Spreadsheet to calculate PV output with shading

[ericw]

Having read recent threads there is a clear need for a simple way of determining the output of a PV array under shading conditions.

The attached spreadsheet is designed to do just that for an array of PV panels consisting of a single string.

All that is needed is to insert the number of substrings with the desired illumination and it generates the Power v Voltage characteristic curve for the array.

It is then the function of the MPP algorithm in the inverter to choose the operating point on this curve which gives the maximum power output.

To avoid confusion with the term "string", which is normally used to describe a set of series connected panels I have chosen "substring" to describe the set of series connected individual cells in parallel with a bypass diode. A typical panel will contain 3 substrings each containing 20 cells.

The data (on the Panel Data tab) is the I-V figures extracted from the datasheet of a typical 60 cell 240w panel.

An assumption has been made that reverse bias voltage on shaded cells is insufficient to reach the breakdown voltage of the cell.

The consequence of this is that increasing the number of shaded cells in a single substring beyond one, has only a very tiny effect.
While this seems contrary to most expectations, the fact that as more cells are put reverse bias, the voltage is split between them, means the assumption is even more likely to be valid.

[StBarnabas]

Hi
Eric. This looks useful. Are you assuming Rsh=Inf and Rs=0? Are you assuming T=25 degrees centigrade over the entire array?
Sean

[ericw]

Sean,
I hopefully skirted around such modelling issues by using the published V-I curve for the forward characteristics.  In attempt to get smooth curves I found the largest picture published on the web and converted it into the table in the spreadsheet, hence the some of the rather strange current values chosen.

As usually is the case the datasheet will put the product in the best light so I think that they are 25 degree temperature curves.

On reflection I realise that I havent included the dynamic forward resistance of the bypass diode for the shaded substrings. This will not be a problem when working on a multipanel system but may need to be considered if checking a single panel setup.

Eric

[StBarnabas]

Eric
published datesheets normally only cover the 4th quadrant: the curve from I_sc to V_oc. (approx 0-0.6V per cell for silicon). If you are working with shaded cells you need the IV curve from around -6V to zero depending on the number of cells per bypass diode. The gradient of this curve is  dominated by R_sh, which can be around 300 Ohms/cm^2. (Provided you are less than the breakdown voltage). For my cells which are 15.6 cm square R_sh is in the order of 1 Ohm. You can estimate this from the gradient at V=0. Regarding the bypass diode what voltage are you using for switch on? Schottky are often used (semiconductor/metal rather than PN) ast they have a lower switch on voltage.

[ericw]

Sean,

As I am working at the substring level the I-V curve for the substring in the -V, +I quadrant is dominated by the bypass diode characteristics.

I made the assumption that the bypass diode conducted at 0.7v and had zero slope resistance both of which are dubious.
However a quick web search for bypass diode specs shows voltage drops of 0.9v for si diodes or 0.5v for schottky ones at a few amps.
So in practice while it could be improved its not that bad. (modify the -2.1 (i.e. 3*0.7) value in the characteristics table)

The other assumption was that the cell current did not increase as a cell went into reverse bias - again this is not strictly true as the cell, in practice and as your equivalent circuit shows, will have a soft breakdown characteristic. This increase in current will cause a corresponding rise in current for the whole substring as it goes into reverse bias. However at this point the bypass diode is also starting to conduct so any increase in the current in cell branch of the circuit will just slightly soften the curve of the forward knee of the diode.

So I think the net result is that error in the assumed terminal voltage of a reverse biased (shaded) substring is probably less then 0.5v out.

When you move up to the panel or string level this voltage is in series with the foward voltages of the other substrings so the resulting error in the terminal voltage of a panel/string is probably less than that from factors such as temperature and production variations.

[GavinA]

interesting project.

We've developed our own slightly more rough and ready version of estimating the shading impact on systems performance. Basically using google sketchup to model the system and shading through the year, manually estimating the %  impact of the shading on output for each hour of the day for the mid point of each month.

We then use PVWatts to supply average hourly performance estimates for that particular systems orientation and slope angle based on the closest available weather station data, convert this again to percentage figures and then combine this with PVGIS output estimates for that particular locality.

erm, if that makes any sense at all.

anyway, main point being that you can use the PVWatts site to estimate the hourly output you'd expect from an unshaded system of any orientation / slope angle to plug in to any model you develop. Whether you then want to go on to use this combined with PV GIS to get greater geographic accuracy depends how many steps you want in your process / how accurate you want it to be.

[StBarnabas]

Hi Eric
posibly your configuration is different to mine, but I have 2 bypass diodes per 36 cells on my panels (Yingli YL110 (156)), connected across 18 cells each. If only one cell is shaded the 17 others will have a combined voltage at MPP of c 0.5x17=7.5V, hence a single cell would have to go below C -8V before the bypass diodes switch on. I tend to assume the shaded cells have about 10% or so of the irradiance as the cells in direct sunlight. In my system it takes about 3 cells per string for the bypass diodes to switch on. Including  R_sh in reverse bias makes a big difference. If R_sh was ignored, then I agree that 1 shaded cell would normally be enough to activate the bypass diode, but I'm sure in my configuration this will not happen even with 1 cell with zero irradiance. I can dig out a few plots tomorrow if interested.

Gavin
I have used Google Sketchup (or more accurately one of my students has). I have not used PVWatts but the site looks interesting.

[ovonrein]

I'm not sure this is right, Sean.  Your 17-cell calculation would apply to panel-MPPT (SolarEdge, Enecsys) but your signature suggests that you are using a string-inverter.  Since a single shaded cell would attempt to force I down on the entire panel-string, there would be a very large number of cells needing to move up in V along their sunny IV curves to throttle down to the shaded I.  Assuming that each sunny cell hops up by 0.05V (+10%), then you need 160 sunny cells to force the shaded cell into reverse bias.  Sounds a lot but that's not quite 5 panels.  So if your string has >5 panels, it is quite interesting that you should need to shade 3 cells before the diode trips.

Perhaps a question of contrast, ie how far apart the IV curves are.

[StBarnabas]

Hi Ovonrein
Let me try to convince you. I naturally could be wrong.
In my system I have a single string of 936 cells (26x36).
Every cell can have a different voltage but all have to have the same current.
Assuming all cells are subject to 1000W/m^2 (and the usual STC conditions)  at MPP  each cell will pull about 6A and have a voltage drop of about 0.5V.

If we now shade one cell, this not going to dominate. I would expect the global current to drop very slightly, however what can change dramatically for the shaded cell is voltage.

Taking an extreme case of 0W/m^2, from the principle of superposition we can replace the  current source with an open circuit. The cell diode will be hard switched off and can also be considered open circuit. The shaded cell will look like R_sh in series with R_s. The overall resistance will be about 1 Ohm giving c -6V across the cell. All the other 935 cells will have about 0.5V across each cell.

As far as the bypass diode is concerned only the 18 cells in the chain are important. The other cells and MPPT etc will influence the current through these cells, but their voltage  is not important as both ends of the diode will float with this voltage.

The bypass diode will conduct if the summed voltage across all 18 cells is less than about 0.5V, but as 17 of the 18 cells will have about 0.5V the shaded diode would have to sit at about -8.5V or have 8.5A flowing through.

I still can see how a single cell can turn off the bypass diode unless R_sh is higher. In any event R_sh dominates the gradient IV curve in reverse bias  below avalanche.

[ovonrein]

If we now shade one cell, this not going to dominate. I would expect the global current to drop very slightly, however what can change dramatically for the shaded cell is voltage.

That's the bit I'm stuck on.  I am not sure it is a matter of "domination".  All these cells are switched in series (across their sub-string, across their panel and across the inverter string) so the cell on the lowest IV curve dictates the max current at which the inverter string can operate.  I think that all the cells on that string must move along their respective IV curves to find the spot where they produce no more than the shaded cell.  Did I get this wrong?  Thanks.

[StBarnabas]

lets put it another way. The MPPT will try to find the maximum power point.
The dark cell looks like a 1 Ohm resistor.
Say instead of shading the cell we added a 1 Ohm resistor in series with the array. We would have 936 cells irradiated with 1000W/m^2 in series with 1 Ohm. We will get a power drop of about 6W, a voltage drop of about 6V, but a very marginal reduction in current.
The situation with one completely shaded cell is almost exactly the same only that there are 935 cells irradiated with 1000W/m^2 in series with 1 Ohm. In no way does the single cell dominate.

If R_sh did not exist then things would be entirely different as R_s will be in the order of milli ohms. Without R_sh then reverse voltage would be controlled by the IV curve of the internal diode, which will avalanche at say -15V, this would be easily enough to turn on the bypass diode (or possibly fry the cell in the absence of a bypass diode). If R_sh were higher, say 2 Ohms then 1 shaded cell would be enough to trigger bypass. This could well be the case with Eric's cells

Hope this Helps

[ericw]

Sean,
I now understand what you are saying and agree with your point. It is going to make the simple analysis rather less simple.
Leakage currents in the amps region at first do not sound reasonable until you realise the area of the cell is vastly bigger than normal diodes.
It would be nice to be able to get a good value for RSH but all of references I have found just concentrate on the max power region and (in)conveniently ignore it.

While in principle it ought to be possible to get it from the slope of the forward I-V curve close to 0v, I suspect the published datasheet graphs suffer from "illustrator's licence" in this region and are not to be trusted.

Can you think of a simple practical test that we might be able to persuade a friendly installer to do on a spare panel to get a value.
Measure the current with ~1v applied to a dark panel ?

[ericw]

Sean,
I found this reference http://webs.uvigo.es/carrillo/publicaciones/SPEEDAM2010_REC0405_PV_SHADOWS.pdf in which figs 2 & 3 have numbers which when scaled by 3 to give around the forward current of a 240w panel seem to tie in with a value of 1 ohm

[ovonrein]

The dark cell looks like a 1 Ohm resistor. Hope this Helps

Perhaps.  I think you go one step further in your analysis.  The dV of a myriad sunny cells sends the one shaded cell into reverse bias.  As soon as that reverse bias is established, the ability of the cell to conduct (burn) current completely changes (increases relative to forward bias).  Once in reverse bias, in other words, the cell no longer throttles the circuit quite so badly and the sunny cells can drop again (some) in V (and produce more W, though much less than when all sunny).  Thus somewhat less reverse biased, the shaded cell does not trip the diode quite as early as my calculation would imply.  Like that?

[StBarnabas]

Eric
thanks. Looks like a good link. I will try to study it in detail later, but the graphs looks very similar to the ones I produce for the StB system. http://www.navitron.org.uk/forum/index.php/topic,10201.30.html. With Polycrystalline panels I understand something like 300 Ohms/cm^2 is fairly typical. In forward bias there is little to be gained by going much above this. The best Single Gap Silicon cells are about 26% efficient using PolyPearl technology, but it is very expensive to make them.
The Wikipedia article  http://en.wikipedia.org/wiki/Theory_of_solar_cells is quite good.

[img]http://upload.wikimedia.org/wikipedia/commons/thumb/a/a9/I-V_Curve_RSH.PNG/800px-I-V_Curve_RSH.PNG[img]

Ovonrein
I'm not sure I follow you. What do you mean by dV? Is this a slope of some sort if so with respect to what?  Do you mean dV/dI (wrt current) or something else?
The ability of the cell to conduct (burn) current.  Sorry I'm not sure what you mean. I understand the term burn in terms of energy or power but to me current flows. Sorry I am genuinely confused. It could well be that you have an alternative analysis technique?

Sean