312 Alternators in Parallel. 



When l 2 n 2 = 2Rr + r 2 the total power remains the same, 

 whatever the phase difference, the leading machine sup- 

 plying the whole of the controlling power, and there is no 

 variation of power + or — in the external circuit. 



Thus it would seem desirable, so as to have no fluctuations 

 of current in the external circuit, to make l 2 n 2 — 2Rr + r 2 . 



P — P 



Considering the expression for * * in equation (3), 



±1 + X 2 



we find that it is a maximum for variation of In, when 



, 2 ,_ (2Rr + r 2 )(R + r-Rcos2tt) 



in - R + r + Rcos2« i- • • W 



so that when a is very small, In — r. 



This is the same result that Hopkinson arrives at (see 

 Fleming's 'Alternating Current Transformer,' vol. ii. p. 356), 

 and In may not be reduced beyond this minimum value 

 without serious loss of control. 



P — P 



Again tt — ^ i s a maximum for a given value of In by 



variation of a when 



_ R(2Rr + R 2 -ZV) 

 COSZa ~(R + r)(2Rr + R 2 + Prc 2 )' " ' ' W 



P — P 



so that if In is very small the ratio ^ — ^ rapidly increases 



to a maximum for a very small difference in phase. 



At first sight this might appear to be an argument in 

 favour of having the self-induction as small as possible, but 

 on consideration it will be seen that the alternators would 

 then be very " stiff/' in the same sense as a sailing boat is 

 " stiff " as opposed to " crank/' and that the least alteration 

 in the working of the engine would not only cause large 

 currents to surge backwards and forwards between the two 

 alternators, but in addition would affect considerably the 

 current in the external circuit. 



This rigid control is decidedly to be avoided, for it is im- 

 possible so to regulate two engines that they will work 

 exactly at the same number of revolutions, and some fluctua- 

 tion of the engines is to be expected in speed. 



Some elasticity then is required in the system, whereby a 

 small alteration in speed of the engine should 



(1) Not affect the power in the external circuit, 



(2) Damp down the surging currents, 



(3) Give maximum control. 



