Flux Linkages

It was stated in Section 3-3 that magnetic lines of flux close upon themselves. As a result it is possible for magnetic flux lines to link electric circuits in much the same manner as flux lines link the windings on the cores in Figs. 3-16 and 3-17 and the manner in which the flux in the toroid of Fig. 3-9(a) links the turns in the winding. Another example of flux linking a circuit is the turn shown in Fig. 3-9(b).

In the case of a winding having N turns and the same value of flux Φ links all the turns, the flux linkages are expressed by

[3-47]

There are many cases, however, in which the different turns of a winding serve to link different amounts of flux. Electric motors and generators usually have windings in which the turns are distributed among slots, an arrangement which makes for differing amounts of flux linking the turns. Figure 3-24 shows the stator of a 3-phase synchronous motor. The coil ends of the stator winding are visible on the right-hand side of Fig. 3-24.

Consider a winding in which the fluxes Φ₁, Φ₂, Φ₃,... Φ_n link N₁ N₂ N₃....,N_n turns respectively where N₁ N₂, N₃, etc. may each be one or more turns, then from Eq. 3-54 we have

and the total flux linkages will be

or

[3-48]

Figure 3-24. Stator of a 3-phase synchronous motor. (Courtesy of Westinghouse Electric Corporation.)