Well, when rigging solar (or batteries), "string" means "in series". So when you say "string of nine", that means "string of nine panels wired in series", and of course those two strings would then be wired in parallel...because if the two strings of nine were wired in series, then it wouldn't be two strings of nine, it would be one string of eighteen.
Then again, when you say, "paired up to give 24v". That implies that they are 12v panels wired as 9 series strings of two panels per string, and the nine series strings would then be paralleled.
The problem with shading, is that it not only drops the amperage, it also drops the voltage. If the voltage drops "too much", then it will be too low to charge a battery. Say you have a 24v battery bank. You need to have the array always putting out around 30v or more or you won't be able to push the "24v nominal" battery bank up to full charge voltage, which for a "24v nominal" battery bank would probably be at least 28.8v.
Here's how a typical solar panel is laid out internally:
Note the three bypass diodes (orange blocks). Those are there to protect shaded cells. If you feed power through a solar cell, then it becomes a radiant heating element. So in this pic, there are 24 cells. They are all wired in series. Say one is shaded. Well now you are feeding the power of the other 23 cells through that one shaded cell and it's operating as a heating element. It might overheat and be damaged.
So the bypass diodes will bypass part of the series string of 24 cells if the voltage of that section drops too far.
Solar cells all put out around 1/2 volt. So in this example, 24 cells in series would put out 12v. Rigged with 3 bypass diodes, if one section is shaded (or maybe even just one cell in a section), then that section gets bypassed, and now there are only 16 cells in series (the other 8 have been cut out). Okay fine, but the voltage of 16 1/2 volt cells in series is only 8v.
So using the solar panel in the pic, which puts out a max of 12v, if we're trying to charge a "12v nominal" battery, we need to get it up to say 14.4v. So there's no way the panel in the pic could actually charge a 12v battery. We'd need two of them rigged in series. That would give us an array voltage of 24v.
Now say we get shading and one section of one panel is bypassed. That drops the array voltage from 24v down to 20v (8 cells got cut out at 1/2v per cell). If another section got shaded and bypassed, it would drop the array voltage to 16v. Either way, it's still enough to charge a "12v nominal" battery. But if one more section gets bypassed, the array voltage would be down to 12v, and that's not enough.
Now, in real life, "12v nominal" solar panels have at least 30 cells (15v Vmp) or 32 cells (16 Vmp). Most common is 36 cells for a Vmp of 18v. With three bypass diodes (12 cells per diode), the voltage of an 18v panel with one section bypassed would drop to 12v, and with two sections bypassed would drop to 6v. So any shade that causes a section bypass, also causes the voltage of the panel to drop far enough that it won't charge a 12v battery.
So let's say you have two 18v panels (wired in parallel for an array voltage of 18v), and one has a section bypass. That panel is now down to 12v. It isn't producing a high enough voltage to charge the battery, so it basically does nothing. You've now lost 50% of your array output.
But if you rigged them in series, then you would have an array voltage of 36v. One section bypassed, would drop the array voltage to 30v, which would still be plenty to charge a 12v battery. Another section bypassed, and your array voltage is down to 24v, which is still enough. Another section bypassed, and you're down to 18v, which is still enough.
So rigging the two panels in parallel, a single section bypass in one panel drops the entire array output by 1/2. But if rigged in series, a single section bypass only drops the array output 1/6. Two section bypasses drops the array output 1/3. Both are better than 1/2.
Thus, in general, for shade tolerance, series is always better.
But...(and there's always a "but")...
Rigging the array for a higher voltage, increases the voltage mismatch between array and battery, and the greater the mismatch, the greater the inefficiency, and the less power you harvest. And that will happen constantly. So the voltage mismatch can cause the system to work constantly at a lower efficiency. Bad news.
So now it depends on the charge controller. With a PWM controller, the voltage mismatch matters, so you don't want to rig the array voltage any higher than you have to. So with 18v panels charging a 12v battery, you would always rig the array in parallel.
But with an MPPT controller, the voltage mismatch no longer matters, since the MPPT adjusts the voltage, which PWM can't do. If you've got 18 x 18v panels, you could actually rig them in a single series string of 18 and have an array voltage of 324v. With such a high array voltage, you could have a whole bunch of sections bypassed due to shading, and still have a voltage plenty high to charge a 12v, 24v, 48v or even 96v battery bank.
And that is how you would always do it with an MPPT controller and an array mounted at a fixed location, like a house.
But...
If you rig the entire array in series, if there is any break in the circuit anywhere, the whole array stops working. There's not much chance of that happening to an array mounted to the planet, but an array mounted on a vehicle is a different story. Vibration, tree limbs, etc. can cause a loose or broken connection. So for a mobile installation, you want redundancy.
You didn't say what voltage your solar panels operate at. You didn't say how many watts they produce. You didn't say if you are going to use MPPT.
I'm going to assume based on what you said, that they are "12v nominal" solar panels, so you'll need at least two in series to get 24v. Okay, then you will have to have series strings. Again, the smallest you could get away with are 9 series strings of two panels per string, and the nine series strings paralleled.
Say they are actually 18 Vmp with three bypass diodes. Two in series would give a Vmp of 36v, and again, for a 24v battery bank, the array has to stay at 30v or more. A single section bypass on a series string of two panels would drop the output of that string of two panels to 30v. Fine. Another section bypass and the voltage of the series string of two panels, drops to 24v, and that's too low to charge a 24v battery bank.
So now you've got to work out a tradeoff between shade tolerance, and redundancy.
If you rigged 3 panels in series, you would have 6 series strings which you could then parallel. If any one string of 3 panels quit working, then you would lose 1/6 of the array output. Pretty good in terms of redundancy. And the string of three would have an array voltage of 54v. A single section bypass on a string would drop that to 48v. Two would drop it to 42v. Three to 36v. Four to 30v and that's as low as you can go and still charge a 24v battery. So pretty good in terms of shade tolerance as well.
4 panels per series string wouldn't work, because you'd end up with one string that only has two panels in it. The series strings have to have either 2, 3, 6 or 9 panels per string.
Two panels per string gives a lot of redundancy, but not as much shade tolerance. Rigged that way if you lose a string, you only lose 1/9 of the array output, but only two section bypasses and that string is out of commission. You could rig for 6 or 9 panels per string and increase shade tolerance, at the cost of decreasing redundancy. If using 6 panels per string, if a string stops working, you lose 1/3 the array output. If using 9 per string and a string quits, you lose 1/2 the array output.
But rigging 3 panels per string, if you lose a string, you only lose 1/6 of the array output and you've still got good shade tolerance.
So that's probably how I'd rig it -3 panels in a series string, 6 series strings paralleled.
(Disclaimer: Provided of course that you are using an MPPT charge controller and that my assumptions (wild-assed guesses) about your solar panel and battery bank voltages are correct.)
[And...to those nit-pickers out there who've actually been paying attention to what I've said over the years, I *have* somewhat revised my thinking on the series vs. parallel question in recent years. So yes, you caught me.
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