## Power (kW), Energy density (kWh) and Range (km)

The objective of this article is to explain the differences between power and energy and explain why these concepts are important for electric vehicles.

If you are familiar with cars, you are probably familiar with the concept of power. Power is what gives the car acceleration and what maintains a car at a given speed. Mechanically power is the product of torque and rpm, so while torque can be multiplied through gearing (by lowering rpm), power is independent of gearing

Now on the electrical side of things power it is important to know that Voltage times Amps = Watts. This is only a measure of instant power, this is the amount of power that flows though an electrical circuit, this does not tell us how long this power can be used. Power is measured in metric units as watts (W) or more commonly kilowatts (1kW=1000W). Technically there is no difference between power produced by an Internal Combustion Engine or an electric motor, though because the torque curves are so different just comparing the peak power of the two motors isn't sufficient. The peak power of an EV is generally decided by the controller, as long as the batteries and motor can handle that power.

Energy is what gives an electric car range. It is the product of power and time (E = P x t) or the product of voltage and amp-hours. Energy is stored in the batteries as chemical energy and is converted to kinetic energy by the motor to make the car move. The measurement used for measuring total electrical energy in a battery pack is called Watt-Hours (Wh) or sometimes Kilowatt-Hours (1kWh=1000Wh). Watt-Hours is a measurement we can use to figure out how much energy we have, i.e. how long can we sustain a given level of power.

If a vehicle takes 10kW to travel 55mph, and the owner wishes to do so for two hours then the energy required to do so is power x time or 10 x 2 = 20kWh. So the owner would need to size the battery pack to contain 20kWh in order to travel that distance.

For example - The Mahindra e2o has 10kWh worth of energy stored in its battery pack at 48 V.

The ampere hours value for the pack can be calculated as follows - 10,000W / 48V = 208 Ah.

So looking at all the numbers of the battery pack, the approximate range can be easily figured out.

The range of the pack is determined by the efficiency (measured in Wh/km) and the total energy stored in your battery pack (measured in kWh)

Can the Mahindra e2o really provide a range of 100kms as advertised?

The weight (mass) of the e2o is 834 kgs and the max speed is 80 kph.

The kinetic energy KE at 80 is 1/2*m*v^2 = 205,925 Joules.

To accelerate to 80 in 20 seconds requires KE/20= 10.3 kW.

For 48 volts system will use 215 amps for 20 seconds, which the 48v, 200 Ahr battery pack can easily provide, but it will use up ~1% of the battery capacity every time a driver makes a rapid start like this.

If it needs to go 100km range at 80 kph, then the battery must supply current for 100/80=1.25 hours.

And based upon the capacity 200Ahr/1.25 hrs = 160 amps it will need to draw during that period, and at 48V that is 48*160= 7680 Watts available to drive at 80 kph.

So it looks like yes the Mahindra e2o could make 100 km range if driven at constant speed and not accelerated very much or very fast this is theoretical using 100% of the battery and without allowing for any losses in the battery pack.

**Power**If you are familiar with cars, you are probably familiar with the concept of power. Power is what gives the car acceleration and what maintains a car at a given speed. Mechanically power is the product of torque and rpm, so while torque can be multiplied through gearing (by lowering rpm), power is independent of gearing

Now on the electrical side of things power it is important to know that Voltage times Amps = Watts. This is only a measure of instant power, this is the amount of power that flows though an electrical circuit, this does not tell us how long this power can be used. Power is measured in metric units as watts (W) or more commonly kilowatts (1kW=1000W). Technically there is no difference between power produced by an Internal Combustion Engine or an electric motor, though because the torque curves are so different just comparing the peak power of the two motors isn't sufficient. The peak power of an EV is generally decided by the controller, as long as the batteries and motor can handle that power.

**Energy**Energy is what gives an electric car range. It is the product of power and time (E = P x t) or the product of voltage and amp-hours. Energy is stored in the batteries as chemical energy and is converted to kinetic energy by the motor to make the car move. The measurement used for measuring total electrical energy in a battery pack is called Watt-Hours (Wh) or sometimes Kilowatt-Hours (1kWh=1000Wh). Watt-Hours is a measurement we can use to figure out how much energy we have, i.e. how long can we sustain a given level of power.

If a vehicle takes 10kW to travel 55mph, and the owner wishes to do so for two hours then the energy required to do so is power x time or 10 x 2 = 20kWh. So the owner would need to size the battery pack to contain 20kWh in order to travel that distance.

For example - The Mahindra e2o has 10kWh worth of energy stored in its battery pack at 48 V.

The ampere hours value for the pack can be calculated as follows - 10,000W / 48V = 208 Ah.

**Range**So looking at all the numbers of the battery pack, the approximate range can be easily figured out.

The range of the pack is determined by the efficiency (measured in Wh/km) and the total energy stored in your battery pack (measured in kWh)

Can the Mahindra e2o really provide a range of 100kms as advertised?

The weight (mass) of the e2o is 834 kgs and the max speed is 80 kph.

The kinetic energy KE at 80 is 1/2*m*v^2 = 205,925 Joules.

To accelerate to 80 in 20 seconds requires KE/20= 10.3 kW.

For 48 volts system will use 215 amps for 20 seconds, which the 48v, 200 Ahr battery pack can easily provide, but it will use up ~1% of the battery capacity every time a driver makes a rapid start like this.

If it needs to go 100km range at 80 kph, then the battery must supply current for 100/80=1.25 hours.

And based upon the capacity 200Ahr/1.25 hrs = 160 amps it will need to draw during that period, and at 48V that is 48*160= 7680 Watts available to drive at 80 kph.

So it looks like yes the Mahindra e2o could make 100 km range if driven at constant speed and not accelerated very much or very fast this is theoretical using 100% of the battery and without allowing for any losses in the battery pack.