Characteristics of SRM Machines (part 4)

Control Signals, Typical Steady-State Characteristics

Although SRM motor is a reluctance machine and has a completely passive rotor, there are three control quantities deciding about the characteristics of the operation of the drive. They are: supply voltage u, initial angle of energizing the phase winding - switch on angle aon and initial angle of de-energizing power sup ply from the winding - switch off angle aoff. Alternative to the switch off angle, the set of the control signals can apply the conduction angle az. The above control angles aon, aoff are meant to be the angles that precede the aligned position of stator and rotor teeth. For a typical supply of the SRM drive the following condition is fulfilled: the conduction angle az > e, where e is the stroke angle. Usually in order to apply the possibilities of driving the mo tor the control is performed in the range:

At the same time, switching on occurs for which is aimed at obtaining a large value of the current in the adequate range of the reduced rotation angle theta_r. The higher values of aon concern SR motors with higher number m of phase windings. Since the number of steady-state characteristics that can be presented for these control variables is large, the presentation here will focus only on selected characteristics calculated for motor B (Zs/Zr = 6/4). The first group of characteristics is performed in the function of the load torque Tl for three values of the supply voltage: U = 1.0, 0,75, 0.5 Un.

+-+-+- Steady-state characteristics of 6/4 SRM drive for U = 1.0, 0.75, 0.5 Un and aon = 51°, az = 36°, as a function of a load torque: a) speed curves b) phase and source currents c) efficiency of the drive.

The presented characteristics in the function of the angle aon indicate that there is an optimum selection of the advance angle for energizing winding which occurs for the examined machine somewhere in the range from aon = 50°…52°, i.e. for aon ˜ 1.7e in this case. Concurrently, the smallest pulsations of the torque are encountered for aon = 42°…46°, i.e. for aon ˜ 1.4e. Hence, it results that the late beginning of the conduction process, e.g. for aon ˜ 1.4e, leads to an uninterrupted current flow in the windings and reduces pulsations. However, the disadvantage thereof is associated with negative torque components originated from current flow in particular phase windings of the motor, which are manifested after the aligned position is exceeded. The presented characteristics don’t illustrate the effect of the conduction angle az on the characteristics, which for the cases is equal to 36°, i.e. az ˜ 1.2e, which corresponds to a standard value.

SRM—Efficiency, Torque Ripple Level

Having three control parameters aon, aoff, u it’s possible to determine the same point of operation of the drive along the mechanical characteristic of the motor n,Tl for a series of various control parameters. Thus, at the same operating point it’s possible to transform energy for various efficiencies and for various levels of torque ripple - Trip. Such research has been presented in, and the general conclusion is that the quasi-optimal selection of control parameters of SRM motors is technically possible. The control values during quasi-optimal operations vary along with rotational speed. For small speeds the control occurs as a result of changing u , for a constant values of aon,, az. In the intermediate range of the rotational speeds the value of the voltage u remains constant, while the switch on angle aon and the conduction angle az increase. Within the range of the high speeds only the angle aon increases, while the remaining parameters of control remain constant. The curves for control variables for a quasi-optimal control of SRM motor are presented.

+-+-+- Change of control variables for a maximum efficiency of SRM drive in respect to change of rotational speed

The preservation of the control in accordance with the principle presented makes it possible to secure the operation of the drive with maximum efficiency. Concurrently, the ripple component of the torque is at a minimum for a given load torque of a motor from the threshold speed n1 as well. The threshold values n1, n2, for which there should be a change in the control manner are relative to the motor's load torque Tl and they are derived on the basis of the minimum current. For the case of the mathematical model of SRM motor discussed here, it’s possible to present electromagnetic torque produced by the motor as the sum of the component torques resulting from the flow of particular phase currents.

This is so because in accordance with the assumptions made during the development of this model, the phase windings are not magnetically linked and the current coming from each of the phases generates a magnetic flux for a single pair of stator teeth regardless of the currents in the remaining phase windings.

In particular, this offers a possibility of graphical presentation of how the control angles aon, aoff affect the history of electromagnetic torque and what values of the control angle are beneficial for the reduction of torque ripple. +-+-+-the development of torque in motor B (Zs/Zr = 6/4) for the rated values of the supply and load. Subsequently the torque of the motor for the control angles selected in a manner in which the pulsations of the torque are the smallest. This occurs for aon = 43° and aoff = 9° , i.e. for the conduction of the phase across az = 34°. In the first of the cases, the pulse component of the torque is equal to 70% of the mean value of the torque, and in the latter case for Trip = 0.72 [Nm], which corresponds to around 27% of the mean torque. This is done at the expense of the reduction o the system's efficiency by 4 per cent points. If the control angles were to be selected at the values aon = 44° and aoff = 10° , the pulsation level would be only equal to 33% , and the efficiency loss would be two times lower, which means 2 percent points. As a result, a compromise with regard to the selection of control parameters is possible with a considerable benefit to the quality of the drive's operation, which is generally characterized by the quasi-optimal curves of the control parameters.

The illustrations of the curves present why for a motor with three phases there is a certain loss of energy efficiency during limiting pulsation. This is so because the flat waveform of torque according to time and reduction of the pulsation occurs for the control angles displaced in the direction of the aligned position of stator and rotor teeth in comparison to the operation in the rated state. In this case we have to do with two phenomena reducing the efficiency: large negative torque component for exceeding the aligned position with the current in the given winding and decrease of the rotational speed of the rotor, which results in the smaller power output of the machine.

The data given concern motor B whereas for motor A (Zs/Zr = 8/6) the effect of the parameters on the level of pulsation is relatively smaller. For this motor the level of pulsation is close to the minimum Trip/ Tav = 32%...40% within a wide range of the control angles and it’s difficult to obtain a level of pulsation below 30%. It’s possible to exceed this boundary; however, this can only occur for the loads of the motor that are greater than the rated load. Concurrently, for the control corresponding to the rated state the waveforms, for aon = 38°, aoff = 10°. In this case, the respective values of the efficiency and torque ripple level are the following: ? = 83.5%, Trip/Tav = 39%. The lowest level of torque ripple, which is equal to Trip/Tav = 32% takes place for the control: aon = 35°, aoff = 10°, and the efficiency is even higher, as it’s equal to ? = 84.8%. The two latest states differ in terms of the value of the power output of the motor due to the definitely different values of rotational speed, which are respectively equal to 3220 [rev/min] and 2780 [rev/min]. As one can see, in SRM motors there is a possibility of reducing the level of pulsation as a result of adequate selection of the control angles aon, aoff. This, how ever, is possible within a limited range and may lead to a slight decrease of the efficiency, in particular for low rotational speeds.

Shapes of SRS Current Waves

The shapes of phase currents reflect the mode of the control of SRM motor and assume specific waveforms depending on the control angles and rotational speed of the rotor. It’s also possible to distinguish the generator operation of the ma chine from the motor regime on the basis of its waveform. --- presents the shapes of the phase current of motor A which differ in terms of the switch off angle aoff, i.e. for a decreasing conduction angle az, equal to az = 30°, 25°, 20°, respectively. One can clearly note the instant when the supply voltage is disconnected and the transfer of the winding to the period in which it returns the energy to the source through the diodes of the bridge. For the example presented for az = 30°, during the return of energy one can easily notice a bulge on the waveform which is associated with the decreasing inductance of the winding after the rotor tooth exceeds the aligned position.

+-+-+- presents the continuous conduction of the phase currents of the SRM motor, which occurs for the late de-energizing of phases, large load and high rotational speed of the rotor. In these conditions the motor operates correctly and demonstrate a low level of pulsation; however, the energy efficiency of the motor decreases considerably due to the large power losses in the windings. This, in turn, brings a hazard of motor failure due to overheating.

In __, one can see that the load does not have a significant effect on the waveform of the current, which is similar for both small (Tl = 0.5 [Nm]) as well as large (Tl = 7.5 [Nm]) load torque of the motor. However, the rotational speed of the drive differs significantly in these two cases, which can be also concluded from static characteristics.