[Lecture Notes in Electrical Engineering] Mechatronics and Automatic Control Systems Volume 237 ||...
Transcript of [Lecture Notes in Electrical Engineering] Mechatronics and Automatic Control Systems Volume 237 ||...
PMSM Sensorless Vector Control System
Based on Single Shunt Current Sensing
Hongyan Ma
Abstract To reduce the cost and volume of permanent magnet synchronous motor
(PMSM) drive system fed by pulse width modulation (PWM) inverter, this paper
presents a single shunt current sensing with rotor-position sensorless control
method of PMSM vector control system. The reference voltage of space vector
pulse width modulation (SVPWM) inverter is researched to implement the
requirements by AC-link phase current reconstruction with single shunt current
sensing. By model reference adaptive system (MRAS), speed estimation method is
investigated to satisfy rotor-position sensorless control. Simulations are tested on a
PMSM vector control system fed by SVPWM inverter. Simulation results demon-
strate the feasibleness and the effectiveness of the single shunt current sensing with
MRAS sensorless control method.
Keywords Single shunt current sensing • MRAS sensorless • PMSM • PWM
inverter
1 Introduction
For permanent magnet synchronous motor (PMSM) having many advantages such
as high ratio of torque to weight and high efficiency, PMSM vector control systems,
which supplied by pulse width modulation voltage source inverters (PWM-VSI),
are widely used in many applications [1]. High performances PMSM vector control
systems depended on the precise information of AC-link currents by AC-link
current sensors and the rotor position by mechanical sensor. To reduce the cost
and volume of inverter, no current sensors control methods based on a single shunt
current sensing to reconstruct three phase AC currents have been proposed by
H. Ma (*)
Department of Electrical Engineering, Beijing University of Civil Engineering
and Architecture, Beijing, China
e-mail: [email protected]
W. Wang (ed.), Mechatronics and Automatic Control Systems, Lecture Notesin Electrical Engineering 237, DOI 10.1007/978-3-319-01273-5_81,
© Springer International Publishing Switzerland 2014
727
researchers [2–4]. The sensorless rotor-position estimation methods like the
Extended Kalman Filter (EKF) algorithm combining with single shunt sensing
and the model reference adaptive method combining with no AC-link current
sensor have been developed [5, 6].
In sensorless AC drive systems, the practical rotor position/speed estimation
method is based on model reference adaptive system (MRAS). In this paper, single
shunt current sensing with the MRAS sensorless method is researched in PMSM
vector control systems supplied by space vector PWM voltage source inverter
(SVPVM-VSI). The validity and feasibility of the researched method are verified
by simulation results of PMSM vector control systems supplied by three phase
voltage source inverter.
2 Single Shunt Current Reconstruction Based on DC-Link
Single shunt current sensing control scheme is reconstructed the AC-link currents
by the measured DC-link current values with single shunt. The voltage vector
diagram of SVPWM-VSI shown as Fig. 1, there are six sectors in the voltage vector
diagram of SVPWM and six active voltage vectors (V1 ~ V6) and two zero vectors
V0 (000) and V7 (111). The reference voltage vector Vr located in sector 1 is only
studied in follows.
In sector 1, the reference voltage vector Vr is synthesized by the two adjacent
active voltage vectors V1, V2. In the linear modulation range, conventional seven
segment SVPWM signals distribution strategy which is to synthesize Vr by using
two adjacent non-zero vectors and one zero vector in one sampling period Ts is
applied, Vr is given as
Vr ¼ T1Ts
V1 þ T2Ts
V2 (1)
qr
1
2
3
4
5
6
2
3Udc
V2 (110)V3 (010)
V4 (011)
V5 (001) V6 (101)
V1 (100)V7V0
Vr
Fig. 1 The voltage vector
diagram of SVPWM-VSI
728 H. Ma
T1 and T2 are the on-durations of the switching state vectors V1 and V2. They can be
calculated as
T1 ¼ffiffiffi3
pTs
Vrj jUdc
sin θr
T2 ¼ffiffiffi3
pTs
Vrj jUdc
sinðπ=3� θrÞ
8>><>>: (2)
Where Udc is DC-link voltage, θr is the angle of Vr.
The on-duration of zero vector T0 can be obtained as
T0 ¼ Ts � T1 � T2 (3)
Used an active voltage vector to PMSM, AC-link phase current is measured by
the DC-link current idc. In Fig. 2, by detecting idc as active vector V1 employed,
a-phase current ia of the motor is achieved; as zero vectors employed, idc equalszero, then the phase current is not measured. In each control period, two phase
currents achieved by the DC-link current idc, the third phase current is determined
by the zero sum of three-phase currents.
As shown in Table 1, the applied voltage vector employed, the responding phase
current is measured from the DC-link current idc.In practice, using single shunt sensing to reconstruct the AC-link phase current,
the precision of reconstructed AC-link phase current is determined by the DC-link
current. In order to achieve a dependable DC-link current idc, the minimum
sampling time Tmin has to be less than the operation period of applied active vector.
PMSM
a
b
c
on
on on
idc
Udc
R
C
Fig. 2 No AC-link current
sensor control in sector 1
Table 1 Voltage vectors and
measured phase currents by idcVoltage vector idc Voltage vector idc
V0(000) 0 V4(011) �iaV1(100) +ia V5(001) +icV2(110) �ic V6(101) �ibV3(010) +ib V7(111) 0
PMSM Sensorless Vector Control System Based on Single Shunt Current Sensing 729
3 Sensorless PMSM Vector Control
3.1 PMSM Mathematical Model
In the d-q rotor reference frame, PMSM mathematical model of is given by the
following equations.
ud ¼ pψd � ψqωþ Riduq ¼ pψq � ψdωþ Riq
�(4)
ψd ¼ Ldid þ ψ r
ψq ¼ Lqiq
�(5)
Tem ¼ pn iqψd � idψq
� �(6)
Where ud and uq stand d-q axis voltages, id and iq express d-q axis currents, ψd
and ψq denote d-q axis flux linkages, R is stator resistance, Ld and Lq are d-q axis
inductances, ψ r is the permanent magnetic flux, Tem and TL are electrical torque andload torque, pn is numbers of pole pairs of the motor, p is d/dt, ω stands for the rotor
speed that is equal to pθ, θ is the actual rotor position.
3.2 Speed Estimation Method Based on MARS
In MRAS method, the current equation of PMSM is chosen as the adjustable model
and the actual PMSM as reference model. The error between currents of the
adjustable model and the currents of the actual PMSM is used to calculate motor
speed.
In the rotating d-q reference frame, the PMSM stator current equations are
d
dt
id
iq
" #¼
� R
Ld
LqLd
ω
� LdLq
ω � R
Lq
2664
3775 id
iq
" #þ ud
Ld� ωψ r
Lqþ uqLq
� �(7)
Considering the convenience of stability analysis, the systemmatrix A is written as
A ¼� R
Ld
LqLd
ω
� LdLq
ω � R
Lq
2664
3775 (8)
730 H. Ma
Let i0d ¼ id þ ψ r
Ld, i
0q ¼ iq, u
0d ¼ ud
Ldþ Rψ r
L2d
, u0q ¼ uq
Lq. Then the simple reference model
form is obtained as
d
dti0 ¼ Ai
0 þ u0
(9)
Speed estimation process described as follows.
The simple parallel connection adjustable model form is
d
dti0¼ Ai
0þ u
0(10)
The state variables error is
e ¼ i0 � i
0(11)
The parallel connection model is
d
dte ¼ Ae
v ¼ De
((12)
If D ¼ I, then v ¼ e.By the Popov super stability theory, the estimation equation of ω can be obtained
as
ω ¼Z t
0
k1ðid0 iq0 � iq0 id
0Þdτ þ k2ðid0 iq0 � iq0 iq
0Þ þ ωð0Þ (13)
Where, k1 � 0, k2 � 0.
Replacing id0; iq0 with id; iq, the estimated speed is obtained as
ω ¼Z t
0
k1½id iq � iq id � ψ r
Ldðiq � iqÞ�dτ þ k2½id iq � iq id � ψ r
Ldðiq � iqÞ�
þ ωð0Þ (14)
Where, id and iq are determined by the adjustable model, id and iq are achieved bythe transformation of the reconstructed three-phase stator currents with single shunt
current sensing control method.
Integrating the estimated speed, the rotor position is
θ ¼Z t
0
ωdt (15)
PMSM Sensorless Vector Control System Based on Single Shunt Current Sensing 731
4 Simulation Study
In order to prove the feasibleness and effectiveness of single shunt current sensing
with MRAS sensorless method, the diagram of PMSM vector control system is built
in Fig. 3. Conventional vector control technique such as id ¼ 0 is applied to the
PMSM drive system.
The simulation parameters are shown in Table 2. The dead time effect is not
considered in simulation.
Figure 4 shows the speed curve. The speed steady-state error between the motor
speed and the reference speed 1,500 rpm is very small. The motor has good
performance under this control strategy. Figure 5 shows PMSM stator current.
The phase current can concord with the reconstruction current. Figure 6 shows
SVPWM
PI
PI
+
wref
= 0idref
id
iq
iqref
ia
idc
Currentreconstruction
PI
dq
ud
uq
PWM
PWM
ua ub+
dq
abc
+ d /dt
ib icSampling
ˆ
R
q
q
q
wq
ab
PWMInverter PMSMDC
MRAS
−
−
−
Fig. 3 Block diagram of single shunt current sensing with MRAS sensorless PMSM vector
control system
Table 2 The simulation
parameters of the motorParameter Value Parameter Value
Ld/mH 7.418 Lq/mH 12.285
R/Ω 0.618 ψ r/V/(rad/s) 0.1128
pn 2 TL/Nm 1.5
732 H. Ma
0 0.2 0.4 0.6 0.8 1 1.2 1.4−200
0
200
400
600
800
1000
1200
1400
1600
t/s
spee
d/rp
m estimation speed
rotor speed
reference speed
Fig. 4 Speed response curve
1.4 1.405 1.41 1.415 1.42 1.425 1.43 1.435 1.44 1.445 1.45-8
-6
-4
-2
0
2
4
6
8
t/s
curr
ent/A
phase current
reconstruction current
Fig. 5 Waveforms of AC-link phase current
PMSM Sensorless Vector Control System Based on Single Shunt Current Sensing 733
the waveform of rotor position. The real rotor position can concord with the
estimated rotor position by MRAS method and reconstructed AC-link phase
current.
This verifies that the single shunt current sensing with MRAS sensorless control
method is effective in PMSM vector control.
5 Conclusion
In this paper, single shunt current sensing control combined with MRAS sensorless
scheme was used for PWM-VSI fed PMSM vector control system. The MRAS
sensorless control used the reconstructed AC-link phase currents to estimate rotor
position. Simulations demonstrated that, in PWM-VSI fed PMSM vector control,
the method that is using single shunt current sensing with rotor position sensorless
control based on MRAS method, is valid and feasible.
Acknowledgements The author thanks the financial support by Beijing Municipal Commission
of Education of China (PHR201108211) and MOHURD project (2011-k8-3).
1.4 1.405 1.41 1.415 1.42 1.425 1.43 1.435 1.44 1.445 1.45-50
0
50
100
150
200
250
300
350
400
t/s
estimated rotor position
rotor position
Rot
or p
ositio
n/�
Fig. 6 Waveforms of rotor position
734 H. Ma
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PMSM Sensorless Vector Control System Based on Single Shunt Current Sensing 735