Synchronous Machines

Under steady-state operating conditions, the physical picture of the operation of a polyphase synchronous machine is simply seen in terms of the interaction of two magnetic fields as discussed in Section 4.7.2. Polyphase currents on the stator produce a rotating magnetic flux wave while dc currents on the rotor produce a flux wave which is stationary with respect to the rotor. Constant torque is produced only when the rotor rotates in synchronism with the stator flux wave. Under these conditions, there is a constant angular displacement between the rotor and stator flux waves and the result is a torque which is proportional to the sine of the displacement angle.
We have seen that a simple set of tests can be used to determine the significant parameters of a synchronous machine including the synchronous reactance Xs or Xd. Two such tests are an open-circuit test, in which the machine terminal voltage is measured as a function of field current, and a short-circuit test, in which the armature is short-circuited and the short-circuit armature current is measured as a function of field current. These test methods are a variation of a testing technique applicable not only to synchronous machines but also to any electrical system whose behavior can be approximated by a linear equivalent circuit to which Thevenin's theorem applies. From a Thevenin-theorem viewpoint, an open-circuit test gives the intemal voltage, and a short-circuit test gives information regarding the internal impedance. From the more specific viewpoint of electromechanical machinery, an open-circuit test gives information regarding excitation requirements, core losses, and (for rotating machines) friction and windage losses; a short-circuit test gives information regarding the magnetic reactions of the load current, leakage impedances, and losses associated with the load current such as I2R and stray load losses. The only real complication arises from the effects of magnetic nonlinearity, effects which can be taken into account approximately by considering the machine to be equivalent to an unsaturated one whose magnetization curve is the straight line Op of Fig. 5.9 and whose synchronous reactance is empirically adjusted for saturation as in Eq. 5.29. In many cases, synchronous machines are operated in conjunction with an external system which can be represented as a constant- requency, constant-voltage source known as an infinite bus. Under these conditions, the synchronous speed is
determined by the frequency of the infinite bus, and the machine output power is proportional to the product of the bus voltage, the machine internal voltage (which is, in tum, proportional to the field excitation), and the sine of the phase angle between them (the power angle), and it is inversely proportional to the net reactance between them.
While the real power at the machine terminals is determined by the shaft power input to the machine (if it is acting as a generator) or the shaft load (if it is a motor), varying the field excitation varies the reactive power. For low values of field current, the machine will absorb reactive power from the system and the power angle will be large. Increasing the field current will reduce the reactive power absorbed by the machine as well as the power angle. At some value of field current, the machine power factor will be unity and any further increase in field current will cause the machine to supply reactive power to the system.
Once brought up to synchronous speed, synchronous motors can be operated quite efficiently when connected to a constant-frequency source. However, as we have seen, a synchronous motor develops torque only at synchronous speed and hence has no starting torque. To make a synchronous motor self-starting, a squirrel-cage winding, called an amortisseur or damper winding, can be inserted in the rotor pole faces,
as shown in Fig. 5.31. The rotor then comes up almost to synchronous speed by induction-motor action with the field winding unexcited. If the load and inertia are not too great, the motor will pull into synchronism when the field winding is energized from a dc source.
Altematively, as we will see in Chapter 11, synchronous motors can be operated from polyphase variable-frequency drive systems. In this case they can be easily started and operated quite flexibly. Small permanent-magnet synchronous machines operated under such conditions are frequently referred to as brushless motors or brushless-dc motors, both because of the similarity of their speed-torque characteristics to those of dc motors and because of the fact that one can view these motors as inside-out dc motors, with the commutation of the stator windings produced electronically by the drive electronics.




1 Magnetic Circuits and Magnetic Materials
2 Transformers
3 Electromechanical Energy Conversion Principles
4 Introduction to Rotating Machines
5 Synchronous Machines
6 Polyphase Induction Machines
7 DC Machines
8 Variable-Reluctance Machines and Stepping Motors
9 Single- and Two-Phase Motors
10 Introduction to Power Electronics
11 Speed and Torque Control
Appendix A Three phase circuits
Appendix B Voltages, Magnetic Fields, and Inductances of Distributed AC Windings
Appendix C The dq0 Transformation
Appendix D Engineering Aspects of Practical Electric Machine Performance and Operation
Appendix E Table of Constants and Conversion