Magnetically Nonlinear Dynamic Models of Synchronous Machines: Their Derivation, Parameters and Applications

This chapter deals with the magnetically nonlinear dynamic models of synchronous machines. More precisely, the chapter focuses on the dynamic models of the permanent magnet synchronous machines and reluctance synchronous machines. A general procedure, which can be applied to derive such magnetically nonlinear dynamic models, is presented. The model is of no use until its parameters are determined. Therefore, some available experimental methods, that are appropriate for determining parameters of the discussed models, are presented. The examples given at the end of the chapter show, how the magnetically nonlinear dynamic models of discussed synchronous machines can be applied. Generally, in all synchronous machines the resultant magneto-motive force and the rotor move with the same speed. This condition is fulfilled completely only in the case of steadystate operation. However, during the transient operation, the relative speed between the resultant magneto-motive force and the rotor can change. In the case of permanent magnet synchronous machines, the force or torque that causes motion appears due to the interaction between the magnetic fields caused by the permanent magnets and the magnetic excitation caused by the stator currents. On the contrary, in the reluctance synchronous machines the origin of motion is the force or torque caused by the differences in reluctance. Most of the modern permanent magnet synchronous machines utilize both phenomena for the thrust or torque production. A concise historic overview of the development in the field of synchronous machine modelling, related mostly to the machines used for power generation, is given in (Owen, 1999). When it comes to the modern modelling of electric machines, extremely important, but often neglected, work of Gabriel Kron must be mentioned. In the years from 1935 to 1938, he published in General Electric Review series of papers entitled ``The application of tensors to the analysis of rotating electrical machinery.’’ With these publications as well as with (Kron, 1951, 1959, 1965), Kron joined all, at that time available and up to date knowledge, in the fields of physics, mathematics and electric machinery. In such way, he set a solid theoretical background for modern modelling of electric machines. Unfortunately, the generality of Kron’s approach faded over time. In modern books related to the modelling and control of