Panel voltage.

[J.P.M.]

The exception perhaps would be corn

What if you stuff the turkey with corn ?

[posplayr]

I guess I better look at an anti-cloud feature for my solar array, I had no idea that my panels might be in danger of over heating on a cloudy day.

Maybe if I put a large fan in front of my panel and break the light fast enough the edge effect will increase my solar output?

[sensij]

All this (as an example) gives, "tau" = M,(t)/U ~~ (8 BTU/deg.F)/105 BTU/hr. deg. F. ~~ .08 hr. ~~ 4 or 5 min.

So, MAYBE not quite the order of magnitude less than you might suggest, but on cursory, or back of the envelope calc, probably a fair amount more than I SWAGGED.

On this topic, panel level data can also offer some insight.

Although panel or cell temperature is not among the reported values, the panel voltage is. It isn't a perfect proxy, but panel voltage should correlate strongly to cell temperature.

7/16 was a recent clear day. 1 pm ambient temp from a local weather station was 80.1 deg F (26.7 C), with a peak temp that day of 85.6 def F (29.8 deg C) at 6 pm. Looking at just one panel, the voltage and current looked like this:

july16.GIF

The data for the panel updates once every 5-10 min. At 13:01, Panel voltage was 26.87 V, current was 8.58 A, and power was 230.62 (reported), 230.54 (calculated I * V).

Now, let's compare that to the data on 7/10, which was a relatively cloudy morning with the sun finally breaking through cleanly at around 12:45 pm. On that day, 1 pm temp was 77.9 F (25.5 deg C), with a peak temp of 81.9 F (27.7 C) at 4 pm.

july10.GIF

You can see how much more sharply the voltage varies here... that alone is a decent indication that the cell temp time constant is at around the sample rate or faster. At 12:59, panel voltage is 27.37, current is 8.55 A, and the power is 235.05 W reported (234.01 calculated).

Relative to the 16th, a difference of 0.5 V equates to about 5 deg C difference (-0.34%/deg C, with 30.4 Vmp). The difference in power is 1.9% (235/230.6), which suggests about a 4.4 deg C difference if temperature were the only factor contributing.

Only 1.2 deg C of that can be explained by the ambient temp from the weather station, so the other 3 ish degrees looks like an integrated effect of the morning clouds. It could be the lower cell temp, but more likely, a difference in rooftop ambient temp with a lower shingle temps from the cloud cover.

On the 10th, just as the clouds were breaking though at SolarEdge timestamp 12:36, the following data were logged: panel V = 27.5 V, I = 9.58, Power = 263.48 (reported) / 263.45 (calculated). This spike in power was also captured by my revenue grade meter, so it looks legitimate. By comparing the voltage with what was reported 30 min later (only 0.13 V difference), it suggests that the power spike contrubted no more than 1 deg C to the cell temp, or that the time constant is so short that the thermal effect is not visible in the data. It also suggests that the spike in power (14%) is almost entirely irradiance driven, since the temperature difference implied by the voltage explains almost nothing of it.

To be sure, this is nothing resembling a proof, and data from many more panels over many more days would be needed to show that the data is good and conclusions can really be drawn from it. However, on the basis of this one comparison, I'd say that thermal time constant is something less than 10 min, and that cloud effect spikes are driven more strongly by irradiance increases (lensing) than by thermal contribution from cells that had been cooler under cloud cover. I think this agrees with the first principles analysis J.P.M. offered above.

If I might futher cite J.P.M. here... take what you want of the above, and scrap the rest.

[posplayr]

I had a look at the data, and I'm not really sure what the data is telling you. I do think I see something different than what you have highlighted.

First thing I would look at is your assumption about voltage being a proxy for temperature. We we know there is correlation and it could be the case based on first principles as well as the manufacture's stated electrical performance sensitivities to temperature. But from an eyeball look at the data, there is something else going on.

When you look to validate a relationship as you have proposed, it is best to see if large transients at least pass the test.
In the first plot of data from 7/17, there are two large current transients and because the panel acts like a current source in proportion to solar irradiance, we can reliably assume there was a solar transient both in the morning at 8:15 am and in the afternoon at 16:45.

Interestingly the average voltage at around 8:15 and 16:45 was about 29.2V and 28.5V respectively. That is 0.7V difference corresponding to about 7 degree C temperature difference which could be accounted for by the ambient temperature. You did not provide a morning temp so I'm just guessing. While those voltage levels might make sense, the voltage transient leave some questions open. Why is the 2 Amp peak to peak (APP) transient in current in the morning generating almost no voltage transient while in the afternoon a much lower 1 APP transient cause a 4 volt output spike which would correlate to 40 degC drop in temperature. It would appear that this spike can not be attributed to a sudden temperature cooling of 40 degC of the panel.

Now if we compare the second cloudy day data to the clear day data, you see some similarities but at the same time discrepancies. The afternoon of 7/10/15(cloudy day) is similar to the afternoon period(sunny day). The cloudy day Solar irradiance has a slightly lower peak (30.5A v.s. 32 amps) and a slightly higher voltage (27V v.s. 26.7V) as you would expect from a less than clear day. However when you look at the relative sensitivity of the changes in APP and the effect on VPP the relation ships seems to change.

On 7/16 a large drop off in solar radiance caused a very large voltage change that can't be attributed to a temperature drop. An on 7/10 the and even larger drop off caused almost no change in the voltage. At the time of the negative solar spikes, both average currents and voltages were the same. So why the big change in voltage response to the change in irradiance?

What this suggests is that while first principles still hold (voltage is related to panel temperature), in order to measure a thermal time constant on the order of the sample rate you are going to have to look for the largest transients. Those transients do not seem to follow the basic thesis, (voltage is a proxy for temperature). You might be able to get some more information by doing a time series analysis between the signals, but it is not clear at what time scale the slowest period correlations between I and A (morning and afternoon average voltages) no longer relate as the transients become larger(and do not correlate).

This data doesn't seem to offer anything with respect to what thermal time constants are nor even any consistency in solar edging effects and the output voltage. Just looking at voltage response to the current down spikes on the afternoons (16:30 ish) of both data sets lacks any consistency to make much of a conclusion at all.


BTW the easy way to measure the thermal time constant is with a thermometer and a tarp.

[sensij]

When you look to validate a relationship as you have proposed, it is best to see if large transients at least pass the test.

More commentary from the clueless guy. Sharp voltage transients are *not* worth weighting heavily, because they are likely indicating that the MPPT algorithm has not caught up to the actual running condition of the panel and there is much more than just temperature effects going on. Perhaps my comment regarding the presence of transients as an indicator of time constant was mistaken, but the <10 min thermal response time is supported also by the more stable data in the set as well.

[posplayr]

More commentary from the clueless guy. Sharp voltage transients are *not* worth weighting heavily, because they are likely indicating that the MPPT algorithm has not caught up to the actual running condition of the panel and there is much more than just temperature effects going on. Perhaps my comment regarding the presence of transients as an indicator of time constant was mistaken, but the <10 min thermal response time is supported also by the more stable data in the set as well.

If you want an eyeball analysis of how long it is taking the panel to heat up here it shows approx 20 min delay between Solar peak and temperature peak. That is not exactly a time constant but provides a clue of the time frames involved.

There are much more involved ways of determining the smoothed curves that I penciled in, but you get the idea.

[sensij]

The clear day data is in the attached spreadsheet, for anyone interested in working with it in more detail. I've included the temperatures recorded by the weather station... nearby, but not exactly the same at my address, I'm sure. I also can't be certain that the timestamps match between the weather station and the inverter; there could probably be 5 min of synchronization error there since the data passed through PVOutput before I grabbed it.

The inverter heat sink temp is also included, with timestamps that should match the panel electrical data. The inverter temp and the panel temp ought to correlate well, with thermal mass / time constant being the biggest contributor to differences between them... but I haven't looked at it yet so don't hold me to it.

DataExport.zip

[bcroe]

just to add some more confusion, the voltage idea assumes the panel is operating
at the Vmp. If the converter was to go into clipping, the panel voltage would be
allowed to rise (decreasing the current). Bruce Roe

[J.P.M.]

My array monitoring is the 5 min. S.P. stuff and probably no better than +/- 5% with some, but not stupendous precision. My fouling measurement attempts are "snapshots" taken at minimum incidence angle for any measurement day (within ~3 min. or so), with the power, and voltage readings taken directly from the string inverter readout as close to the min. incid. angle time as a radio controlled digital clock and my pencil can record.

Early on, I considered the voltage as a way to est. panel temps. and do record the voltage of each of the two strings along with the power into and out of the inverter manually as noted. That may well be a good way to do things, but my experience, FWIW, leads me to wonder, but not because the voltage is not necessarily a linear function of temp. It's probably a decent est., maybe better than thermometer accuracy and measurement method provide, and as I write, and IMO, at least a good backup for my measurements. I prefer to use array voltages as a check/backup to the temp. measurements, as the actual temp. measurements provide more information about individual panel temps. and meter info about the temp. distribution over the array as f(wind vector). FWIW, I'd ask readers to trust me that the agreement between array Voltages and measured temps., without getting lost in a boatload of minutia, seems reasonable, or at least the #'s seem to go in the expected directions at about the same rates with what seems to be reasonable agreement with published panel delta V/delta T. coefficients.

On temp./weather measurements and using nearby data: FWIW, I'd add, that if I have a slight advantage, it may be that my wind and amb. air temp. data (and Global Horiz. irradiance) are taken at the array, measured continuously and recorded in 1 min. increments. That doesn't make them necessarily more accurate in an absolute sense, but I've observed that several nearby Weatherunderground sites, one of which, about 1 1/4 miles away, having identical measuring equipment to mine, all seem to record amb. temps. lower than my roof temp. with wind vectors all over the place. I've observed that those weather factors can have a measureable effect on panel temps. somewhat different than the change in array Voltages, but that's more anecdotal than measureable. The remark here is that other info or data, not as close in time or location, may introduce additional uncertainty. Still, use what is available, but be aware of the limitations. I think my data is a bit better than average, at least in terms of precision, but still little more than a SWAG, if that good. Thinking about it, given that added uncertainty, several consecutive array voltage measurements may be a decent way, or for that matter, the only way, to estimate panel temps. Lots to consider.

That brings us (or me anyway) back to the concepts of a time constant being a bit different (and somewhat slower with respect to changes in irradiance levels) than the actual environmental changes, and how that response time may influence array voltage(s) and efficiencies as the array temp. changes (increases in the case under discussion here) in response to a step change in irradiance due to cloud conditions. My comment way back a page or so ago, was that temporary observed increases in output which, while probably and mostly likely attributable to "lensing" or reflections from clouds in addition to the step increase in irradiance by the appearance of the sun, may PERHAPS have that (lensing) effect made larger by the initially lower array temp. due to a lower irradiance level at the beginning of the "lensing" event. Such lower voltages will allow greater panel efficiencies and thus output, until the panel temps. pick up with those panel temp. changes roughly estimated to maybe a 1st approx. by using the panel time (or array) time constant.

Two other things: On measuring lunar reflected solar radiation: There is a paper or technical note, I can't remember which, in the journal "Solar Energy" from an issue back in the '80's which I haven't had the time or inclination to dig out, among other things described the intensity of solar irradiance from the moon reflected to the earth. Bruce, you weren't the first, unless you were one of the authors of that paper. Second, I had considered the idea of covering one panel and measuring the temp. change as f(time). However, after a little thought, I realized that covering a panel would also change all the heat transfer characteristics of the panel and make the results non applicable to the actual situation, therefore of little use. I've done that many times with thermal collectors, but the time constant there has a slightly different meaning, dealing mostly with flowrates through the collector.

Take what you want of the above. Scrap the rest.

[sensij]

Thanks for contributing. Here is another example, which might also help tease out some truth. Instead of looking at cloud effect, in which temperature and lensing are hard to disentangle, watching what happens when relatively hard shade travels across the panel might offer a purer approach.

First, here is my home. You can see my array is 12 panels with a nearly due south azimuth, 18 deg tilt.

Home.GIF

Just to the west, and 20 ft or so higher in elevation, is a giant palm tree in my neighbor's yard. During part of the year, the tree's shadow swipes across the array. The west end of the array is panel 1, and will see the shade the longest. The east end of the array is panel 12, and the tip of the tree will pass across it fastest.

Here is system data on 4/27/15, showing the drop in power as the tree comes into play.

Evening_Shade_PVO.GIF

Looking at just the power data from panels 1 and 12, the difference in the shade cover is clear

Evening_Shade_SE.GIF

Here, you can see that despite being in shade for ~40 min (panel 12), or ~78 min (panel 1), once the shade clears, they both return to the same exact power curve within the time it takes for a single measurement to be reported. There isn't any sign that operating at a lower power output for the time in shade helped the cells cool in a way that meaningfully affected the power when the sun returned.

I think the voltage behavior of panel 12 jives with the voltage/temp relationship we've been discussing. Narrative: When the shade kicks in, the voltage on panel 12 rises initially (much more than temp explains), then tries to come back down as the MPPT adjusts. The shade is too dynamic though, and the voltage rises again until the shade passes completely. On Panel 1, the shade lasts longer, but is even more dynamic... maybe from some bushes near the base of the tree. The MPPT is never able to completely drop the voltage back to the maximum power point until the shade clears (and another short shade producing object on the ridge follows closely behind).

A couple things... with cloud cover, the surrounding ambient temp would also drop, while the hard shade is less likely to contribute to any environmental cooling. Also, at this time of day, the panels are not working at full power anyway, so the heat load is less than it might be in the middle of the day. I'm not sure how panel 1 could be outproducing panel 12 at any time during the shade event, so I'll have to get up on the roof and watch more closely when it eventually returns.

No conclusions offered here, just more food for thought.

[J.P.M.]

@ Sensij: All of what you report seems pretty reasonable to me. The comments relative to irradiance also affecting the ambient temp. as well as the temp. of other nearby objects and thus the radiant heat transfer are, IMO, certainly valid. Such considerations are also examples of the many considerations of large, small and/or unknown and in any case probably variable inputs that (can) have an effect on panel and array performance both steady state and transient.

I use irradiance, amb. air temp., dew point, wind vector, panel temp., roof temp. (both under the array and "exposed" roof), readouts from the monitor screen for voltage and power in/out of the inverter, and a few other things.

Even before considerations for instrument and measurement limits on accuracy/precision, I'm pretty sure there are a boatload of other things I'm probably not even aware of, much less measuring, that may well influence array performance, even before considerations for how they may influence one another.

Additionally, mine is a probably more than a bit of a fool's errand in the sense that what I'm attempting to estimate (array fouling) is, for the most part, a quantity that is about the same order of magnitude as the accuracy of most of the instruments and methods I'm using. The best realistic hope I might entertain is that by doing the same thing a lot of times in the same way and looking for patterns/trends/tendencies, I might get lucky and add to the body of knowledge for my own and others' future use.

Given all that, and my goal to try to gain some insight to array fouling, the idea of a panel thermal time constant and its influence on lensing effects, while interesting, and a subject I feel somewhat qualified to discuss, is not the main focus of my efforts on the roof.

While rooting around yesterday, I stumbled across a paper that seems to hit a lot of the ideas relative to PV panel time constant issues being bandied about here, one of which being that the time constant for PV panels is more or less intimately and directly linked to the convective and radiative heat transfer coefficients, which, because those coefficients are highly variable, linked and therefore more or less unpredictable, give the panel thermal time constant the same unpredictability.

See: Applied Thermal Engineering, 30 (2010), pp. 1488 - 1495, "A thermal model for photovoltaic panels under varying atmospheric condition.", S.Armstrong, W.G. Hurley.

While not agreeing with all of it, seems to me the paper does a fair job of hitting a lot of the issues that bear on what we're writing about here.

[sensij]

While rooting around yesterday, I stumbled across a paper that seems to hit a lot of the ideas relative to PV panel time constant issues being bandied about here, one of which being that the time constant for PV panels is more or less intimately and directly linked to the convective and radiative heat transfer coefficients, which, because those coefficients are highly variable, linked and therefore more or less unpredictable, give the panel thermal time constant the same unpredictability.

See: Applied Thermal Engineering, 30 (2010), pp. 1488 - 1495, "A thermal model for photovoltaic panels under varying atmospheric condition.", S.Armstrong, W.G. Hurley.

While not agreeing with all of it, seems to me the paper does a fair job of hitting a lot of the issues that bear on what we're writing about here.

Nice paper, it kind of figures that Ireland would be a good place for research related to cloud cover interactions with PV. They don't graphically show a comparison of the model with measured results, and the tabular form suggests there is some effect they are missing, or mis-weighting, based on the accuracy improvement as wind speed increases. Their comments on time to equilibirum (and not just time constant) are roughly consistent with the voltage lag observed by posplayr in my data. I'm not seeing how they are accounting for the diffuse fraction or incidence angle of the solar radiation, but it will take a few more reads to see if that is true or if it matters.

With respect to the fouling study, I take it for what (I think) it is... carefully thought out and executed measurements, using data from a real world system collected with a healthy respect for the unknowns and hard to quantify factors. While the results might not be conclusive in a tight confidence window, they are suggestive, and at least offer order of magnitude estimates for how fouling might affect an array. I enjoy the updates. After the downpour this weekend, I was hoping for a clear day to see if I could detect any change in performance using just the SolarEdge data, but the high altitude clouds didn't quite clear out at midday yesterday, and today is back in the gray.

[J.P.M.]

Nice paper, it kind of figures that Ireland would be a good place for research related to cloud cover interactions with PV. They don't graphically show a comparison of the model with measured results, and the tabular form suggests there is some effect they are missing, or mis-weighting, based on the accuracy improvement as wind speed increases. Their comments on time to equilibirum (and not just time constant) are roughly consistent with the voltage lag observed by posplayr in my data. I'm not seeing how they are accounting for the diffuse fraction or incidence angle of the solar radiation, but it will take a few more reads to see if that is true or if it matters.

With respect to the fouling study, I take it for what (I think) it is... carefully thought out and executed measurements, using data from a real world system collected with a healthy respect for the unknowns and hard to quantify factors. While the results might not be conclusive in a tight confidence window, they are suggestive, and at least offer order of magnitude estimates for how fouling might affect an array. I enjoy the updates. After the downpour this weekend, I was hoping for a clear day to see if I could detect any change in performance using just the SolarEdge data, but the high altitude clouds didn't quite clear out at midday yesterday, and today is back in the gray.

Understood. The paper has a lot of interesting stuff. My "suggested for consideration" takeaways from all this is: It ain't rocket science. None of us knows squat about most of it. Constants aren't and variables won't. And, as I learned about 40 or so years ago, thermal performance estimates and tools used to figure such things out are +/- about 20% or so, about half the time or more, so take your best informed guess and shot. Thinking I can do better is an act of faith (and/or folly).

That's why I limit my suggestions about panel cleaning to folks in similar situations to mine (Ian: maybe a bit more often for you - a SWAG) to hosing down their arrays IN THE EARLY A.M. about every 6 weeks or so, or 6 weeks after a decent rain as about the most precise piece of advice I can give at this time based on what I've measured. That might hold the fouling to about 3% or so as an average working number.

@ Sensij: Dude, respectfully suggest you consider investing $1K and get a Davis Pro II + and mounting it near your array. The world again seems to be running short of unprocessed data. Perhaps time for you to step into the breach.

[SunEagle]

Understood. The paper has a lot of interesting stuff. My "suggested for consideration" takeaways from all this is: It ain't rocket science. None of us knows squat about most of it. Constants aren't and variables won't. And, as I learned about 40 or so years ago, thermal performance estimates and tools used to figure such things out are +/- about 20% or so, about half the time or more, so take your best informed guess and shot. Thinking I can do better is an act of faith (and/or folly).

That's why I limit my suggestions about panel cleaning to folks in similar situations to mine (Ian: maybe a bit more often for you - a SWAG) to hosing down their arrays IN THE EARLY A.M. about every 6 weeks or so, or 6 weeks after a decent rain as about the most precise piece of advice I can give at this time based on what I've measured. That might hold the fouling to about 3% or so as an average working number.

@ Sensij: Dude, respectfully suggest you consider investing $1K and get a Davis Pro II + and mounting it near your array. The world again seems to be running short of unprocessed data. Perhaps time for you to step into the breach.

Looks like the price has come down on those Davis Pro II to about $500. Sure beats sticking your wet finger out the window to determine the weather.

[posplayr]

I think the predominant factor you are seeing in that palm tree shading data is that the building/roof on which the solar panels are mounted has sufficient thermal mass and heat content to mute any self heating effects an individual panel might have.

The return to the same trajectory for both end panels suggests that at that sun angle and solar incidence and similar temperatures due to the roof, the panels will act the same exhibiting little self heating effects. They just plain did not cool off with sun blockage as the rest of the roof is still hot and cooling little due to a single palm tree shadow. That probably explains JPM comment, that he would just throw a tarp on a panel mounted on a hot roof expecting something else. The panel does NOT cool from a tarp as it is being heated from below by the hot roof.

If as Bcroe has, ground mounted panel which are not in proximity to any object of high thermal mass and large exposed sun area, his panels will self heat and exhibit faster thermal characteristics than roof mounted.

The most striking thing to me is how the power from both panels lays right on top of one another. Powers under solar irradiance is almost identical . Unless your end panels just happen to match I suspect that the rest of the panels are also in close statistical alignment as per expectations from binning resolution.

The real message here is that you can suffer a lifetime performance penalty or gain by improving the ambient temperature around your panels. The most obvious for roof mounted is to space them away as much a practical from hot tiles. The power gain is readily quantifiable using the manufacturer's temp coefficients.