In order to determine how big a battery you need, you simple add up how much each of the items will use in an hour, and then how many hours you want the system to function between recharges.
This is measured in Wh (Watt Hours).
Examples (for each hour in use)
Light 7-10Wh
Hot plate 1000Wh (Max power uses 1500Wh but on simmer as little as 200Wh)
Fridge 60Wh (When running it draws 300Wh but it only runs infrequently so about 1300Wh a day)
Fan 60Ws (Fans use a surprising amount of electricity)
You can estimate how much power something uses by looking at its rating in W, and estimating how much it runs in an hour. A light and fan is on all the time so a 5W light uses 5Wh each hour it is on
Then you need to think how long the appliance will be on. If you only use the stove for 10min on Max to boil water that is only 1/6 of an hour at 1500W or (1/6 x 1500) = 250Wh
1kWh = 1000Wh = 1 000 000mWh
The maximum lithium battery you can fly with is 100Wh or 27 000mAh (27 000mAh x 3.7V is about 100 000mWh)
At this time, the Jackery Explorer 100 Plus and Anker Prime 27000mAh are the biggest batteries you can take on a plane. But neither provide 120V for regular lights or a fan. They can be charged only with the solar panels from the same manufacturer.
We recommend a minimum of 2000Wh (540 000mh or 2kW) for a power station to power a home, or way too big to take on a plane
We have created a comprehensive estimator but here are examples:
Refridgerator - 1300Wh
Lights (5h a day) - 250Wh
Each fan (10h a day) - 600Wh
Hot plate (1h at Max) - 1500Wh
Instapot (half hour) - 350Wh
Rice cooker (half hour) - 200Wh
You can see that cooking can quickly drain your battery unless you have solar panels but it is great in emergency with the propane runs out if used judiciously
A battery will recharge when the power is on in about 60-90min depending on capacity and model
A battery never provides its rated capacity because you can't run them down to zero, and inefficiencies. Expect to get about 80% of its rated capacity, so a 1000Wh battery only has 800Wh of usable capacity
If you wanted to add an air conditioner, you system needs to be at least 2-5x
An air conditioner uses 6-8kWh overnight (when solar recharging is not an option), and much more during the day. See also the note on power
This determines how long your battery lasts, but also a battery can only provide so much power so it determines how much you can run at once
This is measured in W (Watts) and is usually listed on all appliances.
Examples (while in use)
Light 7-10W
Hot plate 1500W (Max power)
Fridge 300W (When running)
Fan 60W
The maximum power needed by the battery is the sum of all things that are going to be running at the same time
Even if you are recharging your battery with solar, you still have to stay below the maximum power output of your battery
All this is to say you need about 2000W or 2kWh to run a house at any given time
We created a full spreadsheet to help you estimate but briefly
Refridgerator - 300w
Lights - 5w or hardly anything
Each fan - 60w
Hot plate - 1500W
Rice cooker - 400w
Air conditioner - 1000w
In a pinch you can run the fridge and the hot plate at the same time (300W + 1500W = 2000W)
You can see why you need a much larger power rating to add an air conditioner because it adds 1000W on its own (when running)
With air conditioning you need much more
A 5000BTU air conditioner uses 450W and, of course a 10 000BTU uses 900W, but keep in mind that when they start they can use up to 3x that amount. Batteries are designed to handle short bursts but my not have enough power to start your air conditioner.