Electric Machines: Transients, Control Principles, Finite Element Analysis, and Optimal Design with MATLAB®

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface
Authors
Chapter 1: Electric Machine Circuit Models for Transients and Control
	1.1 Introduction
	1.2 Orthogonal (dq) Physical Model
	1.3 Pulsational and Motion-­Induced Voltages in dq Models
	1.4 dq Model of DC Brush PM Motor (ω b = 0)
	1.5 Basic dq Model of Synchronous Machines (ω b = ω r)
	1.6 Basic dq Model of Induction Machines (ω b = 0, ω r, ω 1)
	1.7 Magnetic Saturation in dq Models
	1.8 Frequency (Skin) Effect Consideration in dq Models
	1.9 Equivalence between dq Models and AC Machines
	1.10 Space Phasor (Complex Variable) Model
	1.11 High-Frequency Models for Electric Machines
	1.12 Orthogonal Models of Multiphase a.c. Machines
	1.13 Summary
	1.14 Proposed Problems
	References
Chapter 2: Transients and Control Principles of Brush–Commutator DC Machines
	2.1 Introduction
	2.2 Orthogonal (dq) Model of DC Brush Machines with Separate Excitation
	2.3 Electromagnetic (Fast) Transients
	2.4 Electromechanical Transients
		2.4.1 Constant Excitation (PM) Flux, Ψ dr
		2.4.2 Variable Flux Transients
		2.4.3 DC Brush Series Motor Transients
	2.5 Basic Closed-Loop Control of DC Brush PM Motor
	2.6 d.c.–d.c. Converter-Fed d.c. Brush PM Motor
	2.7 Parameters from Test Data/Lab 2.1
	2.8 Summary
	2.9 Proposed Problems
	References
Chapter 3: Synchronous Machine Transients and Control Principles
	3.1 Introduction
	3.2 Phase Inductances of SMs
	3.3 Phase Coordinate Model
	3.4 dq0 Model to Three-Phase SM Parameters Relationships
	3.5 Structural Diagram of the SM dq0 Model
	3.6 pu dq0 Model of SMs
	3.7 Balanced Steady State via the dq0 Model
	3.8 Laplace Parameters for Electromagnetic Transients
	3.9 Electromagnetic Transients at Constant Speed
	3.10 Sudden three-phase Short Circuit from a Generator at No Load/Lab
	3.11 Asynchronous Running of SMs at a Given Speed
	3.12 Reduced-Order dq0 Models for Electromechanical Transients
		3.12.1 Neglecting Fast Stator Electrical Transients
		3.12.2 Neglecting Stator and Rotor Cage Transients
		3.12.3 Simplified (Third-Order) dq Model Adaptation for SM Voltage Control
	3.13 Small-Deviation Electromechanical Transients (in PU)
	3.14 Large-Deviation Electromechanical Transients
		3.14.1 Asynchronous Starting and Self—Synchronization of DC—Excited SMs/Lab 3.2
		3.14.2 Asynchronous Self-Starting of PMSMs to Power Grid
		3.14.3 Line-to-Line and Line-to-Neutral Faults
	3.15 Transients for Controlled Flux and Sinusoidal Current PMSMs
		3.15.1 Constant d-­Axis (ψ d) Flux Transients in Cageless SMs
		3.15.2 Vector Control of PMSMs at Constant ψ d0 (i d0 = const)
		3.15.3 Constant Stator Flux Transients in Cageless SMs at cos φ 1 = 1
		3.15.4 Vector Control of SMs with Constant Flux (ψ s) and cos φ s = 1
	3.16 Transients for Controlled Flux and Rectangular Current SMs
		3.16.1 Model of Brushless DC-PM Motor Transients
		3.16.2 DC-Excited Cage Rotor SM Model for Rectangular Current Control
	3.17 Switched Reluctance Machine Modeling for Transients
	3.18 Split-Phase Cage Rotor SM transients
	3.19 Standstill Testing for SM Parameters/Lab 3.3
		3.19.1 Saturated Steady-State Parameters, L dm and L qm, from Current Decay Tests at Standstill
		3.19.2 Single Frequency Test for Subtransient Inductances, and
		3.19.3 Standstill Frequency Response Tests
	3.20 Linear Synchronous Motor Transients
	3.21 Summary
	3.22 Proposed Problems
	References
Chapter 4: Induction Machines Transients and Control Principles
	4.1 Three-Phase Variable Model
	4.2 dq (Space Phasor) Model of IMs
	4.3 Three-Phase IM–dq Model Relationships
	4.4 Magnetic Saturation and Skin Effects in the dq Model
	4.5 Space Phasor Model Steady State: Cage and Wound Rotor IMs
	4.6 Electromagnetic Transients
	4.7 Three-Phase Sudden Short Circuit/Lab 4.1
		4.7.1 Transient Current at Zero Speed
	4.8 Small-Deviation Electromechanical Transients
	4.9 Large-­Deviation Electromechanical Transients/Lab 4.2
	4.10 Reduced-Order dq Model in Multimachine Transients
		4.10.1 Other Severe Transients
	4.11 m / N r Actual Winding Modeling of IMs with Cage Faults
	4.12 Transients for Controlled Magnetic Flux and Variable Frequency
		4.12.1 Complex Eigenvalues of IM Space Phasor Model
	4.13 Cage Rotor IM Constant Rotor Flux Transients and Vector Control Basics
		4.13.1 Cage-Rotor IM Constant Stator Flux Transients and Vector Control Basics
		4.13.2 Constant Rotor Flux Transients and Vector Control Principles of Doubly Fed IMs
	4.14 Doubly Fed IM as a Brushless Exciter for SMs
	4.15 Parameter Estimation in Standstill Tests/Lab 4.3
		4.15.1 Standstill Flux Decay for Magnetization Curve Identification:
		4.15.2 Identification of Resistances and Leakage Inductances from Standstill Flux Decay Tests
		4.15.3 Standstill Frequency Response (SSFR) Tests
	4.16 Split-Phase Capacitor IM Transients/Lab 4.4
		4.16.1 Phase Variable Model
		4.16.2 dq Model
	4.17 Linear Induction Motor Transients
	4.18 Line-Start Self-Synchronizing Premium Efficiency IMs
		4.18.1 Line Start One-Phase—Source Split-Phase Capacitor Self-Synchronizing Induction Motor with PMs in the Rotor’s Flux Barriers
	4.19 Summary
	4.20 Proposed Problems
	References
Chapter 5: Essentials of Finite Element Analysis (FEA) in Electromagnetics
	5.1 Vectorial Fields
		5.1.1 Coordinate Systems
		5.1.2 Operations with Vectors
		5.1.3 Line and Surface (Flux) Integrals of a Vectorial Field
		5.1.4 Differential Operations
		5.1.5 Integral Identities
		5.1.6 Differential Identities
	5.2 Electromagnetic Fields
		5.2.1 Electrostatic Fields
		5.2.2 Fields of Current Densities
		5.2.3 Magnetic Fields
		5.2.4 Electromagnetic Fields: Maxwell Equations
	5.3 Visualization of Fields
	5.4 Boundary Conditions
		5.4.1 Dirichlet’s Boundary Conditions
		5.4.2 Neumann’s Boundary Conditions
		5.4.3 Mixed Robin’s Boundary Conditions
		5.4.4 Periodic Boundary Conditions
		5.4.5 Open Boundaries
			5.4.5.1 Problem Truncation
			5.4.5.2 Asymptotical Boundary Conditions
			5.4.5.3 Kelvin Transform
	5.5 Finite Element Method
		5.5.1 Residuum (Galerkin’s) Method
		5.5.2 Variational (Rayleigh–Ritz) Method
		5.5.3 Stages in Finite Element Method Application
			5.5.3.1 Domain Discretization
			5.5.3.2 Choosing Interpolation Functions
			5.5.3.3 Formulation of Algebraic System Equations
			5.5.3.4 Solving Algebraic Equations
	5.6 2D FEM
	5.7 Analysis with FEM
		5.7.1 Electromagnetic Forces
			5.7.1.1 Integration of Lorenz Force
			5.7.1.2 Maxwell Tensor Method
			5.7.1.3 Virtual Work Method
		5.7.2 Loss Computation
			5.7.2.1 Iron Losses
	References
Chapter 6: FEA of Electric Machines Electromagnetics
	6.1 Single-Phase Linear PM Motors
		6.1.1 Preprocessor Stage
		6.1.2 Postprocessor Stage
		6.1.3 Summary
	6.2 Rotary PMSMs (6/4)
		6.2.1 BLDC Motor: Preprocessor Stage
		6.2.2 BLDC Motor Analysis: Postprocessor Stage
		6.2.3 Summary
	6.3 The Three-Phase Induction Machines
		6.3.1 Induction Machines: Ideal No Load
		6.3.2 Rotor Bar Skin Effect
		6.3.3 Summary
	References
Chapter 7: Thermal FEA of Electric Machines
	7.1 Thermal Models
		7.1.1 The Single-body Thermal Model
		7.1.2 The Two-body Thermal Model
		7.1.3 Equivalent Thermal Circuit (Thermal Network)
	7.2 Thermal Analysis of Electric Machines by Finite Element
		7.2.1 Equivalent Coil Conductivity—Simplified Thermal Model of the Slot
		7.2.2 Boundary Conditions
		7.2.3 The Input Data
	7.3 Steady-state Simulation Results
	7.4 Thermal Transient Analysis of Electric Machines by Finite Element
	7.5 Summary
	References
Chapter 8: Optimal Electromagnetic Design of Electric Machines: The Basics
	8.1 Electric Machine Design Problem
	8.2 Optimization Methods
	8.3 Optimum Current Control
	8.4 Modified Hooke–Jeeves Optimization Algorithm
	8.5 Electric Machine Design Using Genetic Algorithms
	References
Chapter 9: Optimal Electromagnetic Design of Surface PM Synchronous Machines (PMSM)
	9.1 Design Theme
	9.2 Electric and Magnetic Loadings
	9.3 Choosing a Few Dimensioning Factors
	9.4 A Few Technological Constraints
	9.5 Choosing Magnetic Materials
	9.6 Dimensioning Methodology
		9.6.1 Rotor Sizing
		9.6.2 PM Flux Computation
		9.6.3 Weights of Active Materials
		9.6.4 Losses
		9.6.5 Thermal Verification
		9.6.6 Machine Characteristics
	9.7 Optimal Design with Genetic Algorithms
		9.7.1 Objective (Fitting) Function
		9.7.2 PMSM Optimization Design Using Genetic Algorithms: A Case Study
	9.8 Optimal Design of PMSMs Using Hooke–Jeeves Method
	9.9 FEM Based Optimal Design of a PM Spoke Motor: A Case Study
	9.10 Conclusion
	References
Chapter 10: Optimization Design of Induction Machines
	10.1 Realistic Analytical Model for Induction Machine Design
		10.1.1 Design Theme
		10.1.2 Design Variables
		10.1.3 Induction Machine Dimensioning
			10.1.3.1 Rotor Design
			10.1.3.2 Stator Slot Dimensions
			10.1.3.3 Winding End-Connection Length
		10.1.4 Induction Machine Parameters
	10.2 Induction Motor Optimal Design Using Genetic Algorithms
	10.3 Induction Motor Optimal Design Using Hooke–Jeeves Algorithm
	10.4 Machine Performance
	10.5 Conclusion
	References
Index