Synchronous Machines-III Torque-Angle Characteristics Under Transient Conditions

This is the third part of a series of papers on the subject of synchronous machines. The first two were: I. An Extension of Blondel's Two-Reaction Theory, II. Steady State Power-Angle Characteristics. The present paper deals with the power-angle, or torque-angle, characteristics under transient conditions, namely, A. Cyclic variation of impressed torque, B. Sudden angular displacement, C. Synchronizing out of phase. It is shown, as in Fig. 6, that although the slope of the torqueangle characteristic (which is an important factor in the determination of the resonant frequency) under the oscillatory condition is greater over a large range of values of the average angle δ'' than under steady operation, nevertheless in the range of normal operation, i. e., from δ' = 0 to δ' = 25 deg., the two slopes, in the case of salient-pole machines, are practically the same. Hence, it is only in rather rare, special cases that a correction in the slope for the oscillatory condition is necessary. For such cases, Equation 27 gives the correction. Referring to condition B, Fig. 13 shows the steady state torqueangle characteristic and also the characteristics for the condition of sudden angular displacement, the latter occurring from various given points on the steady state curve. The slopes indicated by dotted line segments in Fig. 6 merely correspond to parts of the complete characteristics shown in Fig. 13. The latter are calculated from Equation 46.