A novel technique for torque ripple suppression in BLDC motor drive using switched capacitor based SEPIC converter

ABSTRACT


INTRODUCTION
The brushless DC (BLDC) motor has excellent speed regulation capability enabling it to be widely applicable in industry and domestic applications [1], [2].The primary factor limiting the use of BLDC motors in many industries is the commutation torque ripple they create [2], [3].The torque ripple may even reach up to 50% of the value of the average electromagnetic torque.Therefore, reduction of torque ripple is important for improving the performance of the BLDC motor.
The research on reducing torque ripple in BLDC motor has attracted a lot of attention since last decade [4]- [12].Through literature survey it is observed that commutation torque ripple can be reduced by controlling the rise time and fall time of phase current during commutation [6].Different modulated duty ratio has been applied for controlling the slopes of the incoming and outgoing phase currents as described in [7].The torque ripple can be minimized by applying modulated duty ratio to each phase.Hu et al. and Li et al. [8], [9] presented a different modulation technique for torque ripple minimization using field-programmable gate array (FPGA) algorithm and coordinate transformation theory for both low speed and high-speed operation.The simplest method for torque ripple minimization is application of power modulator along with inverter.The reason for terming the method simplest is that it offers a solution with less complicated circuitry.As a result, different converter topologies have been proposed and studied that offers better reduction of torque ripple [10]- [16].A bidirectional buck boost converter has been used for torque ripple reduction in BLDC drive, however, the mathematical evaluation of torque ripple reduction has not been elaborated as can be seen [11].The bidirectional buck boost converter is integrated with inverter through common three switch leg for BLDC drive which increases the complexity of the control circuitry required for the said drive.A torque ripple minimization scheme for BLDC drive has been introduced based on a newly proposed single-inductor multiple output (SIMO) DC-DC converter using FPGA as illustrated in [12].However, the relation between the converter and torque ripple has not been elaborated.A comparative analysis on torque ripple reduction techniques using four converter topologies has been shown for different operating speed as explained in [13].Moreover, in recent years, it has been observed that hybrid converters also gained popularity for torque ripple suppression in BLDC drive [14]- [19].
Thus, all these studies [11]- [15] proves that the inclusion of a power modulator in BLDC drive circuitry reduces the unwanted torque ripple but none of them reveals any mathematical relationship of torque ripple reduction with the duty ratio of DC-DC converter.In order to understand the introduction of converter for torque ripple suppression, we have established the mathematical relationship between the duty ratio of the converter along with the electromagnetic torque in BLDC drive.The major contribution of this article is this numerical analysis, which will enable the future studies to incorporate the appropriate DC-DC converter for BLDC drive.In this context, switched-capacitor based SEPIC converter has been introduced in this paper that shows a higher voltage boost ratio compared to other converters presented in [20]- [23].The switched capacitor plays a vital role here as it helps to reduce the voltage stress across switches used in converters.
In this paper, the work is introduced in: i) Section 2 presents the mathematical analysis of the torque ripple at the time of commutation and its relation with DC link voltage; ii) The proposed scheme of brushless DC motor drive is put forward in section 3 along with the relation between the duty ratio of converter and torque ripple and a modified switched capacitor-based converter is proposed; iii) The method to perform the experiment, results, and discussions are presented in section 4; and iv) The concluding remark has been described in section 5.

MATHEMATICAL ANALYSIS OF TORQUE RIPPLE DURING COMMUTATION
An equivalent circuit representation of the brushless DC motor drive has been shown in Figure 1.The voltage equation for the three phases in BLDC motor can be represented as (1).The equation for electromagnetic torque is given by (2).
Where, Vno is the neutral to ground voltage, Vr, Vy, and Vz are the terminal voltages of the three phases.The three phase currents are given by ir, iy, and ib.The trapezoidal back emf are given by er, ey, and eb.R is the resistance of the phase winding.Assuming all three phases have same resistance and L is the equivalent inductance of the phase winding.

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The desired waveform of current is rectangular in shape but practically it is not the same.The actual phase current is trapezoidal in shape comprising of finite rise time and fall time due to the presence of stator inductance [23]- [27].The actual shape of phase current obtained is presented in Figure 2. The slope of phase current has a direct impact on the torque ripple of the brushless DC motor.
Assuming very short duration of commutation, we can consider the back emf to be constant during commutation.Then the initial values of voltage at the start of the commutation can be considered as Vr = 0, Vy = Vdc, Vb = 0, er = Ec, ey = Ec, and eb = -Ec.Rewriting (1), using the values of initial condition, we get (3).
The neutral point voltage drop can be written as (4).Substituting the initial values of emf and current in the (2), the torque equation before commutation is given by (5).
Considering high switching frequency of the pulse width modulation and shorter time period for commutation.The effect of resistance can be neglected.The slope of the phase current obtained using the above assumption has been shown in (6).The time taken for the current (ir) to decay and reduce to initial value as shown in Figure 3 can be obtained using ( 6) and has been expressed as (7).The time taken for the current (iy) to rise from 0 to Ic as shown in Figure 3 can be obtained using ( 6) and can be expressed as (8).
Using ( 2), (6), and the initial conditions, the equation of torque during commutation can be obtained.The expression for electromagnetic torque during commutation is given by (9).The torque ripple is the difference between the maximum and minimum electromagnetic torque of the BLDC motor [27][28].Therefore, the torque ripple is expressed as (10).The relationship between DC link voltage and torque ripple can be described using (10).

PROPOSED SCHEME FOR BLDC DRIVE
The schematic diagram of the proposed brushless DC motor drive has been presented in Figure 3.The proposed BLDC drive comprises of SEPIC derived topology integrated with inverter.The proposed DC-DC converter is derived from the conventional SEPIC by connecting switched capacitor cell with it.Unlike classical switched-capacitor based SEPIC converter presented in [22], the proposed converter comprises of one switch, which is required to be controlled.

Switched-capacitor based SEPIC
The circuit diagram of the newly proposed switched capacitor based SEPIC converter has been presented in Figure 4.The mode of operation of the circuit can be divided into two types: i) continuous conduction mode and ii) discontinuous conduction mode.For brushless DC motor drive operation, we have considered only the continuous conduction mode.The continuous conduction mode of operation can be divided into two more modes based upon the switch on and off state of the switch.The circuit operation during switch on and off mode has been shown in the Figures 5 and 6 respectively.
The relationship between the input and output voltage of the proposed converter is given in (11).In (11), D is the duty ratio, that is equal to the ratio of time the switch is on to the total time period.By changing the operating time of the switch S1 of the converter, the output voltage obtained from the converter can be changed.This Vo is fed to the inverter of BLDC drive and acts as the DC link voltage.

Estimation of torque ripple in the proposed BLDC drive
The proposed DC-DC converter is integrated with inverter to run the BLDC drive.Substituting Vdc from (11) in (10), we get (12).

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The equation for torque ripple after the integration of the modified DC-DC converter has been presented in (12).The proposed brushless DC motor drive is operated at different duty ratio of the DC-DC converter.The commutation torque ripple obtained can be calculated using (12).It has been observed that with the change in duty ratio the commutation torque ripple changes.The (10) shows that with change of DC-DC converter, the DC link voltage will change and so does the torque ripple.Therefore, the choice of converter for BLDC drive will become easier for future studies.

RESULTS AND DISCUSSION
The proposed DC-DC converter shown in Figure 4, has been designed for an operating frequency of 50 kHz, taking L1 as 500 µH, C1 as 5 µF, C21 and C22 as 5 µF and C0 as 1 µF.In order to analyze the performance of the proposed converter, a comparative analysis has been performed between single-ended primary-inductor converter (SEPIC) [20], ZETA [21], and SC based ZETA [22].Table 1 shows the comparative analysis of the output voltage of the proposed converter with the above-mentioned converters.The input voltage has been varied from 5 to 30 volt, keeping the duty ratio constant at 65%.The obtained outcome has been presented in Table 1.The total harmonic distortion of the output voltage for all the converters has also been observed for different duty ratio.Table 2 represents the comparative analysis for the mentioned converters at 50 kHz frequency.The comparative analysis presented in Table 2 has been done for an input of 20 volt at a duty ratio of 65%.The output voltage obtained using the proposed converter for an input of 20 voltage is 72 volts with total harmonic distortion of 11.92%, which is a much better output as compared to the previously existing converters presented in [20]- [22].The simulation of the proposed drive is presented in Figure 7.An experimental setup has been developed for verifying the effectiveness of the proposed drive.The experimental test setup for the BLDC drive has been presented in Figure 8.The inverter has been supplied with the output from the DC-DC converter.The Vdc applied to the inverter is varied from 12 to 15 volt.The switches used in the inverter circuit are controlled with the help of signals generated by Arduino-UNO.The designed proposed DC-DC converter is applied to generate the Vdc voltage.The stator back EMF of the BLDC motor is been observed in the oscilloscope.The obtained stator back EMF waveform for one of the three phases in the proposed drive with 15-volt Vdc has been presented in the Figure 9.
As mentioned above, the (12) shows that by varying the duty ratio, the DC link voltage can be controlled, which in turn helps in controlling the ripple in electromagnetic torque of BLDC drive.The Table 3 presents the variation of torque ripple and commutation time with respect to the change in duty ratio of the proposed converter.Moreover, the torque ripple is defined as (14).It can be observed from Table 3 that, with the increase of duty ratio, the commutation time decreases.The torque ripple can be reduced to 16.5% using the proposed simple BLDC drive.
Figure 10(a) illustrates the output current waveform and electromagnetic torque of the proposed drive at a duty ratio of 65%.The BLDC drive has also been operated without using DC-DC converter and the waveform of phase currents and torque is presented in Figure 10 3 that with the integration of the proposed converter, torque ripple percentage has been reduced down to 16.5% at a duty ratio of 85% which is much less as compared to the BLDC drive without any DC-DC converter.33 From the results we may say that, the proposed DC-DC converter offers higher gain of about 7 times the input at a lower duty ratio of 65%.To maintain a lower torque ripple in BLDC, drive high gain converter is a simple solution.Thus, the proposed converter which offers lower THD helps maintain high voltage gain with lower voltage stress across the switch and in turn helps to minimize torque ripple.The proposed drive offers better solution to torque ripple suppression as compared to the complicated modulation technique presented in [8] and complex circuit analysis presented in [26].

CONCLUSION
In this study, a modified switched capacitor-based DC-DC converter has been presented to suppress the commutation torque ripple of BLDC motor drive and in previous section it was compared with other such converter fed drives.The main contribution of this paper lies with the mathematical analysis of the cause of torque ripple and the condition for refraining torque ripple.The detailed analysis of the proposed converter fed BLDC drive is presented and in section experimental results are provided.The results obtained shows that the ripple obtained in the electromagnetic torque of the BLDC drive can be minimized with the application of proposed DC-DC converter without using any complicated control techniques.It can be seen that at duty ratio of 55% the torque ripple is 27.88% and with increase in duty ratio to 85%, the torque ripple reduces to 16.27%.The torque ripple in electromagnetic torque can be minimized by simply modulating the converter duty ratio.

Figure 1 .
Figure 1.Equivalent circuit representation of BLDC motor

Figure 2 .
Figure 2. Phase current of three phases during commutation Figure 3. Proposed BLDC drive circuit

Figure 4 .Figure 5 .Figure 6 .
Figure 4. Switched capacitor-based DC-DC converter )  (1−) −4  3 ] (12) Int J Pow Elec & Dri Syst ISSN: 2088-8694  A novel technique for torque ripple suppression in BLDC motor drive using … (Sunam Saha) Figure10(a) illustrates the output current waveform and electromagnetic torque of the proposed drive at a duty ratio of 65%.The BLDC drive has also been operated without using DC-DC converter and the waveform of phase currents and torque is presented in Figure10(b).The torque ripple obtained in BLDC

Table 2 .
Comparison of converter topologies

Table 3 .
Analysis of commutation time and ripple for proposed drive Duty ratio Commutation time Change in torque Average torque Torque ripple