Balancing Array with Panels at Different Angles

I'm installing an 8-panel solar array on a houseboat. The panels are rated at 270 watts with a Vmp of 31 volts. They will be wired in two strings of four, connected to an array combiner, and then fed to a Magnum PT-100 MPPT controller.
The panels will be mounted to the top of an awning frame on top of the boat. We're having a welder strengthen the frame to handle the additional weight. For simplicity, we're using a fixed mount and since the boat moves we can't angle the panels south. The two sides of the frame rise to a peak in the middle. For aesthetics, simplicity, and to shed rain, we'll mount the panels at the same angle as the frame which is about 7 degrees. Four panels will be on one side and four on the other. That means most of the time some panels will get more direct sun than others.
The effective difference in angle to the sun from the panels on one side to the panels on the other will vary from 0 (when the sun is directly in line with the ridge) to 14 degrees (when the sun is perpendicular to the ridge).
Here's my question: I'm wiring the panels in two strings of four. Should I have one string on each side of the peak or should I have each string a balanced set with two on one side and two on the other. I've been reading about this and I've identified three theories.
Theory A: In each string, place two panels on each side of the peak. This way the strings are balanced with respect to each other they will have the same Maximum Power Point and the MPPT controller will pick a point that's an average best. The downside is that the panels at the less-efficient angle will limit the current of the panels that are at more-efficient angle. So while the strings are optimized, individual panels may not be.
Theory B: Put one string on one side of the peak and the other string on the other side. For a given model of solar panel, Vmp is nearly the same regardless of solar intensity. (I've read graphs of several models to verify this). Therefore, the MPPT controller will be able to find the maximum power point for both strings even though one is at a different angle than the other. The string with the more optimal angle will deliver a larger share of the total current. All panels in a particular string will have the same exposure and so current will not be limited by any particular panel.
Theory C: There won't be a measurable difference between the two methods. So long as a panel is not shaded (as opposed to a less-optimal angle) it can pass through the current from the rest of the string and the total current will be the average of what could be produced from one side or the other of the peak.
Which of these theories is correct? If I had the time I would run an experiment but I don't think I'll get that opportunity.
The panels will be mounted to the top of an awning frame on top of the boat. We're having a welder strengthen the frame to handle the additional weight. For simplicity, we're using a fixed mount and since the boat moves we can't angle the panels south. The two sides of the frame rise to a peak in the middle. For aesthetics, simplicity, and to shed rain, we'll mount the panels at the same angle as the frame which is about 7 degrees. Four panels will be on one side and four on the other. That means most of the time some panels will get more direct sun than others.
The effective difference in angle to the sun from the panels on one side to the panels on the other will vary from 0 (when the sun is directly in line with the ridge) to 14 degrees (when the sun is perpendicular to the ridge).
Here's my question: I'm wiring the panels in two strings of four. Should I have one string on each side of the peak or should I have each string a balanced set with two on one side and two on the other. I've been reading about this and I've identified three theories.
Theory A: In each string, place two panels on each side of the peak. This way the strings are balanced with respect to each other they will have the same Maximum Power Point and the MPPT controller will pick a point that's an average best. The downside is that the panels at the less-efficient angle will limit the current of the panels that are at more-efficient angle. So while the strings are optimized, individual panels may not be.
Theory B: Put one string on one side of the peak and the other string on the other side. For a given model of solar panel, Vmp is nearly the same regardless of solar intensity. (I've read graphs of several models to verify this). Therefore, the MPPT controller will be able to find the maximum power point for both strings even though one is at a different angle than the other. The string with the more optimal angle will deliver a larger share of the total current. All panels in a particular string will have the same exposure and so current will not be limited by any particular panel.
Theory C: There won't be a measurable difference between the two methods. So long as a panel is not shaded (as opposed to a less-optimal angle) it can pass through the current from the rest of the string and the total current will be the average of what could be produced from one side or the other of the peak.
Which of these theories is correct? If I had the time I would run an experiment but I don't think I'll get that opportunity.
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2.1 Kw Suntech 175 mono, Classic 200, Trace SW 4024 ( 15 years old but brand new out of sealed factory box Jan. 2015), Bogart Tri-metric, 460 Ah. 24 volt LiFePo4 battery bank. Plenty of Baja Sea of Cortez sunshine.
Solar panels are "current mode" devices... And the current is the result of sun on the panel. Less sun, less current.
There is the argument that when using MPPT type charge controllers that follow a temperature corrected Vmp-array, that you should have a separate controller for each plane of panels. If the panels are close to the same temperatures, then Vmp-array should be similar too.
Short answer, measure the current and voltage from your array (two parallel strings) and see what the results are. If they are what you expect (typically, around 77% of panel power rating is an average "best you will get" output on a typical clear spring/fall day).
You can experiment too... Very easy if you put a switch/circuit breaker in each parallel string. Turn off one string and measure the current/voltage. Then do the same with the other string. If the Vmp voltage is more than ~10% different between the two planes, then it would be possibly worth while to have two different MPPT controllers. If Vmp-plane is less than 10% different, then they are close enough for government work. The fact the current is different from the two planes is not relevant for this experiment (if the current is too different, then perhaps you have shading/wiring/panel problem--assuming both are in full sun overheat sunlight).
Don't be surprised if you cannot measure the difference between the two arrays--10% difference is difficult to measure with standard tools and no reference--Natural variations will tend to swamp differences that are 10% or less.
My two cents...
-Bill
BB, thanks for the guidance. From your input, it appears that "Theory B" from my original post is the correct one. Whether I use one controller or two, each string should be on the same plane. Two controllers would be optimal but I'm not likely to see much difference with one.
I agree with you regarding wire size and an 80 foot round trip. I would however be concerned with shadowing on those long strings. Being a houseboat you at least don't have masts, booms, sails and lines to contend with.
2.1 Kw Suntech 175 mono, Classic 200, Trace SW 4024 ( 15 years old but brand new out of sealed factory box Jan. 2015), Bogart Tri-metric, 460 Ah. 24 volt LiFePo4 battery bank. Plenty of Baja Sea of Cortez sunshine.
2.1 Kw Suntech 175 mono, Classic 200, Trace SW 4024 ( 15 years old but brand new out of sealed factory box Jan. 2015), Bogart Tri-metric, 460 Ah. 24 volt LiFePo4 battery bank. Plenty of Baja Sea of Cortez sunshine.
It sounds like you've now got a solution that will work well for you. I have a slightly similar setup on my bus, with four panels on each side of the roof walkway - when they all lay down against the roof for travel they are at 21 degrees down, but they can be raised to level or to 21, 33 or 45 degrees up depending on the season. The idea is that if parked pointing east or west the panels nearest south stay down against the roof and the other side's panels are raised up, and if parked pointing north or south I'll raise all eight panels to level. Each side of panels is wired in parallel and feeds its own charge controller so it really doesn't matter at all if each side is getting different insolation, then each CC feeds its own separate bank of four batteries. In effect I have two separate systems in parallel, and they each run through a 250 amp Schottky diode before being combined for the DC house loads and inverter: the diodes prevent one bank backfeeding into the other. It sounds more complicated than it is - I have complete redundancy in case one system fails or needs work (important when boondocking off the grid, maybe a long way from anywhere), and it will allow me to replace each bank of batteries at different times if needed, though I don't ordinarily plan on doing so. If one side of panels is completely shaded I'll still have power from the other side, and if only some panels on one or both sides are shaded I'll still have power because they're wired in parallel. So far, so good.
John
40' Crown bus with 2kW of tiltable panels on the roof:
Eight Sharp 255W, two Morningstar TS-MPPT-60, Magnum MS2000, Champion C46540 generator converted to propane, eight golfcart batteries, and maybe a small Exeltech inverter for the fridger.
Southern California