Look back at the diagram. The top of the power curve is called the "maximum power point" - for what should be obvious reasons. That particular voltage/current point is the absolute maximum number of watts you can get out of the panel at this particular point in time. A more sophisticated charge controller can track this point by sweeping across the range of voltage/current values and finding the maximum power. My main array of 8 panels is hooked up to a MPPT charge controller (a Midnite Classic 200, which runs around $600). If I load things up enough to get them at max power point, they're operating at about 116V/13.8A/1600W (two strings of 4 panels in series instead of one string of 2 like my morning panels). It's a good solar day. The MPPT controller converts that power into what my battery bank (and the rest of my system) wants - about 27A at 59V. This is the insides of a Midnite Classic 200, and it's a fairly complicated bit of circuitry (this unit can handle up to 4500W of panel on a 72V battery bank). This is only doing the maximum power point tracking and DC-DC conversion - it's not even outputting an AC waveform!
What happens when I don't need all that power (assuming the batteries are full)? If my AC compressor is turning, I need about 1.6kW. Shut that down, I'm pulling about 950W. Where does the excess power go? It simply doesn't get produced in the first place. A charge controller can restrict the energy drawn by drawing less current than the maximum power point, which lets the voltage float up towards the open circuit voltage (you could also draw more current, but that's a far less stable way to operate). When I'm pulling 950W, my main array is running at 133V/5.1A/678W, while my morning panels make up the rest (actually, they produce what they can, and the main array makes up the rest). The system only draws as much as is actively being used.
So, going back to the curve: If I try to draw more than whatever the peak power of my panels are (in current conditions), the voltage (and power) collapses. If I tried to pull 2A out of my morning panels when they were facing east and only able to source 1.3A, the voltage would collapse to 0V and the power would drop to zero. What if I try to pull 2A out of them when they're swung out and able to produce 7.4A? Well, I can pull 2A for as long as I want.
The key here is that you cannot pull more than the maximum power from a panel - even by a little bit - without suffering a massive voltage and power collapse. You can operate below the maximum power point easily enough, but it's hard to identify the maximum power point without sweeping through the whole range to find it.
They also, because they're feeding the grid, have zero surge capability. A 320W microinverter can never source more than 320W, which is fine, because the panel will generally not produce more than 320W. There are conditions where it can, but they're unlikely for roof mounted panels (a very cold, very clear winter day would seem like a case, but the panels aren't typically aligned to take advantage of low winter sun). When the inverter can't process everything the panel could produce, it's called "clipping," and it's really not that big a problem as long as it's not many hours a year.
But, because of these requirements for the operating environment, microinverters are significantly cheaper to build. They just need to be able to find max power point and shove that power onto an existing waveform.
An off grid system typically has two different devices - a charge controller (the Midnite Classic shown above) and an inverter (sometimes more than one of each in parallel). These are separate devices, and cost a good bit more than a microinverter of comparable power. But, they also work with the battery bank, and have to deal with more amps. A 320W microinverter will typically consume around 10A on the DC side and output about 2.5A on the AC side. My charge controller tops out around 75A on the battery side, and my inverter can pull 125A from the battery bank (peak current). I've got a massive low frequency inverter that weights about 40lb (for stationary use, I consider power density in inverters an anti-feature - I'd rather have a massive inverter than a tiny one, because they tend to last a lot longer). My inverter is rated at 2kW, but can source up to 6kW briefly if needed.
Some of the newer systems use a high voltage DC coupled setup - this is how the DC Powerwalls work (which was the Powerwall 1, and was advertised for the Powerwall 2, but then cancelled). For this, you have a very high voltage string of panels (typically 400VDC, either from panels in series or from power optimizers, which are basically a microinverter that outputs high voltage DC), the battery bank hangs on that bus, and the inverter swallows 400VDC and puts out AC. This works better for higher power systems, but it's not a very common off grid layout.
Worth noting on batteries: They suffer age related degradation as well as as cycle based degradation. You cannot keep any battery alive forever, even if you don't use it. Lead acid chemistries (flooded, sealed, AGM, whatever) are rarely good past about 10 years, though if you were to keep them really cold you could probably manage it (some of the industrial cells are rated for 15 years, but they're quite a bit more expensive). Lithium... eh. It supposedly lasts longer, but I treat accelerated lifespan tests as a general guideline to compare batteries instead of full truth. I make a lot of money on dead lithium, and there's a lot of ways to kill them. They also require heating in the winter or you'll get lithium plating while charging (which is also a way to kill the capacity).
Let me offer a general guideline on batteries: Any time you put any sort of battery into a power system, the system will never "pay for itself." There may be specialty cases where this isn't true, but it's a solid first order approximation you should be aware of.
What happens when I don't need all that power (assuming the batteries are full)? If my AC compressor is turning, I need about 1.6kW. Shut that down, I'm pulling about 950W. Where does the excess power go? It simply doesn't get produced in the first place. A charge controller can restrict the energy drawn by drawing less current than the maximum power point, which lets the voltage float up towards the open circuit voltage (you could also draw more current, but that's a far less stable way to operate). When I'm pulling 950W, my main array is running at 133V/5.1A/678W, while my morning panels make up the rest (actually, they produce what they can, and the main array makes up the rest). The system only draws as much as is actively being used.
So, going back to the curve: If I try to draw more than whatever the peak power of my panels are (in current conditions), the voltage (and power) collapses. If I tried to pull 2A out of my morning panels when they were facing east and only able to source 1.3A, the voltage would collapse to 0V and the power would drop to zero. What if I try to pull 2A out of them when they're swung out and able to produce 7.4A? Well, I can pull 2A for as long as I want.
The key here is that you cannot pull more than the maximum power from a panel - even by a little bit - without suffering a massive voltage and power collapse. You can operate below the maximum power point easily enough, but it's hard to identify the maximum power point without sweeping through the whole range to find it.
Microinverters Versus Charge Controllers/Off Grid Inverters
A typical grid tied solar system is built with microinverters. These are a combination MPPT tracker and inverter for each solar panel, normally in the 280-320W range, though that's creeping up with time as panel output increases. The output from these synchronizes with the grid - typically 120VAC and 60Hz, in the US. However, they're very simple devices. They don't have onboard frequency generation - they can only work when given a voltage waveform to synchronize against. They also only work at maximum power point - that's their whole point, and when the grid is up, they're connected to what is, from the perspective of a microinverter, an infinite sink. So they sit there, finding the maximum power point, and hammering amps out onto whatever waveform the grid is feeding them.
They also, because they're feeding the grid, have zero surge capability. A 320W microinverter can never source more than 320W, which is fine, because the panel will generally not produce more than 320W. There are conditions where it can, but they're unlikely for roof mounted panels (a very cold, very clear winter day would seem like a case, but the panels aren't typically aligned to take advantage of low winter sun). When the inverter can't process everything the panel could produce, it's called "clipping," and it's really not that big a problem as long as it's not many hours a year.
But, because of these requirements for the operating environment, microinverters are significantly cheaper to build. They just need to be able to find max power point and shove that power onto an existing waveform.
An off grid system typically has two different devices - a charge controller (the Midnite Classic shown above) and an inverter (sometimes more than one of each in parallel). These are separate devices, and cost a good bit more than a microinverter of comparable power. But, they also work with the battery bank, and have to deal with more amps. A 320W microinverter will typically consume around 10A on the DC side and output about 2.5A on the AC side. My charge controller tops out around 75A on the battery side, and my inverter can pull 125A from the battery bank (peak current). I've got a massive low frequency inverter that weights about 40lb (for stationary use, I consider power density in inverters an anti-feature - I'd rather have a massive inverter than a tiny one, because they tend to last a lot longer). My inverter is rated at 2kW, but can source up to 6kW briefly if needed.
Some of the newer systems use a high voltage DC coupled setup - this is how the DC Powerwalls work (which was the Powerwall 1, and was advertised for the Powerwall 2, but then cancelled). For this, you have a very high voltage string of panels (typically 400VDC, either from panels in series or from power optimizers, which are basically a microinverter that outputs high voltage DC), the battery bank hangs on that bus, and the inverter swallows 400VDC and puts out AC. This works better for higher power systems, but it's not a very common off grid layout.
Batteries
You need batteries in an off grid system for two reasons: Energy storage is the obvious reason, but they also cover peak power demands. Lots and lots of things in a typical home draw far, far more startup power than they do peak power. Anything with a motor is likely to do this, and compressors are particularly bad about this (fridges, freezers, air conditioners, etc). Pretty much any semi-inductive load is going to be a pain to start in terms of current requirements. Again, using data I have handy, my air conditioner pulls about 700W running, but it pulls somewhere around 2kW, very briefly, when starting. My system is designed for this sort of load (my inverter is a 2kW unit with a 6kW peak surge current capability), but you have to be able to handle that, or the system won't work. If you have purely resistive loads, there's still a startup surge - a typical bulb draws more current on starting as resistance goes up with temperature (you can radically extend the life of incandescent bulbs by putting a negative temperature coefficient resistor in series with them, and this was a popular trick with aircraft landing lights before LEDs got bright enough). This is another reason off grid inverters tend to be large and heavy - they have to be able to provide that peak power. Most off grid inverters have a peak power delivery of 2-3x their sustained power delivery, and mine is on the high end, peaking at 3x rated.
Worth noting on batteries: They suffer age related degradation as well as as cycle based degradation. You cannot keep any battery alive forever, even if you don't use it. Lead acid chemistries (flooded, sealed, AGM, whatever) are rarely good past about 10 years, though if you were to keep them really cold you could probably manage it (some of the industrial cells are rated for 15 years, but they're quite a bit more expensive). Lithium... eh. It supposedly lasts longer, but I treat accelerated lifespan tests as a general guideline to compare batteries instead of full truth. I make a lot of money on dead lithium, and there's a lot of ways to kill them. They also require heating in the winter or you'll get lithium plating while charging (which is also a way to kill the capacity).
Let me offer a general guideline on batteries: Any time you put any sort of battery into a power system, the system will never "pay for itself." There may be specialty cases where this isn't true, but it's a solid first order approximation you should be aware of.
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