I 3 o ALTERNATING CURRENTS 



70. Magnitude and Phase of Current for 

 Various Conditions of Load. Overload Capacity 



By assuming various positions for OE relatively to 0V, we can 

 determine the load with which the motor is capable of dealing for 

 each position of OE, and the magnitudes and phase relations of OE 

 and 01 relatively to 0V. This might be done graphically, but more 

 accurate results may be obtained by calculation, as follows : 



If = angle by which the motor e.m.f. is in advance of the p.d., 

 r = resistance, and pL = reactance of armature, then we have 



OK = (V 2 + E 2 + 2VE cos 0)4 (1) 



I --^2=, (2) 



\/r 2 +^ 2 L 2 



E 



sin a = VVD sin (3) 



UK 



4, = TT - (e + tan- 1 ^ - o)= TT - tan" 1 ? - (0 - ) . (4) 



\ T / T 



driving power = El cos ^ (5) 



The above five equations enable us to find the values of I and 

 the driving power for various values of S ; V and E being maintained 

 constant. 



For given values of V and E, the relations connecting and I, 

 and and driving power, may be graphically exhibited by means 

 of curves. Such curves have been plotted in Figs. 98 and 99, for 

 the case of a motor whose armature has a resistance of 0'2 ohm, and 

 a reactance of 2 ohms, the p.d. being maintained constant at 1000 

 volts throughout. The different curves relate to different values of 

 the motor e.m.f., i.e. to different excitations. The ascending portions 

 (shown dotted) of the power curves in Fig. 99 correspond to a con- 

 dition of instability. For, let us suppose that the motor is running 

 under conditions corresponding to a point on the dotted branch of 

 one of the power curves, and let there be a slight increase of load. 

 This will cause a retardation of the rotor, i.e. a decrease of 9 the 

 angle by which the motor e.m.f. is in advance of the p.d. Now, along 

 the dotted branch of a curve a decrease of 6 will be accompanied by 

 a decrease of driving power, so that the retardation will go on, and 

 the motor will drop out of step. On the other hand, if we suppose 

 a slight decrease of load to take place, acceleration will result, 

 increasing, and with it also the driving power, so that the accelera- 

 tion will go on until the top of the curve is passed, and some point 



