GATE EE

Single-Phase Induction Motors GATE Quick Notes - Electrical Engineering

Lecture Notes

SEC 01

Fundamentals

1Single-Phase Induction Motor - Basics
1Key Characteristics

  • Not self-starting - Zero starting torque

  • Single-phase AC supply creates pulsating magnetic field

  • Requires auxiliary starting arrangement

  • Power rating: Typically up to 1 kW

Construction:

SEC 02

Double Field Revolving Theory

1Double Field Revolving Theory

A pulsating magnetic field can be resolved into two rotating magnetic fields of equal magnitude, rotating in opposite directions at synchronous speed.

Mathematical Expression:

\[\phi(t) = \phi_m \cos(\omega t) = \frac{\phi_m}{2}[\cos(\omega t) + \cos(-\omega t)]\]

Where:

1Slip Relations

Forward Field:

Backward Field:

1Important

At standstill: \(s_f = s_b = 1\), hence net torque = 0

SEC 03

Equivalent Circuit

1Equivalent Circuit

Circuit Parameters:

SEC 04

Torque Analysis

1Torque Characteristics

Forward Torque:

\[T_f = \frac{K_1 \phi_m^2 R_2' s}{(R_2')^2 + (sX_2')^2}\]

Backward Torque:

\[T_b = \frac{K_2 \phi_m^2 R_2' (2-s)}{(R_2')^2 + ((2-s)X_2')^2}\]

Net Torque:

\[T_{net} = T_f - T_b\]
1Key Points
SEC 05

Starting Methods

1Starting Methods
1Why Starting Methods Required?

Single-phase induction motors have zero starting torque due to equal and opposite torques from forward and backward rotating fields.

1. Split-Phase Starting:

2. Capacitor Starting:

3. Capacitor Start-Capacitor Run:

1Capacitor Starting - Details

Capacitor Value for Starting:

\[C_s = \frac{1}{2\pi f X_C}\]

Where \(X_C\) is chosen to get 90° phase shift.

Starting Torque with Capacitor:

\[T_s = \frac{K V^2}{2} \left[\frac{R_2'}{s} - \frac{R_2'}{2-s}\right]\]
1GATE Important
SEC 06

Power Relations

1Power Analysis

Input Power:

\[P_{in} = V I \cos \phi\]

Stator Copper Loss:

\[P_{cu1} = I^2 R_1\]

Core Loss:

\[P_{core} = \text{Hysteresis loss + Eddy current loss}\]

Air Gap Power:

\[P_{ag} = P_{in} - P_{cu1} - P_{core}\]

Rotor Copper Loss:

\[P_{cu2} = s \times P_{ag}\]

Mechanical Power Developed:

\[P_{mech} = (1-s) \times P_{ag}\]

Output Power:

\[P_{out} = P_{mech} - P_{friction} - P_{windage}\]
SEC 07

Efficiency and Power Factor

1Efficiency and Power Factor

Efficiency:

\[\eta = \frac{P_{out}}{P_{in}} = \frac{P_{mech} - P_{mechanical\ losses}}{P_{in}}\]

Power Factor:

\[\cos \phi = \frac{P_{in}}{V I}\]

Typical Values:

1GATE Focus

Single-phase motors have lower efficiency and power factor compared to 3-phase motors of same rating due to backward rotating field losses.

SEC 08

Special Types

1Shaded Pole Motor

Construction:

Working Principle:

Characteristics:

SEC 09

GATE Problem Types

1GATE Problem Categories

1. Equivalent Circuit Problems:

2. Starting Method Analysis:

3. Performance Calculations:

4. Conceptual Questions:

SEC 10

Key Formulas

1Important Formulas for GATE
1Must Remember

  • Forward slip: \(s_f = s\)

  • Backward slip: \(s_b = 2 - s\)

  • Net torque: \(T = T_f - T_b\)

  • Rotor copper loss: \(P_{cu2} = s \times P_{ag}\)

  • Mechanical power: \(P_{mech} = (1-s) \times P_{ag}\)

  • Synchronous speed: \(N_s = \frac{120f}{P}\)

  • Slip: \(s = \frac{N_s - N}{N_s}\)

Efficiency:

\[\eta = \frac{P_{out}}{P_{in}} = \frac{(1-s)P_{ag} - P_{mech\ losses}}{P_{in}}\]
SEC 11

Summary

1Quick Revision Points

  1. Single-phase motors are NOT self-starting

  2. Double field revolving theory explains operation

  3. Starting methods create phase difference between windings

  4. Capacitor starting gives highest starting torque

  5. Efficiency and power factor are lower than 3-phase motors

  6. Equivalent circuit has forward and backward components

  7. Slip relations: \(s_f = s\), \(s_b = 2-s\)

  8. Applications: Fans, washing machines, small pumps

1GATE Tip

Focus on torque analysis, starting methods, and equivalent circuit problems. Understand the concept of forward and backward rotating fields.