BEE108 Rotating Electric Machines: Electro-mechanical Energy Conversion

Unit Overview: BEE108 Rotating Electric Machines

• Course Title: Bachelor of Science (Electrical Engineering) BEE108: Rotating Electric Machines.

• Specific Focus: Tutorial on Electro-mechanical Energy Conversion Principles.

• Software Requirements:     - MATLAB/SIMULINK     - PSCAD

• Hardware Requirements: N/A.

Learning Outcomes

• Fundamental Principles: Explain the fundamental principles behind electro-mechanical energy conversion and calculate the relation between motor rated power and torque (Bloom's Level 3).

• DC Machines: Describe the principle of operation of DC machines, the function of the commutator, and the different types of DC machines based on field winding connections (Bloom's Level 2).

• 3-Phase Synchronous Machines: Explain the theory of 3-phase synchronous machines and the relation between excitation and power factor (Bloom's Level 2).

• Induction Machines: Explain the fundamental theory of 3-phase and single-phase induction machines, the various types of machines, and their control aspects (Bloom's Level 2).

• Efficiency and Construction: Discuss the construction of AC machines and the ways of enhancing motor efficiency (Bloom's Level 4).

• Testing Procedures: Describe the procedure for testing AC machines and perform these tests in a simulated environment to calculate motor parameters (Bloom's Level 3).

Assessments Summary

• Assessment 1: Weekly Quizzes     - Type: Multiple-choice quiz questions.     - Weighting: $10\%$ of total unit marks.     - Timing: Weekly.     - Learning Outcomes Assessed: All (Topics 2 to 11).

• Assessment 2: Invigilated Test     - Type: Short/long answer questions and numerical problems.     - Weighting: $20\%$ of total unit marks.     - Timing: During Topic/Week 7.     - Learning Outcomes Assessed: 1, 2, 4 (Topics 1 to 6).

• Assessment 3: Practical (Report) & Pre-recorded Presentation     - Type: Practical project using software and research on state-of-the-art solutions.     - Weighting: $30\%$ of total unit marks.     - Timing: End of Topic/Week 11.     - Learning Outcomes Assessed: All (All topics).

• Assessment 4: Invigilated Exam     - Type: Mixed theoretical answers and engineering problems.     - Weighting: $40\%$ of total unit marks.     - Timing: Exam Week.     - Learning Outcomes Assessed: All (All topics).

Unit Content Topics

• Topic 1: Electro-mechanical energy conversion principles     - Comparison between electrical and magnetic circuits.     - Energy and Co-energy.     - Induction.     - Forces and torques in magnetic fields and balance equations.

• Topic 2: DC Machines Part 1 (Generators)     - Separately excited DC generators.     - Self-excited DC generators.     - Shunt generators.     - Load characteristics of DC generators.

• Topic 3: DC Machines Part 2 (Motors)     - Working principles and types of DC motors.     - Speed control.     - Faults, inspection, and maintenance.

• Topic 4: Synchronous Machines Part 1 (Generators)     - General aspects and operation.     - Synchronizing methods (single phase & three phase).     - Classification.

• Topic 5: Synchronous Machines Part 2 (Motors)     - Operation, construction, and excitation.     - V-curves and inverted V-curves.     - Characteristics.

• Topic 6: Induction Machines - Part 1     - Principles of single-phase AC machines.     - Equivalent circuits.     - Zero starting torque issues and split winding construction.     - Universal motors (based on DC series motors).

• Topic 7: Induction Machines - Part 2     - Principles of 3-phase induction motors/generators.     - Equivalent circuits, leakage resistance, and reactance.     - Starting behavior and the role of back EMF.

• Topic 8: Control of 3-phase motors and Industrial Applications - Part 1     - Torque-speed characteristics of cage and slip ring motors.     - Crawling and cogging problems.     - Impact of voltage reduction on motor torque.

• Topic 9: Control of 3-phase motors and Industrial Applications - Part 2     - Assisted starting in weak systems.     - Motor starting methods and braking.     - Selection based on characteristics.     - Direct-on-line (DOL) and reversible motor circuits.

• Topic 10: Testing of Motors and Generators     - DC tests, No-load tests, Blocked rotor tests.     - Heat Run tests.     - Component tests.

• Topic 11: Special Machines     - Stepper motors, Permanent-Magnet DC motors.     - Servo motors, Brushless DC motors.     - Brushless Synchronous generators.

• Topic 12: Unit Review     - Final review of content, student work review, and clarification of outstanding issues.

Electromechanical Energy Conversion Foundations

• Definition: The process of changing the form of energy from electrical to mechanical or vice versa is called electromechanical energy conversion.

• Generators: Devices that convert mechanical energy into electrical energy to provide electricity.

• Motors: Devices that convert electrical energy into mechanical motion and work.

• Electromechanical System Components:     - Electrical systems and mechanical systems are joined by a coupling field.     - Coupling Field: Can be electrical or magnetic.     - Losses: Losses occur at every stage of the system; therefore, it is never an ideal system.     - Efficiency: A critical consideration during machine selection due to existing losses.

Questions & Discussion: Machine Selection and Operation

• Question: What basic factors should be considered while selecting a machine?     - Nature of the electric supply.     - Types of drives.     - Types of loads.     - Electrical characteristics.     - Service capacity and rating (specifically Size and Cost).

• Question: Compare motor and generator in terms of torque.     - In a Motor: Electromagnetic torque is produced by the interaction of electric current with a magnetic field. This torque is used to drive a load. The load provides a mechanical torque that opposes the electromagnetic torque.     - In a Generator: Electric current is generated when mechanical torque is applied to turn conductors through a magnetic field. This mechanical torque is opposed by an electromagnetic torque resulting from the current's interaction with the magnetic field.

• Question: What are the basic methods to produce an EMF?     - 1. An electromagnetic force (EMF) is created by the interaction of two magnets.     - 2. A coil possessing magnetic flux can create an EMF similar to a permanent magnet.

• Question: Where does maximum energy storage take place in a DC machine?     - Options: a) Stator; b) Rotor; c) Air gap.     - Answer: Maximum energy storage occurs in the Air gap. The predominant energy storage occurs here because the properties of the magnetic circuit are determined by the air gap dimensions.

• Question: Explain methods for innovating conversion systems.     - Modern techniques utilize new motor types and modern power controllers.     - Controllers using power electronics offer energy-efficient, user-friendly, and high-performance drives.     - Advantages: Considerable energy savings; ability to limit currents to pre-recorded values during starting, overload, or unbalanced supply; prolonged equipment life.

Magnetic Circuit and Electromagnetic Principles

• Comparison of Circuits:     - Electric Circuit: Applied voltage causes a current $I$ to flow.     - Magnetic Circuit: Applied magnetomotive force ($\mathcal{F}$) causes flux ($\phi$) to be produced.

• Magnetic Circuit Variables:     - $\mathcal{F}$ = Magnetomotive Force (measured in Amp.Turn or $A.T$).     - $\phi$ = Flux of the circuit (measured in Weber or $Wb$).     - $\mathcal{R}$ = Reluctance of the circuit (measured in $A.T/Wb$).     - Fundamental Equation: $\mathcal{F} = \phi \mathcal{R}$.

• Key Laws:     - Ohm’s Law: Electromotive force (EMF) produces a current proportional to the path's conductivity.     - Ohm’s Law for Magnetic Circuits: Electric current constitutes a magnetomotive force (MMF) producing magnetic flux proportional to the path's permeability.     - Lenz’s Law: The polarity of induced EMF in a coil causes a current that opposes any change in the magnetic flux.     - Motor Action: A magnetic field exerts a force on a current-carrying conductor.     - Generator Action (Faraday’s Law): A conductor moving through a magnetic field (or a magnetic flux changing with time through a coil) will have an EMF induced in it.

Mathematical Principles of Induction and Force

• Induced EMF Calculation:     - For a conductor of length $l$ moving at speed $v$ in flux density $B$: $e = lv \times B$.     - The direction is determined by the "right-hand rule" for cross products.     - For a coil of $N$ turns: $e = -(\frac{d\phi}{dt})$. Note: The minus sign indicates Lenz's law opposition and is often neglected in magnitude calculations.     - General expression related to inductance ($L$) and current ($I$): $e = \frac{d\phi}{dt} = L(\frac{di}{dt}) + i(\frac{dL}{dx})(\frac{dx}{dt})$.     - In a magnetically linear system, self-inductance is independent of current but is a function of displacement $x$ in systems with moving parts.

• Lorentz Force Law:     - Determines force ($F$) on a particle of charge $q$ in electric ($E$) and magnetic ($B$) fields: $\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})$.     - Pure Electric System: $F = qE$.     - Pure Magnetic System: $F = q(v \times B)$.     - Force Density ($f$): For continuous charge distribution, where $\rho$ is charge density ($charge/volume$) and $J$ is current density ($J = \rho v$): $f = \rho E + J \times B$.

• Torque Factors:     - Torque requires two forces/coupling forces acting at different angles (not $180^{\circ}$).     - Depends on: Current through the coil, length of the current-carrying coil, and the magnetic field passing through the coils.

The Energy Method and Energy Balance

• Conservation of Energy Principle: Energy is neither created nor destroyed, only changed in form.

• Lossless Magnetic Energy Storage System:     - Electric terminal: Variables are voltage ($e$) and current ($I$).     - Mechanical terminal: Variables are force ($f$) and position ($x$).     - Energy Balance Equation: $dW_{elec} = dW_{mech} + dW_{fld}$.     - $dW_{elec} = ei dt = i d\lambda$ (Differential electric energy input).     - $dW_{mech} = f_{fld} dx$ (Differential mechanical energy output).     - $dW_{fld}$ = Differential change in magnetic stored energy.

• State Variables: Magnetic stored energy ($W_{fld}$) is a state function uniquely specified by values of flux linkages ($\lambda$) and position ($x$).     - $dW_{fld} = i d\lambda - f_{fld} dx$.     - Determining Force: $f_{fld} = -\frac{\partial W_{fld}(\lambda, x)}{\partial x}$.     - For linear systems where $\lambda = L(x)i$: $W_{fld} = \frac{1}{2} L(x) i^2$.

• Multiple Electrical Terminals:     - Independent variables: $\theta, \lambda_1, \lambda_2$.     - $dW_{fld}(\lambda_1, \lambda_2, \theta) = i_1 d\lambda_1 + i_2 d\lambda_2 - T_{fld} d\theta$.     - Linear system Co-energy ($W'_{fld}$): Simplified torque/force determination using current as a terminal variable.

Numerical Worked Examples

• Example 1: Magnetic Circuit and Reluctance     - Problem: Core path length $= 40\,cm$, gap $= 0.05\,cm$, area $= 12\,cm^2$, $\mu_r = 4000$, $N = 400$. Fringing increases air gap area by $5\%$. Find total reluctance and current required for $0.5\,T$ in gap.     - Solution Details:         - Effective gap area: $1.05 \times 12 = 12.6\,cm^2$.         - Total Reluctance: $\mathcal{R}<em>{total} = \mathcal{R}</em>{core} + \mathcal{R}_{gap}$.         - Equation used: $NI = B A \mathcal{R}$.

• Example 2: Induced EMF     - Given: $N = 220$, $A = 0.09\,m^2$, $B_1 = 0.2\,Wb/m^2$, $B_2 = 0.05\,Wb/m^2$, $t = 0.02\,s$.     - Calculation: $e = -N A \frac{B_2-B_1}{dt} = -220 \times 0.09 \times \frac{0.05-0.2}{0.02} = 148.5\,V$.

• Example 3: Force on a Conductor     - Given: $B = 4 \times 10^{-3}\,T$, $l = 55\,cm = 0.55\,m$, $I = 6\,A$, $\theta = 90^{\circ}$.     - Calculation: $F = BIl \sin(\theta) = 4 \times 10^{-3} \times 6 \times 0.55 \times \sin(90^{\circ}) = 0.0132\,N$.

• Example 4: Aeroplane Wing EMF     - Given: $l = 22\,m$, $v = 45\,m/s$, $B_{vertical} = 3 \times 10^{-5}\,T$.     - Calculation: $\epsilon = Blv = 3 \times 10^{-5} \times 45 \times 22 = 0.0297\,V$.

• Example 5: Force and Torque Inclination     - Given: $B = 0.9\,T$, $I = 20\,A$, $l = 0.3\,m$.     - Scenario 1 ($\theta = 90^{\circ}$): $F = 0.9 \times 20 \times 0.3 = 5.4\,N$.     - Scenario 2 ($\theta = 30^{\circ}$): $F = 5.4 \times \sin(30^{\circ}) = 2.7\,N$.

• Example 6: Relay Stored Energy     - Parameters: $N = 1000$, $g = 2\,mm$, $d = 0.15\,m$, $l = 0.1\,m$, $I = 10\,A$.     - Function of position $x$: $W_{fld} = 236(1 - \frac{x}{d})\,J \times 10^0$.

• Example 7: Complex Torque in Multiply-Excited System     - Inductances: $L_{11} = (3 + \cos(2\theta)) \times 10^{-3}$, $L_{12} = 0.3\cos(\theta)$, $L_{22} = 30 + 10\cos(2\theta)$.     - Result for $i_1 = 0.8\,A, i_2 = 0.01\,A$: $T = -1.64 \times 10^{-3} \sin(2\theta) - 2.4 \times 10^{-3} \sin(\theta)$.

• Example 8: Mechanical Power     - Given: $\tau = 50\,N.m$, speed $= 1500\,r/min$.     - Calculation (Watts): $P = \tau \omega = 50 \times (1500 \times \frac{2\pi}{60}) = 7854\,W$.     - Calculation (Horsepower): $P = \frac{7854}{746} = 10.5\,hp$.

• Example 9: Three-Legged Core Flux     - Core Regions: Core divided into four regions (reluctances $\mathcal{R}<em>1, \mathcal{R}_2, \mathcal{R}_3, \mathcal{R}_4$).     - Total Reluctance: Calculated as $\mathcal{R}</em>{total} = \mathcal{R}<em>1 + ((\mathcal{R}_2 + \mathcal{R}_3) \parallel \mathcal{R}_4)$.     - Flux Divider Rule: Used to find individual leg fluxes: $\phi</em>{centre} = \phi_{total} \times \frac{\mathcal{R}_4}{\mathcal{R}_2 + \mathcal{R}_3 + \mathcal{R}_4}$.

System Efficiency and Applications

• Types of Losses During Conversion:     - Core losses (Iron losses).     - Electrical losses (Copper losses).     - Mechanical losses.

• Examples of Electromechanical Devices:     - Speakers, Alternators, Typewriters.     - Amusement rides, Hydraulic systems.     - High-speed automation production lines, Robotics.     - Systems using Programmable Logic Controllers (PLC).

References

• Bakshi, U.A. & Bakshi, M.V., Electrical Machines – II.

• Umans, S., Fitzgerald and Kingsley's Electric Machinery, 7th Ed., 2013.

• Chapman, S. J., Electric Machinery Fundamentals, 5th Ed., 2012.

• Gieras, Jacek F., Electrical Machines: Fundamentals of Electromechanical Energy Conversion, 2017.

• Mukerji, S. K., Khan, A. S., & Singh, Y. P., Electromagnetics for Electrical Machines, 2015.