102 SYNCHRONOUS MOTORS 



utilizing Fig. 46. Knowing the value of P and assigning a value to 

 I w , the equation, 



PZ~ ^l w ii)L'l w Id 

 can be written as follows: 



M ...... (a) 



Taking, in Fig. 46, a point AI on the right line DQ, as a center, 

 let a circle be described with a radius equal to EI. Let Oi be the 

 intersection of this circle with the right line A 2 X. The values of 2 

 and Id can then be immediately deduced. We find 



and I d =-DAi. 



z 



These values introduced in equation (a) will give, for example, 



Should this value be greater than M, it is because the point AI was 

 located too near D. If, on the contrary, the value N is less than 

 M, it is because the point AI is too far from D. The point AI may 

 be moved until the values found for 3 and Id give a value for N equal 

 to M. We can also proceed otherwise. Having found, quite easily, 

 by the above method, two positions such as AI and AI' which give, 

 for the polynomial N, two values, one a little too large (N) and the 

 other a little too small (N"), a point, AI', can be obtained by 

 interpolation such that 



A l 'A l _ N-M 



A l "A 1 '~W^N 7 '' 



This gives the desired value of the power, P, with a sufficient degree 

 of approximation for practical purposes. 



Influence of the Wave-Form of E.M.F. The shape of the E.M.F. 

 curves of the generator and motor should approach the sinusoidal 

 form as much as possible in order to avoid instability and low efficiency. 

 Let us first suppose that only one of the two machines departs from the 

 sinusoidal form. By virtue of Fourier's theorem, its E.M.F. can be 

 considered as the resultant of the superposition, upon a principal 

 sinusoidal, of higher harmonics, i.e., of sinusoidals of higher frequency 

 (odd multiples). 



