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## Über dieses Buch

This book is a result of the author's work which was initiated about a decade ago and which, in the meantime, has resulted in his Ph.D. Thesis and several technical papers. The book deals with accurate modeling of electric machines during transient and steady states, a topic which has been usually avoided in the literature. The modeling techniques herein take into account all machine peculiarities, such as the type and connection of its windings, slotting, and saturation in the iron core. A special emphasis in the book is given to the exact physical interpretation of all phenomena which influence the machine's transient behavior. Besides the Introduction, the book has five chapters. The second chapter describes basic concepts of the magnetic equivalent circuit theory and has examples of magnetic equivalent circuits of several types of machines with their node potential equations. In the third chapter the transform matrices w' and w" of A.C. wind­ ings are derived. These matrices playa very important role in the magnetic equivalent circuit theory because they connect the quantities from the ma­ chine's magnetic equivalent circuit, branch fluxes, and mmfs with the ma­ chine's phase currents and fluxes.

## Inhaltsverzeichnis

### 1. Introduction

Abstract
Transient states are characteristic of every physical system that has energy storage elements. Any change of state in such a system is accompanied by a change of accumulated energy in it. The accumulated energy can increase or decrease only gradually. An infinite source of power would be necessary to support an instantaneous change of energy. An infinite source of power is not physically feasible; therefore transients will always take place in a finite time.

### 2. Magnetic Circuits

Abstract
The key idea in creating a magnetic equivalent circuit for a given electromagnetic device is to generate enough elements to reflect all properties of a device on the one hand, and not have too many elements which could unnecessarily slow down the computation without a significant gain in accuracy, on the other. The two opposite demands end up in a compromise — a magnetic circuit that minimizes the computational time for a given accuracy. The logic of the generation of such a circuit will be explained in the following sections. Before this, the legality of representation of a part of a device by one element (permeance) will be proven. Namely, in the MEC concept it is assumed that the flux is constant in a whole element, or, in other words, that there are no wave phenomena in the device. In that case the device is at a quasi-stationary state and it is legal to define flux tubes in the magnetic field. The flux tubes are the basis of the whole MEC method.

### 3. Winding Transform Matrices

Abstract
The main purpose of the magnetic equivalent circuit method is to relate phase fluxes to phase currents of an electric machine in a way that will as best as possible reflect all peculiarities of a device. Node potential equations that were derived in the previous chapter helped establish connections between magnetic scalar potentials in a machine and stator and rotor tooth fluxes. In this chapter relations between phase and tooth fluxes and values of mmf sources and phase currents will be defined.

### 4. Extended System of Machine Algebraic Equations

Abstract
In Chapter 2 algebraic equations that connected scalar magnetic potentials with branch fluxes in magnetic equivalent circuits for different types of electromagnetic devices were derived. Branch fluxes in a magnetic equivalent circuit are always tooth fluxes in a machine. Generally, those equations can be written in the form
$$Au = {\Phi_t}$$
(4.1)

### 5. Machine System of Differential Equations and Complete System of Algebraic Equations

Abstract
An electric machine communicates with the outer world through its electrical and mechanical terminals. Energy received through the terminals is converted into another form or stored as magnetic field or kinetic energy. Electromechanical energy conversion is a time-invariant process, as shown in Chapter 2. Force (torque) does not depend on the time rate of change of state variables but on the state variables themselves. Stored magnetic energy, Li2/2, and kinetic energy, 2/2, cannot change instantaneously because it would demand an infinite source of power. The gradual change of energy means that not only the state variables but also their time derivatives, written in the form of ordinary differential equations, define the state in a machine.