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### EV Charging - How long? How much? How far?

##### 9 August 2021

The most common questions we get relate to electric vehicle charging rates and costs, so we thought we would try to answer these questions.

Along with this we also thought we would give the basic maths and also the technical reasons things might not always seem as they should.

To start with, in addition to the vehicle battery, there are usually two electronic devices that impact electric vehicle charging. Both of these significantly impact things:

**The vehicle**- all electric vehicles have on-board charge controllers. These absolutely limit the maximum power that than can be pushed at the battery to charge it. They form part of the specification of the vehicle. There are at least two of these in the vehicle, one for AC charging and one for DC charging. Some cars also have more than one charge controller for the AC or DC circuits**The charging equipment**- the most common type is the AC chargepoint. This is what you will typically buy for the home or office normally delivering up to 32 amps per phase (more on this later) usually costing £1,000 or less. There is DC charging equipment, often located at service stations, which will deliver between 20kW and 350kW (why not amps?) and usually cost between £5,000 and £100,000 each.

**How long will my car take to charge?**

The vehicle battery is specified in kWh (kilowatt hours) while the power to charge is specified in kW (kilowatts). As such the maths to work out the time to charge is pretty simple - it is the vehicle battery size divided by the maximum charging power that can be pushed at the battery to charge it.

A simple typical example is a 58kWh battery charged at 7.4kW. This will take 58kWh / 7.4kW = 7.84 hours (7 hours 50 minutes) to charge.

**What is my battery size?**

Vehicle manufacturers quote the 'full' capacity of the battery when it is new.

It is often not stated that the battery cannot be discharged below 10% and it is often recommended that it is not charged above a certain amount, for example 80%.

This means that a vehicle specified as having a 58kWh battery may only have a recommended maximum capacity of 41.76kWh when new. The maths for this is: 58kWh * ((100% - 10%) * 80%) = 41.76kW. This reduces the time required to 'fully' charge but is more important when we look at how far a charge will take you (more on this later).

**What is the maximum charging power?**

The absolute maximum charging power is limited by the vehicle. No matter what charging equipment you use you cannot exceed this vehicle limit. This is determined by the on-board charge controllers.

This limit will be different for AC and DC charging with a typical vehicle specification perhaps being 11kW AC and 100kW DC. For this specification no AC chargepoint, however powerful, can push more than 11kW at the battery and no DC charging equipment can push more than 100kW at the battery.

This is not the end of the story! As the maximum charging power is also limited by the chargepoint.

For DC charging equipment there is an absolute power limit for any given charging unit. A vehicle might be able to take 100kW but a 50kW DC chargepoint cannot deliver more than 50kW and a 75kW unit cannot deliver more than 75kW. As with DC charging equipment, AC charging equipment also has a maximum power limit, for example 7.4kW.

The absolute maximum charging power for a specific charging session is therefore the lower of the vehicle and the charging equipment specification for the type of charge being delivered, be that AC or DC.

This means that each charging location for a given vehicle will take different times to provide a full charge.

To work this time out you need to know the type of charge, DC or AC, the maximum specification of the vehicle charge controller for the charge type as well as the maximum power of the charging equipment. The time to charge is then the 'nominal' (see above) vehicle battery capacity divided by the lower of the vehicle charge controller power and the charging equipment for the type of charge being delivered.

Based on a nominal vehicle battery capacity of 41.76 kWh with 11kW AC and 100kW DC charge controllers:

A

**300kW**DC chargepoint will take 41.76kWh /**100kW**= 0.42 hours (25 minutes)A

**100kW**DC chargepoint will take 41.76kWh /**100kW**= 0.42 hours (25 minutes)A

**50kW**DC chargepoint will take 41.76kWh /**50kW**= 0.84 minutes (50 minutes)

A

**22kW**AC chargepoint will take 41.76kWh /**11kW**= 3.80 hours (3 hours 48 mins)An

**11kW**AC chargepoint will take 41.76kWh /**11kW**= 3.80 hours (3 hours 48 mins)A

**7.4kW**AC chargepoint will take 41.76kWh /**7.4kW**= 5.64 hours (5 hours 38 mins)

**What is ****MY**** maximum charging power?**

**MY**

So if you have a chargepoint at home or at work and want to know what it can do. This gets a bit technical as our electricity grid and Ohms law come into play here, however the maths is still pretty simple.

In the UK we have a three phase electrical grid operating at 230 volts. However, most domestic properties are only supplied with a single phase supply. Further, the maximum current that a AC chargepoint can operate at is typically no more than 32 amps.

By applying Ohms law, where power = volts * amps, the maximum power available from a single phase 32 amp supply in the UK is 230 volts * 32 amps = 7360W roughly 7.4kW. Using a three phase supply, not typically available in domestic properties, this would be 7.4kW per phase or a total of 3 * 7.4kW = 22.2kW.

Without installing a 32 amp supply for a chargepoint, many households will revert to charging equipment that uses a three pin plug. Rather than delivering 13 amps, the maximum that a standard UK domestic socket will deliver, plug in charging equipment will usually only work at 10 amps. Again by applying Ohms law this equates to 230 volts * 10 amps = 2.3kW.

Using the same nominal vehicle battery capacity of 41.76kWh with an 11kW AC charge controller

A

**7.4kW**AC chargepoint will take 41.76kWh /**7.36kW**= 5.64 hours (5 hours 38 mins)A

**3.6kW**AC chargepoint will take 41.76kWh /**3.68kW**= 11.35 hours (11 hours 21 mins)A

**2.3kW**AC charging lead will take 41.76kWh /**2.3KW**= 18.16 hours (18 hours 10 mins)

There are many vehicles, even new models, that have on-board charge controllers that are less 7.4kW. The maximum charging power may then again be limited by the vehicle and not the charging equipment.

There are also some quite odd outcomes. For example, some vehicles that have on-board AC charge controllers rated at 11kW will not charge at anything like 11kW using a UK single phase supply. The reason for this is that an 11kW charge controller may be limited 16 amps per phase. Running single phase this would only give 230 volts * 16 amps = 3.68kW while at three phases it would give the full 11kW - 3.68kW * 3 = 11.04kW.

To allow higher single phase charging some vehicles have more than one charge controller for AC charging with one operating at a higher current on a single phase.

**How much will is cost to charge?**

Electricity is charged in kilowatt hour (kWh) units. As such the maths to calculate the cost of fully charging an electric vehicle is pretty simple. All you need to know the size of the vehicle battery and the electricity tariff being applied. With these two values the cost to fully charge is the battery size * the unit price of electricity.

Currently the average price for a unit of electricity purchased directly from the grid during the day is £0.1436/kWh. For a nominal battery of 41.76kWh the full cost to fully charge will be 41.76kWh * £0.1436/kWh = £6.00

By using off peak tariffs, typically available at night for between 4 and 7 hours, tariffs of £0.7/kWh or less are available. Provided you can fully charge your vehicle during off peak hours the cost, again for a nominal battery of 41.76kWh, will be 41.76kWh * £0.07/kWh = £2.92

When out and about the cost to charge at a public charging station varies considerably. Some public charging stations will charge around £0.35/kWh while some can be as much as £0.79/kWh. This can make the cost to charge over 10x more expensive than charging at home or at work.

A

**£0.07/kWh**tariff to fully charge a 41.76kWh battery is**£2.92**A

**£0.15/kWh**tariff to fully charge a 41.76kWh battery is**£6.26**A

**£0.35/kWh**tariff to fully charge a 41.76kWh battery is**£14.62**A

**£0.79/kWh**tariff to fully charge a 41.76kWh battery is**£32.99**

**How far can I go when I charge?**

The total distance an electric vehicle can travel on a full charge is dependent on the battery size. However the distance it can travel for a given amount of charge is dependent on the efficiency of the vehicle.

Every electric vehicle has a specified efficiency even though this is often not published. It does however make a great deal of difference. Currently efficiencies range from around 200Wh/mile to over 400Wh/mile.

Again the maths to work out how far a given charge will take the vehicle is pretty simple. It is the amount of charge delivered divided by the efficiency. So all that is needed is the amount of charge delivered in a given time together with the vehicle efficiency.

But ..... the amount of charge delivered is dependent on the charging equipment and the vehicle charge controller as discussed above. Working out the distance a given time charging will give you may need a calculator. Fortunately the vehicle will normally calculate this for you and display this on the instrument panel while you are charging in terms of miles per hour (mph).

The distance a given charge will give you can be calculated quite easily for any vehicle at any charging station. For example at a 50kWh DC charging station for a vehicle with a 100kW DC charge controller and an efficiency of 210W/mile a 15 minute charge will deliver 12.5kWh (50kW * 0.25 hours = 12.5KWh or 12500Wh) of charge. At an efficiency of 210Wh/mile this will give 12500Wh / 210Wh/mile = 59.52 miles.

Working on a typical 300Wh/mile efficiency, the following distances for 15 minutes of charge can be used as a rule of thumb for any given charging power. This is provided that the vehicle charge controller is not limiting the power being delivered

**2.3kW**(a typical home three pin AC charging cable) -**1.92 miles (7.68mph)****3.6kW**(a typical domestic AC slow charger) -**3 miles (12mph)****7.4kW**(a typical domestic AC fast charger) -**6.2 miles (24.8mph)****22kW**(a typical commercial or public AC charging point) -**18.3 miles (74.4mph)****50kW**(an typical older generation DC rapid charger) -**41.6 miles (166.4mph)****75kW**(a typical newer generation DC rapid charger) -**62.5 miles (250mph)****150kW**(a newer generation DC rapid charger) -**125 miles (500mph)****300kW**(a DC hyper rapid charger) -**250 miles (1000mph)**