Sensorless Commutation Method for Low-Voltage BLDC Motors Based on Unfiltered Line Voltage

This study presents a filterless and sensorless commutation method for low-voltage brushless DC motors. The proposed method utilizes controlled DC-link inverter instead of the Pulse-Width Modulation (PWM) scheme. Therefore, motor voltages and currents become free from the high-frequency noise of PWM switching, thereby decreasing motor losses. Consequently, the method does not require any Low-Pass Filter (LPF) and it does not involve speed-dependent phase delay caused by the LPF. However, current commutation deteriorates waveform of line voltages. Thus, specific functions are defined to compensate for the current commutation spikes and remove false zero-crossing points of line voltages. Furthermore, the use of unfiltered line voltages eliminates the requirement of any phase shifter. Hence, the main superiority of the proposed method over preceding sensorless commutation methods is the simultaneous elimination of the phase shifter and LPF, which makes the method simple and cost-effective. The simulation and experimental results show the effectiveness and validity of the method.


Introduction
Brushless DC (BLDC) motor is widely used in the industry due to its high efficiency, low maintenance, light weight, and compact structure.The BLDC motors require the information of rotor position to perform current commutation in stator windings.However, the position sensors increase the complexity of system con-figuration as well as motor cost and size [1], [2] and [3].Sensorless control methods have been introduced to cope with the abovementioned restrictions.
In [4] and [5] commutation points were extracted by detecting Zero-Crossing Points (ZCPs) of line voltage differences which were sampled during Pulse-Width Modulation (PWM) on time.Another method utilized a Z-source inverter to supply BLDC motor and sampled the voltage of the inactive phase in shoot-through vectors to detect its ZCPs [6].The ZCPs of phase back Electro-Motive Force (EMF) advance inherently actual commutation points by 30 • .Hence, a phase shifter is demanded to determine the commutation points correctly.The phase shifting process makes the sensorless commutation technique more sophisticated because it needs the high-cost Digital Signal Processor (DSP).Although the methods used in [4], [5] and [6] need no Low-Pass Filter (LPF), they require a particular PWM switching pattern to sample the motor voltages accurately.
Filtered line voltages that comprise the corresponding line back EMFs have been used in [7], [8] and [9] to estimate the commutation instants.The LPF, which is used to suppress high-frequency noise due to PWM switching of the inverter, causes speeddependent phase delay that increases as rotor speed increases.The phase delay of the estimated position prevents the phase current from aligning with the rotor position.Therefore, it generates torque ripples that reduce the average torque and motor efficiency.Consequently, LPF limits the high-speed operation capability of BLDC motors [10].In [9], phase delay caused by LPF was nearly compensated only at the rated speed of the motor by adjusting the hysteresis band of the comparators.Hence, this approach is inappropriate for variable speed drives.In [11] and [12], specific methods were presented based on shifting the ZCPs of heavily filtered line voltages by either 90 − α or 150 − α degrees.These methods were complicated and required variable phase shifting.The technique presented in [13] also used line voltages.However, it was more complicated and needed two-step filtering and virtual neutral point.
In [14], [15] and [16], speed-independent functions are used to detect the commutation instants.The calculation of the speed-independent functions is complicated because they depend on the measured voltages, currents and the derivatives of the currents.Other studies have been dedicated to correction of the rotor position error.For example, commutation instants are adjusted by forcing the current integrals of the two half periods to be equal in 60 degrees conducting period [17].It is reported that the effect of the estimated position error reflects on the current waveform.Hence, the current waveform is used as an index to compensate for the commutation error [18].In the other study, a self-correction sensorless method is introduced based on the difference of the terminal voltage of the inactive phase between the beginning and the end of commutation interval [19].
The contribution of this study is an improvement of sensorless commutation of BLDC motors by the simultaneous elimination of the LPF and phase shifter.Commutation spikes of the unfiltered line voltages are investigated in detail in Sec. 2.Then, specific functions are presented in Sec. 3. to compensate for the false ZCPs caused by current commutation.The estimation error of the proposed and conventional methods are analyzed in Sec. 4. The simulation and experimental results are provided in Sec. 5. and Sec. 6. , respectively, to verify the effectiveness of the proposed approach.The results justify that the method can be easily implemented using simple circuits without any need for high-cost DSPs.Furthermore, the estimated commutation signals are phase-delay-free because no LPF is used anymore.Hence, the method can increase the operating range.Finally, conclusions are given in Sec. 7.

Spikes of Unfiltered Line Voltages
Usually, the PWM method is used to control BLDC motors.However, some studies have proved that supplying BLDC motor with a controlled DC-link inverter leads to high efficiency [20] and [21].Figure 1 shows the equivalent circuit of a three-phase Y-connected BLDC motor which is fed by a full-bridge inverter, and a buck converter is used in front of the inverter to regulate the DC-link voltage by the duty cycle of switch S 7 .Figure 2 shows the simulation waveforms of the phase current obtained from the PWM and controlled DC-link inverter schemes.It is evident that the PWM method causes the large high-frequency ripple in the stator current which inevitably increases copper and iron losses.Furthermore, the controlled DClink inverter could provide more stable performance for sensorless control of a BLDC motor than the PWM method [11], [12], [13], [20], [21], [22] and [23].
The voltage equations of the BLDC motor shown in Fig. 1 are given as: where V ag , V bg , and V cg are the motor terminal voltages with respect to the DC-link ground g.The stator phase currents are indicated by i a , i b , and i c .The stator resistance, stator inductance and motor neutral point voltage relative to the ground g are denoted by R, L, and V Ng , respectively.The maximum value of the back EMFs can be defined as: where K e and ω m are the motor voltage constant and angular velocity, respectively.The trapezoidal back EMF voltages which are indicated by e a , e b and e c can be expressed as: where θ e is electrical angular position of rotor and F stands for the trapezoidal function which can be given as: The inverter switches S 1 -S 6 turn on and off only when they perform the current commutation.Therefore, the motor terminal voltages do not contain undesirable high-frequency switching noise, and thus, no LPF is employed anymore.Consequently, the proposed method does not involve the speed-dependent phase delay caused by LPF. Figure 3 shows the three line voltages along with the corresponding phase currents.
When the BLDC motor operates with 120 • conduction mode, there are six combinations of the stator excitation in a fundamental cycle.Under regular conduction interval, only two of the three phases are conducting at any time, and the other phase is unexcited.By performing current commutation every 60 • , the commutation intervals will emerge.During the commutation intervals, the three phases conduct because the commutation needs a finite time due to the stator windings inductance.The six regular conduction intervals and six commutation intervals are indicated in Fig. 3 and Tab. 1.
Tab. 1: Six regular conduction and six commutation intervals.

Sec. Interval
Conducting devices It can be seen from Fig. 3 that the current commutation causes four voltage spikes in each line voltage waveform; while only two of them cross the horizontal axis and cause zero-crossing errors.Let us calculate the amplitude of line voltage V ac during the critical commutation spikes which make false ZCPs in the line voltage waveforms (see Fig. 3 and highlighted rows in Tab. 1).Consider Sec. 3 in which switches S 1 and S 2 are conducting, and commutation instant comes and makes switch S 1 turn off and switch S 3 turn on.This switching leads to transferring current from a-phase to b-phase.As mentioned before, due to the inductance of stator windings, the current of a-phase does not decrease to zero immediately.Hence, diode D 4 conducts until i a becomes zero.This current commutation causes a spike in the waveform of line voltage V ac which is indicated as Sec. 3 to 4 in Fig. 3.The equivalent circuit during this commutation interval is shown in Fig. 4(a).By applying KVL to the path traced from a to c, the amplitude of line voltage V ac is obtained as −V D − V f , where V D and V f denote diode and transistor forward voltage drops, respectively.Now, let us consider the negative half cycle of line voltage V ac .Consider Sec. 6 in which switches S 4 and S 5 are conducting, and commutation instant reaches and makes switch S 4 turn off and switch S 6 turn on.The current of a-phase does not decrease to zero instantly, so it makes diode D 1 conduct until i a becomes zero.This current commutation generates a spike in the waveform of line   voltage V ac which is indicated as Sec.6 to 1 in Fig. 3.The equivalent circuit of the motor and inverter during this commutation interval is shown in Fig. 4(b).By applying KVL to the path shown in Fig. 4(b), the amplitude of line voltage V ac is obtained as It can be concluded that the absolute value of the line voltages during the commutation intervals is the sum of the forward voltage drops on the diode and transistor V D + V f .In the case of a low-voltage BLDC motor, V D + V f is large enough to be detected compared to the peak value of line voltages.That is not the case, however, if a high-voltage BLDC motor is considered.Hence, in this study, we focus on low-voltage BLDC motors.

Compensation for Commutation Spikes
We define a function for line voltage V ac as: where Sign operator is defined as: Figure 5 shows line voltage V ac and its function.Elliptical contours indicate the two commutation spikes in the function of the line voltage.The voltage of a-phase relative to the ground (V ag ) is also illustrated in Fig. 5. V ag can be expressed as: The maximum value of back EMFs, E, is always less than V dc /2.Hence, according to Eq. ( 7), V ag indicates a positive value except within the interval from 5π/6 to 5π/6+θ C3 in which D 4 is conducting and the amplitude of V ag is −V D .This interval coincides with the first spike of voltage V ac .Hence, we define a Sign function for V ag as: The above function can compensate for the first spike of voltage V ac by utilizing the logical equation: where + stands for OR operator.Figure 5 depicts the function S ag and the resultant signal (Z a ).As can be seen, the function S ag compensates for the first spike of the function S ac .However, the effect of the second spike still deteriorates the resultant signal Z a .By detailed investigation on the waveform of voltage V ag , another fact is discovered that the amplitude of V ag is greater than the DC-link voltage only in the interval from 11π/6 to 11π/6 + θ C6 which coincides with the second spike of the line voltage V ac .In this interval, c 2019 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING diode D 1 is conducting and the value of V ag is V dc +V D .Accordingly, we define another function as: where V ug is the voltage of the positive rail of DClink to the ground.Figure 6 shows voltage V ua , its function S ua , and the signal Z a obtained from Eq. ( 9).As evident from Fig. 6, the function S ua can be used to compensate for the second spike of voltage V ac by using the logical equation: where • stands for AND operator.The resultant spikefree commutation signal C a is illustrated in Fig. 6.The same process is applied to the other two unfiltered line voltages, namely, V ba and V cb .Accordingly, the appropriate functions which are required to compensate for the spikes caused by current commutation are defined as: The commutation signals of b-and c-phases can be extracted as: The proposed logical equations for generating six gating signals of the inverter from three estimated commutation signals can be derived as: where subscripts kH and kL (k = a, b, c) stand for high-side and low-side power devices of the inverter.

Voltage Drop on Stator Resistance
The proposed method uses the line voltages to detect the ZCPs of the line back EMFs indirectly.Although the line voltages comprise the relevant line back EMFs, estimation error is inevitable because of voltage drop on the stator winding resistance.Assume that a-and c-phases are conducting and b-phase is unexcited.The indicated area in Fig. 7 corresponds to the mentioned interval.As can be seen, the back EMF of b-phase increases until it reaches its maximum value.The ideal commutation point for transferring current from a-phase to b-phase is the instant in which e b equals e a .However, in practice, the ZCPs of the line voltages are used to estimate the commutation points.Assume that the phase inductance is small enough to be neglected.In this case, when e ba = 0 the line voltage can be expressed as: which means that the ZCPs of the line voltages do not coincide with those of the line back EMFs.Hence, the inverter switches keep their states unchanged until the line voltage crosses zero.The line voltage can be expressed as: Substitution of the back EMFs defined in Eq. ( 3) in Eq. ( 16) gives: Fig. 8: The LPF used in the conventional sensorless methods.
The commutation point is detected when V ba reaches zero.Hence, the rotor position estimation error can be derived as: where the peak value of the back EMF can be extracted as: By substituting Eq. ( 19) into Eq.( 18), the phase delay caused by the voltage drop on stator resistance can be expressed as:

Phase Delay Due to LPF
The LPF is used in the conventional sensorless commutation methods based on filtered voltages of the motor.Figure 8 shows a common LPF which is utilized in the conventional sensorless methods.The transfer function of the LPF can be given as: The value of the phase delay caused by the LPF can be expressed as: where ω e is the electrical angular velocity of the rotor and ω c is the cutoff frequency of the LPF.It can be concluded from Eq. ( 22) that the LPF causes the speed-dependent phase delay in the estimation of rotor position.

Simulation Results
Table 2 lists the specifications of the BLDC motor which is used to run the simulations in MAT-LAB/Simulink.To verify the effectiveness of the proposed method, we have compared its results with those of the conventional method based on ZCPs detection of the filtered line voltages.We choose the cutoff frequency of 2 kHz for the LPF of the conventional method to make a compromise between the phase delay of the LPF and its capability to remove the highfrequency noise.
The line voltage, phase current, electromagnetic torque, rotor speed, ideal Hall signal obtained by the Hall-effect position sensors placed within the motor, and the estimated commutation signals obtained from the proposed and conventional methods are shown in Fig. 9 and Fig. 10, respectively.These simulation results are given under the intermediate load at a speed of 15000 r•min −1 .By comparing the electromagnetic torque and phase current waveforms, it can be deduced that the proposed method causes less distortion in the current and torque waveforms than the conventional technique.The phase current and torque of the con- ventional method involve large high-frequency ripples that cause a decrease in the motor efficiency.Furthermore, the estimated commutation signal obtained from the proposed method has a good match with the ideal Hall signal.For the proposed method the commutation angle error is about 3 • , whereas it is significant and about 14 • for the conventional method.The small difference between the ideal Hall signal and the estimated commutation signal obtained from the proposed method is due to the phase delay resulting from voltage drop on the stator resistance.In the case of the conventional technique, the error caused by the voltage drop on the stator resistance superimposes to the error resulting from the LPF.
We repeated the simulation under different rotor speeds and phase currents to compare the position estimation error of the proposed method with that of the conventional method.Figure 11 shows the simulated performance of the proposed and conventional methods at different speeds, from 5000 to 20000 r•min −1 , under various load conditions with phase current of 0, 0.5, 1, 1.5, 2, and 2.5 A. In all the conditions, the commutation angle error of the proposed method is smaller than that of the conventional method, as expected.Due to the phase delay caused by LPF, the commutation angle error for the conventional method is significant at high speeds.Hence, as mentioned before, the conventional method is not suitable for a wide range of speed.On the contrary, increasing or decreas- ing the rotor speed does not affect the performance of the proposed method significantly.
Let us analyze the effect of the estimation error of the rotor position on smooth torque generating capability of the BLDC motor.Assume that the current commutation from c-phase to a-phase is performed with a phase delay of θ d from the ideal commutation point.In this case, by ignoring the commutation interval, the 60 • period of Sec. 2 can be expressed as: During this interval, the phase currents can be expressed as: The electromagnetic torque produced by the BLDC motor is given by: where K t is the torque constant of the motor.Substituting Eq. (24) and Eq. ( 4) into Eq.( 25) gives: c 2019 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING Accordingly, the average electromagnetic torque of the motor can be expressed as: Figure 12 shows the electromagnetic torque of the BLDC motor when current commutation happens with a phase delay.This figure and Eq. ( 27) justify that the maximum torque occurs at θ d = 0 with K t I. Clearly, the larger the rotor position estimation error, the larger the torque ripple.In other words, the average electromagnetic torque produced by the BLDC motor decreases with increasing the estimation error of the rotor position.Therefore, the proposed method improves the efficiency and performance of the position sensorless drive of the BLDC motor by decreasing the estimation error of the rotor position.Figure 13 shows the waveforms of V ac , i a , rotor speed, load torque, and electromagnetic torque with sudden load change.The load torque has been increased suddenly from 0.01 to 0.037 N•m and after a while decreased from 0.037 to 0.01 N•m.As can be seen, the proposed sensorless commutation method has the effective performance for a sudden load change.Figure 14 shows the waveforms of V ac , i a , and rotor speed with speed change.The speed command has been increased from 4000 to 15000 r•min −1 .As can be seen, the proposed sensorless commutation method has the effective performance, and the motor continues to run during the transient conditions.

Experimental Results
Figure 15 shows the designed circuit to generate the proposed functions S ac , S ag , and S ua that are required to extract the sensorless commutation signal of a-phase, namely, C a .We have implemented the proposed method using low-cost LM339 comparators, CD4071 OR gate, CD4081 AND gate, and CD4069 logic inverter.Table 3 lists the prototype's parts and their cost from Amazon.com during November 2018.The Total cost of the proposed method is less than $10.
In circuits 1 and 2 shown in Fig. 15, voltages V ag , V ug , and V cg are fed to the subtracters to generate voltage V ac and V ua .In the next step, these voltages are   The experimental waveforms of V ac , V ag , and V ua along with their sign functions S ac , S ag , and S ua are illustrated in Fig. 17.They justify the capability of the designed circuits to generate the compensator functions accurately.The experimental waveforms of the line voltage, phase current, ideal Hall signal and the estimated commutation signal at speeds of 10000 and 15000 r•min −1 are shown in Fig. 18 and Fig. 19, respectively.The position error resulted by the proposed method is negligible and about 4 • .The estimated position error of the proposed method is not significantly affected by the rotor speed, as expected.Furthermore, the phase current has the acceptable rectangular waveform.

Conclusion
This study presents a new sensorless commutation method for BLDC motors.The proposed method uses unfiltered line voltages.Thus, neither LPF nor phase shifter is required.The specific functions are introduced to compensate for the commutation spikes.The commutation signals are derived by the proposed logical equations.The simulation and experimental results prove the validity of the proposed method.Compared with the conventional sensorless methods, the proposed method has advantages as follow: • Wide speed range due to the elimination of the LPFs.
• Simple and easy-to-implement due to the absence of the phase shifter.
• Cost-effective: The proposed method can be easily implemented using simple comparators without any need for high-cost DSPs.
• Precise commutation: position error and torque ripple are reduced due to the elimination of the LPFs.
• Insensitive to operating speed and load conditions.

Fig. 1 :Fig. 2 :
Fig. 1: The equivalent circuit of the Y-connected BLDC motor and its inverter topology based on the buck converter.
c 2019 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING

Fig. 4 :
Fig. 4: Equivalent circuit of the motor and its inverter during commutation interval.

Fig. 5 :
Fig. 5: Function Sag used to compensate for the first spike of Vac and the resultant signal Za.

Fig. 6 :Fig. 7 :
Fig. 6: Function Sua used to compensate for the second spike of Vac and the extracted commutation signal Ca.

Fig. 9 :Fig. 10 :
Fig. 9: Simulated waveforms of the proposed method under intermediate load at speed of 15000 r•min −1 (from top to bottom): unfiltered line voltage, phase current, electromagnetic torque, ideal and estimated commutation signals, and rotor speed.

Fig. 11 :
Fig. 11: Comparison of the simulated phase-delay vs. rotor speed under various load conditions for the proposed and conventional methods.

Fig. 12 :
Fig. 12: Effect of the current commutation delay on torque generating capability of BLDC motor.
c 2019 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING