Watt Hour

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

Tesla Model Y

A Tesla Model Y has an energy consumption of 288 Wh/mile.1

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 roughly 8 kWh of electricity per day, somewhat above Ofgem’s medium-user average across all home sizes.2 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.

Production Energy

By production energy we are talking about how many Wh of battery would be needed per year of production.

Let us use the example of a vehicle with a battery pack that has a total energy content of 83 kWh and that we will make 50,000 vehicles every year.

83 kWh x 50,000 = 4,150,000 kWh required per year

4,150,000 kWh = 4,150 MWh = 4.15 GWh

Pack Size versus Application

  • iWatch ~1Wh
  • Mobile ~ 10Wh
  • Tablet ~30Wh
  • Laptop ~50Wh
  • eBike ~500Wh
  • Home PV storage ~10kWh
  • Electric Car ~100kWh
  • Electric Lorry ~500kWh

References

  1. InsideEVs, 2024 Tesla Model Y Long Range AWD Gets 3.5 Miles/kWh EPA Energy Consumption, reporting official EPA/fueleconomy.gov ratings
  2. Ofgem, Typical Domestic Consumption Values for gas and electricity

See also: Ohm’s Law, Kirchoff Laws