CHAP. XII] INDUCTANCE OF WINDINGS 219 



per phase, such as are indicated for instance in Fig. 15. Then 

 the inductance of a machine, per pole per phase, is given by the 

 equation 



...... (148) 



where (Peq is an empirical value of the equivalent permeance 

 per pole per phase. This formula presupposes that all the 

 partial linkages are replaced by the equivalent complete linkages 

 embracing all the C pp conductors. Moreover, the value of (P^ 

 is such as to take into account the inductive action of the other 

 phases upon the phase under consideration. The total inductance 

 of the machine, per phase, depends upon the electrical connec- 

 tions in the armature winding. If all the p poles are connected 

 in series, the foregoing expression for L P p must be multiplied 

 by p; if there are two branches in parallel, the inductance 

 of each branch is %pL PP , and the combined inductance of the 

 whole machine is i(ipZ/ PP ) = {pL PP . 



The leakage inductance of a machine is usually determined 

 by sending through it an alternating current of a known frequency, 

 under conditions which depend upon the kind of the machine 

 (the field to be removed in a synchronous machine, and the 

 armature to be locked in an induction machine). From the 

 readings of the current of the applied voltage and the watts 

 input, the reactance x of the machine is calculated (after elim- 

 inating the ohmic drop). Then, knowing the frequency /of the 

 supply and the number of poles of the machine, the inductance 

 L PP =x/(2nfp) per pole is calculated. Substituting into eq. 

 (148) this value of L PP and the known number of conductors 

 Cpp, the equivalent permeance (P^ per pole per phase is deter- 

 mined. By performing such tests on machines built on the 

 same punching, but of different embedded lengths, the permeance 

 due to the embedded parts of the winding is separated from 

 that due to the end-connections; the values so obtained are then 

 used in new designs. 



The leakage permeances in the embedded parts are pro- 

 portional to the widths of these parts in the direction parallel 

 to the shaft, in other words, to the length of conductors which 

 are surrounded by the leakage lines. Experiment shows that 

 the permeance of the paths in the air-ducts and around th< 

 end-connections is also approximately proportional to the lengths 



