Chapter 4 - Modeling and Analysis of Synchronous Machines

Abstract

This chapter discusses the synchronous machine model based on dqO coordinates. To visualize steady-state saturated magnetic fields, numerical solutions are presented for no-load, full-load, and short-circuit conditions. It presents the fields for permanent-magnet machines and switched-reluctance machines and addresses the two possible reference systems. A synchronous machine is a complicated electromagnetic device, and it is very important for the operation of power systems. Detailed models are needed to analyze its behavior under different operating conditions and to understand their impact on the power system. The second-order mechanical equation of a synchronous machine can be decomposed into two first-order differential equations: one for the mechanical angular velocity of the rotor ωr and the other for the mechanical rotor angle δ. Linear reactances are assumed and amortisseur windings are neglected except for some out-of-phase synchronization results and for reclosing events. Most machines have very weak damper windings and, therefore, this assumption is justified. Frequently synchronous machines or permanentmagnet machines are used together with solid-state converters, that is, either rectifiers as a load or inverters feeding the machine. The application examples relate to the calculation of synchronous reactances, the investigation of various fault conditions including reclosing, and the calculation of the amortisseur current for subtransient faults such as line-to-line, line-to-neutral, and balanced three-phase short circuits. The design of synchronous machines and permanent-magnet machines for wind-power and hybrid drive applications, respectively, is discussed. Finally, approaches for analyzing static and dynamic eccentricities, shaft fluxes, and bearing currents are outlined.