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Modeling of permanent magnet synchronous machine with fractional slot windings
Abstract
This paper focuses on simulation of permanent magnet synchronous machine (PMSM) with fractional-slot windings (FSW) in Modelica. Modeling of the electrical machines with object-oriented approach is shortly described, and a new Modelica library for simulation of electrical machines is introduced. The results of simulation of PMSMs with fractional slot windings are presented and explained. Special attention is paid to the higher harmonics and subharmonics produced by the winding and their influence on machine operation.
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Part I: Introduction. Chapter 1: Introduction to Modeling and Simulation. Chapter 2: A Quick Tour of Modelica. Part II: The Modelica Language. Chapter 3: Classes, Types, and Declarations. Chapter 4: Inheritance, Modifications, and Generics. Chapter 5: Components, Connectors, and Connections. Chapter 6: Literals, Operators, and Expressions. Chapter 7: Arrays. Chapter 8: Equations. Chapter 9: Algorithms and Functions. Chapter 10: Packages. Chapter 11: Annotations, Units, and Quantities. Part III: Modeling and Applications. Chapter 12: System Modeling Methodology and Continuous Model Representation. Chapter 13: Discrete Event, Hybrid, and Concurrency Modeling. Chapter 14: Basic Laws of Nature. Chapter 15: Application Examples. Chapter 16: Modelica Library Overview. Part IV: Technology and Tools. Chapter 17: A Mathematical Representation for Modelica Models. Chapter 18: Techniques and Research. Chapter 19: Environments. Appendix A: Modelica Formal Syntax. Appendix B: Mathematica-style Modelica Syntax. Appendix C: Solutions for Exercises. Appendix D: Modelica Standard Library. Appendix E: Modelica Scripting Commands. Appendix F: Related Object-Oriented Modeling Languages. Appendix G: A Modelica XML Representation. References. Index.
This paper presents a permanent magnet model which takes temperature dependencies and demagnetization effects into account. The proposed model is integrated into a magnetic fundamental wave machine model using the modeling language Modelica. For different rotor types permanent magnet models are developed. The simulation results of the Modelica are compared with measurement results. Additionally, the fundamental wave model is compared to a finite element analysis in order to assess the applicability of the proposed model.
The windings concentrated around the teeth offer obvious advantages for the electrical machines with radial air-gap, because the volume of copper used in the end-windings can be reduced. The Joule losses are decreased and the efficiency is improved. These machines are still limited to applications of subfractional power and they generally present a reduced number of phases. In the three-phase machines, the concentrated winding is too often restricted to a winding with a short pitch of 120 electrical degrees, i. e., to a winding with performances reduced compared to the traditional structures. But there is a significant number of three-phase structures that can support a concentrated winding if the number of poles is increased. In this article, the authors present a synthesis of the structures of three-phase machines with concentrated windings. In the first part, the structures with a regular distribution of the slots are presented. A systematic method is proposed to determine the windings and the performances are discussed. In the second part, the authors present original structures of three-phase machines with concentrated windings that use an irregular distribution of the slots. A specific method to identify these structures is described, and a comparative analysis of the performances of the original and traditional structures is performed by using a field calculation software.
A design approach is presented for achieving optimal flux-weakening operation in surface permanent-magnet (SPM) synchronous machines by properly designing the machine's stator windings using concentrated, fractional-slot stator windings. This technique makes it possible to significantly increase the machine inductance in order to achieve the critical condition for providing wide speed ranges of constant-power operation. The conditions for optimal flux weakening can be achieved while simultaneously delivering sinusoidal line-to-line back-electromotive-force waveforms and low cogging torque. A closed-form analytical model is described that can be used to design SPM machines to achieve optimal flux-weakening conditions. This technique is applied to design a 6-kW SPM machine that achieves constant-power operation over a wide speed range. Performance characteristics of this machine are compared using both closed-form and finite-element analysis.
The windings concentrated around the teeth offer obvious advantages for the electrical machines with radial air-gap, because the volume of copper used in the end-windings can be reduced. The Joule losses are decreased, and the efficiency is improved. These machines are still limited to applications of sub-fractional power and they generally present a reduced number of phases. In the three-phase machines, the concentrated winding is too often restricted to a winding with a short pitch of 120 electrical degrees, i.e., to a winding with performances reduced compared to the traditional structures. But there is a significant number of three-phase structures which can support a concentrated winding if the number of poles is increased. In this article, the authors present a synthesis of the structures of three-phase machines with concentrated windings. 1) In the first part, the structures with a regular distribution of the slots are presented. A systematic method is proposed to determine the windings and the performances are discussed. 2) In the second part, the authors present original structures of three-phase machines with concentrated windings which use an irregular distribution of the slots. A specific method to identify these structures is described, and a comparative analysis of the performances of the original and traditional structures is performed by using a field calculation software.
The windings concentrated around the teeth offer obvious advantages for the electric machines with radial air-gap, because the volume of topper used in the end-windings can be reduced. The Joule losses are decreased and the efficiency is improved. These machines are still limited to applications of subfractional power and they generally present a reduced number of phases. In the three-phase machines, the concentrated winding is too often restricted to a winding with a short pitch of 120 electric degrees, i.e. to a winding with performances reduced compared to the traditional structures. But there is a significant number of three-phase structures which can support a concentrated winding if the number of poles is increased. In this article, the author present a synthesis of the structures of three-phase machines with concentrated windings. In the first part, the structures with a regular distribution of the slots are presented. A systematic method is proposed to determine the windings and the performances are discussed. In the second part, the authors present original structures of three-phase machines with concentrated windings which use an irregular distribution of the slots. A specific method to identify these structures is described and a comparative analysis of the performances of the original and traditional structures is performed by using a field calculation software.
This paper focuses on the selection of a fractional-slot winding for permanent-magnet (PM) machines. The choice of the proper combination of the number of slots and number of poles, together with the corresponding winding layout, has a strong impact on the PM machine performance, in terms of torque density, torque ripple, magnetomotive force harmonic content, and induced rotor losses, as well as the capability to limit the short-circuit current and other fault-tolerance features. Considering these characteristics, this paper aims to help the PM machine designer to select the proper winding configuration, giving useful indications. The winding choice criteria are given using analytical equations, so that their implementation is easy. In this way, the collection of such criteria becomes a helpful tool in the design process.
Chapter 4 concentrates on discussing leakage flux components, their nature, and calculation resulting in leakage inductances, which have a significant impact on machine performance. Expressions for the permeance factor of single-layer and double-layer windings in connection with the shape of the slots are derived and applied in some examples. Correction of the permeance factor because of the skin effect is shown, and the skewing factor and skew leakage inductance are defined. All components of leakage inductance are discussed in detail.
This paper thoroughly investigates the impact of the winding layer number and the choice of magnet type on the performance characteristics of surface permanent magnet (SPM) machines with fractional-slot concentrated windings designed for wide speed ranges of constant-power operation. This is accomplished by carefully examining the performance characteristics of three different SPM machines designed for the same set of performance requirements drawn from an automotive direct-drive starter/alternator application. These results show that double-layer stator windings yield lower torque ripple and magnet eddy-current losses than single-layer windings, but can contribute to a lower overload torque capability. Although the adoption of sintered magnets leads to the highest machine torque density, bonded magnets result in a significant reduction of the magnet losses because of their much higher value of resistivity
Previous work has shown that it is possible to design surface permanent magnet (SPM) synchronous machines using fractional-slot concentrated windings to achieve wide speed ranges of constant-power operation. A closed-form analytical technique is now available to rapidly analyze candidate SPM machine designs using concentrated windings and tune them to meet the critical condition for optimal flux weakening. This analytical tool is used to demonstrate that optimal flux weakening can be achieved in SPM machines that are varied over wide ranges in several key dimensions including machine pole numbers, diameter-to-length aspect ratios, and output power ratings. Performance requirements for a 6 kW direct-drive automotive starter/alternator machine are used as the starting point for the scalability investigation. Finite element analysis results are presented to confirm the validity of key results
Fractional-slot concentrated-winding (FSCW) synchronous permanent magnet (PM) machines have been gaining interest over the last few years. This is mainly due to the several advantages that this type of windings provides. These include high-power density, high efficiency, short end turns, high slot fill factor particularly when coupled with segmented stator structures, low cogging torque, flux-weakening capability, and fault tolerance. This paper is going to provide a thorough analysis of FSCW synchronous PM machines in terms of opportunities and challenges. This paper will cover the theory and design of FSCW synchronous PM machines, achieving high-power density, flux-weakening capability, comparison of single- versus double-layer windings, fault-tolerance rotor losses, parasitic effects, comparison of interior versus surface PM machines, and various types of machines. This paper will also provide a summary of the commercial applications that involve FSCW synchronous PM machines.
The aim of here is to define an index of the rotor losses induced by the magnetomotive force (MMF) space harmonics in fractional-slot permanent magnet (PM) machines. Such an index facilitates a rapid discrimination of the various fractional-slot PM machines, based on the numbers of slots and poles. For the sake of generality, a simple model of the rotor losses is adopted to compute such an index of rotor losses. However, the index behaviour follows that of rotor losses computed by means of more complex models.
The paper focuses on the optimal selection of a fractional-slot winding for PM machines. The choice of the proper combination of slots and poles, and the corresponding winding layout, has a major impact on the PM machine performance, such as torque ripple, torque density, harmonic contents and then induced rotor losses, as well as capability to limit the short-circuit current and other fault-tolerance features. Among the very large possibilities to choose a winding configuration, the paper gives useful indications for a proper selection considering several aspects. The winding choice criteria are given using analytical equations, so that their implementation results to be easy. In this way, the collection of such criteria becomes an helpful tool in the design process.
Three-phase fractional-slot PM machines are more and more used in many applications. In spite of the several advantages, these machines exhibit high contents of space harmonics in the air-gap MMF distribution, whose amplitude depends on the particular combination of number of slots and poles. The main consequence of such harmonic contents is the induced losses in the rotor. The aim of this paper is to link the rotor losses to the combination of slots and poles of the PM machine. The effort is to determine a general rule to single out easily if a machine topology is suitable or not, as far as the rotor losses are concerned. Both overlapped and non-overlapped coil fractional-slot windings are considered.
The torque to MMF ratio of a permanent magnet machine with concentrated windings is normally much lower than for the more traditionally used distributed windings. BLDC and AC machines with concentrated windings usually have a slot pitch of only 2/3 the length of the pole pitch, which results in a poor fundamental winding factor of 0,866. This can be compared to the ideal winding factor of one, which can easily be acquired using distributed windings. However, by choosing better combinations of the pole and slot numbers for a machine with concentrated windings, the winding factor can be substantially increased. Moreover, it is also possible to achieve low cogging torque without skewing, simply by selecting appropriate combinations. The presented theory includes both single- and double-layer configurations of concentrated windings. The theory is verified by using FEM analysis. This paper describes methods for designing high performance permanent magnet machines with concentrated windings.
This paper thoroughly investigates the impact of the winding layer number and the choice of magnet type on the performance characteristics of surface permanent magnet (SPM) machines with fractional slot concentrated windings designed for wide speed ranges of constant-power operation. This is accomplished by carefully examining the performance characteristics of three different SPM machines designed for the same set of performance requirements drawn from an automotive direct-drive starter/alternator application. These results show that double-layer stator windings yield lower torque ripple and magnet eddy current losses than do single-layer windings, but can contribute to a lower overload torque capability. Although the adoption of sintered magnets leads to the highest machine torque density, bonded magnets result in a significant reduction of the magnet losses because of their much higher value of resistivity.
Theory and design of fractionalslot pm machines
- N Bianchi
- M Prè
- L Alberti
N. Bianchi, M. Prè, and L. Alberti, "Theory and design of fractionalslot pm machines," in IEEE IAS Tutorial Course notes, IAS'07 Annual
Meeting, Sponsored by the IEEE IAS Electrical Machine Comittee.
CLEUP, Padova (Italy), 2007.