We have two cars. One is a fully-electric car, and the other is a diesel.

Up until recently, the plan we had with our electricity supplier for the electric car was a flat fee per month, and an “all you can eat” plan. This made the choice of which car to drive a no-brainer: take the electric car whenever possible.

However, due to the rising price of energy, our supplier is changing their plan to a new pricing structure. The new price will be

750 DKK per month flat fee + kWh * (average electrical price – 2.25)

The reasoning behind this pricing is explained on their website – I won’t bother getting into that.

Our problem is that it made the decision of which car to drive (looking at it from a purely economic point of view) complicated. If we park the electric car, it still costs us 750 DKK / month + the price of diesel in the other car. On the other hand, if we drive the electric car, it costs us something that’s difficult to calculate when you’re heading out to the car in the morning with only one cup of coffee in you…

It turned out that figuring out this problem was the most interesting math that I did this week. I ran the calculations first in Matlab, and then duplicated them in Excel (for compatibility’s sake) to find out how to deal with this.

The variables are:

- Average electricity price in DKK / kWh (available as a downloadable Excel file from this page)
- Fossil fuel Price in DKK/litre (in my case, that’s diesel)
- Average consumption of the electric car in kWh/100 km
- Average consumption of the fossil-fueled car in litres/100 km
- Total number of km driven per month
- The flat monthly rate we’re going to be charged
- The price per kWh that we’ll be charged on top of the flat rate

(in our new plan, that will be the average electricity price per kWh – 2.25)

The result is two plots:

- The one on the left shows the price of driving each car individually, based on the total number of km driven in the month, as a function of how many of those km are driven in the electric car.
- The green line shows the cost of driving the electric car
- The red line shows the cost of driving the fossil-fuel car

- The one on the right shows our total price, as a function of how many of the total number of km driven are driven in the electric car.

So, as you can see in the plots above, at the current prices, and using the average consumption values for our two cars, the more we drive the electric car, the more money we save. Looking at the plot on the right, if we park the electric car (0 km on the X-axis), we’ll spend about 2800 DKK. If we only drive the electric car (2000 km) then we’ll spend about 1100 DKK. Quite a savings!

However, what happens if prices change?

This shows the same information about the cars – I’ve just changed the prices to 9 DKK/kWh for electricity and 16 DKK/litre for diesel. (I’m just making some numbers up here… this is not a prediction…)

Now you can see in the plot on the right that we’ll spend about 2850 DKK if we park the electric car for the month and only drive the diesel; if we drive ONLY the electric car, we’ll spend about 2910 DKK. (which, admittedly, is an increase of less than the price of a pizza)

In case you are in the same position as we are, and the little Excel calculator I made might be useful, you can download it here. However, I make no promises about its reliability. Don’t send me an email because I screwed up the math – fix it yourself. :-)