Bo TAN, Xingyun GUO, Jun ZHAO, Xiofng DING, Wi FANG

a School of Electronic Information Engineering, Xi’an Technological University, Xi’an 710021, China

b Marketing Service Center of State Grid, Hebei Electric Power Co., Ltd, Shijiazhuang 050021, China

c Xi’an Aviation Institute of Computing Technology, Aviation Industry Corporation of China, Xi’an 710065, China

d School of Automation Science and Electrical Engineering, Beihang University, Beijing 100083, China

e Chinese Flight Test Establishment, Xi’an 710089, China

KEYWORDS Back-EMF detection;Brushless DC motors;Commutation control;Electric drive;Internal power angle

Abstract High-speed Brushless DC Motors(BLDCMs)usually adopt a sensorless control strategy and operate in three-phase six-state drive mode.However,the sampling errors of the rotor position and the driving method increase the Internal Power Angle(IPA),resulting in a decrease in the efficiency of the system. Conventional IPA reduction strategies are either sensitive to motor parameters, or ignore diode freewheeling during the commutation process, or require additional current sensors.In this paper,a new strategy to reduce the IPA is proposed.Firstly,a Zero-Crossing Point(ZCP)detection method for the back-EMF without filter is proposed to reduce the sampling errors of the rotor position.Secondly,the relationship between the non-energized terminal voltage and the ZCP of the corresponding back-EMF is analyzed. The non-energized terminal voltage that has completed the diode freewheeling is divided into two triangles by half of the bus voltage. When the IPA is suppressed,the areas of the two triangles are equal.Thirdly,an advanced angle for reducing the IPA is obtained through a PI regulator which can eliminate the deviation between the two areas.Finally,both a simulation model and an experimental circuit are built to verify the proposed control strategy.

1. Introduction

All-electric aircraft has become the development trend of future aircraft. Fuel cells have the advantage of high energy density and can meet the needs of aircraft endurance. However,as the altitude of the aircraft increases,fuel cells generally require an electric air compressor to supply oxygen.The speed of the air compressor motor is generally higher to reduce the volume and weight of the air compressor. Brushless DC motors have the advantages of high efficiency and high power density. High-speed brushless DC motors are especially suitable for driving air compressors for aviation fuel cells.In addition to compressors, all-electric aircraft also include applications with similar operating conditions, such as electric propulsion and electric environment control.By increasing the speed of the drive motor, its power density can be increased.

Generally, high-speed Brushless DC Motors (BLDCMs)have higher fundamental frequency and smaller phase inductance. If the three-phase inverter with PWM modulation method is adopted, the switching frequency of the power device in the three-phase inverter will be relatively high,which will result in high switching loss. Moreover, in order to suppress the phase current ripple, a power inductor is generally connected in series with each motor winding, which will increase the volume of the drive. In addition, the PWM interferes with the non-energized terminal voltage, increasing the error and the detection complexity of the rotor position. In order to solve the above problems,we employ a drive topology based on a buck converter to regulate voltage and a threephase inverter for commutation. In this driving mode, the switching frequency of the power device is reduced,and power inductors are omitted. Moreover, the interference to the nonenergized terminal voltage caused by PWM is reduced.

For the high-speed BLDCM,the sensorless control method based on back-EMF Zero-Crossing Point (ZCP) detection is usually adopted. The electromagnetic power of BLDCM is proportional to the dot product of the current vector and the back-EMF vector1. Hench, if the load torque is constant, the RMS value of the phase current is the smallest when the Internal Power Angle (IPA) between the current vector and the back-EMF vector is minimal. However, the sampling errors of the rotor position prevent the motor from operating at the ideal commutation point, resulting in an increase of the IPA.Moreover,even if BLDCM commutates at the ideal commutation point,the value of IPA is still large due to the motor inductance. The motor inductance causes the phase current to lag behind the back-EMF in the three-phase six-state driving mode2. Therefore, there are two methodologies for reducing the IPA.One is to reduce the sampling errors of the rotor position,and the other is to advance commutation before the ideal commutation point.

In sensorless control, the ZCP of the back-EMF is usually detected according to the non-energized terminal voltage.However,the freewheeling of the diode will introduce harmonics to the terminal voltage,which are related to the parameters and operating conditions of the BLDCM. The harmonics can cause the failure of ZCP detection of the back-EMF.The Low-Pass Filter(LPF)is usually adopted to suppress these harmonics. However, the LPF will inevitably introduce phase delay and estimation errors of the rotor position. The sampling errors of the rotor position introduced by the filter can be eliminated by direct or indirect methods.

In the direct methods, some scholars considered to avoid the use of filters or compensate for the delay directly based on the parameters of BLDCM and the LPF. In Ref.3, the masking signal method was proposed without filter delay. In order to obtain the ZCP of the back-EMF, a resistor network consisting of three resistors was required to obtain the virtual neutral point voltage. In Refs.4–6, the phase delay caused by the LPF was calculated and eliminated according to the filter parameters and the motor velocity. In Refs.7–8, the scholars proposed to combine the PWM synchronous measurement strategy with automatic calibration, and added a hysteresis comparator to reduce the LPF delay and the integrator offset error.

The indirect methods eliminated the instantaneous or integral difference between the motor terminal voltage or the line voltage before and after the commutation to reduce the rotor position errors. In Refs.9–10, the commutation position was determined in such a way that it generated the symmetric terminal voltages of the non-energized phase at the beginning and end of the commutation. In Refs.11–14, a fast commutation instant shift correction method based on detecting the deviation of line voltage or terminal voltage before and after the commutation point was proposed. Ref.15compensated the commutation error based on the difference in the integral of the virtual center point voltage within 60° before and after the commutation.

The above methods can reduce the rotor sampling errors caused by the LPF.However,none of these methods took into account the IPA caused by the motor inductance.Some of the methods required to measure the virtual neutral point voltage.Also, the direct methods were sensitive to motor parameters,LPF parameters,and motor operating conditions.The indirect methods ignored the effect of the diode freewheeling on the terminal voltage.

Under the premise that the ideal commutation point has been obtained, the high-speed torque characteristics of the BLDCM can be further improved by adjusting the advanced commutation angle16. Ref.17defined the commutation point by detecting the phase difference between the rotor flux and the integral of the phase current.In Ref.18,the advanced angle was calculated in real time according to the phase current, the inductance and the flux linkage established by magnet of the motor. Ref.19determined a phase advanced angle for quasisquare waveform of phase current delay based on the Fourier series of the phase voltage waveforms. The above methods were sensitive to motor parameters, and required current sensors in hardware or Fourier expansion and phase discrimination in software.

In summary,for the methods to reduce the sampling errors of the rotor position, most of them were sensitive to motor parameters,LPF parameters,and motor operating conditions,or ignored the effect of the diode freewheeling on the terminal voltage. For the methods of advancing commutation, most of the existing methods were sensitive to motor parameters, and highly relied on the complex hardware and software. In this paper, a new strategy to reduce IPA for the high-speed BLDCM is proposed, which can solve the above problems of inaccurate back-EMF ZCPs detection, sensitivity to parameters, and complicated software and hardware. Firstly, when detecting the ZCPs of the back-EMF, the interference of the diode freewheeling to the terminal voltage is considered, thus improving the detection accuracy of the back-EMF ZCPs.Secondly, the authors explore the relationship of the nonenergized terminal voltage which has completed diode freewheeling and the bus voltage waveform. Finally, the output waveform of the terminal voltage and bus voltage are directly used to calculate the advanced angle. The calculation process does not involve the motor parameters and current values.Hence, the strategy is also independent of motor inductance parameters and does not need extra current sensors.

This paper is organized as follows. In Section 2, the detection principle for the ZCP of the back-EMF without filter is introduced. The proposed IPA control method is described in Section 3.In Section 4 and 5,the simulation results and experimental results are analyzed to verify the method. The conclusions are drawn in Section 6.

2. Detection principle for back-EMF ZCP without filter

The common topology of a high-speed BLDCM is shown in Fig.1.Vdcis the power supply voltage.According to the topology,the method of‘‘masking signal”verified in Ref.3is simplified in this paper,which avoids the step of detecting the neutral point voltage in the original method. The improved ZCP detection method for the back-EMF without filter is analyzed and implemented as follows.

2.1. Analysis of non-energized terminal voltage

The ZCP of back-EMF is usually detected by the nonenergized terminal voltage. For example, when T1 and T6 are turned on and phase C is non-energized,three-phase terminal voltages uaM, ubMand ucMcan be expressed as

Assume that the three-phase windings of the motor are symmetrical, and the Fourier expansions of the three-phase back-EMFs are expressed as

Therefore,the ZCP of the back-EMF uxZP（x = a，b，c)can be detected by comparing uxM（x = a，b，c)with U/2 as shown by the black dots in Fig. 2. If uxM>U/2, uxZPwill be 1; if uxM

In Fig. 2, there are 6 states of the ideal back-EMFs ea, eband ec. is used to mark the back-EMF states, which ranges from 1 to 6. Between t1and t4, ea>0, eb<0 and ec>0, we can define the back-EMF state as ‘‘101” and n=1. Similarly,the other five states of the back-EMFs can be defined.

In the commutation process, if T2 is turned off and D5 is freewheeling, during D5 freewheeling, the ucMvoltage is approximately equal to the bus voltage, which will interfere with the definition of the back-EMF state and change it from normal‘‘010”to abnormal‘‘011”,as shown in the red circle of Fig. 2. Taking into account the influence of the diode freewheeling, the invalid ZCPs of the back-EMFs are shown by the green dots in Fig. 2.

2.2. Judgment of back-EMF ZCPs

There are 6 valid comparing states of three-phase terminal voltages in a 360°electrical period,as shown by the black dots in Fig.2.And there are 12 invalid states as shown by the green dots. The timing sequences of uxZPare shown in Table 1.

Fig. 1 Power topology of high-speed BLDCM.

Fig. 2 Relationship between three-phase terminal voltage and one-half of bus voltage.

Table 1 Relationship between back-EMF and terminal voltage.

In Table 1, i is used to indicate the validity of uxZPwhich ranges from 1 to 3. When i=1 at t1，t4，t7，t10，t13and t16， uxZPis valid and the back-EMF state is updated to uxZP. When i=2 or i=3 uxZPis invalid and the back-EMF state is maintained.

However,when the motor is lightly loaded or unloaded,the freewheeling process is very short. After filtering by the parasitic capacitance of the comparison circuit and the acquisition circuit, the freewheeling process collected by the FPGA is incomplete, and the detection method cannot be used.

Theoretically, for pump loads, the motor torque increases as the velocity increases. When the motor is lightly loaded at low speed, the IPA is also small. The fixed delay filtering method of the terminal voltage described in Appendix A is used to detect the back EMF. As the velocity of the motor increases, the freewheeling process is gradually clear due to the increase in load. Then the back-EMF detection method will be switched to the proposed detection method in Section 2.Through the analysis in this section, three conclusions can be obtained as follows:

(1) The ZCPs of back-EMF can be detected by comparing the non-energized terminal voltage with half of the bus voltage.

(2) The detection of back-EMF ZCPs without filter can be realized based on the timing sequence of uxZP.

(3) When diode commutation period is short, the proposed method is not applicable.

3. Proposed IPA control method

When the BLDCM commutates at the ideal commutation point, the voltage vector generated by the inverter is synchronized with the back-EMF. However, the phase inductance of BLDCM causes the current vector delay as shown in Fig. 3.In other words,even if the motor operates at the ideal commutation point, the IPA is not suppressed. Therefore, it is necessary to introduce a compensation angle φ for the motor to commute in advance, which is shown in Fig. 4.

It can be derived from Refs.17,20–21that when the IPA is eliminated by introducing the advanced angle φ, the midpoint of the phase current non-conducting region is the ZCP of the corresponding back-EMF, which means Δt1=Δt2as shown in Fig. 4. According to this rule, the compensation angle can be obtained by the difference between Δt1and Δt2to reduce the IPA.However,the midpoint detection of the phase current non-conducting region requires three additional phase current sensors. Moreover, the regulation of the motor rotational velocity affects Δt1and Δt2, which causes Δt1≠Δt2even if the IPA is zero. Fortunately, an interesting feature of the terminal voltage can solve the above two problems. The new method proposed in this paper is not affected by the velocity regulation and without additional current sensors.

Taking the non-energized phase C as an example, when iccompletes the diode freewheeling, S1is the triangular area Fig.3 Relationship between back-EMF and phase current when motor is ideally commutated.composed of the terminal voltage and half of the bus voltage before the back-EMF ZCP, and S2is the triangular area after the back-EMF ZCP as shown in Fig.3 and Fig.4,respectively.

Fig. 4 Relationship between back-EMF and phase current.when IPA is suppressed.

When the motor speed is ω1, S1is expressed as

The difference of the two areas can be obtained as

It can be seen from Eq. (9) that there is no direct relationship between the areas and the motor speed.Under the premise that the IPA has been eliminated,when the motor speed is constant, we have ω1= ω2and Δt1=Δt2. Thus, Δφ1=Δφ2is obtained. Then we can obtain that ΔS=0 according to Eq.(9). But, when the motor speed is regulated, the value of ΔS is difficult to obtain directly since ω1≠ω2and Δt1≠Δt2. However, there is a special relationship between Δφ1and Δφ2.

Because the back-EMF is a symmetrical trapezoidal wave,the ZCP of the back-EMF is the midpoint of the π/3 commutation process. According to Fig. 4, Eq. (10) and Eq. (11) can be obtained.

where φ1is the lead angle when the motor speed is ω1,and φ2is that when the motor speed is ω2.

In order to get the relationship between Δφ1and Δφ2, the relationship between φ1and φ2needs to be obtained. It has been derived in the previous work18that the theoretical lead angle is only related to the parameters and the load of the motor, which is demonstrated in Appendix B for the sake of conveniently reading.The motor parameters can be considered constant in a short time scale, because the parameters change slowly, such as temperature. Therefore, the theoretical lead angle is approximately only related to the load torque during the adjacent conduction period16,18.

Since the load of a high-speed BLDCM is usually a pump with a smooth load change, the theoretical lead angle can be approximately constant between t3and t5in Fig. 4. It means that φ1=φ2. According to Eq. (10) and Eq. (11), we can obtain that Δφ1= Δφ2. In this case, it can be obtained from Eq. (9) that ΔS=0.

In summary, the IPA of the motor can be reduced according to the difference between S1and S2for a typical pump load.First,ΔS and zero are used as the feedback and reference of a PI regulator,respectively. Then,the lead angle φ is calculated based on the results of the PI regulator, and finally the commutation point is advanced to reduce the IPA.

It can be seen from Eqs.(7),(8)and(9)that only the motor terminal voltage and the half bus voltage are involved during the calculation of S1, S2and ΔS. When the three-phase windings of the motor are symmetrically and evenly distributed,and the power devices adopt the same type devices and drive circuits, and the heat sink is shared, it can be approximated that the phase current, phase inductance, phase resistance,and the voltage drop of power device will not affect the calculation result. In addition, although the actual back-EMF of BLDCM is generally not an ideal trapezoidal back-EMF, the Fourier decomposition of the actual back-EMF can still be expressed as Eq. (4). Only the fundamental and harmonics amplitudes of the actual back-EMF are different from those of the ideal back-EMF, and the amplitudes do not affect the calculation result ΔS=0 in Eq. (9). Without considering the magnetic saturation, as long as the three-phase windings are guaranteed to be symmetric, ΔS=0 is effective when the IPA is reduced.

This idea has the following two benefits:

(1) The idea is suitable for the actual non-ideal back-EMF and is insensitive to the inductance parameters of motor.

(2) No phase current sensor is involved.

The overall control block diagram is shown in Fig.5,where the proposed IPA control is highlighted in blue background.The functions of each module are described as follows.

‘‘Comparison circuit”:it is used to get the uxZP（x = a，b，c)states by comparing the terminal voltage with U/2 through comparators.

‘‘Zero-crossing judgement”: the module is used to obtain the valid back-EMF ZCP signal ‘‘ZCPx” .

‘‘Integral logic”:it is adopted to calculate S1and S2according to Eq. (7) and Eq. (8).

‘‘Delay calculation”: the module is used to generate π/6 electrical degrees delay.

‘‘Logic synthesis”:this module generates drive signals of T1 to T6 according to the desired commutation angle θcand the back-EMF ZCP signal ‘‘ZCPx”. For example, when ‘‘ZCPx”is ‘‘101” and the corresponding zero crossing point is delayed by θc, T5 is turned off, and T1 and T6 are turned on.

The flowchart of the detection process is shown in Fig. 6.

Firstly, uxZP（x= a，b，c) is detected by ‘‘Comparison circuit”. Secondly, the back-EMF ZCP of the non-conducting phase is extracted by the ‘‘Zero-crossing judgement”. Thirdly,‘‘Integral logic” calculates S1and S2. Then, ΔS is calculated and used as the feedback of the discrete PI controller, and the output of the PI controller is adopted as the advanced angle φ .The desired commutation angle θcis got by delaying the ZCP of the back-EMF by π/6-φ electrical degrees.Finally, the motor commutation is controlled by the ‘‘Logic Synthesis” module according to θc.

The following points should be noted.

The first point is that the control frequency of the PI controller in Fig. 5 is equal to the commutation frequency of BLDCM. When the commutation frequency increases, the integration time of PI becomes shorter. Therefore, in order to ensure that the integral coefficient of the PI controller is constant, the integral coefficient of the PI controller is constant,and the integral coefficient of the motor should be inversely proportional to the commutation frequency.

Fig. 6 Flowchart of detection process.

The second point is that,the proposed method is not applicable when the three-phase back-EMFs are asymmetric. The eccentricity between the stator and the rotor is the main reason of the three-phase back-EMF asymmetry, because the magnetic flux is continuous. However, in the process of motor machining and assembly, the guarantee of concentricity is a key technological process, and its accuracy has strict factory inspection standards. The probability of three-phase back-EMF asymmetry is low.

The third point is that,this method needs to work under the premise that the voltage generated by the inverter leads the back-EMF by within 30°. The relationship among the leading angle, freewheeling time, motor parameters, power supply voltage and motor operating conditions will be studied in the following work.

Fig. 5 System overview of proposed method.

4. Simulation

Since the IPA is not easy to observe in real time in the experiment, it is necessary to observe the characteristics of IPA under different control methods through simulation.

The simulation model is built in the MATLAB/Simulink environment to verify the proposed IPA control strategy.The simulation model is consistent with Fig. 5, except that the buck circuit is replaced by a controllable voltage source.The motor model is built based on a 209 W BLDCM, and the motor parameters are shown in Table 2. High-speed sensorless BLDCMs typically drive the pump whose velocity and torque vary smoothly, thus applying a ramp-based speed reference and load torque curve to the motor model.

The simulation waveforms are shown as Figs. 7–10, in which (a) shows the simulation waveforms of the traditional method and (b) shows the simulation waveforms of the proposed method under different torques and speeds,respectively.φDis the value of the IPA.

Table 2 Specifications of BLDCM.

Fig. 7 Simulation waveforms under 10000 r/min, 0.04 N.m.

Fig. 8 Simulation waveform under 10000 r/min, 0.08 N.m.

Fig. 9 Simulation waveforms under 20000 r/min, 0.04 N.m.

It can be seen that S1

By comparing Fig. 7(a) with Fig. 8(a), the average IPA increases as the torque increases under the traditional method.Under the proposed method, the average value of IPA is always approximately 0, regardless of the change in load torque as shown in Figs. 7(b) and 8(b). This conclusion can also be verified by Fig. 9 and Fig. 10.

Fig. 10 Simulation waveform under 20000 r/min, 0.08 N.m.

Table 3 Advanced angle simulated by proposed method.

It can be seen from Figs. 8(a) and 10(a) that the average IPA is less affected by the change in motor speed under the traditional method.Under the proposed method,the average IPA is always approximately 0, which is also not affected by the change in motor speed as shown in Figs. 8(b) and 10(b). It can also be obtained by Fig. 7 and Fig. 9.

The average advanced angle φavgby the proposed method is shown in Table 3, and it can be found that φavgis mainly related to the load torque and is less affected by the rational velocity.

Considering that the permanent magnet is easy to demagnetize at high temperature, we simulate the waveforms when the permanent magnet is gradually demagnetized by 20%with the proposed control method. The motor’s given speed and load torque are constant, respectively 20000 r/min and 0.08 N.m.It can be seen from Fig. 11 that the lead angle (φ) and phase current (ic) increase with the increase in the demagnetization degree of the permanent magnet. The areas of S1and S2remain the same, and the positive and negative peak-to-peak values of the IPA (φD) are approximately equal. This shows that when the motor parameters change, the lead angle will be automatically adjusted accordingly to ensure a better control effect.

5. Experiments and analysis

5.1. Experimental platform construction

In order to further verify the proposed method, a prototype was designed and manufactured.The parameters of the prototype BLDCM are shown in Table 2. The experimental platform consists of five parts: the designed drive control board,the high-speed BLDCM, a magnetic powder brake, a power supply and an oscilloscope, as shown in Fig. 12. The power supply provides power to the drive control board. The load is provided by the magnetic powder. The device connection of the designed PCB is shown in Fig. 13.

The FPGA(EP4CE6E22C8N) receives the three-phase terminal voltages uxM（x = a，b，c) and bus voltage Vdcsampled by two AD7357s through the SPI bus, and gets the ZCP of the back-EMF collected by the ‘‘Zero-Crossing Detection”(ZCD) circuit through the IO port. FPGA detects the back-EMF ZCP according to Table 1, and calculates ω, T30°(the time corresponding to 30°electrical angle) and ΔS. ΔS and ω are transmitted to the DSP (TMS320F28335). DSP generates a PWM signal to the buck circuit and calculates the advanced angle φ according to ω and ΔS.Then,DSP transmits the advanced time φ/ω to FPGA.The FPGA delays the back-EMF ZCP by the time of （T30°-φ/ω) to obtain the actual commutation point. The low on-resistance IRFB4410Z is selected as power transistor to reduce the conduction loss,and it has been proved in Section 2 that the voltage drop of current flowing through the on-resistance of the MOSFET has no effect on the proposed method.

The collection interface of FPGA mainly includes SPI and IO port. The SPI bus clock is 20 MHz, and the sampling frequency is 1 MHz. The acquisition frequency of IO port is 20 MHz.When the motor speed is 20000 r/min,the control frequency of DSP is 2 KHz.

In the experiment, the sampling time and application time should also be compensated. The delays of controller signal acquisition and signal transmission mainly include the software delay and the hardware delay. Software delay mainly contains delays of ZCP detection, AD acquisition, integration logic, logic synthesis and PI calculation. The hardware delay mainly includes delays of AD conversion, comparison circuit,drive circuit and power circuit. In the experiment, we use FPGA and DSP to complete the software. Among them, the PI calculation is undertaken by DSP,and the rest is completed by the FPGA. The clock frequency of FPGA is 40 MHz, and its software works can be finished in 8 clock cycles. The delay time is 200 ns. In PI calculation, DSP calculates φ of the next commutation point based on the current ΔS. This delay is determined by the working characteristics of the brushless DC motor and is related to the motor speed. When the motor operating condition is stable, PI calculation delay can be ignored. In terms of hardware delay, we adopt AD7357 with high-speed synchronous acquisition characteristics, whose sampling delay time is 3.5 ns. IR2130 is used as the drive circuit. Its typical turn-on delay time is 675 ns, and the typical turn-off delay time is 425 ns. The IRFB4410Z is adopted for power devices, its typical turn-on delay time is 16 ns, and the turn-off delay time is 43 ns. Based on the above analysis, the average delay time of software and hardware is 780 ns.Combined with 40 MHz clock of the FPGA,the software compensation time is designed to be 31 cycles.

Fig. 11 Simulation waveforms when permanent magnet is demagnetized by 20% at high temperature under 20000 r/min, 0.08 N.m.

Fig. 12 Functional block diagram of drive control board.

Fig. 13 Experimental setup.

It should be pointed out that, when the motor rotor is at a standstill, the proposed method will not be applicable. Therefore, we adopt a three-stage starting strategy to start the motor, under which the motor is rotated to a certain speed in the external synchronization stage11,22. When the speed reaches 3000 r/min, the system switches to the selfsynchronous operation state, and IPA control is introduced.In the IPA control process, the slope of the given speed ramp is set to 4000 r/s. However, there will be an engineering problem here,which is the surge current when switching from external synchronization to self-synchronization. Aiming at the surge current problem,we have sorted out the following ideas:In the external synchronization,the commutation angle is corrected in real time according to ΔS.When the motor reaches a certain speed, it is smoothly switched to self-synchronization.The idea will be studied in the future work.

5.2. Experimental result

Fig. 14 Experimental waveform under 10000 r/min, 0.04 N.m.

Fig. 15 Experimental waveform under 10000 r/min, 0.08 N.m.

The IPA is difficult to test directly in the experiment, whereas the IPA can be indirectly indicated by the relationship between S1and S2. The experimental results including traditional control and the proposed control are shown in Figs.14–17.In the waveforms, the blue line represents the neutral point voltage ush, which can be equivalent to terminal voltage; the pink line represents one-half of the bus voltage;the green line represents the phase current.

Fig. 16 Experimental waveform under 20000 r/min, 0.04 N.m.

Fig. 17 Experimental waveform under 20000 r/min, 0.08 N.m.

The diode freewheeling time has been marked in the experimental waveform. From Figs. 14–17, we can observe that when the load torque is higher, the diode freewheeling time is longer, and the bus voltage ripple of the buck circuit is higher.

From the red circles in Figs. 14–17, we can see that it is S1

Moreover, when the torque or the speed is too high, the phase current will lag behind the back-EMF at a large angle due to the motor inductance. At that time, there will be no intersection between the terminal voltage and the half bus volt-age. The back-EMF ZCP detection method will fail. In the case of the proposed method,the two voltages can be adjusted to be the same value regardless of speed and load, thereby reducing IPA. The experimental average advanced angles are shown in Table 4, which are consistent with the value shown in Table 3.

Table 4 Experimental advanced angle by proposed method.

Table 5 Comparison of experimental phase current RMS values.

The phase current RMS values are affected by the IPA.The comparison results of the phase currents RMS values are shown in Table 5. Compared with the traditional method,the phase current RMS values are reduced by the proposed method. As the velocity and load torque increase, the effect of current reduction becomes more obvious. In the case of 20000 r/min and 0.08 N.m, the copper loss of the BLDCM can be reduced by 7.2%. In Table 5, PCu1is the copper loss of the traditional method, PCu2is the copper loss of the proposed method, and ΔPCuis the percentage of copper loss reduction.

Fig. 18 Dynamic experimental waveform when motor accelerates from 1000 r/min to 4000 r/min.

Fig. 19 Dynamic experimental waveform when motor decelerates from 4000 r/min to 1000 r/min.

In order to verify whether the proposed method is still effective when the motor velocity and load change, we also conduct dynamic experiments. Due to the limitation of the loading platform and the motor, we adopt two identical lowspeed motors to carry out dynamic experiments, one of which is used as an electrical motor and the other is used as a generator.The output of the generator is connected to a three-phase symmetrical power resistance.

In the experiment, in order to explain the relationship between the three-phase terminal voltages and the half bus voltage more clearly,we connect the ground of the oscilloscope to half the bus voltage, and connect the oscilloscope probe to the three-phase virtual neutral point,which is ushin Fig.18 and Fig. 19. The neutral point voltage can represent the terminal voltage, and the intersection of the neutral point voltage and one-half bus voltage is the ZCP of the terminal voltage.

We accelerate motor speed from 1000 r/min to 4000 r/min,and then reduce the speed from 4000 r/min to 1000 r/min.The dynamic waveforms are shown in Fig. 18 and Fig. 19, from which we observe the relationship between the neutral point voltage and the phase current. In the waveforms, the blue line represents the neutral point voltage ush;the pink line represents one-half of the bus voltage U/2; the green line represents the phase current ic. It can be seen that the intersection (pink point)of the neutral point voltage and one-half of the bus voltage coincides with the midpoint of the phase current nonconduction area during acceleration and deceleration of the motor. And the area of the triangle formed by the neutral point voltage and one-half of the bus voltage before the intersection is equal to that after the intersection.

This experiment shows that the method proposed in this paper can maintain IPA at a low level during acceleration and deceleration of the motor. Therefore, when the motor speed and load change, the motor can still run stably.

6. Conclusions

In this paper, an IPA control strategy for the high-speed BLDCM is proposed.First,the accurate ZCPs are determined to eliminate position sampling errors. Then, the commutation compensation angle is calculated based on the integral characteristics of the non-energized terminal voltage which has completed diode freewheeling and the bus voltage. Finally, the motor is commutated in advance to reduce the IPA.Compared with other existing methods, the proposed strategy has two benefits.

(1) The phase current sensor is eliminated.

(2) The strategy is suitable for the actual non-ideal back-EMF of BLDCM and insensitive to the inductance parameters of the motor.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 51877006); the Key R&D Program of Shaanxi Province, China (No. 2021GY-340 and 2020GY-140); the Aeronautical Science Foundation of China(No. 20181953020).

Appendix A. Fixed delay filtering method of terminal voltageIn engineering, the fixed delay filtering method of terminal voltage is generally adopted to detect the back-EMF. This method is based on the principle that the high and low levels of the back EMF in the terminal voltage have a longer duration, while the level duration of the freewheeling process is shorter. Thus, a filter with a fixed delay time is designed in the FPGA. When the FPGA receives the edge change of the terminal voltage, it judges the duration of the level. When the duration exceeds the fixed delay time, the edge change is considered to be a valid back-EMF ZCP. We delay valid back-EMF ZCP by 30° electrical angle, plus the fixed delay time of the filter. Then the commutation point can be obtained. On the contrary, if the duration does not exceed the fixed delay time, the edge change can be considered as the interference caused by the freewheeling process. The level duration of the freewheeling process is related to the motor parameters, load and velocity. The maximum level duration of the freewheeling process can be calculated or tested, which can be used to design the fixed delay time of the filter.

The fixed delay filtering method is suitable for the unobvious freewheeling signal when the motor phase current amplitude is low. On the contrary, the detection of back-EMF ZCPs without filter is suitable for clear freewheeling signals,when the motor phase current amplitude is higher.

Under the topology adopted in the paper,the magnitude of the DC output current of the buck circuit is approximately equal to that of the motor phase current.The above two methods can be switched by judging the magnitude of the DC current.In order to avoid the frequent switching between the two methods, a comparator with hysteresis can be designed. It should also be pointed out here that the DC current fluctuates with the operation of the brushless DC motor,which will cause misjudgments. The following two current calculation methods can avoid the judgment fault.

Method 1Calculate the average value of the DC current in 1/6 of the electric cycle.

Method 2Detect the phase current at the midpoint of each conduction period.

Appendix B. Derivation process of theoretical advanced angleDuring the analysis in Section 3 of this paper,the final expression of advanced angle φ in Ref.18is referenced, which is only related to the phase current, inductance and magnetic flux of the motor.

According to the principle that the IPA is suppressed at the midpoint of the sector, the dynamic equation of the motor winding was given in Ref.18, as shown in