TOWARD THE DESIGN OF OPTIMAL SYNCHRONOUS RELUCTANCE MOTORS

E. V. Kononenko, G. I. Lukiyanov

(Presented by the scientific seminar of the Departments of Electrical Machines and General Electrical Engineering)

In connection with the expansion of the field of application of synchronous reluctance motors (SRM), especially in systems of frequency control of rotational speed, studies of optimal ratios in their design are becoming topical. One of the possible directions in designing SRMs is the development of an independent series of motors. However, such a solution to the problem involves large expenditures and difficulties and is hardly economically advantageous at a scale of production measured in tens or hundreds of thousands per year. Theoretical studies, as well as the results of experimental investigations of prototypes of improved SRMs, show that SRMs with sufficiently high energy indices can be made on the basis of existing series of general-purpose asynchronous motors. In this case the stator core and all the remaining assemblies and parts are taken from the corresponding asynchronous motors, with the exception of the rotor core. In addition, the number of turns and the cross section of the conductor may be changed in the stator winding. A number of foreign firms engaged in the development and manufacture of SRMs likewise seek to make them on the basis of existing series of standard asynchronous motors. Such a direction in the development of SRMs appears at present to be the most expedient and has the following advantages:

1) Maximum unification and standardization of parts and assemblies, as well as manufacturability of the design, are ensured.

2) The volume, time required, and cost of design work are reduced.

3) The amount of newly developed equipment and tooling is reduced.

4) Production of SRMs can be organized in the same shops as that of asynchronous motors and does not require extensive preparation of production. These circumstances lead to the fact that introducing SRMs into production will require considerably less time and expense than preparing production of individually designed motors.

At the same time, all the geometrical ratios found in asynchronous motors generally cannot be taken as the basis for designing SRMs, because the latter possess a number of fundamental differences from asynchronous motors and must satisfy specific requirements. In addition, the series of general-purpose asynchronous motors with ratings of 0.6–100 kW

is constantly being improved. All this creates the need to establish regularities and relationships for the selection of electromagnetic loadings, principal dimensions, and internal geometry, making it possible to design SRMs that are optimal under given conditions.

At present, when designing optimal electrical machines, for most series-produced machines the economic criterion is taken as the optimality criterion—the minimum of total costs, which includes the costs of manufacturing and operating the machine. In the total costs of an SRM, operating expenses predominate, and in optimization the expenses associated with energy indicators—efficiency and power factor—are mainly subject to change. Therefore, in design one should strive for sufficiently high values of these indicators. However, in some cases the level of energy indicators may be limited by the technical requirements imposed on the motor by operating conditions. In this connection, let us analyze some technical requirements for SRMs and evaluate their possibilities from the standpoint of satisfying these requirements.

1. Starting characteristics

SRMs are started in the same way as induction motors. The choice of the required values of the starting characteristics depends on the intended purpose of the motor. In most cases, SRMs must ensure reliable starting and synchronization at full load. For this it is necessary that the values of the starting torque \(M_p\), the pull-in torque \(M_{\mathrm{in}}\), and the minimum and maximum torques in asynchronous operation be not less than the rated torque. In general, providing such characteristics when designing SRMs on the basis of induction motors is possible. This is confirmed by the data in Table 1. Table 1 gives the starting characteristics and rated data obtained as a result of tests of prototypes made on the basis of induction motors of the AO2 series. It should be noted that in design serious attention must be paid to \(M_{\mathrm{in}}\), since its value is decisive.

The pull-in torque depends mainly on the parameters of the starting winding, the maximum torque of the SRM in synchronous operation (or overload capacity), and the moment of inertia of the rotating masses. As \(M_t\) increases, the pull-in torque increases. However, the energy indicators deteriorate in this case. For example, for the prototype SRO 31-6, with \(M_t = 1.51 M_n\), tests yielded \(M_{\mathrm{in}} = 0.96\), \(\eta_n = 76.4\%\), \(\cos\varphi_n = 0.675\).

Table 1.

In order to obtain \(M_{\mathrm{in}} = 1.0\), the overload capability would be increased to 1.69. In this case the efficiency decreased by 1.83%, and the power factor by 6%. Consequently, an increase in \(M_{\mathrm{in}}\) should primarily be achieved by rational design of the starting winding. One such method is to reduce the active resistance of the winding, for which purpose the starting cage should be made complete. In doing so, it is necessary to take into account the permissible magnitude of the starting current, which is limited by the heating of the windings during starting. For an SRM, the permissible starting-current multiple may be taken as 5.5–7.0 (as in asynchronous motors). If the motors are intended for operation in speed-control systems using thyristor frequency converters, then a reduction in the starting-current multiple can be achieved by selecting the appropriate law of voltage variation as a function of frequency during starting. In some cases, the quantity limiting the starting characteristics may be the value of the minimum torque in the asynchronous mode.

2. Overload capability

The overload capability of an SRM should be chosen somewhat smaller than that of an asynchronous motor. This is explained by the following circumstances. An increase in the load torque above the maximum torque developed by an asynchronous motor leads to stoppage of the motor, with the resulting consequences. Under these conditions an SRM falls out of synchronism and continues to operate in the asynchronous mode with a small slip. When the overload disappears, the motor is automatically pulled into synchronism. Therefore it is sufficient to choose the overload capability of an SRM equal to 1.4–1.5. In addition, as already noted above, choosing a large value of \(M_m\) worsens the energy indices.

3. Rated data

It is seen from Table 1 that experimental SRM prototypes, within the same frame sizes, have the same rated power as asynchronous motors, with a somewhat lower power factor (by 15–20%). The overheating of the stator winding does not exceed that permissible for insulation class E.

When an SRM operates in frequency speed-control systems, additional requirements are imposed on the motors for stable operation over the entire control range. Investigations in this area show that the region of stable operation is strongly affected by the values of the synchronous inductive reactances, the law of voltage regulation as a function of frequency, the parameters of the rotor winding, etc. Changes in the rotor design aimed at improving the energy indices lead to an expansion of the self-oscillation region.

Thus, analysis of the requirements imposed on the motor by operating conditions, and of the SRM characteristics, shows that designing an SRM that simultaneously satisfies all requirements is a rather complex problem.

When designing an SRM on the basis of asynchronous motors, the stator geometry is fixed. Consequently, the required characteristics can be obtained by changing the number of turns of the stator winding and the design of the rotor core. In this case, the design of optimal SRMs consists in finding the optimal ratios of electromagnetic loadings and the optimal rotor geometry.