During power-system disturbances, the relative speed between the resultant flux and the rotor causes eddy currents to be induced in the rotor iron structure and an induction-motor or induction-generator torque to be developed owing to the amortisseur winding; both these effects damp out the synchronousmachine oscillations. Damping has been considered previously as directly proportional to the slip of the rotor with respect to synchronous speed for a single-machine study, and with respect to instantaneous frequency of Thevenin's equivalent e.m.f. for a multimachine study; this is erroneous and can lead to a substantially different assessment of power-system transient stability, as is shown by illustrative examples. It is indicated that the conclusions drawn from a single-machine study for damping purposes (as is sometimes done in the literature) are not really applicable to a multimachine study; and, moreover, it cannot be said with certainty that the damping will be positive or negative. The damping torque depends on the instantaneous slip between the rotor and the resultant flux, and requires knowledge of synchronous-machine torque/slip characteristics. V e v' d , X' q T" 9 ~1 D H K D eu, /o 80 8 1 List of symbols = damping power = braking power due to negative-phase-sequence current = braking power due to rapidly decaying d.c. component = negative-phase-sequence current component = d.c. component = negative-phase-sequence resistance = positive-phase-sequence resistance = infinite bus voltage = external reactance = direct-axis saturated reactance = quadrature-axis saturated reactance = Potier reactance = direct-axis transient reactance = quadrature-axis transient reactance = direct-axis subtransient reactance = quadrature-axis subtransient reactance direct-axis open-circuit transient time constant direct-axis open-circuit subtransient time constant : quadrature-axis open-circuit subtransient time constant • damping torque coefficient inertia constant slope of asynchronous characteristics expressed as p.u.-torque/p.u.-slip for synchronous machine synchronous angular velocity system nominal frequency phase angle of O at the beginning of time interval At phase angle of 0 at the end of time interval A/ phase angle of E q at the beginning of time interval Af phase angle of E q at the end of time interval A/
IntroductionIn power-system planning, various studies are normally carried out to ascertain the ability of a power system to overcome disturbances. Owing to the generally long and tedious calculations necessary, the following assumptions have been made in the past for treating synchronous machines, to achieve simplification: (a) constant flux linkages (b) transient salience neglected (c) damping torques neglected (d) voltage-regulator and -governor effects neglected (e) saturation neglected Moreover, stability has been determined by the first swing of the machine. Many of the above assumptions are self-com-