By M. M. Botvinnik (Auth.)
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Extra info for Asynchronized Synchronous Machines
The problem of stability according to the angle <5(θ) does not arise in the case of AS generators, but at the same time a new problem crops up — speed stability of the AS generator. In this latter respect, the type of line in which it is being used is irrelevant, that is, it does not matter how long it is; this is the basic reason why AS generators are used for long distance transmission, but the speed stability of AS generators is limited nevertheless. The range of permissible variations in slip ±SOL is, as follows from formula (68), determined by the magnitude of the ceiling excitation voltage, the transmission parameters and the steady state operating conditions of the generator.
Taking into account also the equations: Δδ= — — zls mcos vt; (52) %Uo + Cdo = t / o o cos <50 ; %iqo+eqo = U00 sinoo, we obtain the following set: — xpAid + — pAed + ( 1 + s0)zAiq ω8 ω8 + + (l + so)Aea = —U00Asm—(œ8 cos vt cos <50-h v + ν sin vt sin <5o) ; ( 1 + s0)xAid + ( 1 + s0)Aed —- xpAiq co8 — — pAea = U00Asm— } (53) (ω8 cos vt sin δο — — ν sin vt cos δ0) ; ( 1 - 1ήμΤχρΑιά + ( 1 + Tp)Aed = AEd8 ; (1 - 1ο)μΤχρΑι, + (1 + Tp)Aeq = AEq8 ; JpAs + eaoAiq + iqoAed -eq0Aid-id0Aeq = 0. Since the voltages AEd8 and AEq8 are linear functions of the magnitude As — Asm sinv/ (and its derivative), it is clear REGULATION IN OASES OP DEVIATION 29 t h a t t h e v a r i a b l e s A i a , A i q , A e a a , n d A e q will also be linear functions of sin vt and cos vt.
Hence a very important conclusion can be drawn, namely that the total losses in the rotor windings of an AS machine are equal to the losses in the rotor winding of a normal synchronous machine. The second term in equation (66a) determines the power of the excitation system necessary to preserve a power balance. 7oo(ao + aiSo)cosu4, (67) χ equal to the second term of expression (66a). When So^O this magnitude is positive and energy is fed to the stator from the excitation system; when So>0 the value of Δ Ρ becomes negative and surplus energy is fed to the excitation system from the stator.