Unit 3: Fundamentals of Electrical Machines

1. Fleming’s Rules

Fleming’s rules relate the direction of the magnetic field, motion (force), and current in electrical machines.

Fleming’s Left-Hand Rule (For Motors)

Applicable to DC Motors. It determines the direction of the force (motion) acting on a current-carrying conductor placed in a magnetic field.

• Method: Stretch the thumb, forefinger, and middle finger of the left hand such that they are mutually perpendicular to each other.
• Assignments:
  • Forefinger: Direction of Magnetic Field () (North to South).
  • Middle Finger: Direction of Current ().
  • Thumb: Direction of Force/Motion ().
• Principle: When a current-carrying conductor is placed in a magnetic field, it experiences a mechanical force.

Fleming’s Right-Hand Rule (For Generators)

Applicable to DC Generators. It determines the direction of the induced current (EMF) when a conductor moves within a magnetic field.

• Method: Stretch the thumb, forefinger, and middle finger of the right hand such that they are mutually perpendicular.
• Assignments:
  • Thumb: Direction of Motion of the conductor ().
  • Forefinger: Direction of Magnetic Field ().
  • Middle Finger: Direction of Induced Current/EMF.
• Principle: Electromagnetic Induction (Faraday’s Laws).

2. The Transformer

A transformer is a static device that transfers electrical energy from one circuit to another through magnetic coupling without a change in frequency. It can raise (step-up) or lower (step-down) voltage levels.

Mutual Inductance and Mutual Coupling

• Mutual Inductance (): The property of two coils such that a change of current in one coil induces an EMF in the adjacent coil.
• Coupling Phenomena: When an alternating current flows through the primary coil, it generates an alternating magnetic flux. This flux travels through the magnetic core and links with the secondary coil. According to Faraday’s Law of Electromagnetic Induction, this changing flux induces an EMF in the secondary coil.
• Coefficient of Coupling (): A measure of the magnetic coupling efficiency between two coils. implies 100% flux linkage.

Working Principle of Transformer

1. Primary Input: An AC voltage is applied to the primary winding.
2. Flux Generation: An alternating flux () is established in the magnetic core.
3. Flux Linkage: This flux links both the primary and secondary windings.
4. Induced EMF:
   • Primary: Self-induced EMF () opposes (Lenz’s Law).
   • Secondary: Mutually induced EMF () is generated.
5. Output: If a load is connected to the secondary, current flows.

Concept of Turns Ratio ()

The transformation ratio relates the voltages, currents, and number of turns:

Where:

• : Number of turns in primary and secondary.
• : Voltages.
• Step-up Transformer: (Output voltage increases).
• Step-down Transformer: (Output voltage decreases).

Transformer on DC Supply

A transformer cannot operate on DC.

• Reason: DC provides a constant current, creating a constant magnetic flux.
• Consequence: Since induced EMF depends on the rate of change of flux (), no back EMF is generated in the primary winding.
• Result: The primary winding acts as a pure low resistance. According to Ohm's law (), excessively high current flows, causing the transformer winding to burn out.

Instrument Transformers

Used in AC systems for the measurement of high voltages and currents using low-range instruments.

1. Current Transformer (CT):
   • Step-up transformer (Voltage up, Current down).
   • Connects in series with the line.
   • Used to measure high current using a standard 5A ammeter.
2. Potential Transformer (PT):
   • Step-down transformer (Voltage down).
   • Connects in parallel.
   • Used to measure high voltage using a standard 110V voltmeter.

Auto-Transformer

A transformer with only one winding shared by both primary and secondary circuits.

• Working: Part of the energy is transferred by induction (transformer action) and part by conduction (direct electrical connection).
• Advantages: Uses less copper (cheaper), higher efficiency, better voltage regulation.
• Disadvantages: No electrical isolation between input and output.
• Application: Variacs (variable voltage supply), starting induction motors.

General Applications of Transformers

• Power System: Transmission and distribution (Stepping up voltage for transmission to reduce losses; stepping down for distribution).
• Electronics: Impedance matching, power supplies, isolation.
• Measurement: Instrument transformers (CT/PT).

3. DC Machines (Motors and Generators)

Working Principles

• DC Generator: Converts Mechanical Energy Electrical Energy.
  • Based on Dynamically Induced EMF. When armature conductors cut the magnetic flux, EMF is induced (Direction: Fleming's Right-Hand Rule).
• DC Motor: Converts Electrical Energy Mechanical Energy.
  • Based on Lorentz Force. A current-carrying conductor in a magnetic field experiences torque (Direction: Fleming's Left-Hand Rule).
  • Commutator Function: Acts as a mechanical rectifier (in generators) or inverter (in motors) to ensure unidirectional torque.

Classification of DC Machines

Classified based on the excitation of the field winding:

1. Separately Excited: Field winding is supplied by an external DC source.
2. Self-Excited: Field winding is supplied by the machine's own armature.
   • Shunt Wound: Field winding in parallel with armature (Constant speed characteristics).
   • Series Wound: Field winding in series with armature (High starting torque).
   • Compound Wound: Combination of series and shunt windings (Cumulative or Differential).

Starting of DC Motors

Why is a starter needed?

• At the instant of starting, speed , so Back EMF is zero.
• Armature current equation: .
• Since and armature resistance is very low, the starting current is dangerously high (10–20 times rated current).
• Solution: A starter adds external resistance in series with the armature during starting to limit the current. Once speed picks up and builds, the resistance is cut out.
• Types: 3-Point Starter (for Shunt/Compound), 4-Point Starter.

Speed Control of DC Motors

Speed equation:

1. Flux Control (Field Control): Varying flux by varying field current.
   • Used for speeds above rated speed.
2. Armature Control (Rheostatic Control): Varying voltage across armature by adding series resistance.
   • Used for speeds below rated speed.
3. Voltage Control (Ward-Leonard Method): Varying the applied voltage . Provides smooth control over a wide range.

Applications of DC Motors

• DC Shunt Motor: Lathes, centrifugal pumps, fans, blowers (Constant speed applications).
• DC Series Motor: Electric traction (trains), cranes, hoists, elevators (High starting torque required).
• DC Compound Motor: Rolling mills, shears, punches (High starting torque + prevents overspeeding at no load).

4. Induction Motors (AC)

Working Principle of Three-Phase Induction Motor

1. Stator Excitation: A 3-phase AC supply is given to the stator winding.
2. Rotating Magnetic Field (RMF): This creates a magnetic field rotating at synchronous speed ().
3. Induction: The RMF cuts the stationary rotor conductors. By Faraday's law, EMF is induced in the rotor.
4. Current Flow: Since the rotor circuit is closed (shorted), current flows in the rotor bars.
5. Force Generation: The current-carrying rotor conductors interact with the stator magnetic field, producing a force (torque).
6. Rotation: According to Lenz's law, the rotor rotates in the same direction as the RMF to catch up with it. It runs at speed (where ).

Working Principle of Single-Phase Induction Motor

• Problem: A single-phase supply produces a pulsating magnetic field, not a rotating one. Therefore, single-phase motors are not self-starting.
• Solution (Double Field Revolving Theory): The pulsating field is resolved into two rotating fields moving in opposite directions. To start, an auxiliary means is required to create a phase difference.
• Starting Methods:
  1. Split Phase: Uses a starting winding with different resistance/inductance to create a phase shift.
  2. Capacitor Start: A capacitor in series with the auxiliary winding creates a large phase shift (), producing high starting torque.
  3. Shaded Pole: Uses a copper ring on part of the pole to delay flux, creating a sweeping effect.

Applications of AC Motors

1. Three-Phase Induction Motors:
   • "Workhorse of Industry" due to ruggedness and low maintenance.
   • Industrial drives, large water pumps, lathe machines, drilling machines, conveyors, flour mills.
2. Single-Phase Induction Motors:
   • Split Phase: Washing machines, small fans, centrifugal pumps.
   • Capacitor Start/Run: Refrigerators, air conditioners, compressors (High starting torque).
   • Shaded Pole: Toys, hair dryers, small cooling fans (Low torque).