Energy density vs voltage battery

Question

I find on this website the following sentence:

It is said that higher voltage battery have higher energy density. But it appears to me not so evident:

If I consider the 2 following batteries:

If I approximate the cells of the battery to capacitors, I get for the cells in series:

$$ E = \frac{1}{2}*\frac{C_{cell}}{N_{cell}}*(N_{cell}*V_{cell})²\\ = \frac{1}{2}C_{cell}N_{cell}V_{cell}² $$

Then for the cells in parallel, it is more simple:

$$ E = \frac{1}{2}C_{cell}N_{cell}V_{cell}² $$

So I get exactly the same energy density. So what explains that energy density is higher for a high voltage battery?

Answer 1

There are a number of ways you can find a grain of truth in 'higher voltage is better', through unstated assumptions, and deciding what to keep constant in the comparison.

• For the same Ah, higher voltage will give you more energy.

However, to change the voltage of a battery, you are generally changing the chemistry, and therefore everything else about the battery. It then simply becomes a statement of watt.hours = voltage * ampere.hours for any given battery.

• If you have several batteries, then a series connection will give you higher voltage, lower current, for the same power.

This means the cables connecting it to the load can be smaller. While this may seem like a minor consideration, consider an electric vehicle. If you want to shift 60 kW power from batteries to motor, then a 12 V battery would have to deliver 5 kA, requiring very thick bus-bars rather than cable. A 600 V battery 'only' has to deliver 100 A, using 'starter cable' sized cable. Alternatively, for the same size cables, a high voltage battery will deliver more power.

A similar, or possibly even more important consideration, is how fast the car can be charged, as the flexible 'hose' from the charger station to the car is likely to be longer than cables in the car between battery and motors.

The energy and power involved is exactly the same with either low or high voltage battery arrangement, only the (commercially very important) practicality changes.

Answer 2

The energy stored in a battery is given by the known formula E=L= Q∙ΔV. That is, for a 12V, 100Ah battery we have: E=100Ah∙12V=1.2kWh. If we consider a capacitor with capacity C=100Ah/12V=30kF the energy accumulated in it is: E=C∙V²/2= 600Wh which is exactly half of the energy accumulated in the battery. You can't think of the battery as a capacitor.