High-Precision Sensorless Drive for High-Speed BLDC Motors ...

1528 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 33, NO. 2, FEBRUARY 2018

High-Precision Sensorless Drive for High-SpeedBLDC Motors Based on the Virtual Third

Harmonic Back-EMFXinda Song , Bangcheng Han, Shiqiang Zheng , Member, IEEE, and Jiancheng Fang

Abstract—In order to improve the performance of the high-speed brushless direct current motor drives, a novel high-precisionsensorless drive has been developed. It is well known that the in-evitable voltage pulses, which are generated during the commuta-tion periods, will impact the rotor position detecting accuracy, andfurther impact the performance of the overall sensorless drive,especially in the higher speed range or under the heavier loadconditions. For this reason, the active compensation method basedon the virtual third harmonic back electromotive force incorporat-ing the SFF-SOGI-PLL (synchronic-frequency filter incorporatingthe second-order generalized integrator based phase-locked loop)is proposed to precise detect the commutation points for sensor-less drive. An experimental driveline system used for testing theelectrical performance of the developed magnetically suspendedmotor is built. The mathematical analysis and the comparable ex-perimental results have been shown to validate the effectiveness ofthe proposed sensorless drive algorithm.

Index Terms—High-speed brushless direct current (BLDC),phase-locked loop (PLL), sensorless drive, virtual third harmonicback electromotive force (back-EMF).

I. INTRODUCTION

IN RECENT years, owing to the advantages of its compact-ness, maintenance, high efficiency, and low cost, the brush-

less direct current (BLDC) motors are getting more and moreattention in many areas like the blower and compressor, espe-cially in the high-speed applications [1]–[3]. Commonly, thespeed of the high-speed motor could reach up tens of thou-sands revolutions per minute (r/min) according to the bearing

Manuscript received September 1, 2016; revised November 17, 2016 andFebruary 11, 2017; accepted March 20, 2017. Date of publication March 28,2017; date of current version November 2, 2017. This work was supported inpart by the National Key Research and Development Program of China underGrant 2016YFB0500804, in part by the National Major Project for the Devel-opment and Application of Scientific Instrument Equipment of China underGrant 2012YQ040235, and in part by the National Natural Science Foundationof China under Grant 61421063. Recommended for publication by AssociateEditor I. Slama-Belkhodja. (Corresponding Author: Bangcheng Han.)

X. Song, B. Han, and S. Zheng are with the School of Instrumentation Sci-ence and Opto-electronics Engineering, Beihang University, Beijing 100191,China, and also with the Beijing Engineering Research Center of High-Speed Magnetically Suspended Motor Technology and Application, Beijing100191, China (e-mail: [email protected]; [email protected];[email protected]).

J. Fang is with the School of Instrumentation Science and Opto-electronics Engineering, Beihang University, Beijing 100191, China (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2017.2688478

[4], [5]. Meanwhile, the load power of the motor developed forthe blower type applications is increasing with the motor speed[6]. Therefore, precise detecting of the rotor position for the sen-sorless drive scheme is essential to ensure the high efficiencyand low loss of the overall system, especially in the high-speedrange.

It is well known that for the operation of the inverter in theBLDC control system, six discrete rotor position signals in onerotating cycle are required. Conventionally, the rotor positiondetecting methods can be classified into two categories: themechanical position sensor-based methods and the sensorlessmethods. The typical sensors include the resolver [7], the en-coder, [8] and the Hall-effect sensor [9], which are traditionallyused in the mechanical position sensor-based methods. How-ever, these mechanical sensors need special arrangements to bemounted as well as increasing the cost, which limits the applica-tion in the high-speed motors. Hence, more and more researchesare focused on the sensorless-based methods.

Numerous of sensorless-based methods have been reported inthe preresearches, which mainly contain the back electromotiveforces (back-EMFs)-based method, the third harmonic-basedmethod, the integration-based method, the phase-locked loop(PLL)-based method, the flux linkage estimation-based method,and the other sensorless method. Among the sensorless drivemethods, the most popular category is the back-EMF-basedmethod. The back-EMF sensorless method is firs proposed byKenichi Iizuka through extracting the back-EMF zero cross-ing points (ZCPs) of the terminal voltage [10]. On this basis,many sensorless methods based on the terminal voltage havebeen developed, and obtained good performances in the certainapplications [11]–[13]. However, since the back-EMF is verysmall when the motor’s speed is nearly zero, the performance ofthe sensorless method based on the terminal voltage back-EMFis still not satisfied, especially in the high-speed motor applica-tions, where the phase resistance and phase inductance are muchsmall. The third harmonic-based methods provide a better solu-tion, in which the commutation points can be extracted from thethird harmonic of the back-EMF. Moreira [14] pointed that thethird harmonics of the back-EMF kept a constant phase relation-ship with the rotor flux for any motor speed and load condition,and a sensorless commutation control had been developed in awide speed range. Francesco Bonanno used the third harmoniccomponent of the stator voltage to estimate the air-gap flux and

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SONG et al.: HIGH-PRECISION SENSORLESS DRIVE FOR HIGH-SPEED BLDC MOTORS BASED ON THE VIRTUAL THIRD 1529

the torque in the DSC scheme for induction motor drive [15]. Anapplication of third harmonic back-EMF-based sensorless rotorposition estimation has been demonstrated to both BLDC andBLAC motor in [16], and the proposed method is utilized in theflux-weakening mode successfully. Liu and Zhu [17] proposeda rotor position estimator based on the continuous signal of thethird harmonic back-EMF for permanent magnet synchronousmotor sensorless control system, and the proposed estimatorachieved accurate rotor position estimation and obtained out-standing dynamic performances. However, the applications ofthe methods mentioned above are usually in the low-speed mo-tor applications. In addition, the large noise interference limitsits application. Another category is the integration-based sensor-less method. The back-EMF integration method is used in [18]to extract the rotor position by integrating the back-EMF of theunexcited phase. In [19], a Kalman filter is used in a back-EMFintegration-based sensorless method for reluctance machines tosmooth the noise. Nevertheless, an error accumulation problemat low-speed range impacts its performance. Moreover, most ofthe aforesaid methods need the neutral wire in the sensorlesscontrol. However, the neutral wire is usually not provided tomost of the BLDC motors. In [20], based on the virtual neutralvoltage, a sensorless rotor position detecting method has beenutilized. However, the performance in the high-speed range isnot mentioned. Cui proposed a hybrid sensorless drive methodfor the high-speed BLDC motor based on the virtual neutralvoltage in [21]. Although the proposed sensorless method ob-tained satisfied performance in a wide speed range, the commu-tation error resulting from the freewheel diode conduction is notdiscussed.

On the other hand, the commutation error is one of the mostconcerning problems in the BLDC motor dive system, sinceit has drawbacks of the inaccurate hardware parameters, dif-ferent load conditions, and the variable operating temperature,especially in the high-speed applications. As a result, manyefforts have been done to limit the commutation errors in thepreresearches. An error-compensation circuit is proposed tocompensate the commutation error in [22]. But the high-speedperformance is not mentioned. In [23], a fuzzy model-basedestimator for the error of the estimated position angle and theclosed-loop compensation method are proposed, while the er-ror of the estimated position angle is decreased to 2%. Yet theestimation algorithm is complicated for the high-speed motorcontrol scheme. A hysteresis comparator is applied to compen-sate the commutation error in [24]. However, the performance ofthe compensation method in high-speed range and under heav-ier load conditions are not mentioned, although the proposedmethod presents a good performance in a wider speed range. In[25], a straightforward method of the commutation angle self-compensation based on the dc-link current is utilized with a goodperformance in a large speed range. Unfortunately, the mechan-ical hall-effect sensors are used in this research and the reliableof the method is limited. In [26], a closed-loop compensationmethod based on the integration difference of the virtual neu-tral voltage is proposed to compensate the commutation errors,and obtained satisfied performance in a wide speed range. How-ever, the impact of the voltage pulse due to the freewheel diode

conduction is not discussed deeply. Another popular technicalin high-speed applications is the PLL-based method, which hasthe advantages as simplicity, robustness, and effectiveness. Shen[27] proposed a sensorless control method based on the PLL andthe third harmonic back-EMF integration in an ultrahigh-speedrange. The commutation error is significantly reduced by theproposed ASIC-based sensorless controller, whereas the neutralwire is needed to obtain the third harmonic back-EMF. As a con-clusion, to the best of the authors, the proper sensorless controlmethod for the wide speed range BLDC motors has not beenfully investigated in the previous researches, which meets the re-quirements of compensating the commutation error adaptively,does not need neutral wires, and operating in the high-speedrange under various load condition simultaneously.

The main contribution of this paper is that a novel high-precision sensorless drive method for BLDC motors is proposed.The proposed method can compensate the commutation erroradaptively in a wide operating range, and does not need theneutral wire at the mean time. In order to catch the accuratecommutation points, an SOGI-PLL (synchronic-frequency fil-ter incorporating the second-order generalized integrator basedphase-locked loop) incorporating the virtual third harmonicback-EMF scheme is used in the proposed method. Meanwhile,a synchronic-frequency filter (SFF) is put up as a prefilter toimprove the performance of SOGI-PLL. Thus, the rest of thispaper is organized as followS. In Section II, the control schemeof the high-speed BLDC motor drive system in the wide speedrange is first briefly introduced. Then, the traditional sensorlessdrive method based on the virtual third harmonic back-EMF isshown, as well as the commutation error analysis. Section IIIpresents the main idea of the proposed high-precision sensorlessdrive based on the high-precision commutation points detection.The experimental setup is given in Section IV, and the experi-mental results are illustrated to validate the effectiveness of theproposed method. Moreover, some important conclusions canbe found in Section V.

II. ORIGINAL SENSORLESS DRIVE METHOD OF HIGH-SPEED

BLDC MOTORS

A. Control Scheme of High-Speed BLDC Motors

The typical applications of the high-speed BLDC motor con-tain the aeration blower for sewage treatment and the air com-pressor. The feature of the applications is that the motor’s loadis increased with the rotating speed. On another hand, since thespeed range of the high-speed motor is always above tens ofkr/min, the winding inductance and resistance of the high-speedmotor are always much lower than the traditional low-speed mo-tors. Therefore, a hybrid control scheme is used in this paper,which combing the pulsewidth modulation (PWM) techniqueand the pulse-amplitude modulation (PAM) technique [29]. ThePWM technique is applied in the start stage and the low-speedrange to overcome the large phase current. With the speed in-creasing, the back-EMF is gradually becoming higher. Whenthe value of back-EMF is large enough, which can counter-act the dc-link voltage, the PAM technique is adopted. Underthe PAM control in the high-speed range, the 60° commutation

1530 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 33, NO. 2, FEBRUARY 2018

Fig. 1. Diagram of the motor drive circuit.

control is used and the speed of the rotor is regulated by ad-justing the dc-link voltage. The advantage of the hybrid controlscheme combing PWM and PAM is that the scheme guaranteesthe efficient operation of the high-speed BLDC motor in thewide speed range.

B. Sensorless Drive Method Based on the Virtual ThirdHarmonic Phase Back-EMF

The diagram of the motor drive circuit is shown in Fig. 1.As can be seen in Fig. 1, three signals (Hall A, Hall B, Hall C)are needed for the commutation operations of the three-phasevoltage source inverter (VSI) through the commutation logicand the drive circuit. In the mechanical position sensor-basedcontrol method, these three signals are obtained by the hallsensors. In the sensorless drive methods, these three signals areobtained through the sensorless detecting method.

As shown in Fig. 1, the three Y-connected resistors are usedto detect the rotor position signal. In the preresearches, themost popular technique to obtain the rotor position signal is touse the voltage between the neutral point “N” and the virtualneutral point “S” (uSN ), which is the so-called third harmonicback-EMF method. However, the neutral wire is not provided orexpensive to have access in many applications. Therefore, thevirtual third harmonic back-EMF method is discussed in [14],where the rotor position signal is acquired from the voltagebetween the virtual neutral point “S” and the midpoint of thedc-link “P” (uSP ).

According to Fig. 1, the phase back-EMFs can be describedas

⎧⎪⎨

⎪⎩

eA =√

2E cos(ωt)

eB =√

2E cos(ωt − 2π/3)

ec =√

2E cos(ωt + 2π/3)

(1)

where E is the back-EMF virtual value.By a simple calculation based on the Kirchhoff’s voltage law,

usp can be expressed as

usp =uAG + uBG + uCG

3− ud

2(2)

Fig. 2. Relationships between the phase back-EMFs, the third harmonic back-EMF, usp , and the commutation points.

where ud is the dc-link voltage.In the six-step inverter operation sequence, each stage con-

tains two periods: the commutation period and the normal con-duction period. Take the stage of the current transfer from phaseC to phase A for instance. During the commutation period, VT2is switched off and VT4 is switched on. Because of the phaseinductance, the current of the excited phase (phase A) cannotbe completed built immediately. Then, simultaneously, VT3,VT4, and D5 are conducted in the commutation period. At thesame time, the terminal-to-ground voltages can be expressed asuAG = 0, uBG = ud , and uCG = ud . Combining (2), usp canbe written as usp = 1/ 6ud . In the normal conduction period,only VT3 and VT4 are conducted, leading to completely cur-rent establishment of the excited phase (phase A). So, uAG = 0,uBG = ud , and uCG = eC + uNG . Combining (2), usp can beexpressed as

usp =13

(

eC − eA + eB

2

)

. (3)

Since the same situations occur in the other stages, the fre-quency of usp is three times as that of the phase back-EMF,which means that usp has the same ZCPs as the third har-monic back-EMF. Fig. 2 illustrates the relationships between thephase back-EMFs, the third harmonic back-EMF, usp and thecommutation points.

As can be seen in Fig. 2, the frequency and the ZCPs of usp arethe same as that of the third harmonic back-EMF. Contrastingwith usn , usp is different with the third harmonic back-EMFof the phase back-EMFs because the derivation contains nothird harmonic back-EMF component. Therefore, for strictlyspeaking, this sensorless drive method cannot be called as thethird harmonic back-EMF-based method. For facility analysis,it can be called as the virtual third harmonic back-EMF-basedmethod, and usp can be called as the virtual voltage difference.Traditionally, the ZCPs of usp can be detected by commutation

SONG et al.: HIGH-PRECISION SENSORLESS DRIVE FOR HIGH-SPEED BLDC MOTORS BASED ON THE VIRTUAL THIRD 1531

Fig. 3. Performances of the virtual voltage difference (usp ). (a) Advancedcommutation operation; (b) lagged commutation operation; (c) common com-mutation operation in low-speed range; and (d) common commutation operationin high-speed range.

signals detection circuits, which are usually mainly consisted ofa low-pass filter and a voltage comparator.

C. Analysis of the Commutation Error

When advanced commutations or lagged commutations ap-pear, the accuracy of the commutation points detection will beinfluenced, which can be seen in Fig. 3(a) and (b). In order

to compensate this kind of commutation error, the integration-based compensation method has been proposed in prior research[26]. It can be seen that in Fig. 3, in this kind of compensationscheme, usp is integrated from the occurrence of the first com-mutation point to the occurrence of the second commutationpoint (Sprior), and from the occurrence of the second commu-tation point to the occurrence of the third commutation point(Safter), respectively. It can be noted that the advanced commu-tation is reflected by Sprior > Safter , and the legged commuta-tion is reflected by Sprior < Safter . When the two integrationsare equal (Sprior = Safter), the ZCPs of usp are regarded asaccurate. And then the commutation error is corrected, whichcan be seen in Fig. 3(c). A PI adjustor is always used to controlthe difference between Sprior and Safter , and the aim of the PIadjustor is Sprior − Safter = 0.

However, usp actually contains pulses during the commuta-tion period due to the freewheel diode conduction. The integra-tion of the voltage pulse will be always added into Safter , whichwill make Safter always larger than Sprior when the accuratecommutation appears. But the output value of the PI adjustorwill be regulated to achieve Sprior = Safter . For this reason,Sprior increases and Safter decreases. As a result, the little ad-vanced commutation occurs. This problem is not seriously in thelow-speed range because the time of the commutation period (tc )is short and the advanced degree is small in the low-speed range,which can be seen in Fig. 3(c). Nevertheless, the voltage pulsewill appear wider in the high-speed range as shown in Fig. 3(d).According to the analysis in [26], the time of the commutationperiod can be written as

tc = −τ ln13

(ud + 3

√2

2 E)

IoR + 13

(ud + 3

√2

2 E) (4)

where τ = (L − M)/R is the time constant, Io is the ini-tial current of the conducting phase in the beginning of thecommutation.

It can be noted that from (4), the first reason of tc becominglonger in the high-speed range is that the load of the motor be-coming heavier in the high-speed range. So the current of theexcited phase takes long time to build. The second reason isthat the fundamental cycle is relatively short in the high-speedrange. As a result, in the high-speed range, the voltage pulseswill remarkabley impact the accuracy of the commutation pointdetection. Based on the aforesaid discussion, the conclusion canbe obtained that the performance of the virtual third harmonicback-EMF-based sensorless drive method and the integration-based compensation method cannot be satisfied for the high-speed BLDC motor applications. Therefore, a proper sensorlessdrive and commutation error compensation method for thehigh-speed BLDC applications should be developed.

III. PROPOSED SENSORLESS DRIVE BASED ON

HIGH-PRECISION COMMUTATION DETECTION

According to the aforesaid analysis, the virtual voltage dif-ference (usp ) has the same frequency and ZCPs as that of the

1532 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 33, NO. 2, FEBRUARY 2018

Fig. 4. usp and the fundamental wave of usp .

third harmonic back-EMF. On this basis, a novel high-precisionsensorless drive method is proposed in this section.

A. Further Discussion of usp

It can be noted in Fig. 3(c) and (d) that, in the commoncommutation operation, usp is very similar with a triangle-wave.Thus, if neglecting the pulse in usp (since the frequency andthe ZCPs cannot be changed), incorporating Fig. 3, usp can beapproximately expressed as

usp(t) =

⎧⎨

⎩

−(

A2 + A

T0 /2 t) (−T0

2 ≤ t ≤ 0)

−(

A2 − A

T0 /2 t) (

0 ≤ t ≤ T02

) (5)

where A is the amplitude of the triangle-wave, T0 is the cycletime of the triangle-wave.

By a Fourier decomposition, (5) can be obtained as

usp(t) =

−

⎛

⎜⎜⎜⎜⎝

4A

π2 cosω0 t︸ ︷︷ ︸

u s p 1 (t)

+4A

π2

[∑n

i=1

1(2n + 1)2 cos(2n + 1)ω0 t

]

︸ ︷︷ ︸u s p h ig h (t)

⎞

⎟⎟⎟⎟⎠

(6)

where usp 1(t) is the fundamental component of usp(t),usp high(t) is the sum of the high-order harmonic componentsof usp(t).

It is interesting to note that usp is also consisted of the funda-mental wave and high-order harmonics from (6). Fig. 4 showsusp and the fundamental wave of usp in one plot (the high-orderharmonics are not shown since they are not used in the follow-ing analysis). Therefore, according to the aforesaid analysis, thefundamental wave of usp has the same frequency and ZCPs asthe third harmonic back-EMF. It should be pointed out that theapproximation of usp above will not change the frequency andZCPs of usp , since the unconsidered distortion can be consid-ered as the others harmonics of usp , which will not change thefrequency and ZCPs of usp . In another word, the time of thecommutation period (tc) will not impact the ZCPs of usp 1(t). Itis to say that the equivalent ZCPs of usp can be obtained withoutthe impaction of the length of tc . It also should be pointed thatthe usp wave will not change with the selection of the axis. If the60° point in Fig. 4 is selected as the zero point of the horizontal

Fig. 5. Block diagram of the single-phase PLL based on SOGI.

axis, the minus sign in functions (5) and (6) can be eliminated.Therefore, in order to simplify the followed analysis, the minussign is eliminated in the followed discussion.

B. Proposed High-Precision Commutation Points DetectingMethod

Based on the aforesaid analysis, if the fundamental wave ofusp (usp 1(t)) can be exactly extracted, the precise ZCPs of uspcan be obtained, so as the commutation points. Hence, it attractsthe authors to give a suitable process to extract the precise ZCPsby using the fundamental wave of usp for the efficient sensorlessdrive in the wide speed range. Meanwhile, the proposed sensor-less drive will not be impacted by the voltage pulse in the widespeed range. In order to achieve this purpose, a hybrid signalprocessing has been used in the proposed sensorless method.

1) PLL Processing: The PLL technique has been widelyused in many industry applications, and also has the satisfiedperformance in high-speed motor drive system. Owing to theadvantages like simple digital implementation, desired perfor-mance under frequency condition, and low computation burden,the PLL based on SOGI has been received much attention re-cently [30]. So, the single-phase SOGI-PLL technique is usedin the proposed process, which aims to synchronize the outputsignal with the input signal as well as acquire the rotor positioninformation.

Fig. 5 shows the block diagram of the single-phase PLL basedon SOGI. The SOGI-PLL consists of the phase detector (PD),the loop filter (LF), and the voltage controlled oscillator (VCO).The SOGI, which is contained in the PD, is used to generate theorthogonal signals.

By using a simple mathematical calculation, the characteristictransfer functions of the SOGI can be expressed as

Gα (s) =vα (s)vin(s)

=kω̂s

s2 + kω̂s + ω̂2 (7)

Gβ (s) =vβ (s)vin(s)

=kω̂2

s2 + kω̂s + ω̂2 (8)

where k is the damping factor (usually a constant term), and ω̂is the estimated frequency (ω0 is the fundamental frequency ofthe input signal).

It can be noticed that Gα (s) exhibits as a band-pass filter witha center frequency of ω̂ from (7). The damping factor k deter-mines the pass-band of Gα (s). The lower k leads to a narrowerbandwidth and better filtering capability. Meanwhile, Gβ (s)

SONG et al.: HIGH-PRECISION SENSORLESS DRIVE FOR HIGH-SPEED BLDC MOTORS BASED ON THE VIRTUAL THIRD 1533

exhibits a low-pass filtering behavior. If ω̂ = ω0 , vα (s) willmatch in amplitude and in phase with the fundamental wave ofthe input signal of PLL (vin(s)). And vβ (s) will match in am-plitude but with a phase difference of 90° with the fundamentalwave of the input signal of PLL (vin(s)) under the same condi-tions. Assuming that vin = A0cosω0t, and combining (7) and(8), the output signals of the SOGI block (vα (s) and vβ (s)) canbe derived as

vα (s)=A0cos ω0t+Aαcos(ω0

√1 − 0.25k2t

)e−0.5kω0 t

(9)

vβ (s)=A0sin ω0t+ Aβ sin(ω0

√1 − 0.25k2t

)e−0.5kω0 t

(10)

where Aα and Aβ are the functions of A0 and k, respectively.So considering Fig. 5 and combining (9) and (10), the output

signal of the PD can be expressed as (11) at the bottom of thispage.

In steady state (ω̂ = ω0), the output signal of the PD decaysto zero (ε(s) = 0), which can be calculated from (11). Whereasif the input signal of PLL (vin ) contains large harmonics like theexpression as (6), the output signal of the PD [ε(s)] will containa harmonic component in steady state, which can be written as

εhigh(s) =n∑

h=2

Ahsin hωht cos ω̂t −n∑

h=2

Ahsin(

hωht +hπ

2

)

sin ω̂t.

(12)

The harmonics components (εhigh(s)) will cause the band-width of the LF to be smaller, which will deteriorate the transientresponse [28]. Moreover, it becomes severe in the low-speedrange. In this case, it is necessary to filter out the high-orderharmonics of the SOGI-PLL’s input signal. In this paper, theinput signal of SOGI-PLL is usp . From the aforesaid discus-sions, usp contains large odd harmonic components. As a re-sult, a novel signal processing is applied to limit the high-orderharmonics.

2) SFF Processing: The block diagram of SFF is demon-strated in Fig. 6, which is used as the prefilter of SOGI-PLL[31]. In Fig. 6, Xin and Xout are indicated as the input andoutput signals of the SFF, respectively. a is the constant gain,sin (θ̂) and cos (θ̂) are the reference signals, where the phasedifference between them is 90°. The SFF has the character ofprecisely extracting the fundamental wave from the input signal(Xin ), which is illustrated in the following analysis.

Fig. 6. Block diagram of SFF.

Assuming that the input signal (Xin ) contains harmoniccomponents, it can be expressed as

Xin = xin(t) = V0sin(ω0t + ϕ0)︸ ︷︷ ︸

X 1

+∑

Vhsin(ωht + ϕh)︸ ︷︷ ︸

Xh ig h

(13)where V0 , ω0 , and ϕ0 are the amplitude, frequency, and the phaseof the fundamental component of Xin , respectively; Vh , ωh andϕh are the amplitude, frequency and the phase of the h-orderharmonic component of Xin , respectively; X1 and Xhigh are thefundamental and h-order harmonic components, respectively.

According to Fig. 6, the output signal Xout can be derived as

Xout = sin(θ̂)a∫ [

(X1 + Xhigh)sin (θ̂)]

+ cos (θ̂)a∫

[(X1 + Xhigh)cos (θ̂)

]. (14)

It is noted that x1(t) and x2(t) contains the direct currentcomponents and the ac components. During the integral pro-cessing, the correlation theorem can be used, which can filterout the ac components. Thus, combining with (12) and (13), theac components contained in x1(t) and x2(t) can be filtered outby using of the integrate processing. So the output signal of theSFF (Xout) can be obtained as

Xout = 0.5V0 sin (ω0t + ϕ0). (15)

Compared with (13) and (15), it can be focused that the outputsignal of the SFF (Xout) has the same frequency, the samephase and 0.5 times of the amplitude with the input signal ofthe SFF (Xin ). In another word, although the amplitude of Xoutis smaller than Xin , the fundamental wave can be extracted byusing the SFF, precisely. The amplitude can be easily adjustedby adding a constant gain to Xout . The closed-loop transferfunction of the SFF can be expressed as

H(s) =as

s2 + as + ω20

. (16)

It can be noted that, when s = jω0 , the gain of H(s) equalsto 1. It indicates that the fundamental wave of Xin can passthe SFF without attenuation. When s = jωh , the sharpness

ε(s)=vβ (s)cos ω̂t−vα (s)sin ω̂t=A0sin(ω0−ω̂t)−[Aαcos (ω0

√1−0.25k2t)sin ω̂t−Aβ sin(ω0

√1 − 0.25k2t)cos ω̂t

]e−0.5kω0 t

(11)

1534 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 33, NO. 2, FEBRUARY 2018

Fig. 7. Proposed active compensation block diagram based on incorporating SOGI-PLL with SFF.

of the SFF can be adjusted by the factor a. The gain of (16)is depended on a, which equals to the inverse of the quality-factor. In the startup range (nearly zero speed), the real part ofthe poles is small (= 0.015), which means that the stabilitymargin of the SFF is small in the very low-speed range. Soit can be considered that the SFF is stable in the whole speedrange. Additionally, according to (16), the SFF behaves as a low-pass filter when ω0 = 0 (zero speed), and behaves as a SFF aslong as ω0 �= 0, even with very low speed as ω0 = 0.1 Hz(6 r/min for one pole pairs motor). In addition, the sharpnessof the SFF is growing with the motor speed increasing, whichmeans the effectiveness of the SFF is rising in the high-speedrange. As a result, the proposed SFF filter is stable in the wholespeed range with satisfied extraction characteristics of operatingfrequency.

3) Incorporating SOGI-PLL With SFF: From theaboveaforesaid discussion, a novel sensorless drive method,which is based on the single-phase SOGI-PLL incorporatingthe SFF, is proposed. The whole block diagram of the proposedcompensation is shown in Fig. 7.

As can be seen in Fig. 7, an SFF is located at the upstreamof the single-phase SOGI-PLL to prefilter the harmonic compo-nents, which is contained in the input signal (usp ). The referencesignals of the SFF (sin (θ̂) and cos (θ̂)) are generated by usingthe estimated rotor position angle naturally, which is producedfrom the output signals of the SOGI-PLL. Besides, the referencesignals are returned to the SFF by two feedback paths. The ref-erence frequency for VCO (ω0) is obtained by the conventionalcommutation signals detection circuit, which is explained ear-lier. There are two reasons to obtain the reference speed by usingthe traditional speed acquire technique. First, since the originalusp is processed by the filter processed circuit, the impact of thevoltage pulses to the rotor’s speed is very limited. Therefore, theobtaining of the motor rotating speed can be seemed as reliable.Second, as analyzed earlier, the stability margin of the SFF isrelatively small at very low-speed range. Therefore, it will im-prove the performance at very low-speed range by using thetraditional method to generate the reference speed value. Addi-tionally, because of the existing of the prefilter of the SOGI-PLL(the SFF), the damping factor k is chosen as 1.5 for a relativewide bandwidth of SOGI.

As can be seen in Fig. 7, an SFF is located at the up-stream of the single-phase SOGI-PLL to prefilter the harmonic

components, which is contained in the input signal (usp ). Thereference signals of the SFF (sin (θ̂) and cos (θ̂)) are generatedby using the estimated rotor position angle naturally, which isproduced from the output signals of the SOGI-PLL. Besides,the reference signals are returned to the SFF by two feedbackpaths. The reference frequency for VCO (ω0) is obtained by theconventional commutation signals detection circuit, which isexplained above. There are two reasons to obtain the referencespeed by using the traditional speed acquire technique. First,since the original usp is processed by the filter processed cir-cuit, the impact of the voltage pulses to the rotor’s speed is verylimited. Therefore, the obtaining of the motor rotating speed canbe seemed as reliable. Second, as analyzed above, the stabilitymargin of the SFF is relatively small at very low-speed range.Therefore, it will improve the performance at very low-speedrange by using the traditional method to generate the referencespeed value. Additionally, because of the existing of the prefilterof the SOGI-PLL (the SFF), the damping factor k is chosen as1.5 for a relative wide bandwidth of SOGI.

According to the aforesaid analysis, it can be known that thebandwidth of the LF will be reduced due to the input signal’sharmonic component, which will further impact on the controlsystem’s response. But the problem is almost disappeared byusing the proposed incorporating method, since the fundamentalcomponent of the input signal has been extracted by the SFFefficiently. Hence, the key of the discussion is to choose anappropriate bandwidth of the PLL.

The close-loop transfer function of the PLL, which from ε(t)to θ̂ (t) is expressed as

Φ(s) =−(Kps + Ki)s2 + Kps + Ki

. (17)

Setting Kp = 2ρ and Ki = ρ2 , another expression of (17)can be expressed as (18), which has equal roots as (17) [28].

Φ(s) =−(2ρs + ρ2)s2 + 2ρs + ρ2 (18)

where ρ is a positive constant. The bandwidth of Ф(s) is 2.48ρ,which can be obtained by a simple calculation. Therefore, theproblem is concentrated on selecting the value of ρ.

As the harmonics of usp have been prefiltered by the SFF, alarger bandwidth of the PLL can be selected without consideringthe impact of the high-order harmonic noises. Furthermore, for

SONG et al.: HIGH-PRECISION SENSORLESS DRIVE FOR HIGH-SPEED BLDC MOTORS BASED ON THE VIRTUAL THIRD 1535

Fig. 8. Overall high-speed magnetically suspended BLDC experimental setupcontrol block based on the proposed sensorless drive scheme.

the high-speed BLDC motor, the bandwidth should be largerthan that of the conventional low-speed motors, since the speedrange of the high-speed motor is much wider. Therefore, byconsidering the bandwidth of the speed controller and the currentcontroller, the bandwidth of Ф(s) can be designed, so that theparameters Kp (= 2ρ) and Ki (= ρ2) can be acquired.

4) Extra Degree Compensation: Although the proposed ro-tor position detecting method is accurate enough, the rotorposition detecting error may be appears a few times in thewhole speed operating range due to the sampling accuracy ofthe AD module. For this reason, an extra rotor position degreecompensation link is used.

The compensation link consists of a difference integrationmodule and a PI adjusting module. The difference integrationmodule obtained the integration from the occurrence of the firstcommutation point to the ZCP of the fundamental wave of usp ,and the integration from the ZCP of the fundamental wave of uspto the second commutation point, respectively. The PI regularis used to control the difference between the two integrations.The aim of the PI regular is that adjusting the difference be-tween the two integrations equals to zero. The working principleof the extra degree compensation link is similar as the tradi-tional integration-based compensation scheme, which is shownin Fig. 3. Compare to the traditional compensation scheme, themost difference is that the fundamental wave of the usp is used.Since the fundamental wave of the usp contains no voltage pulse,the extra degree compensation link can further compensate thecommutation error effectively.

IV. EXPERIMENTAL EVALUATION

Because of that the impeller of the developed aeration bloweris being processed, an experimental driveline system used fortesting the electrical performance for the high-speed magneti-cally suspended BLDC motor is built. The overall high-speedmagnetically suspended BLDC experimental setup controlblock based on the proposed sensorless drive scheme is shownin Fig. 8. As illustrated in Fig. 8, the magnetically suspendedmotor is connected with the magnetically generator by a flex-ible coupling. A variable resistor is taken as load. The PWMmethod is adopted below the switching speed, and the PAM

TABLE ITEST PARAMETERS

Variable Value

No. of pole pairs, P 1Rated dc voltage 430 VRated current 70 ARated Power 30 kWRated speed, n 48 000 r/minTorque constant, Kt 0.0857 N·m/ALine-to Line back-EMF constant, K e−l in e 0.0082 V/r/minRotational inertia, J 0.0021796 kg·m2

Phase resistance, R 35 mΩPhase inductance, L 195 μHMutual inductance, M 40 μH

Fig. 9. Experimental platform. (a) Drive system. (b) Experimental motors.

technique is applied when the switching speed is achieved. Afront-end phase-controlled rectifier can provide an adjustabledc-link voltage when the PAM worked, while the back-endVSI achieves the commutation control. The phase lag angleand the software retarding are compensated by using the com-mutation delay calculation module. The difference integrationand the PI module are used to generate the commutation com-pensation degree. Then, the final compensation angle can beobtained. The displacement signals (Sm and Sg ) and the currentsignals (im and ig ) are sampled to control the magnetically sus-pended bearings in the BLDC motors. The specification of theexperimental magnetically suspended BLDC motor is shown inTable I. Fig. 9 shows the photograph of the experimental plat-form, which consists of the drive system and the experimentalBLDC motor.

To test the effectiveness of the proposed method in the wholespeed range, several experimental results are shown in thefollowing.

A. Experiment 1—Performance Under No-Load Conditions

Fig. 10(a) shows the experimental results (iA , uA , uAB , andusp ) in the startup stage. The startup stage contains three steps:preposition, force synchronous operation, and sensorless opera-tion, which is the so-called three-steps startup method. Thereare two reasons to select this startup method: the first oneis that the performance in the high-speed range is relativelymore important for the high-speed motor than the transient statein the low-speed range; the second one is that the three-stepsstartup method will provide sufficient stability margin, which is

1536 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 33, NO. 2, FEBRUARY 2018

Fig. 10. Experimental performances of the proposed method in the low-speedrange. (a) Startup stage. (b) 5000 r/min with PWM.

relatively small at nearly zero speed according to the afore-said analysis. It can be seen in Fig. 10(a), in the force syn-chronous operation, the current ripple is large due to the inaccu-rate commutation. When the sensorless operation is applied, thecurrent ripple decreases since the commutation signals is accu-rate, which is obtained from the proposed method. The rotor po-sition angle is detected through the proposed sensorless method,and it is automatically switched from the force synchronous op-eration to the sensorless operation when the sensorless methodprovides reliable position information. The switch speed is usu-ally around 150 r/min. It can be seen that the proposed methodworks reliably in the startup stage.

As introduced previously, the PWM–PAM combining con-trol method is adopted. As followed, the switching speed (fromPWM to PAM) is usually around 5000 r/min (the current rip-ple is increasing with the speed in the PWM mode). Therefore,the upper bound speed is set at 5000 r/min. Fig. 10(b) showsthe experimental results at the speed of 5000 r/min, in whichthe experimental performance is satisfied. Usually, the satisfiedperformance can also be obtained in the conventional sensor-less method, in which the noise is filtered by the low-pass filter.However, by using the proposed method, the accurate commu-tation signals are gotten from the noisy signal without addingextra hardware (such as the low-pass filters).

Fig. 11. Experimental performances of the proposed method in the high-speedrange. (a) PWM–PAM switching stage. (b) 48 000 r/min with PAM.

In order to test the effectiveness of the proposed sensor-less drive method in the high-speed range, the experimentalresults in the PWM–PAM switching stage and 48 000 r/minhave been shown in Fig. 11. As aforementioned, the PAM con-trol model will be triggered when the motor’s speed reaches5000 r/min. The performance at the transition process is pre-sented in Fig. 11(a). It can be seen that under PAM controlmodel, the fluctuations of the phase current (iA ) and voltage(uA ) are decreased compared with that under the PWM controlmodel, since the commutation notches generated at the fre-quency of the PWM are vanished. Furthermore, the loss of themotor will be reduced and the motor efficiency will be improvedbecause the current ripple decreasing. Also, it can be seen inFig. 11(b) that the proposed sensorless drive can be effectivelyoperated in the high-speed range. So, the proposed sensorlessdrive method can be utilized in the whole speed range.

Fig. 12 shows the details of the signals (vα and vβ ) containedin SOGI-PLL both in the low-speed range and high-speed range.The experimental performance at 1000 r/min can be seen inFig. 12(a). It can be noted that vα and vβ contain no obviousdistortion, and quite similar as the standard sine curve. The fastFourier transform (FFT) analysis of vα has been shown next,which shows that vα contains very little high-order harmoniccomponents. Meanwhile, the Lissajous curve drawn by vα and

SONG et al.: HIGH-PRECISION SENSORLESS DRIVE FOR HIGH-SPEED BLDC MOTORS BASED ON THE VIRTUAL THIRD 1537

Fig. 12. Experimental performances of signal details of the SOGI-PLL in-cluding the estimated vα and vβ , the FFT analysis, and the Lissajou curves.(a) Performances at 1000 r/min. (b) Performances at 48 000 r/min.

Fig. 13. Experimental results of rotor position estimations, the blue curvesare the estimated rotor position angle and the red curves are the precise rotorposition angle for comparison. (a) Without compensation. (b) With SOGI-PLLprocessing. (c) With SFF-SOGI-PLL processing.

vβ shows a satisfied phase cycle, since the high-order harmoniccomponents are filtered out. The similar experimental perfor-mance at 48 000 r/min can be seen in Fig. 12(b).

To verify the effectiveness of the proposed SFF-SOGI-PLL-based rotor position estimation, the experimental results of therotor position angle estimations are shown in Fig. 13. The pre-cise rotor position angle curve (the red curve) is given in a sameplot for comparison, which is obtained by an encoder. Fig. 13(a)illustrates the experimental results of the traditional virtual thirdharmonic phase back-EMF-based sensorless method withoutany compensations under 48 000 r/min, while Fig. 13(b) showsthe experimental results with SOGI-PLL processing, followedby the experimental results with SFF-SOGI-PLL processingunder the same experimental conditions in Fig. 13(c). It can benoted that in Fig. 13(a), the estimated rotor position curve fluctu-ates dramatically, thus the estimated error occurs. The maximumvalue of the estimated error is around 10°. The experimental re-sult in Fig. 13(b) presents a better performance, although it also

Fig. 14. Comparable experimental results at 48 000 r/min with 100% load.(a) With the traditional compensation method (Sprior = Safter ). (b) With theproposed sensorless drive method (SFF-SOGI-PLL).

contains estimated error obviously. On the contrary, the esti-mated rotor position angle with the proposed SFF-SOGI-PLLmethod processing, which can be seen in Fig. 13(c), containslittle estimated error. The estimated error is reduced in 1◦.

B. Experiment 2—Performance Under Load Conditions

For further validating the effectiveness of the proposed sen-sorless drive algorithm, the experimental performance underload conditions has been shown in this experiment.

Fig. 14 shows the comparison experimental performanceand the relationship among iA , uA , and usp at 48 000 r/minwith 100% load. As aforementioned, the advanced degree isincreasing with the motor speed and load. Therefore, the ad-vanced degree under the full load conditions at the highestspeed is the largest value as well as the reason that the au-thors choose to show the accuracy performance under the high-est speed conditions. Fig. 14(a) indicates the performance withthe traditional compensation method aforementioned (in Fig. 3,i.e., Sprior = Safter). As can be seen in Fig. 14(a) that, dueto the voltage pulse during the commutation period, the in-tegration of the voltage pulse has been add to Safter . As aresult, the advanced commutation appears, and the advanced

1538 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 33, NO. 2, FEBRUARY 2018

Fig. 15. Comparable experimental performance of the commutation error, thecommutation signals and the FFT analysis at 48 000 r/min with 100% load.(a) With the traditional compensation method (Sprior = Safter ). (b) With theproposed sensorless drive method (SFF-SOGI-PLL).

commutation error cannot be eliminated according to the afore-said analysis. The waves are distorted due to the advanced com-mutation. Fig. 14(b) presents the performance with the proposedsensorless drive method (with SFF-SOGI-PLL processing). Ob-viously, the accurate commutation appears under the proposedsensorless drive method, and the distortion has been furtherimproved.

In order to show the accuracy of the proposed sensorless drivemethod more obviously, Fig. 15 shows the commutation signalsand the FFT analysis, which are under the same conditions asthat in Fig. 14. The ideal commutation signal, usp and the FFTanalysis of usp have been shown to present the relationship ofthem. As shown in Fig. 15(a), the advanced degree is 9.64°with the traditional compensation method. Under the proposedsensorless drive method, it can be noted in Fig. 15(b) that theadvanced degree is decreased to 0.85°. The residual commu-tation error is mainly caused by the residual harmonics in theestimated signals, although the performance is satisfied in thispaper’s research. The extracted fundamental wave of usp (usp 1)

Fig. 16. Comparable experimental results with a step load applying. (a) Withthe traditional compensation method (Sprior = Safter ). (b) With the proposedsensorless drive method (SFF-SOGI-PLL).

and the FFT analysis of usp 1 have also been shown in Fig. 15.As shown, the high-order harmonics have been almost filteredout, which are severely contained in usp .

To further show the experimental performance of the tradi-tional sensorless method and the proposed sensorless method,a load step experiment has been done at 30 000 r/min as shownin Fig. 16. The load is dramatically changed from 10% to 90%full load. The load is changed through switching the load resis-tance box with different resistance values. The two results are

SONG et al.: HIGH-PRECISION SENSORLESS DRIVE FOR HIGH-SPEED BLDC MOTORS BASED ON THE VIRTUAL THIRD 1539

Fig. 17. Experimental results comparisons of the overall efficiency under thetwo compensation method.

obtained under same experimental conditions. It can be notedthat the current ripple is smaller under the proposed sensorlessdrive method than that under the traditional sensorless method.According to the aforesaid analysis, the commutation is moreprecise than that of the traditional compensation method. Thewaves of usp and usp 1 are also shown in Fig. 16. It can beseen that usp 1 has been extracted effectively, and the advantagedistortion with Sprior = Safter compensation has been limitedeffectively in the proposed method with SFF-SOGI-PLL. It alsocan be noted that, when the load is sharply changed from 10%load to 90% load, the maximum estimated error is 8.7° un-der traditional sensorless method, and that under the proposedsensorless drive method is within 1°. As a conclusion, the pro-posed method presents a further improved performance than thetraditional method.

C. Experiment 3—Efficiency Comparison

In order to evaluate the efficiency performance of the pro-posed sensorless method, the experimental results comparing ofthe overall efficiency are shown in Fig. 17. The overall efficiencyis defined as the ratio of the generator’s output power to the mo-tor’s input power in this paper, and the powers are recorded bytwo power analyzers (WT1800). It can be noted that in Fig. 17,resulting from the precise commutation points obtained by theproposed sensorless drive method, the overall efficiency is im-proved compared with that of the traditional method, especiallyin the high-speed range.

V. CONCLUSION

The sensorless drive method, which is based on the third har-monic back-EMF or the virtual neutral voltage, has been widelyused. However, the commutation error is significant due to thedetection of inaccurate ZCPs, which is caused by the voltagepulse during the commutation process, especially for the high-speed applications. In this paper, a novel high-precision sensor-less drive method based on the virtual third harmonic back-EMF

has been developed. In the proposed method, the single-phaseSOGI-PLL is used to estimate the rotor position, while the SFFis adopted as a pre-filter to filter out the harmonics contained inthe input signal, which will impact the effectiveness of the PLL.Compared with the traditional sensorless drive methods basedon the third harmonic back-EMF or the virtual neutral voltage,the proposed method has several advantages:

1) the proposed novel sensorless drive based on the virtualthird harmonic back-EMF can be operated in a wide speedrange with only one voltage signal;

2) the rotor position precise detection has been greatly im-proved by using the proposed method (SFF-SOGI-PLL),which can be worked efficiently without the impact of thevoltage pulse during the commutation method; and

3) the proposed method can provide reliable sensorless com-mutation signals in a wide speed range and improve theoverall efficiency of the motor.

As the three-steps startup technique is used in the startuprange to ensure the properly work of the system, the proposedmethod is suitable for such the industrial applications as blowerand compressor, of which the motor does not need to frequentlystartup.

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Xinda Song was born in August 18, 1981. Hereceived the M.S. degree from Taiyuan Universityof Technology, Taiyuan, China, in 2011, and thePh.D. degree in precision instrument and machin-ery from the Beijing University of Aeronautics andAstronautics, Beijing, China, in 2016.

He is currently a Postdoctoral Research Fellowin the School of Instrumentation Science and Opto-electronics Engineering, Beijing University of Aero-nautics and Astronautics, where he is also a ResearchMember of the Key Laboratory of Fundamental Sci-

ence for National Defense, Novel Inertial Instrument and Navigation SystemTechnology. His research interests include high-speed permanent magnet motorcontrol and power electronics.

Bangcheng Han was born in February 1974. Hereceived the M.S. degree from Jilin University,Changchun, China, in 2001, and the Ph.D. degreefrom Changchun Institute of Optics, Fine Mechanicsand Physics, Chinese Academy of Sciences,Changchun, in 2004. In 2004, he was a PostdoctoralResearch Fellow in the School of InstrumentationScience and Opto-electronics Engineering, BeijingUniversity of Aeronautics and Astronautics, Beijing,China.

In 2006, he joined Beijing University of Aeronau-tics and Astronautics. He is currently a Professor in the School of Instrumen-tation Science and Optoelectronics Engineering. He has over 50 journal andconference publications. His research interests include mechatronics, magneticsuspension technology, and attitude control actuator of spacecraft.

Shiqiang Zheng (M’12) received the Ph.D. degreein electrical and electronics engineering from theBeijing University of Aeronautics and Astronautics,Beijing, China, in 2011.

He is currently an Associate Professor inthe School of Instrumentation Science and Opto-electronics Engineering, Beijing University of Aero-nautics and Astronautics, where he is also in theBeijing Engineering Research Center of High-SpeedMagnetically Suspended Motor Technology andApplication. He was a Visiting Scholar from May

2015 to May 2016 in the Advanced Robotics Center, National University of Sin-gapore, Singapore. His research interests include magnetic bearing technologyin high-speed rotating machinery and attitude control actuators of spacecraft.

Jiancheng Fang was born in 1965. He received theB.S. degree from the Shandong University of Tech-nology (now Shandong University), Jinan, China, in1983, the M.S. degree from Xi’an Jiaotong Univer-sity, Xi’an, China, in 1988, and the Ph.D. degree fromSoutheast University, Nanjing, China, in 1996.

He is the Chinese Academy of Sciences fellowand the Vice-President of the Beijing University ofAeronautics and Astronautics, Beijing, China. He hasauthored or coauthored more than 150 paper and fourbooks. He has been granted 35 Chinese invention

patents as the first inventor. His current research interests include the attitudecontrol system technology of spacecraft, novel inertial instrument and equip-ment technology, inertial navigation, and integrated navigation technologies ofaerial vehicles.

Dr. Jiancheng has the special appointment Professorship with the title ofCheung Kong Scholar by the Ministry of Education of China and the Li KaShing Foundation. He is in the first group of Principal Scientists of the NationalLaboratory for Aeronautics and Astronautics of China. He received the first-class National Science and Technology Progress Award of China as the thirdcontributor in 2006, the first-class National Invention Award of China as thefirst inventor, and the second-class National Science and Technology ProgressAward of China as the first contributor in 2007.

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