Electric Generation

We have studied motors and the main motor equation lets us understand the generation of power in an electric generator.

Recall that the speed is proportional to the generated voltage and that the torque is proportional to the current flowing.

This doesn’t change when the motor is being used as a generator.

In the case of a motor, we applied electrical power to a motor and received mechanical power at the output of the motor.

In the case of a generator, we apply mechanical power to the motor shaft and we generate electrical power that we use in an electrical load.

Electrical Output

If we know the speed that the motor is spinning at, we know the voltage generated. This voltage will be applied to the internal resistance of the motor and the electrical load. Using Ohm’s Law, we can determine the current.

Knowing the current, we can determine the mechanical torque that must be applied to the motor to maintain that motor speed.

Note that this relationship changes when we change the equivalent resistance of the electrical load.

Gearing

We often want to run generators at high speed to create high voltages and low currents to minimize losses.

However, wind turbine blades spin relatively slowly. To convert the slow mechanical input of the blades to the rapid spin of the generator, we use gears.

The gear ratio is the ratio of the RPM of the generator to the RPM of the mechanical input. A bicycle chain is a familiar model and we can calculate the ratio by dividing the number of teeth on the front chainwheel by the number of teeth on the back sprocket.

Exercise

You have a motor/generator with a Kv value (this is the voltage constant in units of RPM/volt) of 8.2 RPM per volt. We spin the motor at 100 RPM and connect it to an electrical load of 20 ohms.

How much torque do we have to apply to the motor to maintain the speed of the motor.

If we have a gear of 48 teeth at the mechanical input and 12 teeth at the motor, what is the RPM and torque at the mechanical input.