Sinusoidal Control of a Single Phase Special Topology SRM, Without Rotor Position Sensor

Nicolae-Daniel IRIMIA, Alecsandru SIMION, Ovidiu DABIJA, Sorin VLĂSCEANU, Adrian

MUNTEANU "Gheorghe Asachi" Technical University of Iasi, Faculty of Electrical Engineering, 700050, Iaşi,

Romania; sckummi@yahoo.com

Abstract. This paper presents the sinusoidal control of a single phase variable reluctance motor of special topology, without any rotor position sensor. A sinusoidal AC current source was used for the energizing of the stator phase winding, considering the cases when only positive alternations or both alternations of the supply current waveform were utilized. A specialized electrical circuit was designed in order to connect the power supply to the terminals of the stator phase winding. Simulations were performed using Matlab / Simulink software package.

1 Introduction

This paper presents the sinusoidal control of a single-phase special topology variable reluctance machine (VRM), considering the cases when only positive alternations or respectively both alternations of the supply current waveform were used to energize the stator phase of the motor. In this work are also presented: the parameters of the single-phase special construction VRM, Simulink block diagrams corresponding to the sinusoidal control of the single-pole variable reluctance machine, the results of the simulation obtained with Matlab/Simulink software package and also some conclusions.

2 The Sinusoidal Control Principle of the VRM

Figure 1(a) presents the sinusoidal control principle of a single-phase variable reluctance machine, in case of the positive currents alternations used to energize the stator coil of the motor. At the top of the figure is presented the ideal waveform of the stator phase inductance of the machine, where can be observed the two limits corresponding to the unaligned and respectively aligned positions of the rotor compare to the stator pole. In the middle of the figure are presented the waveforms of the alternating currents for zero electromagnetic torque. At the bottom of the figure are presented positive alternations of the currents corresponding to a non-zero electromagnetic torque developed by the machine. It can be seen that by using only the positive alternations of the current for energizing the stator phase of the machine, the developed torque can reach the maximum value, without any negative torque production. This is achieved due to the presence of the positive current alternation only on the portion of the positive slope of the motor inductance, for a corresponding load torque. The angular velocity of the variable reluctance machine is about 314rad/s for this situation.

In the figure 1(b) is presented the sinusoidal control principle of a single-phase VRM, in case of both alternations of the current waveform. At the top of the figure is presented the ideal inductance waveform of a single-pole VRM, while in the middle of the figure is the phase current waveform for zero electromagnetic torque and at the bottom of the figure is shown the movement of the stator current waveform to the position where the torque developed by the machine corresponds to the shaft load torque if any (and also the friction torque). The higher the value of the load torque, the more obvious is the movement of the current waveform to the position of the positive slope inductance. The reason is that the necessary electromagnetic torque developed by

the machine increases proportional with the value of the load torque which is applied to the rotor shaft. For increasing the value of the electromagnetic torque, the average of the stator phase current corresponding to the portion of positive slope inductance must increase accordingly; at the same time, the average of the phase current on the portion of the decreasing inductance must decrease so that the negative torque production to decrease accordingly.

(a) (b)

Figure 1: Sinusoidal control principle of a single-phase VRM for: (a) positive current alternations and (b) both stator current alternations.

3 The Parameters of the Single-Phase Special Construction Variable Reluctance Machine (VRM)

The variable reluctance machine used in this paper is a single phase, single pole, axial type magnetic flux, special topology motor. The parameters of this machine are presented in Table 1.

Table 1: Single-phase switched reluctance motor parameters. Stator resistance (Ω) 0.6

Inertia (kg·m2) 0.003 Friction (N·m·s) 0.0005

Initial speed Ω0 (rad/s) 0.0 Initial position θ0 (rad) 0.0

Unaligned inductance at 1A (H) 0.0414 Aligned inductance at 1A (H) 0.0892

Unaligned inductance at 20A (H) 0.0369 Aligned inductance at 20A (H) 0.0531

Maximum current (A) 20 Maximum flux linkage (V·s) 1.062 Nominal voltage supply (V) 230

4 Simulink Block Diagrams Corresponding to the Sinusoidal Control of the Single Phase VRM

Figure 2 presents the Simulink principle scheme for the sinusoidal control of the single phase VRM in case of positive alternations of the stator phase current. It is well known that a current source (the ideal AC Current Source 1 in this case) should never be let without a load connected to its terminals, because of the very high induced voltage amplitude that could appear. Thus, for the negative current waveform alternations (when the current through the stator phase winding is zero), a special circuit was developed for reducing the power losses to a minimum. This circuit is represented by the R1 and R2 resistors and also the D1 diode. In case of the positive waveform alternations, the current flows only throw the stator phase winding, by the D2 diode, thus energizing the coil.

While the voltage across the terminals of the AC current source is positive, the IGBT1 is maintained in the conduction state, short-circuiting the R3 resistor. The main role of the R3 resistor is to dissipate any remained energy accumulated in the magnetic field of the machine’s stator phase, after the current through the power source changes its flow direction.

This control technique has the main advantage that is relatively simple to implement, has no need of any sensor position or many controllable power semiconductor devices. The main disadvantage is the need to initially drive the rotor to a certain speed for synchronising with the frequency of the stator phase current imposed by the power source.

The signal provided by the position sensor from the figure is used only for the scope visualization.

Figure 2: Simulink block diagram for the sinusoidal control of the VRM, positive current alternations.

Figure 3 presents the Simulink block diagram corresponding to the sinusoidal control of a single-pole VRM, in case of both alternations of the stator phase current. For permitting the changing of the current direction through the stator phase, a special circuit provided with four IGBTs was designed.

Figure 3: Simulink principle scheme for the sinusoidal control of the VRM, both current alternations.

5 Simulation Results

The results of the simulation were obtained using the Matlab/Simulink software package. Some of these results are presented as follows.

Figure 4 presents the waveforms corresponding to the start-up regime of the single-phase VRM in case of the sinusoidal control method using only positive current alternations. The value of the load torque is zero for this situation. The frequency of the stator phase current is 50 Hz and its amplitude is about 20 A. It can be observed that the angular velocity of the rotor is self-maintaining around the value of 314 rad/s (with a maximum variation of about 6 rad/s from it), corresponding to the frequency of the phase current. Also, it can be seen that only the positive alternations of the stator phase current were utilized in this situation. The average of the electromagnetic torque developed by the single-phase VRM varies around 0.157 Nm, which also represents the value of the friction torque (the load torque being zero in this case).

Figure 4: Waveforms of the VRM start-up process, for positive current alternations and no-load torque.

Figure 5 shows a zoom-in of the same waveforms and the same conditions presented in figure 4. It can be observed that only the positive alternations of the stator phase current waveform are used in this situation for energizing the stator coil of the machine. The negative phase voltage value appears because of the inductive character of the stator phase of the VRM.

Figure 5: The zoom-in of the waveforms presented in figure 4.

In figure 6 are presented the waveforms corresponding to the start-up regime of the VRM, in case of the sinusoidal control, using only the positive alternations of the stator phase current. The load torque is 0.16 N·m. It can be seen that the angular velocity of the rotor is self-maintained around the value of 314 rad/s, with a maximum variation of about 2 rad/s to it. The average value of the electromagnetic torque developed by the VRM is about 0.317 N·m (compensating the friction torque and also the load torque).

Figure 6: Waveforms of the VRM start-up process, positive current alternations, load torque: 0.16 Nm.

Figure 7 shows the waveforms corresponding to the start-up regime of the single-phase VRM in case of the sinusoidal control method using both positive and negative stator current alternations. The value of the load torque is zero for this situation. The frequency of the stator phase current is 50 Hz and its amplitude is about 20 A. The angular velocity of the rotor is self-maintaining around the value of 628 rad/s, with a maximum variation of about 2 rad/s from it.

Figure 7: Waveforms of the VRM start-up regime, for both current alternations and no-load torque.

6 Conclusions

The sinusoidal control of a single-phase special topology variable reluctance machine presented in this paper, in case of positive and respectively both stator currents alternations, has the main advantage that is relatively simple to implement, has no need of any sensor position or even many controllable power semiconductor devices. The main disadvantage is represented by the need to initially drive the rotor to a certain speed for synchronising with the frequency of the stator phase current imposed by the power source.

Acknowledgment - This paper was realised with the support of POSDRU CUANTUMDOC “DOCTORAL STUDIES FOR EUROPEAN PERFORMANCES IN RESEARCH AND INOVATION” ID79407 project funded by the European Social Found and Romanian Government.

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