# number of electric vehicles that can be charged with specific amount of energy

I used minutely sampled wind speed data for one year to calculate the yield power from specific wind turbines to be used in electric vehicles charging station.

I am supposed to calculate the number of electric vehicles that can be charged within each day given the total constant energy from wind turbine.

My question is:

How many batteries can I charge using a 100 kW supercharger if I have energy of 45 MWh for one day? Battery capacity is 50 kWh, it takes 21 min to fully charged (or up to 80% for example) using 100 kW supercharger.

• To start predicting the power available from the wind you need 10 years worth of data as there are natural variations between years ie dome years can be high and others low. There was a paper about it a while back - you should do a search... – Solar Mike Feb 25 '20 at 17:59

## 2 Answers

There isn't enough information in the question to give a reliable answer. But here are some possible crude answers, just in case you are being tested on basic arithmetic and the relationship between power and energy.

1 kWh is an amount of energy equivalent to 1 kW for 1 hour. It's also the amount of energy equivalent to 10 kW for 0.1 hour, or 0.01 kW for 100 hours. It's just constant power multiplied by time; or, in a more complex but more realistic case, power integrated over time.

1 MWh = 1000 x 1 kWh.

There are 24 x 3 = 72 lots of 20 minute intervals in a day. That means that a single 100kW charger could, at most, charge 72 vehicles for 20 minutes each in a day. This would be 24 hours x 100 kW = 2,400 kWh = 2.4 MWh, assuming that the batteries' states of charge would allow constant charging at the full 100 kW. That's way in excess of your 45 MWh available from the wind turbine each day on average.

Another way to look at it, is to assume that the number of chargers is not a limit - if demand increases, more will get built. In that case, if in a day you have 45 MWh available, and each charge is 33.33 kWh (100 kWh x 20 minutes), then you can charge 45,000 / 33 which is around 1,350 vehicles.

For a somewhat more realistic problem to the solution , you need to know when power is demanded, and when it is supplied. There will be trade-offs between not using power when it's generated, having chargers standing around unused most of the time, having people waiting for a charger, and building battery storage.

But actually, in reality, you just wouldn't do it this way at all. You plug the wind turbines into the grid, and sell the power to the market. You plug the chargers into the grid, and buy power from the market. That way, all the needs of balancing supply and demand are carried out by the system operator, and they can do it far more economically than anyone else, because they're aggregating everyone's demand and everyone's supply.

It would be very unusual to have a wind turbine power a charging station without having a buffering device for energy storage such as an electrolyser or a battery of its own. But if it's a textbook calculation and these things are not there, then one approach is given below.

The limiting factor for battery charging is the current. If it takes 21 min at the supercharger to charge 80%*50 = 40 kWh, then the current is 40 kWh/(100 kw * 21/60) = 1.14 Amps. This is the max charging current to the battery. So one way to solve the problem is to look at the minute by minute amperage from the wind turbine and use the minimum of the current from the WT and the max charging current.