Let us consider a method of expanding the basic system of equations for accounting higher spatial harmonics. We turn our attention, for example, again to Table 3.4 of Chap. 3 where synchronous mode was considered for salient pole frequencycontrolled machines. In this table are given four groups of magnetically coupled loops No. 1–No. 4; they are consolidated by common EMF frequency in rotor loops: \( \upomega_{\text{ROT}} = 6\upomega_{1} \). Loops No. 1 and No. 2 correspond to spatial order \( {\text{m}}_{\text{DIR}} = 1 \), and loops No. 3 and No. 4 to order \( {\text{m}}_{\text{DIR}} = 7 \).
Currents, voltages and complex amplitudes for groups of loops No. 1 and No. 2 are determined by equations of basic system given in Sect 14.5. It contains 14 equations with 14 unknowns and considers spatial harmonics in rotor and stator loops of order \( {\text{m}}_{\text{DIR}} = 1 \) (see 14.5.1–14.5.3). Let us note that the calculation of rotor currents with frequency f = 300 Hz assumes that the distribution of these currents is found for EMF period equal to T; complex amplitudes of MMF and flux density harmonics are found from their distribution curve according to methods given in Chaps. 12 and 13, herewith, expansion period of this distribution curve is also equal to T.
We proceed to groups of loops No. 3 and No. 4
\( \left( {{\text{m}}_{\text{DIR}} = 7} \right) \). Peculiarities of time harmonics of orders Q
_{DIR} = 1 and Q
_{DIR} = 13 at m
_{DIR} = 7 were considered in Chap.
3; the equations defining these peculiarities are marked by sign (*). They consist in the fact that both time harmonics at m
_{DIR} = 7 correspond to sign S = 1 entered in Chap.
3. Let us list additional unknowns in determining the spatial harmonic m
_{DIR} = 7:

three phase currents of stator and three phase voltages of stator; their frequency f = 50 Hz. (Q_{DIR} = 1);

three phase currents of stator and three phase voltages of stator; their frequency f = 650 Hz. (Q_{DIR} = 13);

two components of complex amplitudes of field induction in air gap.
These 14 unknowns are determined from the system of equations similar to the basic one (see 14.5.1, 14.5.3). Let us note that the calculation of rotor currents with frequency f = 300 Hz assumes that the distribution of these currents is found for EMF period equal to \( \frac{\text{T}}{{{\text{m}}_{\text{DIR}} }} = \frac{\text{T}}{7} \); complex amplitudes of MMF and flux density harmonics are found from their distribution curve according to methods given in Chaps. 12 and 13, herewith, expansion period of this distribution curve is also equal to T/7.
We consider peculiarities of physical process at simultaneous currents flow in groups of magnetically coupled loops No. 1 – No. 4; they are consolidated by common EMF frequency in rotor loops: \( \upomega_{\text{ROT}} = 6\upomega_{1} \), i. e. f = 300 Hz. It is noted above that complex amplitudes of MMF and flux density harmonics in a basic system for group of loops No. 1, No. 2 are found for the expansion period equal to T. However, complex amplitudes of MMF harmonics and of flux density harmonics for currents of this group, are calculated with the expansion period \( \frac{\text{T}}{{{\text{m}}_{\text{DIR}} }} = \frac{\text{T}}{7} \).
As a result, we obtain that in air gap there is the additional resulting field of rotor currents with period equal to T/7. This field corresponds in rotor loops to EMF and currents with frequency f = 300 Hz, which is characterized by two complex amplitudes of flux density.
From this point of view, groups of magnetically coupled loops No. 1 and No. 2 (with stator frequencies f = 250 Hz and f = 350 Hz) and loops No. 3 and No. 4 (with stator frequencies f = 50 Hz and f = 650 Hz) can be considered as electromechanical energy converter.
As stated above it follows that both systems of equations should be added with two more equations; each of them is determined by rotor current with frequency f = 300 Hz in the form of flux density components sum for loop groups No. 1, No. 2 and No. 3, No. 4 with identical period equal to T, T/7. Thus, with account of harmonics of order \( {\text{m}}_{\text{DIR}} = 7 \) we obtain except for 14 unknowns of the basic system additional 16 unknowns; the order of system of equations in comparison with that of the basic is increased to 30.
The stated method of accounting higher harmonics by expansion of the basic system of equations is simple and based on physical representations of processes in machine with nonsinusoidal power supply. Calculation practice shows that before further expansion of this system by including each next group of higher harmonics, it is expedient to make assessment of this expansion. For example, losses in machine rotor and stator windings can be chosen as assessment criteria. Considering that with harmonics order growth, MMF and flux density amplitudes decrease, and the increment of these losses will also decrease; respectively, the expansion extent of basic system of equations is determined in the selection of this criterion by calculation accuracy of losses set preliminarily. This practical assessment allows us to limit the number of harmonics used for the calculation.