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: m_hy71@163.com

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

References

1. Mohamed B (2005) Implementation and experimental investigation of sensorless speed control

with initial rotor position estimation for interior permanent magnet synchronous motor drive.

IEEE Trans Power Electron 20(6):1413–1422

2. Liu Yan, Shao Cheng (2007) Reconstruction strategies for phase currents in three phase voltage-

source PWM inverters. Info Control 36(4):506–513 (In Chinese)

3. Chu Jianbo, Hu Yuwen et al (2010) Phase current sampling reconstruction for inverter. Trans

China Electrotech Soc 25(1):111–117 (In Chinese)

4. Blaabjerg F, Pedersen JK et al (1997) Single current sensor technique in the DC link of three-

phase PWM-VS inverters: a review and a novel solution. IEEE Trans Ind Appl 33

(5):1241–1253

5. Yuan Xibo, Li Yongdong, Feng Lichao (2009) Low cost sensorless control of PMSM for

air-conditioner compressor application. Electr Drive 39(5):15–19 (In Chinese)

6. Sun Kai, Huang Lipei (2010) Sensorless over-modulation control of PMSM-compressor

systems. J Tsinghua Univ (Sci Technol) 50(1):18–22 (In Chinese)

PMSM Sensorless Vector Control System Based on Single Shunt Current Sensing 735