Automated Optimization for Electric Machines, Study notes of Power Electronics

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MULTIPHYSICS

SIMULATION BY DESIGN

FOR ELECTRICAL MACHINES,

POWER ELECTRONICS,

AND DRIVES

IEEE Press 445 Hoes Lane Piscataway, NJ 08854

IEEE Press Editorial Board Tariq Samad, Editor in Chief

Giancarlo Fortino Xiaoou Li Ray Perez Dmitry Goldgof Andreas Molisch Linda Shafer Don Heirman Saeid Nahavandi Mohammad Shahidehpour Ekram Hossain Jeffrey Nanzer Zidong Wang

Copyright © 2018 by The Institute of Electrical and Electronics Engineers, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada.

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CONTENTS

PREFACE vii

ACKNOWLEDGMENTS xv

CHAPTER 1 BASICS OF ELECTRICAL MACHINES DESIGN AND MANUFACTURING TOLERANCES 1 Marius Rosu, Mircea Popescu, and Dan M. Ionel

1.1 Introduction 1 1.2 Generic Design Flow 3 1.3 Basic Design and How to Start 4 1.4 Efficiency Map 16 1.5 Thermal Constraints 19 1.6 Robust Design and Manufacturing Tolerances 22 References 42

CHAPTER 2 FEM-BASED ANALYSIS TECHNIQUES FOR ELECTRICAL MACHINE DESIGN 45 Ping Zhou and Dingsheng Lin

2.1 T–Ω Formulation 45 2.2 Field-Circuit Coupling 56 2.3 Fast AC Steady-State Algorithm 70 2.4 High Performance Computing—Time Domain Decomposition 82 2.5 Reduced Order Modeling 93 References 106

CHAPTER 3 MAGNETIC MATERIAL MODELING 109 Dingsheng Lin and Ping Zhou

3.1 Shape Preserving Interpolation of B–H Curves 109 3.2 Nonlinear Anisotropic Model 115 3.3 Dynamic Core Loss Analysis 125 3.4 Vector Hysteresis Model 137 3.5 Demagnetization of Permanent Magnets 150 References 162

CHAPTER 4 THERMAL PROBLEMS IN ELECTRICAL MACHINES 165 Mircea Popescu and David Staton

4.1 Introduction 165 4.2 Heat Extraction Through Conduction 167

v

PREFACE

ELECTRIC MACHINES are being used in wide and novel applications throughout the world, driven by the need for greater power efficiency in the trans- portation, aerospace and defense, and industrial automation markets. The automotive sector is driven by the need for hybrid and electric vehicle technology to meet ever- stringent miles-per-gallon standards. The aerospace and defense sectors are focused on replacing existing power transfer technologies in an aircraft such as the central hydraulic system, with fault-tolerant electric power, where major subsystems such as engine starting, primary flight control actuation, pumps, and braking would be controlled and driven electronically. In the US industrial sector, over 40 million elec- tric motors convert electricity into useful work in manufacturing operations. Industry spends over $30 billion (US) annually on electricity, dedicated to electric motor- driven systems that drive pumps, fan and blower systems, air compression, and motion control. Globally, 42% of all electricity is used in power industries, where two-thirds of this is consumed by electric motors. There is a clear global demand for a comprehensive design methodology to support these new applications and satisfy power efficiency requirements. With the present trend of global industrial automation, the application of elec- tric drive systems (including power electronics and drive control) is expected to grow rapidly in the next decade. In the automotive sector, the utilization of power electron- ics and their control to drive electric motors can significantly contribute to control environmental pollution. In addition, intensive environmentally clean photovoltaic and wind energy resources also show a bright future. As part of electric drive systems, the power semiconductor devices at the heart of modern power electronics are under continuous development. The improved technology in semiconductor processing, device fabrication, and packaging to pro- duce high-density, high-performance, high-reliability, and high-yielding microelec- tronic chips, together with new semiconductor material discovery, made possible significant reduction in energy consumption, driving these systems to an incredible economical price. Without doubt, these achievements force the control strategy techniques to evolve rapidly to the newly created drive conditions and adapt to the overall sys- tems performance requirements. In recent years, soft switching converters became the center of interest when compared with more conventional hard switching converters due to their major advantages such as:

 (^) Minimization of switching loss  (^) Improved efficiency

vii

viii PREFACE

 (^) Improved reliability due to soft stress  (^) Reduced electromagnetic emission

The continuous growing interest in the electric drive area relates to the intel- ligent power electronics modules, where the power and the control are embedded in the same package and interface directly with logic signals. For variable frequency drives, the converter modules and control are mounted directly on the machine for the low and medium power applications.

READERS’ ADVANTAGE

The book is mainly addressed to design engineers, application engineers, technical professionals, and graduate engineering students with a strong interest in electric machines and drives. The comprehensive design approach described in this book supports new appli- cations required by technologies, sustaining high drive efficiency. The highlighted framework considers the electric machine at the heart of the entire electric drive. The book delivers the multiphysics know-how based on practical electric machine design methodologies. Simulation by design concept elevated in the book constitutes the new paradigm that frames the entire highlighted design methodology, which is described and illustrated by various advanced simulation technologies.

Which Design Problems Are We Trying to Solve?

Throughout this book, we apply knowledge of design best practices into multiphysics and multidomain simulation processes to address a complete electrical machine and drive design. In the face of global competition, electric machine manufacturers, like manu- facturers in most industries, are searching for ways to reduce cost, optimize designs, and deliver them quickly to market. Companies able to achieve these objectives hold a competitive advantage in the marketplace. The ability to predict design performance with simulation software without the time and expense of constructing prototypes plays a significant role in creating this competitive advantage. Several computation approaches are available to predict electric machine per- formance, including classical closed-form analytical analysis, lumped parameter models based on the determination of detailed parameters from finite element anal- ysis, and nonlinear time-domain finite element analysis. Each method has advan- tages and disadvantages. Selecting the best method may not be straightforward because it requires the user to understand the differences among the calculation methods. The fundamental issue differentiating these methods is the trade-off among model complexity, accuracy, and computing time. Engineers use a combination of these calculation techniques as the optimal solution to simulate electric machine performances.

x PREFACE

motion is presented, the numerical technique related to multiply connected regions is highlighted, and it also presents the algorithms used for nonlinear iterations and strategies to accelerate the nonlinear convergence. Filed-circuit coupling technology is explained and specific algorithms used to reduce the computation time to reach steady-state conditions are described. High-performance computing (HPC) is a key technology, increasing the capacity of solving large design spaces and reducing sig- nificantly the total time computation by solving the time steps on magnetic transient problem simultaneously rather than sequentially. All technologies highlighted in this chapter are explained through sets of case studies.

Chapter 3: Magnetic Material Modeling

This chapter introduces advanced magnetic material modeling capabilities employed in numerical computation. From isotropic nonlinear characteristics to anisotropic behavior corresponding to grain-oriented magnetic materials, the chapter describes the implementation aspects and detailed modeling techniques. Lamination topologies are considered based on special modeling technique with emphasis on core loss com- putation. Advanced magnetic modeling on vector magnetic hysteresis is presented and specific case studies are used to highlight the computational merits.

Chapter 4: Thermal Problems in Electrical Machines

In this chapter, the heat generation and extraction in electrical motors are investi- gated. Using the three thermal paths—conduction, convection, and radiation—an electromagnetic device can be cooled within the acceptable limits for the environ- ment and corresponding application. A highly efficient electrical machine is required in most industrial fields, but the high efficiency is not telling us the full story of a good motor performance. The losses—electromagnetic and mechanical—must be dissi- pated from the machine into the ambient and the mode in which the cooling system manages to do that represents the key in a reliable and high-performance electrical machine. Within the chapter, the theoretical aspects of thermal management are illus- trated with a state-of-the-art collection of practical examples for cooling electrical machines published in the literature.

Chapter 5: Automated Optimization for Electric Machines

This chapter discusses optimization as applied to electrical machine design. Some commonly used optimization methods are explained. Case studies illustrating the utility of systematic design optimization to compare different machine topologies, to develop design rules, and to quantify the effect of different design features are included.

Chapter 6: Power Electronics and Drive Systems

This chapter describes the entire drive system from semiconductor as the main com- ponent of any modern power electronics circuit to more complex topologies that

PREFACE xi

include active components to rectify the energy, reduce harmonic distortions, and correct power factors in various drive systems. Electrical machines need drive sys- tems to be correctly controlled if they need to be operated at variable speed. This can be achieved by modulating the energy flow to/from them. The chapter also high- lights the need of multiphysics studies for such designs to account for thermal analysis under certain cooling conditions. For instance, inverter modules need a careful design approach as losses vary continuously during normal operation. Poor thermal manage- ment can lead to overheating and thus degrade the reliability of the components.

FRAMING THE MULTIPHYSICS DESIGN

METHODOLOGY

The electric machine is a very complex device, being multidomain by nature involv- ing electromagnetics, thermal, and mechanical aspects. The multiphysics method- ology built around the core of electric machine design encompasses a systematic approach to develop a platform where comprehensive analysis is the key to under- stand and design a complex drive system to predict their performances and analyze their robustness. The multiphysics simulation technology enables users to design, analyze, and deliver efficient, optimized electric machine and drive designs. As shown in Figure 1, the first step in the overall workflow is to develop design requirements. Those requirements may be created within a particular design organiza- tion, or they may be provided from a purchaser of the electric machine. Requirements may include machine speed, output power, input power, torque, efficiency, thermal properties, weight, size, etc. At this stage, motor sizing and model creation take place,

Design requirements

• Template-based
• Spreadsheet

Performance

Stage III Cooling

Stage II

Stage I

Stage IV (^) Manufacturability

• Electromagnetics
  • Thermal
    • Structural

Figure 1 Multiphysics design methodology.

PREFACE xiii

The flexibility of such a design flow is provided by the data exchange among all physics involved, providing various design adoption alternatives. The multiphysics design flow can be further detailed at each and every individ- ual stage. In spite of this granularity, the Chapter 1 will focus on Stage I regarding the generic design flow for topology selection during a motor design to examine the process of basic design.

Marius Rosu Ping Zhou Dingsheng Lin Dan Ionel Mircea Popescu Frede Blaabjerg Vandana Rallabandi David Staton

ACKNOWLEDGMENTS

THE AUTHORS are grateful for the tireless efforts, assistance, and guid- ance of the Wiley-IEEE Press editorial staff who brought to reality this book project. We are thankful to the many colleagues who provided technical insights, com- ments, and suggestions. We are especially indebted to our partners, collaborators, and customers who supported and diligently demanded continuous progress on software technology enabling us to thriving innovation. We owe a great debt of gratitude to our families for their unconditional support and continuous encouragements. This book could not be written to its fullest without ANSYS Inc.’s support and continuous engagement for which we are grateful.

xv

2 CHAPTER 1 BASICS OF ELECTRICAL MACHINES DESIGN AND MANUFACTURING TOLERANCES

Rotor and stator laminations

Rotor and stator cores (stacks)

Stator core and winding

Rotor core and die-cast cage

Figure 1.1 Typical steps for the manufacturing of an electric machine, in this case a line-fed permanent magnet (PM) synchronous motor, which includes in the rotor a die-cast aluminum cage.

the three-phase 18-slot design example from Figure 1.2, which is suitable to be used together with a 16-pole PM rotor [2, 3]. At a first look, concentrated windings, especially in a segmented-modular configuration, tightly packed with a high slot fill factor and short end coils maybe superior to more conventional distributed winding machines, particularly for low-speed applications. Nevertheless, before drawing such generic conclusions, systematic comparisons taking into account the power and speed rating, losses, including winding and core components, the electronic controller should be per- formed following, for example, a large scale automated design process as described in another chapter of the book. A stator core and winding, and a rotor incorporating a shaft, are assembled together with other components, including bearings, end caps, and frame and terminal box to produce an electric machine, as exemplified in Figure 1.3 for a general-purpose three-phase squirrel-cage induction motor and in Figure 1.4 for PM

Figure 1.2 Example of stator modular construction with segmented core and concentrated coils forming a multiphase winding [2, 3]. Versions with a single tooth and coil modules are also possible.

1.2 GENERIC DESIGN FLOW 3

Figure 1.3 Exploded view of a general-purpose National Electrical Manufacturers Association (NEMA) frame squirrel-cage induction motor. Courtesy of Regal Beloit Corp.

synchronous motors with stator concentrated and distributed windings, respectively [4]. It should be noted that the use of PM technology typically results in a higher power density than available from induction machines. A most successful example of combining advanced design techniques, high performance magnetic materials, and enhanced cooling is represented by the recent development of a 100 hp motor for Formula E racing cars [5,6]. This machine shown in Figure 1.5, which employs an 18-slot 16-pole spoke IPM configuration, sets a record for electric traction motors of comparable rating, achieving almost twice the specific torque density per unit of active mass (Nm/kg) than the motor powering the latest generation of the Nissan Leaf electric vehicle.

1.2 GENERIC DESIGN FLOW

In the overall economy of the electric machine design process, virtual prototyping is the most important collection of designing stages when considering design validation

Figure 1.4 PM synchronous motors with interior permanent magnet (IPM) rotors and concentrated (left) and distributed windings, respectively [4]. Courtesy of Regal Beloit Corp.

1.3 BASIC DESIGN AND HOW TO START 5

Physics-based design

Electromagnetics CFD Stress Drive system integration

Sizing

System/circuit design

Design space

Performance Analysis

Figure 1.6 Multiphysics and multidomain electric machine design flow.

the physical dimensions of an electrical machine, we can definitely answer that the electromagnetic toque capability, which can be extracted from the design specifica- tion related to a certain application, will generate enough information to produce an initial magnetic design. And yet this is probably at the same time the most exquisite and intrigued statement one could deliver on such a complex design demand [7, 8]. Simply, following this rationale, the output torque is proportional to rotor vol- ume and tangential force acting on rotor surface known as shear stress. The shear stress is proportional to the product of electric and magnetic loading. Besides elec- tromagnetic torque, the rotor aspect ratio, stator slot diameter ratio, number of poles, and rotational speed are important parameters for design decisions.

TABLE 1.1 Power traction application specifications

Parameter Unit Value

DC supply voltage V 400 Maximum DC current A 700 Maximum line AC current Arms 900 Peak output power kW 235 Peak torque Nm 330 Base speed rpm 7500 Maximum speed rpm 15, Continuous power at base speed kW 80 Continuous torque at base speed Nm 100 Cooling system N/A Liquid System envelope volume mm 270 × 270 × 270

6 CHAPTER 1 BASICS OF ELECTRICAL MACHINES DESIGN AND MANUFACTURING TOLERANCES

The fundamental relationship for torque prediction is the equation which defines the force F acting on a wire of length L carrying a current I in a uniform magnetic field B as

F = B ⋅ I ⋅ L (1.1)

If we consider a uniformly distributed conductor per meter, then we can introduce the shear stress as the ratio between force and area of conductive region. Thus,

F

Area

= B ⋅ A (1.2)

where B is also known as magnetic loading and A is known as electric loading. In any electric machine with radial field concept with the rotor diameter D , the torque is introduced by

T = F ⋅

D

In more general terms, the main parameter defining an electrical machine is the torque or force depending on the device that has a rotational or linear movement, respec- tively. In this design example, we are dealing with a rotational movement, for which the expression that provides the sizing electromagnetic torque is given by

T =

π^2 4

⋅ kw 1 ABD^2 Lstk (1.4)

where kw 1 is the fundamental winding factor, Lstk is the axial active length. A is the electric loading : number of ampere-conductors per meter around the stator surface that faces the airgap.

A =

Total ampere–Conductors Airgap circumference

2 mNph I RMS π D

where Nph represents the total number of turns/phase, I RMS is the RMS phase current and m is the system number of phases. B is the magnetic loading: average flux-density over the rotor surface. If the flux-density is distributed sinusoidal, the fundamental magnetic flux/pole (there are 2 p magnetic poles in the electrical machine) is

𝜙 = B ⋅

π DLstk 2 p

We notice from (1.4)–(1.6) that the torque, electric, and magnetic loading depend on the machine volume in the airgap. Considering also the lossless energy conversion law for an m -phase AC machine,

Electric power = mEI = Mechanical power = T ⋅ 𝜔 p