Rotating Electrical Machines

René Le Doeuff, Mohamed El Hadi Zaïm

• Publisher: Wiley-ISTE
• Year: 2013
• ISBN:
  9781118620632
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Electrical Engineering & Telecommunications
• Index: Technology & Engineering

In this book a general matrix-based approach to modeling electrical machines is promulgated. The model uses instantaneous quantities for key variables and enables the user to easily take into account associations between rotating machines and static converters (such as in variable speed drives). General equations of electromechanical energy conversion are established early in the treatment of the topic and then applied to synchronous, induction and DC machines. The primary characteristics of these machines are established for steady state behavior as well as for variable speed scenarios.

Important new applications for this technology (such as wind turbines, electric propulsion systems for large ships, etc.) are addressed and the book is illustrated with a large number of informative and detailed photographs, provided by various companies at the leading edge of research and applications in the field.

Chapter 1

Main Requirements

1.1. Introduction

The study of rotating electrical machines is a science which is linked with several other topics. In order to make this book easier to read, we are going to summarize the main results and concepts used later on in this introductory chapter:

– sinusoidal systems;

– electromagnetism;

– power electronics.

1.2. Sinusoidal variables

1.2.1. Single-phase variables

1.2.1.1. Timed expressions

An x variable, a timed-sinusoidal function, can be written as:

where X is the rms (root-mean-square) value and is the angular velocity.

1.2.1.2. Vector representation

The x variable defined above can be considered to be the projection on an axis of a vector of length X

rotating anticlockwise at an angular velocity ω (Figure 1.1).

Figure 1.1. Vector representation of a sinusoidal variable

1.2.1.3. Single-phase currents and voltages

If a sinusoidal single-phase voltage v is applied at a Z impedance terminal, current i in this impedance, at steady state, is also sinusoidal, and can be written:

φ being the phase shift between the voltage often chosen as the origin and the current. Conventionally, φ is counted positively when the current is lagging behind the voltage. The instantaneous power supplied to impedance Z is:

[1.1]

is the active power and:

[1.2]

is the pulsating power. It must be noted that this variable, which characterizes the fact that the single-phase power supplied to a receiver is time varying, is cancelled with balanced polyphase systems.

Figure 1.2 shows that voltage is changed into current through a similitude of ratio Z and angle φ.

Figure 1.2. Vector representation of sinusoidal current and voltage

1.2.1.4. Complex representation

Complex numbers are very useful to represent the previous similitude and vector

will thus be associated with complex number

as well as complex number Ī with vector

. They can then be written as follows:

Complex impedance

is also defined by ratio:

It will be set down:

R and X respectively being the resistance and the reactance expressed in Ohms.

is also introduced :

[1.3]

is the apparent power expressed in volt-amperes (VA). Q is the reactive power expressed in volt-amperes reactives (VAr).

1.2.2. 2-phase voltages and currents

A 2-phase voltage system is defined by two voltages in quadrature:

if it is loaded onto a symmetr...

Table of contents

• Cover
• Title Page
• Copyright
• Preface
• Chapter 1: Main Requirements
• Chapter 2: Introduction to Rotating Electrical Machines
• Chapter 3: Synchronous Machines
• Chapter 4: Induction Machines
• Chapter 5: Direct Current Machines
• Bibliography
• Index