Electrical Actuators: Applications and Performance

Chapter 2

Modeling and Parameter Determination of the Saturated Synchronous Machine ¹

The goal of this chapter is to introduce the rational treatment of saturation in synchronous machines. We will limit this study to the case of machines with sinusoidal coupling, the only case where the study of saturation has reached a certain level of maturity. We will not go into all the practical details of the tests involved; we instead refer the interested reader to standards such as [IEC 85] and [IEE 95]. This chapter is divided into three sections. In the first section, we describe the basic notions in a way that does not presume linearity. The second section is dedicated to conventional tests. The models used are mainly linear, but this part ends with the observation that the linear theory is insufficient and with the introduction of the Potier model for smooth pole machines. The third and last section of this chapter is dedicated to the treatment of non-linearities, as well as to the question of equation linearization.

2.1. Modeling of the synchronous machine: general theory

2.1.1. Description of the machine studied and general modeling hypotheses

The machine studied is a conventional machine. It contains two solid parts, stator and rotor, with the latter executing a rotation movement relative to the former.

One of the parts that we can presume as being the stator without losing generality contains a three-phase winding, that is, a symmetrical system with three windings called “phases”. ...