Speaking with experience. I've got a 2008 solar panel and inverter installation. There are, on the roof, enough panels to, theoretically, generate 9.02 kW of power, assuming a nice clear day, at the right temperature, and with the sun's rays hitting the panels perpendicularly.
Having said all that, I have two inverters in the garage, one capable of 4.8 kW output, the other capable of 3.0 kW of output. That's 7.8 kW. Hey!?! Where did the (9.02-7.8) = 1.22 kW go? That's (1.22/9.02)*100 = 13.5% losses!
I should note that I have nifty plots of the power output of the system, Two, maybe three times a year, the two inverters would peak and
slightly flat top at their maximum power. So, most of that 1.22 kW
really disappears. This is not a drill. Where
does it all go?
Just so we're clear on all this: I really, truly am a EE and was and am not scared of math. I investigated this at the time.
- I*I*R losses. One is running significant current through wires and such that total 100 feet or so from the panels to the inverters. Copper has resistance. The power loss in copper goes as current^2 * R.
- Panel mismatches. You guys are going to love this one. In my system, the Big Inverter is connected to an array of panels, where there are strings of 9 panels in series; three of these strings are run in parallel, yielding 27 panels panels total. Now, think about manufacturing variations.
- First, say that a single string of 9 of these panels in series is exposed to sunlight. Without drawing any current, one would have some voltage across that string of 9 panels. Do the same for the other two strings of 9 panels. Bad news: The three strings will not have the same voltages. What happens if one string has more voltage than another string? Um. Current would try and flow through the other string, that's what. For that reason, there are Diodes (well, solar panels are diodes, but let's not go there) that prevent reverse current - but that means that one string is doing all the work and the other isn't doing anything. OK, that doesn't actually happen, but wait for step two.
- Second: Say that the inverter has a single string of 9 panels. Since these panels are in series, the current on all these panels are equal. What does the inverter do? It draws current out of the panels. If it tries to draw some ridiculously maximum current, given the resistance of the panels (under sunlight, natch), the voltage will drop. Power is current x voltage; so if V is minimum, it doesn't matter how much current you have, you get No Power. Likewise, suppose one draws a minimal amount of current. Tiny current x bigger voltage = low power, too. So, what the inverter does, is it steps the load up and down until power is maximized.
- Third: Fun, cool: But, MANUFACTURING VARIATIONS!!. There is no guarantee that a bunch of panels, under the same sunlight, will have the same maximum power at the same current. Some will have more; some will have less; and, if one takes them one at a time, the peak (V*I) products will be different for each of the panels. So, just by having them in series, we lose a certain pecentage of the rated power.
- Fourth: It's bad enough that I've got 9 panels in a string. But I've got three strings in parallel. Oops. Even more losses from the maximum possible rated.
- Inverter losses. Inverters got components. Those components get warm when they're working, be they inductors, capacitors, resistors, or just good old wire. There's 1%-2% losses right there, thank-you-very-much.
- Temperatures. I alluded to this earlier. As it happens, silicon solar cells generate an internal voltage when the sun doth shine. The general idea is that current can be tapped out of the anode of the solar panel and returned to the cathode of the solar panel, completing the circuit. However, there Is No Such Thing As A Solar Panel Without Defects. Defects allow ye electrons to go across the barrier backwards. This is very much temperature dependent. The colder the panel is, the less it tends to do this (do my classes in silicon processing appear evident now?), but that's in the winter time, when the sun is down low and not up all that much. When you really want that power is when it's 104F in the shade.. and that's when the panels don't work as good as one would like so much. I happen to have amorphous solar panels; they're much worse at this than all the crystalline ones you guys are running, but both types do this.
So, it's been a number of years since I went through the math, but, in general:
- Most of the losses are in mismatched panels.
- About 1/3 of the losses are in I*I*R getting from the roof to the inverters.
- Rest is in the inverters, a couple more percent.
Where you guys luck out: DC-DC power converters.
Turns out that there's this class of electronic widgetry called a DC-DC converter. It takes in DC voltage and current; then switches this back and forth at $DIETY's own speed through a magnetic, ferritic transformer; on the output side, more transistors and a little filtering convert this to another voltage and current. By fooling around with pulse width modulation, one can go from, say, 20V and 20A (400W) on the input side of such a converter to, say, 10V and 40A on the other. Or by fooling with the PWM in a different direction, for 20V and 20A in, one can get 40V and 10A out. Less about 1%-2% losses in the transistors and ferrites. Main point: this is
adjustable under electronic control.
By the way: These are cheap, on the order of $20-$50 a pop in quantity. And very, very reliable.
So, hang onto your hats. Say one has a string of 10 400W panels. Each panel is directly connected to its own DC-DC converters. On the DC-DC converter output sides, the outputs are all connected in
series. And, through funky electronic control, we tell the collection of these DC-DC converters that their
total voltage shall be 300V. No more, no less. Now, 300V, maximum sunlight or something, so we have 4000W. Nominal current would be 4000W/300V = 13.33A on all the output sides of the power modules. And, at first glance, the voltage per panel would be 400/13.33 = 30V.
Here's where it goes weird. Suppose under that batch of sunlight, one of the ten panels is generating 420W. Another is generating 380W. Another is generating 402W. And so on.
The guy who's generating 420W? Well, the output side still has 13.33A; and we let the output voltage rise to 420/13.33 = 31.5V. The one that's generating 380W? Still got 13.33A, they're all in series, so we get 380/13.33 = 28.5V. The
total voltage is 300V, always: But the voltage on each panel is allowed to
vary, while the current is adjusted by the Big Inverter to maximize power. Under these conditions,
each panel generates the maximum power that it is capable with that sunlight, at that angle, at that temperature. Minus 1% or 2% loss in the DC-DC converter. (Yes, they are that efficient).
So, with you guys and modern solar panels, you lose 1% to 2% in the panels with the DC-DC converters; then another 1% to 2% in the inverter that converts from DC to 240 VAC; and the rest is in I*I*R losses in the wires. That's probably 8% better efficiency, at least, then what I've got on
my roof.
Older attempts at this kind of thing was to put DC to 240 VAC inverters
on each panel. But that's more expensive. Besides.. Note that I mentioned that my hypothetical string of 10 panels had a total voltage of 300V. There's a reason I mentioned 300V: That's what a lot of battery-back up power walls use for a
battery voltage.
If you got more questions, ask 'em. I got answers.
