What Size Battery Would You Need to Power Your House?

These are just D Cell batteries – not Tesla batteries. Rhett Allain

It seems like Tesla might be making a battery for your house. Would that be cool? I think so. But why would you need a house battery? I can think of a couple of uses:

• For an off-grid house you might like to power it with solar or wind power. Unfortunately, neither of these two sources provide constant energy. If you could store the energy in a battery, you could use this during the night or calm weather.


• Many people keep a gasoline powered generator for their house. I have one that I don’t use too often, but it’s awesome when you need it. What if you had a battery that you could use for your house in times of power outages? That would be cool.


• It seems like the power company would like everyone to have a battery. With a house battery, you could reduce power spikes on the grid. When you turn your air conditioner on, it draws a large current for a short period of time(here’s an explanation of why the current spikes). With a battery this current demand could be leveled out (I guess).

But that’s not why you are here, is it? You want to know how big of a battery you would need. Let’s find out.

Battery Size

We need some starting values. First, how long do you want to run your house on a battery? I think Elon Musk (from Tesla) said one week. Got it. The next big thing is the power usage. I think a fair assumption is a constant 2000 Watt power usage. Clearly a house would need more than 2000 watts at some point in the day. However, at night you wouldn’t need much power such that the average for the day could be 2000 watts. If you don’t like that value, you can put your own numbers into the calculations.

If I know the power and the time, I can use the definition of power to calculate the energy stored in the battery.

Having the power in Watts is fine (since a watt is a Joule per second) but I need the time in seconds.

Now I can calculate the stored energy in the battery.

Great. But what the heck is a Joule? Sure, it’s a unit of energy but is that a large amount? Here’s a simple experiment you can do yourself. Take a textbook and put it on the floor. Now pick it up and put it on a table. In order to lift the book, you need energy (to change its gravitational potential energy). A book is about 1 kg and you lifted it about 1 meter. That makes a change in energy of about 10 Joules (don’t forget the gravitational field is 9.8 N/kg). So now you know about Joules.

Now for the battery size. The dimensions of the battery will depend on the type of battery. The current Tesla vehicles use a lithium ion battery. According to Wikipedia, the lithium ion battery has an energy density from 0.9 – 2.23 MJ/L (mega Joule per liter). I would imagine that Tesla would only use THE BEST BATTERIES! That would put its energy density at 2.3 x 10⁹ Joules per cubic meter.

If I call the energy density σ, then I can find the battery volume:

Putting in values for the energy density and the battery energy:

So just half a cubic meter. That’s not too bad. If you want to put this inside your house, you could make it as tall as a wall (let’s say 2.5 meters). Now from a design view maybe a battery should be just 5 cm thick. This means that it would have to be about 4 meters wide. Ok – that wouldn’t work. If increase the thickness to 10 cm, it would just be 2 meters wide. That could work.

Of course, this only really works because of the high energy density for a lithium ion battery. If you used an akaline battery (like AAs) it has a lower energy density at around 1.8 MJ/L such that it would be slightly larger house battery (but not rechargable). You can look at the Wikipedia page on energy density to get an estimate for house batteries of different materials.

Just for fun, what if you made a penny battery (from copper-zinc pennies and acid)? How big of a battery would you need in that case? Here is your answer.

Homework

This is just a perfect story for homework. It won’t be too difficult, so don’t delay and start soon.

• What if you wanted to run your house on AA Cell batteries? From my previous investigation, I found that a AA battery has about 10,000 Joules of stored energy. How many AA batteries would you need and how much space would it take up?


• What if you wanted to run your house on a nuclear power plant that used Thorium? How much Thorium would you need? Use the energy density from Wikipedia.


• According to this news, Apple will build a 130 MegaWatt solar farm to use for its stores and stuff. What if you wanted to run your house completely off grid with solar panels and batteries. How big would the solar panels be? You can assume the Sun gives 1000 watts per square meter with a solar panel efficiency of about 25%. Don’t forget that the Sun won’t always be directly perpendicular to the panels. This post might be useful.