When two synchronous generators in parallel operation, each provided with synchronizing torque of the induction machineries, are driven by the prime movers at different frequencies, or any synchronous generator, connected to net work of power transmission system, provided with synchronizing torque of the induction machineries, is in the state of slip in frequency from that of the net work, there occurs the communication of electrical energy of two distinct kinds. One is the energy communication of the induction machineries, which acts in such a manner, as to decrease the speed or frequency difference, as long as the speed or frequency difference exists. The other is the energy oscillation of the synchronous machineries, which acts in such a manner, as to flactuate the speed or frequency difference, the mean speed or frequency difference being constant.
Dr. C. P. Steinmetz has already studied the case of two alternators, or group of alternators, such as station sections, connected together, while slightly different from each other in frequency, and given many equations relating to this case. But he has neglect to accept the torque of induction machinery in his equation, and absolutely neglect the speed variation during each half cycle of the oscillating torque of synchronous machinery.
Taking the above two items into consideration, the treatments of the transient in those cases, can be introduced to the some mathematical treatments, as those of the transient of the synch onous motor, provided with induction motor torque, to be puled into synchronism with the supply of the fixed frequency. Those treatments has been introduced and studied by the many authors, as Mr. Otto Bdhm, and Mr. L.H.A. Carr. and so on.
However those authors have procecuted their treatments by the aid of the graphical solution of the fundamental differential equation, the writer has introduced the complete integrals of the fundamental differential equations, by adding the term corresponding to the damping torque, proportional to the square of the velocity. Those treatment of the differential equation is absolutely special.
Adding the terms corresponding the damping torque, proportional to the square of the velccity shall be true for the cases, such as the high speed steam turbine driven synchronous generator.
Synchronous condenser, and water wheel driven synchronous generator of large capacity, with powerful ventilating fan attached to the rotor shafts. The writer has, also discussed the speed var ation on both side of the higher speed and lower speed, which can not be neglected in some cases, as in the case of the Ljungstrom turbo-generator set, and of the small momentum synchronous motor, connected to the large capacity synchronous generator.
This paper shall be complementary to that "On the Synchronizing Torque on Ljunggtrom Turbo Generator", on which, however, the writer has discussed about the relation between the oscillating pull in torque and the induction motor torque, in the steady state. On this paper, the writer has studied and discussed the transient state of pulling in period.
The brief sketches, on the whole course of the paper is as follows;-
The writer has given the general equation of motion for both side of generator
I dω/dt+K
2ω2+K
1ω+K0+Bsin∫(ω-ω')dt+A(ω-ω')=K
2ω0 2+K
1ω0+K0
I dω/dt+K'2ω2+K
1'ω'+K0'+Bsin∫(ω-ω')dt+A(ω-ω')=K
2'ω0'2+K
1'ω0'+K0'
From the above two equations, there follows
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