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2015 | Book

Fundamentals Read chapter Read first chapter

Electrical Machines

Mathematical Fundamentals of Machine Topologies

Author: Dieter Gerling

Publisher: Springer Berlin Heidelberg

Book Series : Mathematical Engineering

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik"

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About this book

Electrical Machines and Drives play a vital role in industry with an ever increasing importance. This fact necessitates the understanding of machine and drive principles by engineers of many different disciplines. Therefore, this book is intended to give a comprehensive deduction of these principles. Special attention is given to the precise mathematical deduction of the necessary formulae to calculate machines and drives, and to the discussion of simplifications (if applied) with the associated limits. So the book shows how the different machine topologies can be deduced from general fundamentals, and how they are linked.

This book addresses graduate students, researchers and developers of Electrical Machines and Drives, who are interested in getting knowledge about the principles of machine and drive operation and in detecting the mathematical and engineering specialties of the different machine and drive topologies together with their mutual links. The detailed, but compact mathematical deduction, together with a distinct emphasis onto assumptions, simplifications and the associated limits, leads to a clear understanding of Electrical Machine and Drive topologies and characteristics.

Table of Contents

Frontmatter
1. Fundamentals
Dieter Gerling
2. DC-Machines
Dieter Gerling
3. Rotating Field Theory
Abstract
Induction machines and synchronous machines are rotating field machines. The stator construction of these machine types are principally the same, they differ in the rotor design. The similarity of these machine types are discussed first, later a detailed consideration of induction machine and synchronous machine will follow.
Dieter Gerling
4. Induction Machines
Abstract
Stator and rotor of an induction machine - separated by an air-gap - contain each a symmetric winding in their slots.
Dieter Gerling
5. Synchronous Machines
Abstract
Like the induction machine the synchronous machine contains a stator with three-phase winding (it is a rotating field machine), but the rotor winding is supplied with DC-current. In the following the voltage equations and the equivalent circuit of the synchronous machine will be derived from those of the induction machine.
Dieter Gerling
6. Permanent Magnet Excited Rotating Field Machines
Abstract
Having a synchronous machine and substituting the DC excitation current (which generates a constant magnetic field according to time) by an excitation with permanent magnets, the following is saved
  • voltage source for the excitation current,
  • excitation winding and
  • excitation current supply via slip rings and brushes.
Dieter Gerling
7. Reluctance Machines
Dieter Gerling
8. Small Machines for Single-Phase Operation
Abstract
The generation of electrical energy, its distribution and its industrial application for high-power drives is done by means of three-phase systems with high voltage. For this, three-phase machines are used that produce a torque that is constant in time.
Dieter Gerling
9. Fundamentals of Dynamic Operation
Abstract
A mass m with the velocity \( {\vec{\rm v}} \) has the impulse \( {\rm m}{\vec{\rm v}} \) (kinetic quantity). The sum of all from outside acting forces leads to a time-dependent change of the kinetic quantity.
Dieter Gerling
10. Dynamic Operation and Control of DC-Machines
Abstract
In comparison to the steady-state operation of the DC-machine the energy storage elements (inductivities LA, LF and inertia Θ) have to be considered additionally for the dynamic operation.
Dieter Gerling
11. Space Vector Theory
Dieter Gerling
12. Dynamic Operation and Control of Induction Machines
Abstract
For the calculation of the dynamic operation of the induction machine the general set of equations for rotating field machines (space vector theory, please refer to Chap. 11) can be used. Because of the constant air-gap when neglecting the slotting effect any choice of α(t) is possible.
Dieter Gerling
13. Dynamic Operation of Synchronous Machines
Abstract
In this section the behavior of the synchronous machine will be regarded, if the rotor angle υ is changed by small values Δυ from the operation point (index “0”).
Dieter Gerling
14. Dynamic Operation and Control of Permanent Magnet Excited Rotating Field Machines
Abstract
As already described in Chap. 6, the principle operation of the permanent magnet excited rotating field machine is like follows:
The synchronous machine contains permanent magnets to generate the excitation field, but there is no starting cage present. The three-phase machine is supplied by an inverter which realizes a three-phase current system. As a main difference to what is described in Chap. 6, here no limiting assumptions concerning the time-dependency of the currents is made (especially there is no need for sinusoidal currents).
Dieter Gerling
15. Concentrated Windings
Abstract
Electrical machines with non-overlapping concentrated windings have become an increasingly popular alternative to machines with distributed windings for certain applications. Concentrated winding machines (characterized by the fact that each coil is wound around a single tooth) have potentially more compact designs compared to the conventional machine designs with distributed windings, due to shorter and less complex end-windings.
Dieter Gerling
16. Lists of Symbols, Indices and Acronyms
Dieter Gerling
Backmatter
Metadata
Title
Electrical Machines
Author
Dieter Gerling
Copyright Year
2015
Publisher
Springer Berlin Heidelberg
Electronic ISBN
978-3-642-17584-8
Print ISBN
978-3-642-17583-1
DOI
https://doi.org/10.1007/978-3-642-17584-8