142 ALTERNATING CURRENTS 



The regulation of a machine, however, may be calculated with 

 sufficient accuracy from data obtainable from open-circuit and 

 short-circuit tests. These tests involve very little power supply 

 and do not require any power-absorbing devices. There are 

 three common methods for determining regulation, the syn- 

 chronous impedance or electromotive force method, the magnetomotive 

 force method, and the A. I. E. E. method. The application and 

 limitations of each method will be discussed in some detail. 



66. Synchronous Impedance Method, or Electromotive Force 

 Method. This method is often called the pessimistic method, 

 because it gives a value of the regulation poorer than that actu- 

 ally existing in practice. 



The principle is as follows: The armature reaction is combined 

 with the armature reactance, or what amounts to the same thing, 

 the armature reactance is increased a sufficient amount to allow 

 for the effect of armature reaction. That this may be done can 

 be shown as follows. 



In Fig. 147 a sine distribution of flux along the air-gap is 

 assumed. The line ab is the coil axis. When the coil axis lies 

 along the pole axis oo, as is shown in (a), the flux linking the 

 coil is a maximum. When the coil axis ab reaches position a'b', 

 as shown in (6), the flux linking the coil is zero. Therefore, the 

 flux linking the coil varies with the time and at a frequency equal 

 to the frequency of the induced electromotive force. In position 

 (a), the flux linking the coil is a maximum, and the induced emf. 

 is zero. In position (6), the flux linking the coil is zero, and the 

 induced emf. is. a maximum. It is seen that the emf. induced 

 in the coil reaches its maximum value 90 electrical space-degrees 

 later than the flux linking the coil, and, therefore, later in time. 

 The flux linking the coil may then be said to lead by 90 the 

 emf. which it induces. 



As the flux linking the coil and the emf. induced in the coil 

 vary sinusoidally with the space position of the coil, their 

 instantaneous values may be found by means of rotating vectors. 



These space relations are shown graphically in Fig. 147 (c). 

 When the coil axis ab lies along the pole axis oo the flux linking 

 the coil is a maximum and the induced emf. E' is zero. As the 

 coil axis ab moves to the right, the flux 4> linking the coil decreases 

 sinusoidally and the induced emf. E' increases sinusoidally. 



