36V 315W 9A solar panel system setup

Theoretical math is one thing; putting it in practice is often another. Here are some practical examples.

You have a 100Ah battery. You do not wish to discharge it below 20% of its capacity (0.2C), i.e. its DoD (depth of discharge) should be no greater than 80%. Assuming it starts fully charged, 0.8C (80%) of 100Ah is 80Ah. Before we can calculate watts, we must know the battery voltage as well. Let's say the voltage is 24v: 24 volts x 80 ampere-hours = 1920 watt-hours (Wh), following the W=VA formula and adding the hours.

If the tiny home consumes electricity at the rate of 120 watts over a period of 16 hours, this will equal the 1920 Wh. The watts by themselves are the rate of usage, not connected to time. But 120 watts for a full hour is 120 Wh (watt-hours).

If our 100Ah battery is at 48 volts instead, we have: 48 x 80 = 3840 Wh. If this is consumed at the same rate, it could last for 32 hours (double the time). Otherwise, it could provide power at twice the wattage for the same period of time.

Note that in these calculations, the watts calculated for the output must already include those consumed by the inefficiencies of the inverter, so additional equipment (lights, fans, computers, refrigerator, etc.) get to use what is leftover after the inversion process has used its portion.

Solar panels are a different story. Unlike a battery, whose capacity and charge level may be known, panels have a maximum output rating which may quite seldom ever be reached, and can fluctuate wildly in output due to many factors: angle of incidence of the sunlight, haziness/clarity of the atmosphere, temperature of the panels, shading (clouds, trees, chimneys, dust on the panels, or perhaps even the passing flock of birds), etc. The MPPT of the charge controller may not instantly respond to changing conditions, and some efficiency is lost while it updates to track the maximum power point. All this to say that panels are notorious for not producing their full rated output. Once you have a particular figure in mind as your production goal, it is highly probable that you will want to have panels rated in excess of that goal by a certain margin. Rain, for example, may cut solar output down to a mere 10% or less of that which one would achieve on a sunny day. If one had ten times the panels, one might maintain the desired output even in this adverse condition. Of course, when the clouds vanish again, one would then likely have way more power than could be put to use. This is part of the fun of designing the system--getting things balanced to where one is satisfied with the result. But the panels' output must be carefully matched to the charge controllers' and/or the inverters' power limitations, especially voltage, so panels, inverters, etc. all have a dominoes effect--change one, and the others need to be reconsidered as well.

The details get even stickier: for example learning that some inverters will be damaged if the battery is disconnected from them while the inverter is still connected to the solar panels--and that some batteries (those with a BMS) may automatically disconnect themselves for cell voltages that are too high or too low, or for temperatures too high or low. To mitigate against disasters, one must either design relays into the system that would disconnect the PV array in the event of a battery disconnection, or else use an inverter model that is not sensitive to battery interruptions and can operate without a battery. Some inverters can be "overpaneled" and some cannot. Some DC fuses will protect a system from extreme overload and some will just let the surge pass through! There are so many ways to cobble together a system which in the end may use incompatible components! So many ways to muck it up, even over what might be considered a small and nearly insignificant part! Every part of the installation seems important, and it takes considerable time to research each part and know its characteristics.

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