An inverter output power control based power factor correction (PFC) strategy is being extensively used for permanent magnet synchronous motor (PMSM) drives in appliances because such a strategy can considerably reduce the cost and size of the inverter. In this strategy, PFC circuits are removed and large electrolytic DClink capacitors are replaced with small film capacitors. In this application, the PMSM
d

q
axes currents are controlled to produce ripples, the frequency of which is twice that of the AC main voltage, to obtain a high power factor at the AC mains. This process indicates that the PMSM operates under periodic magnetic saturation conditions. This paper proposes a back electromotiveforce (backEMF) estimator for the highspeed sensorless control of PMSM operating under periodic magnetic saturation conditions. The transfer function of the backEMF estimator is analyzed to examine the effect of the periodic magnetic saturation on the accuracy of the estimated rotor position. A simple compensation method for the estimated position errors caused by the periodic magnetic saturation is also proposed in this paper. The effectiveness of the proposed method is experimentally verified with the use of a PMSM drive for a vacuum cleaner centrifugal fan, wherein the maximum operating speed reaches 30,000 rpm.
I. INTRODUCTION
During the past decade, permanent magnet synchronous motors (PMSMs) have been extensively employed in appliances because of its higher efficiency compared to that of induction motors (IMs)
[1]
. Although IMs used in appliances do not require complex driving circuits, PMSM is often driven by a singlephase diode rectifierfed inverter.
Fig. 1
(a) illustrates the general structure of the PMSM drive used in appliances. PMSM is driven by a singlephase diode rectifierfed inverter, and the power factor correction (PFC) circuits are generally adopted to meet the IEC6100032 harmonic current emission standard, wherein the limits on harmonic currents that can be allowed are listed
[2]
. The appliance industry is highly sensitive to cost competitiveness. An inverter output power controlbased PFC strategy that involves removing the PFC circuits and replacing large electrolytic DClink capacitors with a small film capacitor, as shown in
Fig. 1
(b), is currently gaining attention in the appliance industry because this strategy can significantly reduce the cost and size of the inverter
[3]

[6]
.
Fig. 1
(c) shows the experimental waveforms when the inverter output power controlbased PFC strategy is employed for a PMSM drive.
Fig. 1
(c) also shows that the
q
axis current is controlled to produce ripples with frequency that is twice that of the AC mains, indicating that the PMSM operates under periodic magnetic saturation conditions.
(a) Configuration of a conventional PFC circuitbased PMSM drive. (b) Configuration of a singlephase diode rectifierfed PMSM drive with a small DClink capacitor. (c) Experimental waveforms of the qaxis current, phase current, and DClink voltage when the inverter output power controlbased PFC strategy is employed.
The PMSM position sensorless control is also an important issue in appliances because this control contributes in the cost reduction of the PMSM drive; the back electromotiveforce (backEMF)based sensorless control methods have also been commonly employed in appliances
[7]
. Numerous researches on the backEMF based sensorless control of PMSM have been introduced
[8]

[14]
. The accuracy of the estimated backEMF considerably depends on the model errors because the backEMF is estimated on the basis of the PMSM mathematical model; thus, the performance of the sensorless controlled PMSM drive at high speeds is known to be highly sensitive to the
q
axis inductance error
[15]
. When the inverter output power controlbased PFC strategy is applied to the PMSM drive, the
d

q
axes inductances of PMSM also vary according to the periodic magnetic saturation. An online parameter estimation strategy can be considered to compensate for the effect of inductance variations caused by the periodic magnetic saturation on the estimated backEMF. In
[15]
, the online parameter estimation strategy is employed to estimate the value of the actual PMSM stator inductances during sensorless control; however, the use of online parameter estimation method increases the computation burden, and a zerophase lag estimation of periodically varying parameters at twice the line frequency (at 100 Hz or 120 Hz) is a challenging task. A lookup table (LUT) saving the
d

q
axes inductance values based on the
d

q
axes currents can be considered to compensate for the periodically varying inductances. However, in view of the effects of dynamic inductance
[16]
, the static inductancebased LUT clearly cannot completely compensate for the effects of periodic magnetic saturation in a sensorless controlled PMSM drive.
This paper proposes a highspeed sensorless control strategy for PMSM operating under periodic magnetic saturation conditions. The backEMF estimator is implemented using a disturbance observer presented in
[9]
, and the transfer function of the backEMF estimator is analyzed in detail to examine the effect of stator inductance variations on the accuracy of the estimated backEMF. Analysis shows that the estimated position error at high speeds mainly depends on the product of the
q
axis inductance error and hypothetical
q
axis current. The effect of periodic stator inductance variations on the estimated position error can be easily compensated by using a notch filter with a stop band of twice the line frequency (100 Hz or 120 Hz). The proposed method is applied to a PMSM installed in a vacuum cleaner centrifugal fan, wherein the maximum operating speed reaches 30,000 rpm. Experimental results are presented to verify the effectiveness of the proposed sensorless control method.
II. POWER FACTOR CORRECTION THROUGH INVERTER OUTPUT POWER CONTROL
Assuming a unity power factor condition at the AC mains, the input power
p_{in}
at the AC mains is given as follows:
where
v_{pk}
and
i_{pk}
are the peak values of the AC mains voltage and current, respectively;
θ_{grid}
is the phase angle of the AC mains voltage; and
θ_{grid}
can be sensed from the AC mains voltage using an additional hardware or can be estimated from the DClink voltage ripples
[3]
. In the same condition, the DClink capacitor power
p_{c}
can be calculated as follows
[4]
:
where
ω_{in}
is the angular frequency of the mains voltage and
C_{dc}
denotes the capacitance of the DClink capacitor.
The output power of the inverter
p_{out}
is given as follows:
where
v_{d}
,
v_{q}
vq and
i_{d}
,
i_{q}
are the
d

q
axes stator voltages and currents, respectively, in the rotating reference frame.
Assuming that the the motor drive losses, including a singlephase diode rectifier, DClink capacitors, and a threephase inverter, are negligible,
p_{in}
is equal to the sum of
p_{c}
and
p_{out}
.
p_{in}
and
p_{c}
for a unity power factor condition are given by (1) and (2), respectively; thus, a high power factor at the AC mains can be obtained by controlling
p_{out}
to exactly follow the reference given by
where the superscript “*” denotes the reference value in each variable.
Fig. 2
illustrates the relationship among
p_{in}
,
p_{c}
, and
p_{out}
under a unity power factor condition when the inverter output power control strategy given by (4) is employed. When the power factor is controlled this way, conventional PFC circuits are removed and large electrolytic DClink capacitors are replaced with a small film capacitor; thus the size and cost of the inverter can be significantly reduced compared to the conventional PFC circuitbased inverter
[5]
,
[6]
.
Relationship among the input power, output power, and DClink capacitor power under a unity power factor condition.
Various control strategies have been introduced in
[3
–
6]
to obtain a high power factor at the AC mains through the inverter output power control. In this study, the
d

q
axes current command generation method presented in
[4]
was utilized.
Fig. 3
shows that in the speed controller, the proportionalintegral (PI) controller on the lefthand side outputs a control signal to regulate the rotor angular velocity. Thereafter, the control signal is multiplied by sin
^{2}
θ_{grid}
to generate the reference of the input power
p^{*}_{in}
for a unity power factor at the AC mains. The inverter output power reference
p^{*}_{out}
is obtained by subtracting
p_{c}
, which was calculated using (2), from
p^{*}_{in}
. The PI controller on the righthand side of
Fig. 3
outputs the
q
axis current command to regulate the
p_{out}
, obtained using (3), to follow
p^{*}_{out}
. However, the
d
axis current should also be appropriately controlled to obtain the aforementioned control object. The procedure for the generation of the
d
axis current reference has been introduced in
[4
,
6]
, and the resulting
d
axis current command is given by
where
k_{1}
and
k_{2}
are the gains used in adjusting the power factor at the ACmains, and are selected through experiments or offline calculations; and
ω_{m}
is the mechanical rotor angular velocity.
Detailed structure of a speed controller to achieve a high power factor at the AC mains [4].
Fig. 2
shows that the drawback of the PFC method through the inverter output power control is that torque ripples, the frequency of which is twice that of the AC mains voltage, are generated because of the ripples in the inverter output power. Cost competitiveness is a highly critical issue in the appliance industry; thus, the torque ripples caused by the PFC control can be allowed if the entire performance of the PMSM drive shown in
Fig. 1
(b) is still better than that of IM. For example,
Fig. 2
shows that the inverter output power ripples exert limited effects on the noise level of a vacuum cleaner. However, the periodically varying
d

q
axes stator currents resulting from the inverter output power ripples cause the variation of the stator inductance with the same frequency. Therefore, an indepth study on the highspeed sensorless control for this application is required because parameter errors caused by magnetic saturation degrade the performance of the sensorless position estimator
[15]
.
III. PROPOSED BACKEMF ESTIMATOR FOR THE HIGHSPEED SENSORLESS CONTROL OF PMSM OPERATING UNDER PERIODIC MAGNETIC SATURATION CONDITIONS
 A. Selection of Sensorless Control Strategy Considering Periodic Magnetic Saturation Effects
Various modelbased sensorless control strategies for PMSM have been proposed
[7]

[14]
; however,
Fig. 4
shows that most of these strategies have a common functional block diagram
[17]
. The backEMF or flux is estimated using the voltage commands
v
^{*}
, the measured stator currents
i
, the PMSM mathematical model, and the rotor position and speed are obtained from the estimated backEMF(
ê
) or flux(
) using an additional position/speed estimator.
Functional block diagram of the modelbased sensorless control strategy [15].
The operating characteristics of the modelbased sensorless position/speed estimator is significantly affected by the type of PMSM mathematical model used in the backEMF or flux estimator. The PMSM voltage equation in the stationary reference frame is given by
where
v_{α}
,
v_{β}
and
i_{α}
,
i_{β}
are stator voltages and currents, respectively, in the stationary reference frame:
R_{s}
is a stator resistance;
L_{d}
and
L_{q}
are
d

q
axes stator inductances;
p
is a differential operator;
ω_{r}
and
θ
_{r}
are an electrical rotor angular velocity and position, respectively;
λ_{PM}
is a permanent magnet flux linkage; and
E_{ex}
is the extended EMF introduced in
[8]
.
The second term on the righthand side of (6) represents the backEMFs; the rotor position can be directly acquired from the backEMFs when using the stationary reference frame model. Note from (6) that the backEMFs in the stationary reference frame are AC signals; thus, phase lagging exists between the actual and estimated backEMFs caused by the intrinsic phase delay of the backEMF estimator. This phase lagging increases as the rotor speed increases; thus, the performance of the sensorless control is often degraded at high speeds when using the stationary reference frame modelbased backEMF estimator
[17]
.
The phase lagging problem at high speeds when using the stationary reference frame modelbased sensorless control can be avoided by estimating the fluxes instead of the backEMFs
[14]
. However, considering the specific application where PMSM operates under periodic magnetic saturation condition, the estimated flux signals are AC signals, the frequency of which varies based on the speed; the model errors resulting from the periodic magnetic saturation, caused by the inverter output powerbased PFC control, have a frequency that is twice that of the AC mains voltage. Therefore, compensating for the effect of the periodic model errors on the estimated flux signals is difficult without affecting the phase angle of the estimated flux signals over extensive operating ranges. Nevertheless, the estimated backEMFs become DC signals when using the rotating reference frame model basedbackEMF estimator; thus, separating the periodic magnetic saturation effect from the estimated backEMFs is relatively easy. For this reason, the rotating reference frame modelbased backEMF estimator was employed in this study.
The PMSM voltage equation in the rotating reference frame is given as follows:
By transforming (8) into the hypothetical rotating reference frame, which is the
γ

δ
reference frame presented in
[11]
, the voltage equation of the PMSM can be expressed as follows:
where
v_{γ}
,
v_{δ}
and
i_{γ}
,
i_{δ}
are stator voltages and currents, respectively, in the
γ

δ
frame; Δ
θ
is the angle difference between the
d

q
and the
γ

δ
reference frame, which represents the position error between the actual and hypothetical rotor positions; and
is the angular velocity of the rotating
γ

δ
frame. Equation (10) shows that the backEMFs in the
γ

δ
reference frame are DC signals and contain the position error Δ
θ
; thus, the rotor speed and PMSM position can be estimated from the backEMFs. When using the rotating reference frame modelbased backEMF estimator, the phase lagging between the actual and estimated backEMFs becomes negligible at steadystates; thus, the rotating reference frame model of PMSM is often preferred for the highspeed sensorless control
[11]
. The drawback of the rotating reference frame modelbased backEMF estimator is that the estimated speed is used for estimating backEMFs; thus, the performance of the backEMF estimator can be degraded by the estimated speed error, particularly at low speeds. However, the effect of the speed estimation error on the estimated backEMFs decreases as the speed increases when considering the synchronous operation of PMSM and the lowpass filtering effect caused by the mechanical system inertia.
 B. BackEMFbased Sensorless Speed/Position Estimator in the Rotating Reference Frame
To estimate the backEMF using the rotation reference frame model of PMSM, the disturbance observerbased backEMF estimator, presented in
[9]
, was employed because the overall structure of the estimator is simple and easy to implement.
Fig. 5
illustrates the entire structure of the backEMF estimator.
Fig. 5
also shows that
represent the nominal values of the stator resistance and
d

q
axes stator inductances, respectively;
ω_{est}
denotes the bandwidth of the firstorder lowpass filter;
j
is the imaginary unit (
); and
v_{γδ}
,
i_{γδ}
, and
Ê_{γδ}
are the vector representations of the stator voltages, stator currents, and estimated backEMFs in the
γ

δ
reference frame, respectively.
Therefore,
v_{γδ}
=
v_{γ}
+
jv_{δ}
,
i_{γδ}
=
i_{γ}
+
ji_{δ}
, and
.
Structure of the backEMF estimator [9].
The estimated rotor position error
can be obtained from the estimated backEMFs as follows:
where
ê_{γ}
and
ê_{δ}
are the estimated backEMFs in the
γ

δ
reference frame.
Fig. 6
shows that the estimated rotor speed () and position
() are obtained from
using the phaselocked loop (PLL) type estimator.
Structure of the PLL type speed/position estimator [9].
 C. Analysis of the Effect of Model Parameter Errors on the Estimated BackEMF and Position Errors[17,18]
Fig. 5
shows that the expression of the estimated backEMF is obtained as follows:
From (9),
i_{γδ}
can be derived as
From (12) and (13),
Ê_{γδ}
can be expressed as
Under steadystate and highspeed conditions, it assumed that
is almost the same as
ω_{r}
because of the synchronous operation of PMSM. The voltage error between
and
v_{γδ}
primarily originates from the nonlinearity of the inverter caused by the deadtime; the relative magnitude of the voltage error caused by the deadtime to the inverter output voltage is known to decreas as the speed increases
[19]
. The stator resistance linearly varies based on temperature, and the relative magnitude of the voltage drop at the stator resistance to the inverter output voltage also decreases as the speed increases
[19]
. Therefore, when PMSM runs at highspeeds, the effect of the voltage error caused by the deadtime and the stator resistance variation on the estimated backEMF can be ignored. From these assumptions,
Ê_{γδ}
in (14) can be expressed as follows:
where Δ
L_{d}
and Δ
L_{q}
denote the error between the actual and nominal values, respectively, of the stator inductance;
The term
s
/(
L_{d}s
+
R_{s}
) included in (15) is a firstorder highpass filter. From (15), the highpass filter outputs are observed to be fed into the losspass filter
ω_{est}
/(
s
+
ω_{est}
); thus, the effect of the highpass filtered terms in (15) on
Ê_{γδ}
can be ignored when the cutoff frequency of the highpass filter is higher than that of the lowpass filter. The
d
axis inductance variation caused by the magnetic saturation is also relatively low compared to the
q
axis inductance variation
[20]
. Therefore, (15) can be simplified as follows:
From (11) and (16),
is given by
Fig. 6
shows that the role of the PLLtype speed/position estimator is to regulate
to be zero; thus, Δ
θ
at the steadystate conditions can be derived from (17) as follows:
To confirm the validity of (18), simulations using the PMSM parameters listed in
Table I
were performed. The effect of Δ
L_{q}
on Δ
θ
was examined from the simulation results, and Δ
θ
calculated from (18), wherein
i_{δ}
and
i_{d}
are obtained from the simulation results, was compared with the value measured from the simulation results. In the simulation, the inverter DClink voltage was set to 300 V, which means that the inverter output power controlbased PFC strategy is not employed in the simulation. The reference speed was set to 30,000 rpm, the PWM frequency was set to 15 kHz, and the bandwidth of the backEMF estimator
ω_{est}
was set to 100 Hz.
Fig. 7
illustrates the
d

q
axes inductance variation of PMSM used in this study based on the magnetic saturation.
Fig. 7
also shows that
L_{q}
decreases by up to 30% from its maximum value as the stator of the PMSM is saturated. This result was reflected in the simulations.
PMSM NOMINAL PARAMETERS
The dq axes stator inductance variation based on the magnetic saturation.
Fig. 8
illustrates one case from the simulation results for the highspeed sensorless control of PMSM, where
is set to 6.0 mH and
L_{q}
is set to 20% less than
; and a comparison result between the measured Δ
θ
from the simulation results and the calculated Δ
θ
from (18).
Fig. 8
(a) shows that the estimated position error ranges between 8.5 and 9.7 degrees. By comparing
Fig. 8
(a) with
Fig. 8
(b), note that the analysis of Δ
θ
, given by (18), shows a satisfactory accuracy.
(a) Simulation result for the sensorless control of PMSM under L_{q} error condition. (b) Comparison between the measured and calculated estimated position errors.
 D. Proposed BackEMF Estimator Considering Periodic Magnetic Saturation Effects
When the PFC function is performed by the strategy presented in Section II,
i_{q}
(or
i_{δ}
) has the ripples, the frequency of which is twice that of the AC mains, which is 2
ω_{in}
. From (18), the effect of
pi_{q}
on Δ
θ
clearly becomes small as
ω_{r}
increases; therefore, Δ
θ
at highspeeds primarily depends on Δ
L_{q}
i_{δ}
, and has ripples with the same frequency as 2
ω_{in}
. As analyzed in (15) and (16), the backEMF estimator, which is shown in
Fig. 5
, acts as a lowpass filter with a cutoff frequency at
ω_{est}
. Therefore, the ripples of Δ
L_{q}
i_{δ}
are not filtered out through the backEMF estimator, and exert a direct influence on Δ
θ
. An exact zerophase lag estimation of
L_{q}
is required to compensate for the effect of Δ
L_{q}
i_{δ}
on Δ
θ
. However, these types of application would encounter difficulty, wherein the
d

q
axes currents and voltages have ripples with frequency of 2
ω_{in}
. To cope with this problem, this study proposes a simple method, in which a notch filter is added to the backEMF estimator to filter out the signals with frequency of 2
ω_{in}
.
Fig. 9
(a) illustrates the general block diagram of the proposed backEMF estimator.
Fig. 9
(a) shows that the cutoff frequency of the notch filter is determined by
ω_{n}
, which is set to have the same frequency as 2
ω_{in}
.
Figure 9
(b) illustrates the bode plots of the conventional and the proposed backEMF estimators, shown in
Figs. 5
and
9
(a), respectively, where no parameter errors are assumed; and
ζ
,
ω_{n}
, and
ω_{est}
were set to 0.7, 100 Hz, and 100 Hz, respectively.
Fig. 9
(b) shows that the ripples with frequency of 100 Hz would be filtered out through the proposed backEMF estimator; however, phase lagging is slightly increased at lowfrequencies. The phase lagging can degrade the backEMF estimator performance at transient states; however, this performance degradation caused by the slight increase in phase lagging is negligible for this application because the target application of the proposed backEMF estimator is a vacuum cleaner, which mainly operates at steady states. The effectiveness of the proposed method will be demonstrated through experiments.
(a) Structure of the proposed backEMF estimator. (b) Bode plots of the conventional and the proposed backEMF estimator.
IV. EXPERIMENTAL RESULTS
Experiments were conducted using a vacuum cleaner centrifugal fan to prove the validity of the proposed backEMF estimator for the highspeed sensorless control of PMSM operating under periodic magnetic saturation conditions.
Figure 10
illustrates the experimental setup, wherein the vacuum cleaner centrifugal fan is installed into a box to shelter the noise of the fan during the experiments. The RMS voltage and the frequency of the AC mains are set to 230 V and 50 Hz, respectively. The parameters and the
d

q
axes stator inductances based on the PMSM magnetic saturation are the same as those in
Table I
and
Fig. 7
, respectively. The PMSM load condition is the same as that of a typical fan because PMSM was installed in a vacuum cleaner fan. The rated speed and torque of PMSM are 30,000 rpm and 0.23 Nm, respectively. The PWM frequency of the inverter was set to 15 kHz, and the bandwidth of the current controller was set to 400 Hz using the polezero cancellation technique presented in
[19]
. A film capacitor, with a capacitance of 10 uF, was used for the DClink capacitor.
The experimental setup.
The gains of the speed controller, the block diagram of which is shown in
Fig. 3
, were tuned through several experiments conducted.
Fig. 3
shows that the proportional and integral gains of the first PI controller were set to 0.1 and 0.3, respectively; those of the second PI controller, in charge of outputting
q
axis current reference, were set to 0.002 and 0.5, respectively. The bandwidth of the backEMF estimator
ω_{est}
was set to 628 rad/sec; and
ζ
and
ω_{n}
, used for the notch filter in the proposed backEMF estimator, were set to 0.7 and 628 rad/sec, respectively. Considering the highspeed operation, the time delay caused by the digital implementation of the controller should be compensated by the reliable operation of the current controller and the backEMF estimator. This study utilized the method presented in
[21]
.
The align and go method was utilized to commence PMSM. For this purpose, the first PI controller shown in
Fig. 3
temporarily outputs a constant value to align the PMSM rotor to a specific direction.
Fig. 11
shows that after alignment, PMSM is started using the estimated speed and position of the rotor.
Fig. 11
also illustrates that the phase current
i_{a}
contains ripples, the frequency of which is 100 Hz, during the alignment period.
Fig. 3
shows that this result is due to the structure of the speed controller, wherein the output of the first PI controller is multiplied by sin
^{2}
θ_{grid}
.
Experimental result for the starting of PMSM.
Fig. 12
shows the experimental result of the highspeed sensorless control of PMSM, driven by a singlephase diode rectifier fed inverter with a small DClink capacitor, with the conventional backEMF estimator shown in
Fig. 5
and the speed controller shown in
Fig. 3
.
Fig. 12
shows that the overcurrent protection is triggered during the operation. The speed at the overcurrent protection point is approximately 29,000 rpm, although a maximum speed of 30,000 rpm is required for the vacuum cleaner used in this study. The cause of the excessive phase current in
Fig. 12
, which results in overcurrent protection, is the inordinate estimated position error in the sensorless control.
Experimental result involving the conventional backEMF estimator.
As described in Section III, the estimated position error in the sensorless control of PMSM at highspeeds mainly depends on Δ
L_{q}
i_{δ}
. For this type of application, where a small DClink capacitor is used and the PFC control is achieved by controlling the inverter output power without an additional hardware, Δ
L_{q}
is inevitable and cannot be easily compensated by using the online parameter estimation strategy.
Figure 13
depicts the experimental comparison result between the conventional and the proposed backEMF estimators at 20,000 rpm.
Fig. 13
also illustrates that the conventional backEMF estimator produces ripples in the estimated speed and position errors, resulting in a performance degradation in the highspeed sensorless control of PMSM. By contrast, the proposed backEMF estimator successfully removes the ripples.
Comparison of the estimated speed and position errors between the conventional and the proposed backEMF estimator at 20,000 rpm.
Fig. 14
shows the experimental result with the proposed backEMF estimator at 30,000 rpm, which is the required maximum speed of the vacuum cleaner centrifugal fan used in this study.
Fig. 14
(a) presents that the
d
axis current fluctuates with a frequency that is twice that of the AC mains voltage because the
d
axis current reference is given by (5) to operate PMSM under a voltage constraint condition. The fluxweakening control is essential to operate PMSM at highspeeds under the voltage constraint condition; the
d
axis current reference is often set to a negative value, and the magnitude of the
d
axis current command increases as the motor speed increases
[19]
. The gains (
k_{1}
and
k_{2}
) for the
d
axis current reference generation should be prudently selected to satisfy both the flux weakening and the PFC control purposes. In the experiments,
k_{1}
and
k_{2}
were set to 0.002 and 0.0011, respectively; thus, modifying these gains based on a large variation in machine parameters is necessary.
Fig. 14
(a) shows that the current waveform at the AC mains is not perfectly sinusoidal because of the improper gain tuning in generating the
d
axis current reference. However,
Fig. 14
(b) shows that the measured harmonic current at the AC mains satisfies the regulation of IEC 6100032 (class A)
[2]
. The performance of input current waveform shaping can be improved by utilizing the method presented in
[6]
. However, the effect of the performance of the input current waveform shaping on the sensorless control is insignificant if the harmonic current at the AC mains is regulated within the limit of IEC 6100032 (class A).
(a) Experimental result with the proposed backEMF estimator at 30,000 rpm. (b) Measured harmonic input current.
V. CONCLUSION
This study proposed the compensation method of periodic magnetic saturation effects for the highspeed sensorless control of PMSM driven by inverter output power controlbased PFC strategy. In this strategy, a singlephase diode rectifierfed inverter with a small DClink capacitor is employed without any PFC circuits; the
d

q
axes inductances vary with twice the frequency of the AC mains caused by the specific inverter output power control. The backEMF estimator was designed in the rotating reference frame to easily separate the periodic magnetic saturation effects from the estimated backEMFs. Based on the analysis, the estimated backEMF error at highspeeds mainly depends on the
q
axis inductance error. The estimated position error based on the
q
axis inductance error was also derived and verified through simulations. The analysis also presented that a simple method, wherein a notch filter with the cutoff frequency set to have the same as twice the frequency of the AC mains added to the backEMF estimator, was proposed to compensate for the effect of the periodic
q
axis inductance error on the estimated position error. The proposed method was implemented in driving a vacuum cleaner centrifugal fan, wherein the maximum operating speed reaches 30,000 rpm. The effectiveness of the proposed method was verified through experiments.
Acknowledgements
This study was financially supported in part by Samsung Electronics Co., Ltd.
BIO
KwangWoon Lee was born in Seoul, South Korea. He received the B.S., M.S., and Ph.D. degrees in Electrical Engineering from Korea University, Seoul, Korea, in 1993, 1995, and 1999, respectively. From 2000 to 2002, he was with Samsung Advanced Institute of Technology, Yongin, Korea, where he worked on the development of microelectromechanical system sensor applications. From 2002 to 2007, he was a senior research engineer at the Samsung Living Appliance R&D Center, Samsung Electronics, Suwon, Korea, where he was engaged in research on sensorless motor drive systems for refrigerators and air conditioners. He is currently an associate professor in the Department of Electronic Engineering, Mokpo National Maritime University Mokpo, Korea. His current research interests include power electronics and control, which include AC machine drives, digital signal processingbased control applications, and fault diagnosis of electrical machines.
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