Electrical Machines

Keywords

electric generator, motor, transformer, mutual inductance, electric machine, magnetic coupling, mutual voltage, coupling coefficient, ideal transformer, autotransformer, step-down transformer, step-up transformer

Related Concepts

energy, complex power

• Electrical Machines are devices that convert mechanical energy into electrical energy and vice versa
  • Types of electric machines:
    • Electric Generator: converts mechanical energy into electrical
    • Motor: converts electrical energy into mechanical
    • Transformer: power systems use it to either step up or step down ac voltages/currents
• Mutual Inductance
  • Two loops are magnetically coupled when they affect each other through a magnetic field generated by one of them.
  • Mutual inductance occurs when two coils (or inductance) are close to each other. One of the coil’s magnetic flux, caused by their current, links with the other coil; as a result, it generates voltage in the latter. In other words, mutual inductance is the quantity—measured in henrys (H)—referring to the capacity of an inductor to induce voltage to a neighboring inductor.
    • Thus, the two inductors are magnetically coupled with each other.
  • If a current enters the dotted terminal of one coil, the reference polarity of the mutual voltage is positive at the dotted terminal of the second coil.
  • If a current leaves the dotted terminal of one coil, the reference polarity of the mutual voltage is negative at the dotted terminal of the second coil.
  • If the current enters the same terminals or dots, the coils’ total inductance is an example of series-aiding connection (positive voltage); otherwise, it is an example of series-opposing connection (negative voltage if the dot is at the bottom).
  • The dot, alongside the dot convention, is used to determine the polarity of the mutual voltage
• Transformers
  • Generally, it is a four-terminal device that is made up of 2+ magnetically coupled cois. They use magnetically coupled coils to transfer energy from one circuit to another
• Coupling coefficient
  • , or the coupling coefficient, is the measure of magnetic coupling
• Ideal transformer
  • Has perfect coupling
  • Has 2 or more coils wrapped around a common core , which has high permeability
  • The high permeability causes the flux to link all turns, resulting in a perfect coupling
  • primary and secondary coils have infinete self-inductances
  • step-down transformer
    • secondary voltage < primary voltage
  • step-up transformer
    • secondary voltage > primary voltage
• Autotransformer
  • Has a continuous winding with a tap between the primary and secondary sides. The tap allows for desired turns ratio for stepping up or stepping down the voltage
  • It is a transformer in which both the primary and the secondary are in a single winding.

Reminders

1. If inductance, multiplty by , thus

Formulas

Description	Value
Open circuit mutual voltage
Mutual inductance
Coupling coefficient
Energy
Linear transformer T circuit equivalent
Reflected impedance
Complex power in the primary winding of an ideal transformer
Number of turns in an ideal transformer
Step-down autotransformer circuit
Step-up autotransformer circuit

Sources

1. Class Lecture
2. Electrical Machines (Lecture Slides)