Synchronous machines I — An extension of Blondel's two-reaction theory

Blondel treated salient pole machines by resolving the fundamental space component of m. m. f. along the two axes of symmetry the direct axis of the pole, and the quadrature axis between poles. Using this idea and applying harmonic analysis, Blondevs theory has been extended in the present paper to a comprehensive system of treatment in which the effect of harmonic m. m. fsy as well as the fundamental and also of field m. m. f. in the quadrature axis, as well as in the direct have been taken into account. It is shown that the “armature leakage flux” which causes reactance voltage drop in synchronous operation comprises all fluxes due to armature currents which generate fundamental voltage except the space fundamental component, the latter constituting the total flux of “armature reaction.” Impressing upon the variable air-gap permeance those space harmonics of m. m. f. which are due to the fundamental time component of current and which therefore rotate at various fractional speeds produces odd space harmonics of flux rotating at many different speeds and in opposite directions. Some of these listed in Table I produce fundamental voltage, but most of them generate time harmonics. The former, which are reactive voltages, are only those of the nth space order rotating at one nth speed that is, those which correspond in space order and speed to the harmonic m. m. fs. The corresponding reactances are definitely defined in Appendix C in terms of permeance coefficients, and means are outlined for quantitative determination of such coefficients from graphically constructed field plots. Although, strictly, there areas many field plots required as there are significant m. m.f. harmonics, an approximation, developed in Appendix B, is given in which only one plot is necessary, other permeance waves being derived therefrom. It is shown that only the average term and the second space harmonic of the permeance series affect the fundamental voltage. Hence, unless it is required to calculate the harmonic voltages, only those two terms of the permeance series need to be determined. In the application of the results, the fundamental voltages thus produced by the armature currents are superposed upon that due to current in the field winding, which latter has been previously treated. This gives the vector diagram, Fig. 19, from which the steady state relations are set down in equations. In Part II, the steady-state angle-power relations are developed, including an interpretation of the “reluctance term11 in the power or torque equation. In Appendix D, the vector diagram for salient pole machines is interpreted in terms of the well-known Potier diagram for cylindrical rotor machines. Also the effect of saturation both on anglepower relation and on the value of excitation required under load is discussed. Subsequent papers in the near future will present results which have been obtained from the application of the method and point of view here outlined to the solution of problems relating to abnormal operating conditions of synchronous machines.