Surprising solar calculations

[booster]

I have been messing around with solar calculators again, as I got a question, with some data, about maximum solar gains to expect. The install had seen as much as 37ah of gain per day, measured by the non shunt based PWM solar controller, which is pretty high for PWM with a 17.7v 100 watt panel. I wanted to find out how much energy is really available over a day, as we only see the rated watts of the panel, which is instantaneous and perpendicular at the equator, or the generic 30ah per day for a 100 watt panel.

I did find a better and easier to use sun angle calculator, though, which allows you to just put in a zip code for location, and it does the rest except for elevation.

Sustainable By Design :: sunangle

You still have to enter individual times of day to get an all day estimate, however. I chose to use one hour increments, as it simplifies the amp hour and watt hour parts of the calculations. A full integration of the entire day would be most accurate, but hourly midpoint for the hour should be close enough for this, I hope. You use the Sine of the sun angle for a horizontal panel as that is the useful part, according to the solar folks.

I put together a spreadsheet that does the calculations and charts a graph, once I had done it by hand once to see how it worked out (I am not spreadsheet guru by any definition, so there could be errors, so let me know).




It is pretty self explanatory, as you just enter the sun angles for the various times at the location and date in the angle calculator.

I was very surprised at the results, especially at northern latitudes, even at summer solstice. Basically double the 30ah per day general rule for good sun.

I was also surprised that you only lose under 10% of output and 25* off of perpendicular sun.

I have the spreadsheet as an ODS (open office document) but don't see any way to attach it here. I will send it to anyone who wants it. I put it in a zip file and that seems to work, let me know if it doesn't.

Open Office solar calculator.zip

[Saldar]

I was able to import your OS spread sheet zip directly into Google sheets. (I can't believe it...I must be living in the future.) I can follow your spreadsheet's logic.

I used the alternate SunPostion calculation page (Sustainable By Design :: sunposition) to calculate an array of sun elevations (hour by hour for this case) in one step. Based on your zip code's lat and long, for today, when these elevation angles were placed in your spreadsheet, I got similar surprising results: 857 W/h/d or 69 Ah/day at 12.4V.

Is 70Ah what enters the charger with only half that entering the battery for our benefit? Certainly the charger has losses, and in addition I read "The state of charge of the battery will also affect charge efficiency. With the battery at half charge or less, the charge efficiency may be over 90%, dropping to nearer 60% when the battery is above 80% charged." (I hope that statement is true. I only quote it for other readers; you know all this inside out.) I figured any losses would reduce the 35Ah/day advertised/ideal output. Is the 37Ah/day you measured entering or after the charger?

What surprises me also is that this high 70 Ah/day full sun gain is twice the "generic"/advertised value for a 100 W panel. My basic distrust of my fellow man makes me suspicious of the innocent value. The radians are in the calculations...What could be missing? Is the solar calculator wrong?

I'm very interested in how the solar works on my new van. I don't have much to contribute except to try to validate your calculation. I'm trying right now to recognize any regularities in the numbers and lights my Zamp + 100W panel shows me.

[booster]

Originally Posted by Saldar

I was able to import your OS spread sheet zip directly into Google sheets. (I can't believe it...I must be living in the future.) I can follow your spreadsheet's logic.

I used the alternate SunPostion calculation page (Sustainable By Design :: sunposition) to calculate an array of sun elevations (hour by hour for this case) in one step. Based on your zip code's lat and long, for today, when these elevation angles were placed in your spreadsheet, I got similar surprising results: 857 W/h/d or 69 Ah/day at 12.4V.

Is 70Ah what enters the charger with only half that entering the battery for our benefit? Certainly the charger has losses, and in addition I read "The state of charge of the battery will also affect charge efficiency. With the battery at half charge or less, the charge efficiency may be over 90%, dropping to nearer 60% when the battery is above 80% charged." (I hope that statement is true. I only quote it for other readers; you know all this inside out.) I figured any losses would reduce the 35Ah/day advertised/ideal output. Is the 37Ah/day you measured entering or after the charger?

What surprises me also is that this high 70 Ah/day full sun gain is twice the "generic"/advertised value for a 100 W panel. My basic distrust of my fellow man makes me suspicious of the innocent value. The radians are in the calculations...What could be missing? Is the solar calculator wrong?

I'm very interested in how the solar works on my new van. I don't have much to contribute except to try to validate your calculation. I'm trying right now to recognize any regularities in the numbers and lights my Zamp + 100W panel shows me.

Good information, thanks for the reality check. I had looked at the alternate calculator, but must have had something checked wrong as it would not accumulate like it did now, thanks again.

The 70ah would be coming from the panels, before the solar controller, but on ours, I can see both amps and volts in and out of the controller, and it is over 90% efficient, it appears, so can't be all that cause.

As soon as you have the battery charging involved, and the tapering, all bets are off on learning much. I usually will put a load on to see how much the solar will cover before it starts taking from the batteries. It is harder to do that for all day, with the grossly varying output. The 37ah was not my measurement, as it came from another solar user that has a 100 watt, 17.7v, panel with a PWM solar controller. The controller does the measuring if you reset it to zero before the sun is up and read it after sunset, so it should be the output from the controller.

I know the 30ah is pretty close and lots of folks have also seen that amount on average with good sun. I will say a lot of the folks that are selling the solar use a much higher number than that, nearing the max output of the panel for the whole day. The 30ah we see a lot is more on the user forums, I think, and some of the most reputable sellers have picked it up.

One has to assume that enough glitches happen during the day to drop the output a bunch. Passing clouds, haze, campfire smoke, bird poop, whatever. As you get off max solar angle, the sunlight goes through a lot of atmosphere before it gets to you. I would also bet that most systems, if they are sized well, will be getting into battery tapering during a very good sun day, as it starts very early at about 70% full in many cases. If we got 60ah per 100 watts, our 300w panels would give us over 50% of even our huge 440ah battery bank (352 usable), and would end right at 70% if starting at 20% state of charge.

I know I am going to watch it closely if we ever wind up in very good sun, sitting level, and not moving. It is an easy chore, as long as you remember to reset it and read it at the end, and put enough load on it to keep the solar at max all day.

[Saldar]

I might see where the factor of 2 comes from.

To allow comparisons, the 100W rating of a panel is determined under standard conditions. The standard condition is 1kW hitting one square meter ("peak sun"). I calculated based on my so called "100W" panel's area. At typical 15% efficiency its output turns out to be 100W/hour at that illumination.

In the spread sheet we assume every sun hour is a 100W hour, and add up 12 of those, modulated by the sun angle. Looking at a chart of average solar radiation (Average Solar Radiation | PVEducation) it appears many places net about 6 kWh per m2 per day in mid summer, rather than 12. So I think this is the why the sheet seems to be overestimating by a factor of 2.

You mention "put enough load on it to keep the solar at max all day". Does this mean keeping the battery out of absorption, and/or low enough to accept most of the power coming from solar?

I'll be interested in your sunny day numbers. Mine waits in a parking spot where it gets out of shade only a few hours. The Zamp seems to automatically reset its "Ah" value every morning, and I think this value reports it's daily uptake (tho it probably is partly an idiot light -- how reliably can it know?). Zamp also reports "A" and this appears to be the instantaneous reading. The highest I've seen so far is 6+, for a little while in a parking lot.

[booster]

Originally Posted by Saldar

I might see where the factor of 2 comes from.

To allow comparisons, the 100W rating of a panel is determined under standard conditions. The standard condition is 1kW hitting one square meter ("peak sun"). I calculated based on my so called "100W" panel's area. At typical 15% efficiency its output turns out to be 100W/hour at that illumination.

In the spread sheet we assume every sun hour is a 100W hour, and add up 12 of those, modulated by the sun angle. Looking at a chart of average solar radiation (Average Solar Radiation | PVEducation) it appears many places net about 6 kWh per m2 per day in mid summer, rather than 12. So I think this is the why the sheet seems to be overestimating by a factor of 2.

You mention "put enough load on it to keep the solar at max all day". Does this mean keeping the battery out of absorption, and/or low enough to accept most of the power coming from solar?

I'll be interested in your sunny day numbers. Mine waits in a parking spot where it gets out of shade only a few hours. The Zamp seems to automatically reset its "Ah" value every morning, and I think this value reports it's daily uptake (tho it probably is partly an idiot light -- how reliably can it know?). Zamp also reports "A" and this appears to be the instantaneous reading. The highest I've seen so far is 6+, for a little while in a parking lot.

Interesting, and it appears you are on the right track. Explained somewhat here.

http://www.cengage.com/resource_uplo...061_137179.pdf

It appears from what they say that there is some reduction in intensity because it goes through more atmosphere, but mostly because it covers about twice as much earth with the same crossection of light in the air, than at higher angles. Does make sense. In the sense of applying over a single day, when the angle varies all day, you may also get a similar 1/2 or so. We probably don't need to get the full half, as the 30-35 amps is very common to get, but not 60-70.

I need to do the trig to write the formula to add another modifier to each of the angles to allow for the increase in ground cover per unit energy as the angle decreases.

Good call.

Yes on the very low batteries and/or load. The solar needs to have a place to send the power, or it won't generate it, and that place needs to use the power easily without back voltage.

[booster]

I made a modification to the spreadsheet and my original example now returns 44 and 51ah at 14.4-12.4v, which is a lot more realistic. The solar controller is likely reporting AH at full charge when it is in full charge, so the 14.4 number should be correct (I have an email into Blue Sky solar for confirmation of that).

If people are actually seeing 37 or so, 44 as a top end is pretty likely, but rarely actually achieved.

To test, it will probably be easier just to modify on line of formula in the spreadsheet.

Row 10 W/Hr per 100w panel formula just needs and extra *x8 with the x being the column you are in.

First one would read =PRODUCT(B8 )*100*B8 next on would be C8 I had to leave a space in the first B8 because it kept putting an icon.

[booster]

This should be the updated spreadsheet with the allowance for sun angle on panel area.

Open Office solar calculator.zip