TABLE 66. 1 Typical Synchronous Generator Parametersa alient-Pole rotor Parameter Symbol Round Rotor Damper windings d-axis q-axis 6-1.2 d-axis 0.2-0.3 0.2-0.45 Subtransient reactance d-axis x 0.1-0.25 0.15-0.25 0.2-0.8 Time constants winding open-circuited Tito 4.5-13 3.0-8.0 Stator winding short-circuited Tt 0.03-0.1 a Reactances are per unit, i.e., normalized quantities. Time constants are in seconds. ource: M.A. Laughton and M.G. Say, eds, Electrical Engineer's Reference Book, Stoneham and [McPherson, 1981] are among the basic sources of reference in electric machinery, where ctical aspects are given. An introductory discussion of power system stability as related to synchronous generators can be found in [Bergen, 1986]. A number of handbooks that include subjects on ac as well as dc generators are also available in [Laughton and Say, 1985; Fink and Beaty, 1987; and Chang, 1982 Superconducting Generators The demand for electricity has increased steadily over the years. To satisfy the increasing demand, there has een a trend in the development of generators with very high power rating. This has been achieved, to a great extent, by improvement in materials and cooling techniques. Cooling is necessary because the loss dissipated as heat poses a serious problem for winding insulation. The progress in machine design based on conventional methods appears to reach a point where further increases in power ratings are becoming difficult. An alternative method involves the use of superconductivity. In a superconducting generator, the field winding is kept at a very low temperature so that it stays super conductive. An obvious advantage to this is that no resistive loss can take place in this winding, and therefore a very large current can flow. A large field current yields a very strong magnetic field, and this means that many issues considered important in the conventional design may no longer be critical. For example, the conventional design makes use of iron core for armature windings to achieve an appropriate level of magnetic flux for these windings; iron cores, however, contribute to heat lossbecause of the effects of hysteresis and eddy cur rents--and therefore require appropriate designs for winding insulation. with the new design, there is no need for iron cores since the magnetic field can be made very strong; the absence of iron allows a simpler winding insulation, thereby accommodating additional armature windings. There is, however, a limit to the field current increase. It is known that superconductivity and diamagnetism are closely related; that is, if a material is in the superconducting state, no magnetic lines of force can enter its lterior. Increasing the current produces more and more magnetic lines of force, and this can continue until the dense magnetic field can penetrate the material. When this happens, the material fails to stay supercon ductive, and therefore resistive loss can take place. In other words, a material can stay superconductive until a certain critical field strength is reached. The critical field strength is dependent on the material and its e 2000 by CRC Press LLC© 2000 by CRC Press LLC and [McPherson, 1981] are among the basic sources of reference in electric machinery, where many practical aspects are given. An introductory discussion of power system stability as related to synchronous generators can be found in [Bergen, 1986]. A number of handbooks that include subjects on ac as well as dc generators are also available in [Laughton and Say, 1985; Fink and Beaty, 1987; and Chang, 1982]. Superconducting Generators The demand for electricity has increased steadily over the years. To satisfy the increasing demand, there has been a trend in the development of generators with very high power rating. This has been achieved, to a great extent, by improvement in materials and cooling techniques. Cooling is necessary because the loss dissipated as heat poses a serious problem for winding insulation. The progress in machine design based on conventional methods appears to reach a point where further increases in power ratings are becoming difficult. An alternative method involves the use of superconductivity. In a superconducting generator, the field winding is kept at a very low temperature so that it stays super￾conductive. An obvious advantage to this is that no resistive loss can take place in this winding, and therefore a very large current can flow. A large field current yields a very strong magnetic field, and this means that many issues considered important in the conventional design may no longer be critical. For example, the conventional design makes use of iron core for armature windings to achieve an appropriate level of magnetic flux for these windings; iron cores, however, contribute to heat loss—because of the effects of hysteresis and eddy cur￾rents—and therefore require appropriate designs for winding insulation. With the new design, there is no need for iron cores since the magnetic field can be made very strong; the absence of iron allows a simpler winding insulation, thereby accommodating additional armature windings. There is, however, a limit to the field current increase. It is known that superconductivity and diamagnetism are closely related; that is, if a material is in the superconducting state, no magnetic lines of force can enter its interior. Increasing the current produces more and more magnetic lines of force, and this can continue until the dense magnetic field can penetrate the material. When this happens, the material fails to stay supercon￾ductive, and therefore resistive loss can take place. In other words, a material can stay superconductive until a certain critical field strength is reached. The critical field strength is dependent on the material and its temperature. TABLE 66.1 Typical Synchronous Generator Parametersa Parameter Symbol Round Rotor Salient-Pole Rotor with Damper Windings Synchronous reactance d-axis Xd 1.0–2.5 1.0–2.0 q-axis Xq 1.0–2.5 0.6–1.2 Transient reactance d-axis X¢ d 0.2–0.35 0.2–0.45 q-axis X¢ q 0.5–1.0 0.25–0.8 Subtransient reactance d-axis X² d 0.1–0.25 0.15–0.25 q-axis X² q 0.1–0.25 0.2–0.8 Time constants Transient Stator winding open-circuited T¢ do 4.5–13 3.0–8.0 Stator winding short-circuited T¢ d 1.0–1.5 1.5–2.0 Subtransient Stator winding short-circuited T² d 0.03–0.1 0.03–0.1 a Reactances are per unit, i.e., normalized quantities. Time constants are in seconds. Source: M.A. Laughton and M.G. Say, eds., Electrical Engineer’s Reference Book, Stoneham, Mass.: Butterworth, 1985