Electrical motors and generators formulas

Synchronous Motors

Synchronous motors operate at a constant speed that is directly related to the grid frequency and the number of poles of the motor.

Key Formulas:

Synchronous Speed ()

Where:

• : Synchronous speed (RPM).
• : Grid frequency (Hz).
• : Number of poles.

Mechanical Power of the Motor ()

Where:

• : Mechanical power (Watts).
• : Torque (Newton-meter).
• : Angular speed (rad/s),.

Electrical Power ()

Where:

• : Electrical power (Watts).
• : Applied voltage (Volts).
• : Current (Amperes).
• : Power factor.

Relationship Between Torque and Current

Efficiency ()

Asynchronous (Induction) Motors

Asynchronous motors or induction motors do not operate at synchronous speed; instead, there is a slip between the speed of the magnetic field and the rotor speed.

Key Formulas

Rotor Speed ()

Where:

• : Rotor speed (RPM).
• : Synchronous speed (RPM).
• : Slip.

Slip ()

is generally expressed as a percentage.

Motor Torque ()

Where:

• : Mechanical power (Watts).
• : Rotor angular speed (rad/s).

Input Power ()

Efficiency ()

Power Dissipated Due to Slip ()

Direct Current (DC) Motors

Direct current motors have a simpler and more controllable behavior, as their speed and torque are directly related to the applied voltage and current.

Key Formulas

Motor Speed ()

Where:

• : Motor speed (RPM).
• : Voltage applied to the motor (Volts).
• : Armature current (Amperes).
• : Armature resistance (Ohms).
• : Back EMF constant (Volts / RPM).

Motor Torque ()

Where:

• : Motor torque (Newton-meter).
• : Torque constant (Newton-meter / Amperes).

Electrical Input Power ()

Mechanical Power ()

Efficiency ()

Electric Generators

Electric generators convert mechanical energy into electrical energy. The formulas applied depend on the type of generator (DC or AC), but in general terms, the following equations are relevant.

Key Formulas

Generated Electrical Power ()

Where:

• : Generated voltage (Volts).
• : Generated current (Amperes).

Synchronous Generator Speed ()

Where:

• : Synchronous speed (RPM).
• : Grid frequency (Hz).
• : Number of poles.

Electrical Energy Generated in DC Generators ()

Where:

• : Induced electromotive force (Volts).
• : Machine constant.
• : Angular speed (rad/s).

Required Mechanical Power ()

Generator Efficiency ()

Common Factors in Motors and Generators

Powers and Torque

General relationship of mechanical power and torque

Efficiency

Efficiency in any electrical machine