How clever are you?

N.B. I updated this page on 2023 04 05 based on new information from our suppliers…

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

Originally, 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

799 DKK per month flat fee + kWh * (average electrical price – 0.89)

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

Note that they define the “average electrical price” as the average monthly price for both DK1 and DK2 (Denmark is split into two regions for electricity prices). The calculation is done on a charge-by-charge basis, where the month that’s chosen for the calculation is the month when you unplug the cable at the end of charging your car.

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 799 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…

One thing that makes it even more complicated is the fact that, if we charge the electric car at home, we first pay our normal electricity supplier for the power we used, and we then get reimbursed by the electricity supplier for the electric car by some amount per kWh.

The way the electricity supplier for the electric car calculates this reimbursement is also complicated: They use the average monthly electricity price between 11:00 p.m. and 6:00 a.m. including charges. That number changes but it’s currently defaulting to 1.33 DKK / kWh on this page – look for the “Tilbagebetalingssats” amount in the sidebar on the right called “Tilbagebetaling”. (Note that this value is difficult if not impossible to determine using the NordPool information. The webpage linked above calculates it from the “forventet indkĂžbspris” that you can change yourself on their calculator.

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:

  • Electrical supplier for the electric car:
    • Flat monthly rate for our subscription
    • The amount that they subtract from the average Danish price, per kWh for charging the car (currently 0.89 DKK)
    • The amount that they pay us back to cover a portion of the electrical costs when we charge the car at home
  • The price we pay for electricity for the house
  • Average electricity price in DKK / MWh
    (available from this page. Select the DK1 and DK2 prices for the month of interest. The Excel spreadsheet finds the average of those two values, and adds 25% tax. shown at the bottom in cell B17 in DKK/kWh)
  • Fossil fuel Price in DKK/litre (in my case, that’s diesel)
  • Consumption of the two cars
    • 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 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 if we charge it at a station away from home
    • The red line shows the cost of driving the electric car if we charge it at home
    • The black 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, and we’ll save a lot more money if we don’t charge at home.

Looking at the plot on the right, if we park the electric car (0 km on the X-axis) we’ll spend about 2700 DKK per month. If we only drive the electric car (2000 km on the X-axis) and charge away from home at charging stations, then we’ll spend less than 1000 DKK (green line on the right-hand plot). Quite a savings! If we charge at home, we’ll spend about 2200 DKK (red line on the right-hand plot) – still cheaper than the diesel, but more than double the price of NOT charging at home.

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. :-)

2023 05 19 update: We switched to “spot pricing” for the house electricity. So, this calculation has become dependent on the time of day when we charge the car. As a result, I’ve given up trying to understand it…