Electrical Machines | Lecture - 10 E | Equivalent Circuit of Single-Phase Induction Motors

Step-by-Step Tutorial: Equivalent Circuit of Single-Phase Induction Motors

1. Introduction to Single-Phase Induction Motors:

   • Understand that single-phase induction motors are conceptualized with a single common stator winding and two rotors revolving in opposite directions.
   • Note that the equivalent circuit is based on the double field revolving theory, which is fundamental in single-phase induction motors.

2. Equivalent Circuit Components:

   • Identify the components of the equivalent circuit:
     • Stator impedance: Z1 = R1 + jX1 (where R1 is resistance and X1 is reactance).
     • Rotor impedance: R2/S + jX2 and R2/2 - s + jX2 (where R2 is rotor resistance, X2 is standstill reactance, and S represents slip).

3. Incorporating Magnetizing Reactance:

   • Recognize XM as the magnetizing reactance, representing the flux produced between the stator and rotor in the air gap.
   • Note that the values mentioned are half the actual values, referring to the stator.

4. Equivalent Circuit without Core Losses:

   • Understand that the circuit representation excludes core losses, focusing on the XM branch where flux is produced.

5. Forward and Backward Impedance Calculation:

   • Determine the forward impedance (ZF) under running motor conditions by calculating the impedance using the parallel combination of components.
   • Calculate the backward impedance by replacing S with 2 - S in the forward impedance equation.

6. Torque Calculation:

   • Compute the power developed by the motor using the equation: (1 - slip) / slip * I2s * R2.
   • Calculate torque based on speed in revolutions per second (RPS) using the formula: 1 / (2 * π * n) * (1 - slip) / slip * I2s * R2.

7. Incorporating Core Losses:

   • Include RC (iron loss) in the circuit connected in parallel with XM to represent the complete single-phase induction motor circuit with losses.

8. Advantages and Limitations of Single-Phase Induction Motors:

   • Advantages include smaller size, lighter weight, cost-effectiveness, efficiency, longer life, and versatility in design for household and industrial applications.
   • Limitations involve lower output compared to three-phase motors, poor power factor, lower efficiency, lack of starting torque, and higher cost.

9. Selection Considerations:

   • Understand that single-phase induction motors are preferable in household applications with single-phase AC supply but may be less efficient and more expensive compared to three-phase motors for heavy operations.

10. Conclusion:

    • Review the overview of single-phase induction motors and the preference for three-phase motors in certain scenarios.
    • Acknowledge the importance of single-phase motors in various applications based on their unique characteristics and design flexibility.

By following these steps, you can gain a comprehensive understanding of the equivalent circuit of single-phase induction motors and the considerations associated with their selection and application.