# Analysis of Synchronous Machines, Second Edition by T.A. Lipo

By T.A. Lipo

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Additional resources for Analysis of Synchronous Machines, Second Edition

Sample text

2N t ⁄ ( πP ) , does not enter into the final expression for self inductance. 20. 113) Substituting Eqs. 115) can now be used to find the total inductance of the fourcoil series string. 117) 0 However, the winding function N A1, A2 is zero over pole pitches corresponding to the position of windings A3 and A4 (and vice versa). As a result, the mutual inductance between any two pairs of windings having both a north and south pole is zero. 118) which is the same as Eq. 112). In the analysis above strict attention has been paid to the correct definition of the mutual and self inductances when the four poles of the circuit are considered individually (each having both a positive and negative portion in their winding functions).

Winding B is fixed to the rotor. Since the rotor is free to rotate, the mutual inductance LAB changes with rotor position. 16(a). 15 Mutual inductance example with concentrated coils. wise to the coil side directed into the page, it is evident that γ = θ rm so that Eqs. 90) can also be used to describe this condition. 16(b). The triangular nature of LAB can be more easily visualized if the expression for mutual inductance in the form of Eq. 91) is chosen. 91) 0 Since the turns function nB(φ) is a non-zero constant over the range θrm to θrm + π, and zero elsewhere, it can be interpreted as a function which specifies which portions of the function NA are to be evaluated in the integral.

2 that the MMF drop (and hence flux) is considered positive from rotor to stator. What is desired is the total flux linkage of winding B from current in winding A. 13 Winding placement for mutual inductance calculation. far the placement of winding B has been assumed arbitrary so that an expression for the total flux linkage appears rather hopeless. Note, however, that regardless of the distribution one must have an equal number of conductors directed into the page (x) as out of the page as (•).