Investigation of High Frequency Injection Method
for Surface-mounted PMSM Sensor-less Drive
Yu Zhang, Jie Gu, Zhigan Wu, Jianping Ying
Delta Power Electronics Center (DPEC)
238 Minxia Road, CIMIC Industry Zone, Pudong, Shanghai, 201209, China
Abstract – A novel sensor-less position detection scheme for
surface-mounted permanent magnet synchronous motor
(SPMSM) at standstill and low speed is investigated in this
paper. For synchronous motor’s sensor-less drive, there is
phase error between the synchronous reference frame and the
estimated synchronous reference frame. High frequency
voltage signal is injected into the estimated d-axis voltage, and
the position can be demodulated from estimated q-axis current
due to the small salient-ratio caused by saturation. High
frequency model of the motor is analyzed with projective
geometry between the estimated synchronous reference frame
and the synchronous reference frame. The complex mutual
inductance and stator voltage need not to be introduced.
Feasibility of the proposed scheme is verified with experiments
with a sample motor.
I. INTRODUCTION
Permanent magnet synchronous motor (PMSM)
drives have been widely accepted in many application fields
such as industry, transportation and elevator traction
because of their high efficiency, high power density and fast
respondency. However, traditional drives with position
transducers have problems such as high price, special
maintenance and complexity. So, position sensor-less drives
have caused great investigation interest with the
development of electronics and power electronics.
Generally, position sensor-less control strategy can
be classified into two types. One is based on EMF
observation. In this type, EMF can be observed with voltage
model, observer or Kalman Filters. Angular position can be
decided with EMF information. The performance of this
scheme is fairly good at medium and high speed. However,
the position can hardly be detected at standstill or very low
speed because the magnitude of EMF is proportional to
speed. So high frequency injection scheme is introduced to
solve this problem. The injection scheme has been applied
in reluctance and interior Permanent magnet synchronous
motor (IPMSM) drive, and great progress has been made [1].
For surface-mounted permanent magnet synchronous motor
(SPMSM), high frequency injection scheme is more and
more interested because salient-pole does exist in many
SPMSMs although it is not the dominant. [2] and [3] have
proposed an injection/demodulation scheme which can
solve the problem of small signal-to-noise ratio, low spatial
306
resolution and additional hardware or voltage sensor.
This paper proposes some further investigation
progress about high frequency injection scheme for
SPMSM. A simplified analysis method is deduced
considering estimated phase error between the synchronous
reference frame and the estimated synchronous reference
frame. The measurement experiments are the important part
of verification procedure and reference to select injection
voltage and frequency.
II. HIGH FREQUENCY MODEL AND CONTROL SCHEME
A. Model of High Frequency Injection Signal
The voltage equations of SPMSM on the
synchronous reference frame are represented as follows.
ud   Rs + Ls p − ω r Ls  id   0 
(1)
 +
u  = 
Rs + Ls p  iq  ω r Ψm 
 q   ω r Ls
Where,
p=
d
dt
When the rotor speed of SPMSM is relatively
small compared to the injected frequency, only the high
frequency component of voltages and currents are
considered. By assuming that the high frequency resistance
is sufficiently smaller than the high frequency inductance,
the voltage equations can be represented as followed.
0  idh 
udh  l dh p
u  =  0 l p  i 
qh   qh 
 qh  
(2)
In order to describe the investigation method,
injection voltages is just the same as [2] and [3]. High
frequency voltage signal is injected only on the d-axis in the
estimated synchronous reference frame whose relationship
with synchronous reference frame is shown in fig.1.
uˆ dh  Vc cos(ω c t )
uˆ  = 

0

 qh  
(3)
Symbols with ‘^’ represent parameters in the
estimated synchronous reference frame. Its position θˆ is
derived by position estimation method. In order to make
position sensor-less operation possible, it is necessary to
eliminate estimation phase error ∆θ = θ − θˆ , where θ is
position of synchronous reference frame.
Since currents in synchronous reference frame
cannot be observed in estimated synchronous reference
frame, currents in estimated synchronous reference frame
can also be derived with projective geometry as followed.
q̂
q
iˆdh 
l avg − 12 l diff cos( 2 ∆θ )
Vc
sin(ω c t ) 
ˆ  =
 (6)
1
 − 2 l diff sin( 2 ∆θ ) 
i qh  ω c l dh l qh
ω
Where,
d
lavg =
d̂
∆θ
Fig. 1. Relation between synchronous reference frame and estimated one
(4)
ωref
If there exists anisotropy or saturation in the
magnet circuit of SPMSM, there is high frequency
inductance difference between d- and q- axis, that is, ldiff is
not zero. With the former injection method, the rotor
position estimation error can be obtained from the high
frequency component of current on the q-axis in the
estimated synchronous frame.
(5)
+
Vccos(ωt)
iq_ref
+
-
+
+
-
ω̂
iq_fdb
Udc -
+
uq_out
d,q
SV
PWM
α,β
id_ref
(7)
B. Demodulation of the Carrier Signal
According to (2) and (4), high frequency currents
in synchronous reference frame can be derived as followed.
 1

sin(ω c t ) cos( ∆θ ) 

i
 dh  Vc l dh


i  =
1
 qh  ω c −
sin(ω c t ) sin( ∆θ )
 l qh

, ldiff = ldh − lqh
2
So, current response of high frequency voltage
signal can be derived without introduction of mutual
inductance. Currents in estimated synchronous reference
frame include information about inductance difference
between d- and q- axis.
With projective geometry, high frequency voltages
can be represented as followed.
udh 
 cos(ω c t ) cos( ∆θ ) 
u  = Vc 

− cos(ω c t ) sin( ∆θ )
 qh 
ldh + l qh
6
+
ud_out
id_fdb -
-
θˆ
-
d,q
Observer
BPF
a,b,c
SPMSM
3~
iA
iB
iC
sin(ωt)
Fig. 2. Block diagram of high frequency injection method
With high frequency injection methods for sensorless control, the signal demodulation constitutes a major
demand for signal processing. From (7), the input signal to
position estimation circuit can be obtained via signal
process as in (8).
[
]
i∆θ = LPF iˆqh sin(ω c t ) = −
Vc ldiff
2ω c l dh l qh
If position estimation error is sufficiently small, (8)
can be simplified as followed.
i ∆θ = −
Vc l diff
ω c ldh l qh
⋅ ∆θ = K err ⋅ ∆θ
(9)
So, estimated position can be inferred from the estimation
error by the estimation circuit.
sin( 2∆θ ) (8)
307
Fig.3 shows the procedure of signal processing.
The high frequency component of current on the q-axis
+ Udc -
iˆqh
is derived with the BPF from the q-axis feedback current
iq_fdb. The output of the PI regulator is the estimated
rotational speed. The estimated position θˆ is the
integration of estimated speed.
sin(ω c t )
BPF
I
SIN
GEN
6
SV
PWM
uβh
LPF
Ic'
iˆqh
iˆq _ fdb
uαh
Vc'
f'
PI
iαh
x2 + y2
iah
ibh
ich
α,β
iβh
a,b,c
i ∆θ
PMSM
3~
Fig. 4. Block diagram of measurement algorithm
θˆ
With rotating field excited by high frequency
voltage, currents can be measured to get inductances. By
measuring inductances in one electrical period, ldh and lqh
can be measured. The magnitude of high frequency current
and voltage, and the high frequency inductance on the
measurement axis can be obtained as followed.
Fig.5 and fig.6 show the measurement results of
high frequency inductance of SPMSM at various currents
and various injection frequencies. For the measurement, a
700W SPMSM is used with parameters listed in table.1. In
the figures, ‘Test angle’ is the assumed electrical angular
position of measurement axis.
dθˆ
dt
Fig. 3. Block diagram of position and speed observer
C. Overall Control Algorithm of the Method
Fig.2 shows the block diagram of the sensor-less
drive system including the proposed high frequency
injection algorithm. It consists of the basic field oriented
vector control system, proposed injection method and
demodulation observer shown in fig.3. It can be
implemented with microprocessor-based circuit and power
inverter. Cooperating with proper algorithm to observe
position from EMF at medium and high speed, high
frequency injection method can be constructed into a
overall solution for high performance sensor-less SPMSM
drive.
2
Vc ' = uαh + u βh
2
I c ' = iαh + iβh
X dh = max(
III. INVESTIGATION OF HIGH FREQUENCY MODEL WITH
EXPERIMENTS
2
2
V'
Vc '
), l qh = min( c )
Ic '
Ic '
3.5
High frequency injection method is mainly based
on the inductance difference between d- and q- axis. So the
existence of that difference in SPMSM is very important.
With the increase of frequency, the flux tends to propagate
through the leakage paths in the stator and rotor. That is
called skin effect. It decreases the inductance difference
between d- and q- axis. So, motor properties should be
considered in the model at the injection frequency due to
the skin effect [3].
To verify the high frequency inductance
difference of SPMSM, and possibility to detect the
accurate position with simulation methods, some
measurement has been performed to get the high frequency
inductances.
The method of measurement is to exploit the
SVPWM inverter to supply the SPMSM with high
frequency voltage. The block diagram of the measurement
algorithm is shown in Fig.4. By properly adjusting the
voltage and frequency, the amplitude and frequency of the
current can be used to estimate high frequency inductances.
Reactance X (p.u.)
Vc=0.354(p.u)
3
Vc=0.265(p.u)
Vc=0.177(p.u)
2.5
2
0
42.4
84.7
127.1 169.4 211.8 254.1 296.5 338.8
Test angle (deg.)
Fig. 5. High frequency inductances at various voltage supplies
308
(10)
(11)
(12)
feasibility of high frequency injection scheme for
SPMSM’s position detection at zero and low speed are
analyzed. For injecting and demodulating the high
frequency signal, a proper and simplified model is
proposed. Except the simplified voltage equation and
projective process, no additional variables or equations
should be considered. With the proposed experimental
method, feasibility of the target motor can be verified. The
injection voltage’s magnitude and frequency can be
selected with the reference of those experimental results.
Reactance X (p.u.)
3
f=750Hz
2.5
f=600Hz
2
1.5
0
f=450Hz
62.6
125.2
187.8
250.4
TABLE I
Parameters of Sample SPMSM
Rated Power
700 [W]
Rated Torque
2.2 [Nm]
Number of Poles
6
Rated Current
3.65 [A]
Rated Speed
3000 [rpm]
Resistance (per phase)
1.21 [Ω]
Inductance (per phase)
11.2 [mH]
313.0
Test angle (deg.)
Fig. 6. High frequency inductances at various frequencies
Fig.5 shows the high frequency inductance
characteristics at various supplied voltages where the
frequency is 600Hz. As is shown in the figure, the d- axis
high frequency inductance is a bit larger than that of q- axis.
The high frequency inductance difference (ldiff) between dand q- axis is about 5% of the average (lavg) at all current
supply but it varies while voltage supply is being adjusted.
In fig.6, the ratio of voltage and frequency supply
maintains the same value. It shows that the ratio of
inductance difference varies very slightly at different
frequencies. As in fig.5, the high frequency inductance
difference (ldiff) between d- and q- axis is about 5% of the
average (lavg) at all current supply. From fig.6, it can be
known that higher frequency injection method is used
because the magnitude of impedance increases as the
injection frequency increases.
REFERENCES
[1] Ryoji Mizutani, Takaharu Takeshita and Nobuyuki Matsui,
"Current Model-Based Sensorless Drives of Salient-Pole PMSM at
Low Speed and Standstill", IEEE-IAS 1997, Conference Record of
the 1997 IEEE Ind. Appl. Conference
[2] Ji-Hoon Jang, Seung-Ki Sul, Jung-Ik Ha, Kozo Ide and Mitsujiro
Sawamura, "Sensor-less Drive of SMPM Motor by High Frequency
Signal Injection”, IEEE-APEC 2002, Conference Record of the
2002 IEEE Applied Power Electronics Conference
[3] Macro Linke, Ralph Kennel and Joachim Holtz, "Sensorless
Position Control of Permanent Magnet Synchronous Machines
without Limitation at Zero Speed”, IEEE-IAS 2001, Conference
Record of the 2001 IEEE Ind. Appl. Conference
[4] Ji-Hoon Jang, Jung-Ik Ha and Seung-Ki Sul, “Vector Control of
Surface Mounted Permanent Magnet Motor without any Rotational
Transducer”, IEEE-APEC 2001, Conference Record of the 2001
IEEE Applied Power Electronics Conference
IV. CONCLUSION
In this paper, the high frequency model and
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