AC ELectrical Machines (HTU)

Course Introduction

  • Course Title: AC Electrical Machines

  • Course Code: BEEE 209

  • Instructor: Prince Asabere

  • Contact: 0541033712, pasabere@htu.edu.gh

Lesson Objectives

  • Overview of AC electrical machines.

  • Understand electrical machines and their operations.

  • Mathematical formulation of electrical machines.

Electrical Machines Overview

  • Definition: Devices that convert mechanical energy to electrical energy (generators) or electrical energy to mechanical energy (motors).

  • Key Types of Electrical Machines:

    • Static Electrical Machines

      • No moving parts; includes transformers.

    • Rotating Electrical Machines

      • Involves moving parts; includes motors and generators.

Classification of Electrical Machines

  • Types by Electrical Energy:

    1. DC Machines

    2. AC Machines

AC Machines

  • Definition: AC machines convert electrical energy (alternating current) into mechanical energy and vice versa.

  • Key Characteristic: Alternating current (AC) periodically reverses direction, typically sinusoidal waves.

  • Types of AC Machines:

    • AC Motors

    • AC Generators

Fundamental Principles of AC Machines

  • AC Generators:

    • Based on Faraday’s Law: change in magnetic field induces alternating voltage (EMF).

    • Lenz’s Law: Induced EMF opposes the change that created it, regulating current flow.

  • AC Motors:

    • Based on the Lorentz Force Law: current-carrying conductors in a magnetic field experience a force.

Types of AC Machines

  1. Synchronous Machines:

    • Operate at a constant speed; rotor speed synchronized with AC supply frequency.

    • Used in power generation (alternators) and precision industrial motors.

  2. Induction Machines (Asynchronous Machines):

    • Rotor speed does not match stator's magnetic field speed; slip occurs.

    • Simpler design, robust, cost-effective, commonly used in industry.

Structure of AC Machines

  • Main Components:

    • Stator: Stationary component housing the winding.

    • Rotor: Rotating part that produces torque through interaction with stator's magnetic field.

Stator Details

  1. Parts of Stator:

    • Outer Frame: Body protecting inner parts; either cast or fabricated.

    • Stator Core: Provides magnetic path with high-grade silicon steel.

      • Minimizes losses: hysteresis and eddy currents.

    • Stator Winding: Supplies three-phase winding; connected to terminal boxes.

Types of Rotors

  • Synchronous Machines:

    1. Salient Pole Rotor: High torque, low-speed applications (e.g., hydroelectric generators).

    2. Non-Salient (Cylindrical) Rotor: High-speed machines (e.g., steam turbines).

  • Induction Machines:

    1. Squirrel Cage Rotor: Common, simple design; short-circuited bars.

    2. Wound Rotor: Allows external resistance for control.

Distributed Winding in AC Machines

  • Definition: Coils spread across multiple slots reduce harmonic distortion and improve efficiency.

  • Importance: Produces smoother magnetic field and lower MMF harmonics.

Magnetomotive Force (MMF)

  • Basics: MMF drives magnetic flux through the circuit, generated by current in windings.


  • MMF Equation for Coils:[ ext{MMF} = N imes I ]

    • Where: N = number of turns, I = current.

  • Total MMF: Sum of contributions from all coils.

Examples and Computations

  • Practical calculations for MMF, winding factors and induced EMF using provided formulas.

  • Examples illustrating how to calculate MMF using coil arrangements and induced currents in various AC machine contexts.

Magnetic Concepts

  • Flux Density: Amount of magnetic flux per unit area, measured in tesla (T).


  • Inductance (L): A measure of a coil's ability to store magnetic energy, given by[ L = \frac{N \times \Phi}{i} ] .

  • Power and Torque Relationships: Equations detailing relationships under operational conditions, emphasizing the importance of slip and efficiency.

Special Machines in Electrical Engineering

  1. Stepper Motors: Precise control of position through discrete steps.

  2. Switched Reluctance Motors (SRM): High durability without windings.

  3. Permanent Magnet Synchronous Motors (PMSM): Efficient motors synchronized to AC supply frequency.

  4. Linear Induction Motors (LIM): Produce linear motion directly instead of rotational.

  5. Hysteresis Motors: Continuously synchronous without rotor windings.

  6. Universal Motors: Operate on AC and DC, suitable for household appliances.

Reference Texts

  • Cited multiple academic texts providing foundational knowledge and insights into electrical machines.

Calculations and Examples in AC Electrical Machines

Overview

This section focuses on practical calculations relevant to AC electrical machines, particularly regarding MMF (Magnetomotive Force), winding factors, and induced EMF.

MMF Calculation


  • MMF Equation for Coils: [ \text{MMF} = N \times I ]Where:

    • N = number of turns

    • I = current

  • Total MMF: The total MMF in a system is the sum of contributions from all coils.

Example Calculation for MMF

  • Suppose a coil has 100 turns and carries a current of 2 A: [ \text{MMF} = 100 \times 2 = 200 \text{ A-turns} ]

Winding Factors


  • Winding Factor Calculation:Winding factor can be calculated based on the arrangement of coils (distributed or concentrated) and phase configuration.

Induced EMF Calculation



  • Based on Faraday’s Law of Induction:[ \text{EMF} = -N \frac{\Delta \Phi}{\Delta t} ]Where:

    • N = number of turns

    • ΔΦ = change in magnetic flux

    • Δt = change in time

Example Calculation for Induced EMF

  • If a coil with 50 turns experiences a change in magnetic flux of 0.1 Wb over 0.2 seconds: [ \text{EMF} = -50 \times \frac{0.1}{0.2} = -25 \text{ V} ]

Summary

These calculations provide insights into the operation of AC electrical machines and are critical for understanding their performance under various conditions.