A Power Factor Correction Buck Converter-Fed Switched Reluctance Motor with Torque Ripple Suppression

+e switched reluctance motor (SRM) suffers the main drawback of torque ripples, and a buck converter-fed SRMmotor drive has been proposed to suppress torque ripples and correct a power factor in this paper.+e buck converter reduces the torque ripple by supplying appropriate DC-link voltage; meanwhile, the buck converter realizes a function of power factor correction at ACmains. An enhanced performance has been obtained on speed control and power quality improvement. An experimental SRM motor drive is formed, and the experimental results show that the proposed drive possesses an improved function with suppression of torque ripples and power factor correction.


Introduction
Due to low cost, simple structure, fault tolerance, and good controllability, the switched reluctance motor is widely used in industrial applications as a variable speed drive, particularly in high-speed applications [1-3]. However, the switched reluctance motor suffers from torque ripples, which results in the vibration and noise, restricts its application to a high-performance servo system [4,5,8].
In [23], an active boost converter with a capacitance and an insulated gate bipolar transistor is presented to control the excitation voltage and demagnetization voltage applied to the SRM phases in real time, which can avoid negative torque of the demagnetization phase by controlling the commutation time accurately and reduce the torque ripple effectually in a commutation interval.
In [24], a DC chopper between the rectifier and the power converter of the switched reluctance motor in order to control the DC-link voltage is presented, where the DClink voltage changes with speed, and in the entire speed range, the motor always operates in the single pulse state. Such a control scheme reduces the current gradient and the acoustic noise, and extends the life expectancy of the motor. e authors in [23,24] reduce the torque ripple of the SRM preferably by adjusting the DC-link voltage, but power factor correction (PFC) is not considered. e conventional SRM drive is normally supplied by a diode bridge rectifier and a large DClink capacitor, the diode bridge rectifier draws a pulse current from the AC mains, the accompanying harmonics will exceed the restricts given in the standards [25]. e power supply of SRM drive without power factor correction function leads to harmonic pollution, poor factor, and low efficiency. Hence, the active power factor correction converter is introduced in SRM drive for improving the power quality at AC mains.
In [26], a modified quasi Z-source converter in front of an asymmetric half-bridge converter for the switched reluctance motor is proposed, the quasi Z-source converter not only improves the speed regulation performance of the drive system and reduces the torque ripple by adjusting DC bus voltage according to the operation condition but also reduces total harmonic distortion and improves the power factor by the peak current control.
In [27], a power factor correction converter composed by two cuk circuits with a communal switch fed switched reluctance motor is proposed, the modified cuk converter reduces torque ripples by adjusting DC bus voltage according to speed, and at the same time, it improved the power factor in wide speed range. e authors of [26,27] reduce the torque ripples of the SRM and increase the power factor preferably through the DC converter, but its structure and implementation is relatively complicated. A fine solution for torque ripple suppression of the SRM is to feed the motor with low voltage in the low speed range and to increase voltage accordingly when the speed increases.
A novel simple buck power converter with power factor correction for the SRM is presented in this paper, it not only can control the DC-link voltage to reduce the torque ripple in wide speed range but also can significantly improve the power quality at AC mains, and it does not require a complex algorithm compared with the other control strategies.

Analysis of Torque Ripple
e doubly salient switched reluctance motor has independent phase windings on the stator, and the phase voltage equation is given by where U is the phase voltage, R is the resistance of phase winding, i is the phase current, and L is the phase inductance relying on the rotor position and the phase current. e phase back electromotive force (EMF) E is given by where θ and ω represent the rotor angular position and the rotor velocity, respectively. So, the phase voltage equation can be written as Assuming the magnetism is linear, the phase torque can be given by [5] T where K denotes the change rate of phase inductance with angle.
From equation (4), it can be seen that the torque is proportionate to the square of current. K is a function of the phase-winding current and rotor position in reality, but usually, its variation is much smaller than that in current squared, [28] so the torque stability is mainly determined by the current stability. In a steady state, neglecting the resistance drop, from equation (4), it can be implied that if the phase voltage is equal to the phase back electromotive force, the current will be constant, so the torque will be constant. Since the phase back electromotive force is proportionate to the rotor velocity, the desired voltage of the inverter for SRM drive should vary with the rotor velocity and the desired voltage of the inverter for SRM drive should approximately proportional to the rotor velocity, and then the torque will be smooth. e most commonly used method for the switched reluctance motor is current chopping control, particularly at low-speed and start-up area. e block diagram of the current chopping control for the switched reluctance motor is shown in Figure 1. Due to doubly salient poles and centralized field excitation, the switched reluctance motor is inclined to considerable vibration and acoustic noise. e vibration and noise is particularly notable at low-speed and start-up area in the current chopping control method. e vibration of SRM is caused by the variation of the radial force, and the variation of the radial force is caused by the change of the voltage added to the winding, so the source of the vibration is the change of the voltage.
In the common control method, the voltage added to the winding is full DC-link voltage throughout the entire speed area and the voltage change gradient is maximal, so the vibration and attendant noise is maximal. Moreover, current normally exceeds the hysteresis width in practice, which leads to the larger current ripple along with the larger torque ripple [29].

Buck Converter for SRM
e configuration of the buck converter for the SRM is shown in Figure 2. e buck converter is placed between the diode bridge rectifier and the inverter circuit of the SRM, the output voltage of the diode bridge rectifier is the input voltage of the buck converter, and the output voltage of the buck converter is the input voltage of the inverter circuit of the SRM. e relationship between input voltage and output voltage of the buck converter is indicated by the following equation: where V OUT and V IN represent the output voltage and input voltage, respectively, and D denotes the duty cycle of the switch. A diode bridge rectifier with a capacitor usually results in the low power factor due to a pulsed input current which is far from the sinusoidal wave. A buck converter not only can convert the high input voltage to a low output voltage but also can correct the power factor by shaping the AC input current in the phase with the AC input voltage.
When the input voltage is higher than the output voltage and the power switch T is on, the input current is equal to the current of the inductor, energy from the AC mains is stored in the inductor L, while the power switch T is off, the input current becomes zero, and the inductor energy is transferred to the capacitor C. Figure 3 shows the block diagram of the buck PFC converter control, V IN is a positive sinusoidal full wave rectified by the diode rectifier bridge, V OUT is the DC output voltage of the buck converter, and V SET is the setting DC output voltage of the buck converter. e difference between V SET and V OUT is amplified, V IN is divided, the processed results are input to the multiplier, and V REF is the output of the multiplier, so V REF is a rectified sinusoidal wave whose amplitude is controlled by the output voltage of the buck converter. V REF is compared to the triangular wave, and thus, the PWM wave driving the switching device T is generated, which shapes input current into a sinusoidal waveform in order to be in phase with the utility grid input voltage. e common pulse width modulation technique used in the buck converter usually results in a distortion in the AC input current due to the current ripple of the inductor, and the pulse area modulation technique is an improved control strategy for the buck PFC converter for reducing the harmonic current, which shapes the input current into a sinusoidal waveform by modulating the area of the current pulse [30].
When the current fluctuation in the inductor can be negligible, the input current wave of the buck PFC converter is shown in Figure 4, wave V REF is a rectified sinusoidal wave so as to be in phase with the grid input voltage, and it is compared with the isosceles triangle waveform V car ; the comparison result determines the input current conduction time, and the input current I IN is a sine sequence of pulses. Figure 5 shows the schematic diagram of input current conduction time, the sinusoidal reference wave intersects a triangular carrier at E point, the line segment AB is a horizontal line, T is the period of the triangular wave, and t ON is the input current conduction time of the buck PFC converter in a cycle. Equation (6) can be obtained from Figure 5: where m denotes modulation degree of the sine wave and ω denotes angular frequency of the sine wave. Equation (7) can be derived from equation (6): From the above equation, it can be concluded that the input average current of the buck PFC converter is in proportional to the grid sinusoidal input voltage, and it will be a relatively good sine wave when its high-frequency harmonic components are eliminated with a small filter.

The Proposed Control Strategy for SRM
e full DC voltage leads to high current gradient and then motivates larger torque ripples and larger vibration along Mathematical Problems in Engineering with acoustic noise. Because vibration amplitude is proportional to the rate of voltage change at the step change moment, the torque ripple is also related to the rate of voltage change at the step moment, so the torque ripple and vibration can be suppressed by decreasing the rate of voltage change, and the reduced DC-link voltage leads to reduced current gradient and thus the torque ripple compared with the traditional control method [31][32][33].
In the proposed control strategy, the DC bus voltage is controlled as a function of speed. e buck converter before the power converter outputs the suitable voltage for the switched reluctance motor, and the current of the winding will become smooth. e block diagram of the SRM drive with the buck converter is shown in Figure 6. e rotor position is fed back by the position sensor to the controller, the rotor speed is controlled in the outer control loop, the current is controlled in the inner loop, the error of speed generates the current command, and the error of current generates the switching signals of the power converter. e rotor speed generates the output voltage command to the buck converter.

Experimental Result
To verify the availability of the proposed method, a fourphase 8/6 poles 75 W switched reluctance motor drive system with the buck converter is set up and a TMS320F2812 type DSP is employed for digital implementation of the control algorithm. Figure 7 compares the speed waveforms without and with the buck converter at 300 r/min, and the rated speed of motor is 1500 r/min. As shown in the figure, the speed ripple of the drive with the buck converter is lower than that of the drive without the buck converter, and it implies the torque ripple is suppressed availably with the buck converter. Figure 8 compares the current waveforms without and with the buck converter at 300 r/min, as shown in the figure; the current waveform of the drive with the buck converter is Mathematical Problems in Engineering smoother than that of the drive without the buck converter, and it implies that the torque is smoother. e power factor is the ratio of active power to apparent power, and it consists of the displacement power factor and distortion power factor under the condition that the current waveform is nonsinusoidal. e displacement power factor is the ratio of the fundamental active power to the fundamental apparent power and is often denoted as the cosine of the phase angle between the fundamental voltage wave and fundamental current wave. e distortion power factor is related to harmonic content in current and is equal to the ratio between the root mean square (rms) value of the fundamental current and the root mean square value of the total current. e power factor (PF) can be represented as where I 1 and I T represent the rms value of fundamental current and total current, respectively, θ denotes the phase angle between fundamental voltage and current, and THD represents total harmonic distortion, equal to the ratio of the rms value of the total harmonic component to the rms value of the fundamental component. Figure 9 shows the input current waveform of the buck converter at 300 r/min, it can be seen that the current waveform is closer to the sinusoidal waveform compared with the diode bridge rectifier, and it has less harmonic content; from equation (8), it implies that the property of power factor is enhanced.

Conclusion
A power factor corrected buck converter fed SRM motor drive has been proposed to suppress torque ripples in this paper. e buck converter supplies the desired voltage for SRM drive by controlling the voltage at DC bus and making it vary directly with the motor speed; accordingly, the torque ripple is suppressed. Meanwhile, the front-end buck converter realizes a function of power factor correction at AC mains. An enhanced performance has been obtained on speed control and improvement of power quality at AC mains. Finally, an experimental SRM motor drive is formed to validate the proposed drive, and the results of experiment verify the effectiveness of the proposed drive.

Data Availability
All data, models, or codes generated or used during the study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.  Mathematical Problems in Engineering