Fuel efficiency calculations

Some maths to try and understand the comparative fuel efficiency of vehicles using petrol, diesel and electricity as their fuel. For example, is a 3 mile per kWh electric car more or less fuel efficient than a 80 mile per gallon diesel car? (Spoiler: more)

First we need to understand the energy content of the fuels in question. According to the UK Government there is 9.6kWh of energy in a litre of petrol and 10.9kWh in a litre of diesel. We can then work out the miles per kWh by dividing the miles per gallon figure by 43.5 for petrol cars, and by 49.5 for diesel cars.

So a 50 mpg diesel car is doing roughly 1 mile per kWh. And a 22 mpg petrol car is achieving 0.5 miles per kWh. Almost all electric cars can manage at least 2.5 miles per kWh, so a diesel car would have to do 123.75 mpg to be using its fuel as efficiently as that, and for a petrol car it would be 108.75 mpg. Electric motorbikes can usually achieve twice the fuel efficiency of an electric car, so those figures would be double.

Why is this? Optimistically only about 35% of the actual energy in diesel and petrol is converted into motion, the rest is mainly wasted as heat from combustion of the fuel. Meanwhile electric motors generally turn over 90% of their fuel into motion, with the batteries wasting energy as heat at the extremes of their performance envelope.

Raw fuel efficiency is one aspect, but fuel cost is equally important, i.e. £ per mile. Right now in our part of the UK the cost of petrol is about £1.20 per litre, and diesel about £1.24 per litre. Electricity can cost up to £0.30 per kWh from a commercial fast charger, or as little as £0.045 per kWh on an EV-friendly domestic energy tariff.

To work out the £ per mile we simply divide £5.45 by the fuel efficiency of a petrol car, or divide £5.63 by the fuel efficiency of a diesel car. So our 50 mpg diesel car costs £0.113 per mile, and the 22 mpg petrol car costs £0.248. The electric car calculation is the same, divide the cost of a kWh, say £0.30, by the fuel efficiency, say 2.5 miles per kWh, and in this case get £0.12 per mile.

Purely on fuel costs, a 50 mpg car filled with £1.24 per litre diesel is cheaper to run than a 2.5 mile per kWh electric car charged with £0.30 electricity.

However, charge the electric car overnight at home at £0.045 per kWh and the £ per mile drops to 1.8 pence per mile. Almost a tenth of the £ per mile of the diesel car. And the electric motorbike mentioned above is going to easily cost less than a penny per mile to run.

Finally, if the electricity you charge your car or motorbike with has come from the solar PV panels on your rooftop, then the pure fuel cost is zero...

Agile energy

It has been an ambition to both reduce our energy usage, and clean it up. Our (very) local power station was converted from coal to biomass in 2012, after over 40 years of burning through 1.2m tonnes of coal each year, and then turned off altogether in 2015. Friends of the Earth had claimed that Ironbridge B was the second worst polluting power station in the UK, so I'm not sorry to see it, its dirty electricity and its pink cooling towers go from the landscape.

The key to our twin ambitions is smart meters. Not because they are smart, as they're not, but because the increased frequency of metering enables energy suppliers to offer a much wider range of pricing options. Energy suppliers can offer varying pricing levels during the day, as a mechanism to shift energy usage to times of the day when the electricity on the grid is predominantly coming from clean sources. Something not possible with monthly readings.

Last year our energy provider had contacted us about upgrading our electricity and gas meters to new SMETS2 meters, so we took them up on the offer. Now we have a Landis & Gyr E470 electricity meter and Toshiba SKU1 cellular modem in the outside cabinet. Once or twice a day this automatically sends half-hourly meter readings back to the Data Communications Company (DCC), whom then send our readings onto our energy supplier. Unfortunately our gas meter couldn't be upgraded, so we still have to manually take readings and send these off ourselves. The electricity meter also came with an In Home Display (IHD), which is connected to the meter via ZigBee, so that we can see near real-time usage on a screen in  the kitchen.

IHD, with red LED to indicate excessive power usage

Our energy supplier only offered a fixed rate tariff, so we looked for alternatives and found Octopus Energy. As well as dual rate tariffs, like an Economy 7 tariff, that are aimed at charging electric vehicles overnight, Octopus offer a time-of-use tariff called Agile, where the price of electricity changes every half an hour. And every day.

Agile Octopus tariff for a 24 hour period

If you can change your electricity usage so that you avoid the 4pm to 7pm period, then the cost comes down from the 20p/kWh flat rate we were paying our old energy supplier, to around 7p/kWh. Or less if we're paying attention.

Usage over a 24 hour period

The graph above shows a car charging over night, then being topped up again in the middle of the day after a short trip. During the rest of the day there's about 600W of power being used constantly. Having visibility of this information is the first step to identifying where we can reduce our usage.

A side benefit of chasing the cheap periods in the day is that they correlate well with the times when the electricity on the grid is also the cleanest. Power from wind and solar are the cheapest being fed into the grid, with gas and nuclear being the most expensive. So if the power on the grid is cheap, it is likely to be predominantly from wind and solar.