Watt Hour - Battery Design

A unit of energy equivalent to one Watt of power expended for one hour of time.

Abbreviated as Wh

Watts are defined as 1 Watt = 1 Joule per second (1W = 1 Js^-1)

time is simple 1 hour = 3600 seconds

Hence 1 Wh = 3600 Joules

So the Watt hour (Wh) is a strange unit as it is energy use per unit of time multiplied by time.

However, this unit is easy to use and make simple connections.

Examples

Vehicle Energy

A Tesla Model Y has an energy consumption of 288 Wh/mile.

Hence, if you want to drive 100 miles then you need 288 Wh/mile x 100 miles = 28,800 Wh = 28.8kWh

In the Tesla Model Y it has 21700 cells added together in series (S) and in parallel (P). Hence we get the shorthand 96S46P configuration of cells that we might see in a Tesla pack. This means 46 cells are connected together in a parallel group and this is then connected in series with 95 more of these groups.

If each cell was 5Ah then we would have a total capacity of 46 x 5Ah = 230Ah

and the total nominal voltage of the pack would be 3.7V x 96 = 355.2V

the total nominal energy content of the pack = nominal voltage x capacity = 355.2V x 230Ah = 81,696Wh or 81.696kWh

This is total energy, the usable SoC window will be smaller, around 96% hence the usable energy = 81696Wh x 96% = 78,428Wh

The range of this car with an energy consumption of 288Wh/mile is then 78,428Wh / 288Wh/mile = 272miles

Household Energy

The average 3 bedroom house in the UK uses 8 kWh of electricity per day. If we divide this by the number of hours in a day we get 8 kWh / 24 hours = 0.333 kW. Hence the average power demand of the average house is 333 Watts.

If we have a 100 W incandescent light bulb that is on for 10 hours = 100W x 10h = 1000Wh = 1kWh
Swap this for a 10W LED light bulb that is still used for 10h = 10W x 10h = 100Wh = 0.1kWh

The use of the Watt hour immediately allows us to then translate this into a cost as we generally know how much 1kWh of energy is.