200 ALTERNATING CURRENTS 



116. Short-circuit Test 



We now have one point on the circle P and the line QY, 

 which must contain the centre of the circle. The circle could be 

 drawn if we knew another point on it. Such a point is obtained by 

 determining the magnitude and phase of the short-circuit current, 

 i.e. the current which would be obtained by clamping the short- 

 circuited rotor and applying the normal p.d. to the stator. 



In this form, however, the experiment could only be carried out 

 with extremely small motors, as the currents would be excessive, 

 and a dangerous rise of temperature would result in a very short 

 time. Further, the value so obtained would not be quite correct, as 

 the permeability of the cores would be different from that correspond- 

 ing to normal working conditions. Hence the plan generally adopted 

 consists in applying to the stator a p.d. of amount V s which is 

 sufficient to give rise to a short-circuit current T 8 about equal to the 

 normal full-load current of the motor, the power W s being measured 

 at the same time. If cos S denote the corresponding power factor, 

 we have 



W 

 cos0 s = ~= ....... (2) 



V standing for the line p.d. during the short-circuit test. The 

 short-circuit current I s , which would have been obtained at the full 

 line p.d. of V volts, is then calculated by means of the equation 



the assumption being made that the short-circuit current is directly 

 proportional to the p.d. 



As it is found that the value of the short-circuit current depends 

 on the position of the rotor relatively to the stator, it is best to allow 

 the rotor to run very slowly during this test. 



We can now construct the vector of short-circuit current in our 

 diagram, by laying off 0'P S = I g (Fig. 131), making an angle S , given 

 by equation (2), with the horizontal. This determines a second 

 point P 8 on the circle. The construction is then completed by joining 

 P P, and at the middle point of P P erecting a perpendicular to it. 

 The intersection of this perpendicular with QY gives the centre U of 

 the circle, and the circle may now be drawn. 



In determining the no-load and short-circuit current vectors, it is 

 best to find a number of points on the curve connecting p.d. with 

 current, and to read off the required value from the curve, rather 

 than rely on an isolated reading. This procedure is in any case 



