I want to build a system to power a Tiny Home, and man it's a lot to wrap my head around...

[Doggydogworld]

You asked for watt vs watt-hour corrections, so I'll try. Plus some random comments.

I've built myself a 120 sqft tiny home outside of Houston, Texas on a plot of land I own. I want to do an off-the-grid setup and bring my cost of living down, and a big component of that is Solar Energy. I work from home as a computer programmer, so my energy needs are a bit diverse.

To live there full time you need backup power. Grid or generator.

I need a budget of about 4800w per day

4800 Wh per day or 4.8 kWh per day. About 50 cents worth of electricity in TX. This page has Energy Audit info to help you nail it down.

he gets away with a 4800w system, so that's what I've targeted.

A "4800W system" usually means 4800W of solar panels. Not saying that's what he has, just general lingo FYI.

provide this 4800w daily. Ideally, I'd like to start with something at 4800w initially, then grow it with redundant batteries for prolonged periods of rain,

Again, 4800 Wh. Agree it's best to start small and use backup power for cloudy stretches.

My plan is to get one of those 24V 200aH batteries, which would provide me a capacity of 4800w if I've done my calculations correctly. That would run me $1250.

4800 Wh.
24V * 200 Ah = 4800 VAh
V*A = W (at least for DC) so ....
4800 VAh is 4800 Wh or 4.8 kWh

So I'm doing my calculations based on an average of 4 hours of peak sunlight per day (since I can skirt by with less power in the winter).

Lighting and heating (incl. water heating) take more energy in winter. You can use propane or oil for heat, of course. A/C obviously takes a lot more in summer, but you seem to have that handled.

That's a 315w solar panel. As I understand it, that means the solar panel can produce 315w per hour

315W, not watts per hour. (Watts is already Joules per second, so it's analogous to MPH even though there's no explicit time unit).

at peak sunlight, so at 4 hours of peak sunlight per day worst-case scenario, a single panel is producing 1260w. So I'd need 4 of those panels to produce the 4800w I want my battery to hold in one day? Is that correct?

That's the right math, though real world useful output can be less than napkin math. Sites like PVWatts let you estimate output for your location, panel orientation, etc. I agree with others that new panels are a better deal these days.

I need it to be the size of my solar array, so the inverter would need to be 4800w as well, is that correct?

Inverters are usually rated based on power OUTPUT. If your devices never draw more than 600W then you technically only need a 600W inverter. Anything with a motor will draw a lot more power at startup, so you have to account for that. Same for a microwave.

Finally, I'm looking at a charge controller. What I've read is they need to be the size of my solar array wattage divided by the voltage of my battery. So if my battery is 24V, and my Solar Array is 4800W (technically 5040), I do 4800/24 = 200a.

Four 315W panels is a 1260W array, not 4800W. You have to match your solar charge controller to your array voltage and current. Array voltage and current depend on configuration (series, parallel, mixed). If your panels are nominally 35V and 9A and you put them all in parallel (4P) the array is 35V and 36A. The wiring and connectors often used to connect panels are usually rated for 30A, so you'd have to work around that.

If you connect all four panels in series (4S) it'd be 140V and 9A. The 9A is easy to handle, but you'll need a suitable MPPT controller to convert that voltage down to 24V to charge your battery. PWMs do no conversion. You can also choose 2S2P, for 70V and 18A. That might save a bit on the MPPT.

The solar panels I'm looking at are 72 cell, so unless i'm mistaken I can go with a PWM charge controller to save a little bit of money? I've been looking around and I think a 200 amp PWM controller tends to go for around $1000?

You don't need 200A. Even in 4P your array will only put out something like 36A.

Also, PWM will pull your panels down to 26-28V so your array's peak output would be something like 28V * 36A = 1008W vs. the 1260W the panels are rated at. 4 hours of peak sun equivalent is then only 4.0 kWh vs. the 4.8 you need. It's even less useful energy once you subtract charge/discharge losses, inverter losses, etc. MPPT will drive your panels to their optimum voltage and current, getting you closer to the 4.8 kWh (before losses) you estimated.

Do these numbers sound correct? I'm looking at a rough cost, without wiring or mounts, of about $3000? Is there anything obvious I'm missing? Am I getting myself into trouble here or is this a good starting point for more research? Further, assuming in the future I wanted to add a second battery, what pitfalls should I avoid? And if I wanted to add more solar panels, that would mean I'd need a second inverter, correct? Would it be smarter to size my inverter upfront for any future expansion?

$3k sounds a bit high, but it depends on how much blue you buy.
You can have multiple arrays and multiple charge controllers feed a single battery and inverter. Other odd configs are also possible. Wouldn't worry about that too much right now. Biggest decision is what to use for backup (grid or generator) as that will drive equipment choices. Second decision is battery voltage, I agree with others 48V (or even 12V) is preferable to 24V.

 

[adamantium]

I'm sorry if this is a little too broad of a topic...

If you approach your question from a different angle it might end up being easier to understand. But first, let's clarify that a raspberry Pi can't use more than 15W of power at maximum load since its power adapter is rated at 15W. You almost got it right, its 5V @ 3A not 3V @ 5A. In reality it really can't consume more than about 7W at maximum load without any hats. So it will never consume 40W.

Now back to what you need, to do what you want. I really doubt you use more than 300W of power continuously in your tiny house. Your computer doesn't use anywhere near that amount. Unless you have a coffee pot running all day long or a space heater, or a television, or a large amount of lighting, I suspect you are averaging less than 300W continuously. Let's use some real world examples. I have a 55 inch 4K television that I use as my monitor to my multicore desktop computer. I don't have a graphics card in it. The combined power consumption of the desktop computer and the 4K television is less than 80W at normal load. That's typing and watching television on the computer. It goes up around 110W under moderate load and can exceed 200W combined at full load. So while you are working in the day without lights on, on your raspberry Pi4-B running at average load, you are using probably less than 75W of power depending on your monitor's needs. You can do that all day long with a single 100Ah battery. A 100Ah battery has 100Ah * 12V = 1200Wh of power. To be more specific, you can do that for 16 hours with a single 12VDC 100Ah battery assuming 100% efficiency, or for 12 hours assuming 75% efficiency. So you can easily get an entire day's work out of a single 100Ah 12V battery.

But average load isn't how you calculate what you need. You need to be able to run appliances throughout the day, and some of these have huge power needs. A microwave easily takes 1200W, even the smallest takes 900W. Toasters, hair dryers, space heaters, mixers, can easily each draw 1000-1800 watts of power while they are running. So you need to work out how many of those you will be using each day and how many of them you will be using at the same time. That will determine the size of the inverter you will need.

Also at night how many light bulbs will you be running? The average 60W LED light bulb today uses 7W. You can get 50W, 60W, 75W, 100W versions. You can even buy 12VDC versions of LED bulbs. If you choose to use 12V DC bulbs you don't even need an inverter to run them. You just connect them to your battery. I have AC lamps that I run 12V DC bulbs using a simple AC to 5521DC connector, that are 100W equivalent that use 12W of power, I can run them on an AC/DC adapter rated for 12V @ 1A output (12W) continuously. I don't need more than one of those. They are as bright as any LED plugged into AC. So get some of those and put them in a couple $9 lamps from Amazon and you will have all the lighting you need for 24W. You can run two of those for two days on a single 100Ah battery.

Do you have any 240VAC appliances? It doesn't sound like you have to run an air conditioner. Do you have a gas stove/oven or electric? Do you use a clothes line or an electric dryer? Do you use a washing machine, a dish washer, a refrigerator, a freezer, an iron, a hair dryer, a 3D printer, power tools, etc? Each of those may run several times a day but they do not run continuously. The average RV refrigerator uses about 1-1.5kWh per day. That means just for a refrigerator you will need 1000-1500Wh or a single 100Ah battery at least.

So you need to figure out what your real power consumption is going to be and what a modest expectation for power generation for solar will be to meet those needs. Then you need to size your battery bank to meet that at a minimum, and preferrable at least double that amount so that you have days you can use more, or so that you can use what you need when the sun doesn't shine as much. Like others have said, you will most likely need need a generator if you are going for the minimal solar inverter battery combination.

If you don't have any 240VAC appliances to run and nothing more than a refrigerator and small induction hotplate or something, you don't need to build like you would in a permanent residence. That means you don't need an 12kW hybrid inverter and 30kWh of battery. You can easily get by with the following:

400Ah@12V (3600Wh of usable power per day)
2500W (5000W surge) pure sine inverter

That's 225Ws continuous power for 16 hours a day, or less with bursts of large load for small amounts of time. An RV refrigerator will use 1000-1500Wh of that every day, leaving 130-160W for everything else. A mini fridge will do it for half that (550-850Wh/day)

A 2500W inverter with a 5000W true surge capability can handle anything you throw at it except air conditioning and industrial shop tools, but not everything at the same time. The total cost of these parts currently is around $900 (4 x 100Ah battery is around $720, 2500W pure sine inverter is around $160). Of course you can always spend more for name brands and larger components, but these prices are for parts I own and use. In a tiny home, where are you going to put the rack? Your estimate of $1250 for 200Ah@24V is equivalent in power but almost twice the price of the entire system here. You can configure four 12V batteries in 400Ah@12V or 200Ah@24V or 100Ah@48V.

You probably can get by with 6 solar panels rated at 300W or better if you can get 3 hours a day of direct sunlight on them, more if not. That means a fairly expensive solar charger. If you can find a comparable inverter/charger combo unit that is less expensive, then that would be a good modification. I doubt you will find one those that is less expensive than what I listed here. Make sure you get a real MPPT charge controller for whatever you buy. You can't afford to waste any power from your panels.

Again you will still need a generator to get you through the rainy days, but those are now the least expensive of any of the components. You can get a 5500W dual-fuel DuraMax generator for $550 or so. You would need 4 more batteries ($720 at least) for every day you want power without the sun, so a generator is a better option. (In fact it might be the best option since its the cheapest option for the most power)

If you decide to go with an off-grid inverter charger, then you really need to go with a 48V version. That will reduce the size and cost of your cables, will be a little more efficient, and you will find more options to accommodate that voltage.

Sungoldpower.com has a 48V 6000W off-grid inverter, charger on sale today for $850. I have a new one of those but haven't used it. Its supposed to be a decent starter unit.

I hope that helps.

 

[hrchonda]

while theoretical is part of due diligence some times its better just to do and find out.

my advice,

1) buy a 16 280ah cells + BMS and make a 48v battery. (the best starting point and if more storage is required buy another)
2) buy a victron MPPT and if youve maxed the solar and its not enough, buy another, they talk to each other and its easy to see what 2 mppts combined is outputting at a glance.