as pspice in the past. The R_sh in the example is appropriate for a very well made lab based mono cell. Not a mass produced poply one. I have purchased another panel YL110s are no difficult to find, but I as able to get a YL120 which I think is identical apart from being graded as better performing. I will be able to cover cells completely and get measurements on the panel level