Abstract
This chapter introduces and explains mathematical model of synchronous machines. The model considers three-phase synchronous machines with excitation windings or permanent magnets on the rotor. This model does not include damper windings, which are introduced and explained in Chap. 21. The model represents transient and steady state behavior in electrical and mechanical subsystems of synchronous machines. Analysis and discussion introduce and explain Clarke and Park coordinate transforms. The model includes differential equations that express the voltage balance in stator and rotor windings, inductance matrix which relates flux linkages and currents, Newton differential equation of motion, expression for the air gap power, and expression for the electromagnetic torque. The model development process is very similar to that of the induction machine, which is detailed in Chap. 15. Therefore, some considerations are shortened or removed. The model obtained in this chapter is suitable for both isotropic (cylindrical) and anisotropic (salient pole) machines. This chapter closes with some basic considerations on the reluctant torque and synchronous reluctance machines.
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