# 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).

### 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 ...

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