Fast Control of Filter for Sensor Less Vector Control SQIM Drive With Sinusoidal Motor Voltage

8/14/2019 Fast Control of Filter for Sensor Less Vector Control SQIM Drive With Sinusoidal Motor Voltage

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 5, OCTOBER 2007 2435

Fast Control of Filter for Sensorless Vector ControlSQIM Drive With Sinusoidal Motor Voltage

Suvajit Mukherjee and Gautam Poddar

AbstractA pulsewidth-modulated (PWM) voltage applied toa squirrel-cage induction motor (SQIM) can cause high bearingcurrents, heating of rotor shaft, voltage spike across the motorterminals, etc. Filtering of this PWM voltage to obtain a sinusoidaloutput voltage can be a solution to this problem. However, apassive LC filter makes the dynamic performance of the drivepoor for high-performance control application. In this paper, afeed-forward control strategy for the LC filter is proposed tohave a good bandwidth for the filter output voltage. This filtercontrol strategy is introduced along with a sensorless vector con-trol strategy for the SQIM drive. This complete strategy retainsthe high dynamic performance of the drive even with the LC

filter. In this paper, a three-level converter is used as a voltagesource inverter for the drive to have a less filter-size requirement.The control strategy is verified on a 7.5-hp SQIM drive witha three-level insulated-gate bipolar-transistor inverter and LCfilter. Experimental results validate the high dynamic performanceof the drive with filter.

Index TermsFilter, multilevel converter, sensorless control,squirrel-cage induction motor (SQIM), vector control.

NOMENCLATURE

Ls, Lr Stator and rotor self-inductances referred to thestator.

L0 Magnetizing inductance.s, r Stator and rotor leakage factors. Total leakage factor.Lf, Cf, Rf Filter inductance, capacitance, and resistance.Rs, Rr Stator and rotor resistances referred to the stator.P Number of poles of the motor.is Stator-current vector in the stationary reference

frame.ir Rotor-current vector in the rotor reference frame.iinv Inverter-current vector.iinvd, iinvq d- and q-axes inverter currents.Vs Stator-voltage vector in stationary reference

frame.

Vr Rotor-voltage vector in rotor reference frame.Es Stator-voltage vector after resistance drop in sta-

tionary reference frame.

Vsd, Vsq d- and q-axes stator voltages.Vrd, Vrq d- and q-axes rotor voltages. Angle between the stator and rotor axes.

Manuscript received December 9, 2005; revised October 3, 2006.The authors are with the Department of Electrical Engineering, Indian Insti-

tute of Technology, Kharagpur, West Bengal 721 302, India (e-mail: [email protected]; [email protected]; [email protected]).

Digital Object Identifier 10.1109/TIE.2007.900355

mr, r Rotor-flux angle with respect to the stator androtor axes.

rs, rs - and -axes rotor flux in the stationary referenceframe.

I. INTRODUCTION

IN A NORMAL squirrel-cage induction motor (SQIM)

drive, the motor normally sees pulsewidth-modulated

(PWM) voltages which cause high bearing currents (due to

d/dt) and heating of rotor shaft [1]. In certain applications,shaft voltages [2] can cause direct damage, e.g., sparks in ahazardous environment, and are very undesirable. For a long

cable length between the drive motor and the PWM inverter,

the motor can experience a voltage reflection at the motor

terminals up to two times the applied voltage [3], [4]. This

presents the possibility of serious insulation damage. This is

a matter of big concern for variable speed medium-voltage

drives where the voltage levels are very high. As the voltage

ratings of insulated-gate bipolar transistors (IGBTs) increase

and with the introduction of other high-power fast-switching

devices, such as the integrated gate commutated thyristor, more

medium-voltage PWM voltage-source-inverter (VSI) drives are

being developed and applied. Although they usually employpower converter topologies and switching strategies which are

different from those of low-voltage inverters, the medium-

voltage inverters also generate common-mode voltages and

currents and can have a very high d/dt rate. Naturally, thereare concerns of possible motor shaft voltage, bearing-current

problems, and reflection of high voltage on the motor terminals.

The aforementioned problem can be resolved by applying

variable voltage and variable frequency sinusoidal voltage to

the machine instead of the PWM voltage. Therefore, the filtered

PWM voltage is normally adopted to reduce these problems.

In this paper, a passive LC filter is also used to obtain a

sinusoidal voltage from a PWM inverter. However, there is aninherent problem of a passive LC filter, making the dynamicperformance of a vector control SQIM drive poor. Only few

publications [5][7] deal with the SQIM drive with an output

LCfilter. This paper [5] does not show the dynamical opera-tion of the drive with an LC filter. This paper [6] proposes avector control drive with a dead-beat-controlled PWM inverter.

This paper [7] uses an adaptive full-order observer to control

the motor with an LC filter. The dynamical performances ofthese controllers show undesirable oscillations in torque and

flux responses. In this report, a feed-forward control strategy

for the LC filter is proposed to have a good bandwidth forthe output voltage controller. This enables retention of the high

0278-0046/$25.00 2007 IEEE


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2436 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 5, OCTOBER 2007

Fig. 1. Block diagram of the filter-control sensorless vector control SQIMdrive.

dynamic performance of a sensorless vector control SQIM drive

with the LCfilter.For a better dynamic response and for a minimum fundamen-

tal voltage drop across the choke, the filter size is required to

be low. Since the inverter output voltage harmonics is less incase of a multilevel converter, the amount of filtering required

to obtain the sinusoidal voltage is significantly low as compared

to a two-level converter [8]. Because of this, the filter size and

loss will be less. Hence, the efficiency of the drive will be better.

In this paper, a three-level IGBT converter is used as a VSI for

the drive.

II. FUNDAMENTALS OF BASIC CONFIGURATION

The configuration for the SQIM drive is shown in Fig. 1. The

inverter output voltage is filtered by the LC filter which is

then fed to an SQIM. A three-level inverter, instead of a two-level, is used to have a relatively small LC filter to obtainthe sinusoidal voltage for the motor. In this paper, a sensorless

rotor-flux-oriented vector control strategy is proposed for the

motor control. Filter controller is also developed on the rotor-

flux plane. The motor and the filter analyses are given next to

identify the control method suitable for this configuration.

A. Rotor-Flux-Oriented SQIM Model

The dynamical equations of the motor voltages and currents

are presented here, assuming a symmetrical three-phase ma-

chine [12]. The stator-voltage equation, in the stator coordinate,is furnished as follows:

Vs = Rsis + Lsdisdt

+ L0direj

dt

. (1)

Similarly, the rotor-voltage equation, in the rotor coordinate, is

given as follows:

Vr = Rrir + Lrdirdt

+ L0dise

j

dt. (2)

The important part of the rotor-flux orientation is the rotor-flux vector (r). This rotor-flux vector (r) can be identified in

Fig. 2. Angular positions of the stator and the rotor fluxes with respect to thestator and the rotor axes.

the stator reference frame as follows:

r = Lrirej + L0is = re

jmr . (3)

The relative positions of the stator-flux vector (s) and the

rotor-flux vector (r) with respect to the stator and the rotoraxes are shown in Fig. 2. The stator side (1) is transformed to

a coordinate system that is aligned to the rotor-flux vector by

multiplying ejmr . After rearranging the real and the imagi-nary parts in (1) and (3), the d-axis (along the rotor-flux vector)and the q-axis (perpendicular to the rotor-flux vector) stator-voltage equations are obtained as follows:

Vsd =Rsisd + Lsdisddt

Lsmrisq +1

(1 + r)

drdt

(4)

Vsq =Rsisq + Lsdisqdt

+Lsmrisd+rmr

(1 + r). (5)

Here, mr is the rotor-flux speed with respect to the statoraxis and is equal to dmr/dt. Similar orientation is done onthe rotor side variables by multiplying (2) with ejr to obtainthe dq-axes rotor-voltage (Vrd and Vrq) equations. For squirrelcage motor, Vrd = Vrq = 0. This yields the dynamical equationof the rotor flux (r) and the estimation of rotor-flux frequencywith respect to the rotor, i.e., the motor slip frequency r

isd =1

L0

r +

LrRr

drdt

(6)

r = drdt

= Rrisq(1 + r)r

. (7)

The electromagnetic torque of the motor can also be ex-

pressed in terms of the rotor flux and the q-axis stator currentas follows:

md =2

3

P

2

risq

1 + r. (8)

Finally, the rotor speed (e) follows the relation, which isgiven as follows:

e = mr r. (9)


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MUKHERJEE AND PODDAR: FAST CONTROL OF FILTER FOR SENSORLESS VECTOR CONTROL SQIM DRIVE 2437

B. Sensorless Estimation of Rotor-Flux Vector

In sensorless rotor-flux orientation, the rotor-flux position

mr (Fig. 2) is to be estimated without the information of rotorposition [9][11]. Thus, an indirect method of estimating mris employed here. The stator-flux equation in the stationary

reference frame can be furnished as follows:

s = L0

(1 + s)is +ire

j. (10)

The rotor-flux equation in the stationary reference frame rscan be written as

rs = rej = L0

(1 + r)ire

j +is

. (11)

From (10) and (11), the relation between the stator and the

rotor-flux vectors can be derived as

rs =LrL0

{s Lsis} (12)

where = 1 [1/(1 + s)(1 + r)] is the total leakage factor

of the machine. The stator flux s is estimated from the statorvoltage Vs as follows:

s =

(Vs Rsis). (13)

Substituting (13) into (12), the rotor-flux vector can be

written as

rs =LrL0

(Vs Rsis)

Lsis

. (14)

However, if the stator resistance Rs and the stator voltage Vs arenot estimated accurately, the estimated stator flux s may getsaturated due to the effect of pure integration at low frequency

of operation. This problem is tackled by replacing the pure

integration of (13) with a low-pass filter [10], [11].

Now, the rotor-flux vector magnitude (r) and position of

rotor flux (mr) can be estimated as

rs =rs + jrs

r =2rs +

2rs

mr = tan1

rsrs

. (15)

The rotor-flux frequency with respect to the stator axis is

obtained as follows:

mr = cos mr d sin mr

dt sin mr d cos

mr

dt. (16)

Fig. 3. (a) d-axis motor current controller. (b) q-axis motor current controller.

The differential terms in the aforementioned equation con-

tribute to some noise, which can be eliminated by employing afirst-order low-pass filter.

C. Filter Model in Rotor-Flux Plane

The dynamic equations of the LCfilter at the output of theinverter are as follows:

iinv =CfdVsdt

+is (17)

Vinv =Lfdiinvdt

+ Rfiinv + Vs. (18)

The filter output voltage, i.e., the stator voltage (Vs) of themotor, is to be controlled to its reference value. The reference

values of the stator voltages (Vsd andVsq) are generated by

the rotor-flux-oriented drive controller, as shown in Fig. 3.

These references are in rotor-flux-oriented dq reference frame.Therefore, (17) and (18) are also resolved in the dq referenceframe by multiplying ejmr . The final dq-axes equations aregiven as follows:

iinvd =CfdVsd

dt

CfmrVsq + isd (19)

iinvq =CfdVsqdt

+ CfmrVsd + isq (20)

Vinvd =Rfiinvd + Lfdiinvddt

Lfmriinvq + Vsd (21)

Vinvq =Rfiinvq + Lfdiinvqdt

+ Lfmriinvd + Vsq. (22)

The stator voltages, i.e., the filter output voltages (Vsd andVsq), have the first-order dynamics when the motor currents(isd and isq) and the other underlined terms are feed forwarded

in (19) and (20). The inverter currents iinvd and iinvq are thedriving forces ofVsd and Vsq.


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Fig. 4. (a) Machine model. (b) Rotor speed and the q-axis motor current controller. (c) Rotor flux and the d-axis motor current controller.

The inverter currents iinvd and iinvq also have the first-orderdynamics when Vsd and Vsq, and the other underlined terms arefeed forwarded in (21) and (22). The driving forces of these

dynamical equations are the PWM inverter output voltages(Vinvd and Vinvq).

III. PROPOSED CONTROL METHOD

The proposed sensorless motor control along with the filter

is presented next.

A. Motor Control

The d- and q-axes voltages (4) and (5) represent the first-order dynamics of the stator currents (isd and isq) if theunderlined terms are removed to decouple the d- and q-axes

quantities. Then, PI controllers can control the dq axes cur-rents to their reference values, as shown in Fig. 3. By choos-

ing the proper gain values of the controllers, the closed-loop

transfer functions ofisd and isq become as follows:

isd(s)

isd(s)=

1

1 + sim

isq(s)

isq(s)=

1

1 + sim. (23)

In this paper, the desired time constant im of the motorcurrent controller is selected as 4 ms. Finally, the outputs of

the PI controllers are added to the underlined decoupling terms

of (4) and (5) to get the actual d- and q-axes voltage references.The q-axis current reference, which is equivalent to the

torque command (8) when r is constant, is obtained from the

speed-controller output. A simple PI controller is introduced forthe speed control, as shown in Fig. 4. The estimated rotor speed


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Fig. 5. (a) Closed-loop voltage. (b) Current controllers for theLCfilter.

using (7), (9), and (16) is used as a speed feedback for the speed

controller.

B. Feed-Forward Filter Control

If the underlined terms are removed from the filter (19) and

(20), the d- and q-axes equations become simple first-ordersystem. The transfer functions of this modified system are given

as follows:

Vsd(s)

iinvd(s)=

1

sCf

Vsq(s)

iinvq(s)=

1

sCf. (24)

Therefore, two PI-controllers can control the d- and q-axesvoltages (Vsd and Vsq), as shown in Fig. 5(a). By choosing theproper value ofKpv, the desired time constant dvf ofVsd andVsq controllers can be achieved. The net closed-loop transferfunctions ofVsd and Vsq controllers now become as follows:

VsdVsd

=1

1 + dvfs

VsqVsq

= 11 + dvfs

. (25)

Finally, the feed-forward motor current components isd andisq and the decoupled components, which are shown by theunderlined terms of (19) and (20), are added to the outputs of

the Vsd and Vsq controllers. They generate the actual d- andq-axes inverter-current commands (iinvd and i

invq), as shown

in Fig. 6.

Again, by removing the underlined terms from (21) and (22),the d- and q-axes equations can be transformed to simple first-order equations. The transfer functions of these simple systems

are given as follows:

iinvd(s)

Vinvd(s)=

1

Rf + sLf

iinvq(s)

Vinvq(s)=

1

Rf + sLf. (26)

With proper gain values of the two PI controllers [as shown

in Fig. 5(b)], the closed-loop transfer functions of the inverter

currents become as follows:

iinvdiinvd

=1

1 + difs

iinvqiinvq

=1

1 + difs. (27)

The underlined terms of (21) and (22) are added to these

PI-controller outputs to generate the d- and q-axes voltagecommands of the inverter (Vinvd and V

invq), as shown in Fig. 6.

Here, the actual load voltages Vsd and Vsq are the feed-forwardcomponents of the inverter current controllers. Finally, the

d- and q-axes voltage references go to the space vector mod-

ulator to generate the gate pulses of the three-level inverter ofthe drive (Fig. 6).

After introducing the filter and its controllers, the original

structure (Fig. 3) of the d-axis motor current controller waschanged, as shown in Fig. 7. Similarly, the q-axis motor cur-rent controller also gets modified like the d-axis counter part.Now, it is desired that the motor current controllers retain the

same bandwidth of approximately 1/im (23) for the samedynamical performance of the motor without filter. This means

that the inner filter voltage controllers (Vsd and Vsq) shouldhave the bandwidth of an order higher than that of the motor

current controller. Therefore, the desired time constant (dvf)

of the filter voltage controllers (25) is selected as im/10,i.e., 400 s for this paper. The time constant (dif) of the filtercurrent controllers (iinvd and iinvq) is also taken as 400 s. Thisis achieved by switching the inverter at 5 KHz.

IV. EXPERIMENTAL RESULTS

The experimental verification is carried out on a 7.5-hp

squirrel-cage induction motor. The inverter used in this drive is

a three-phase 10-kVA three-level diode-clamped inverter which

is developed in the laboratory. The switching frequency of the

inverter is 5 kHz. The complete control strategy is implemented

on a digital controller. This digital-control board is based on a

16-b fixed-point digital signal processor. There are two currentsensors to measure the motor line currents and another set of


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Fig. 6. Controller block diagram of theLCfilter.

Fig. 7. Modified d-axis motor current controller with filter.

two line current sensors for the inverter currents. There are two

voltage sensors to measure the stator line voltages. The control

software for the drive is written in assembly language, and the

software execution time is 200 s.

A. Steady-State Performance

Fig. 8 shows the sensorless estimation of the rotor-flux

position (mr) at 25 Hz. Fig. 9 shows the steady-state linevoltage and line current. It confirms that sinusoidal voltage is

applied to the machine instead of the PWM voltage.

B. Dynamic Performance

Fig. 10 shows the response of the torque current (isq) for astep change in the torque-current command (isq). This figure

suggests that the isq has a first-order response with a timeconstant of 4 ms as the controller is designed. Fig. 11 shows

Fig. 8. Experimental waveform of the estimation of rotor-flux position(cos mr and sinmr).

the decoupling of isq and isd during the transient operation.Fig. 12 shows the dynamics of motor voltage (Vs1) during thesudden change of isq. This figure confirms the fast control offilter output voltage without any oscillations. Fig. 13 shows the

rotor speed (e) and the torque current (isq) for a step changein speed command.


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Fig. 9. Experimental waveform of the steady-state motor line current andvoltage.

Fig. 10. Torque current (isq) for a step change in torque-current command(isq).

Fig. 11. Experimental waveform ofisq and isd for a step change in torquecurrent.

V. CONCLUSION

A fast filter control strategy is proposed in this paper for a

sensorless rotor-flux-oriented vector control SQIM drive. The

proposed drive uses a three-level inverter to have a small filter-

size requirement to achieve the sinusoidal voltage at the motor

terminal. Using the proposed feed-forward control strategy for

this filter, a first-order response is achieved for the motor-terminal voltage with a time constant of 400 s. Because of

Fig. 12. Sudden change ofisq and the motor line voltage (Vs1).

Fig. 13. Experimental waveform of speed (e) and isq with a step change in

speed reference.

this fast voltage response, the motor currents are also controlled

with a response time of 4 ms. The experimental results show

the decouple control of the torque current and the rotor flux,

reliable estimation of the rotor-flux position without the rotor

position encoder, etc. Thus, the performances of the sensorless

vector control drive are not sacrificed with the introduction of

the LC filter. However, the motor-terminal voltage remainssinusoidal at all operating conditions. Therefore, the life of the

motor is also expected to be very high.

APPENDIX

MOTOR PARAMETERS

1) Rated power of 7.5 hp.

2) Rated frequency of 50 Hz.

3) Rated speed of 1435 r/min.

4) Number of pole that is 4.

5) Stator line voltage of 415 V.

6) Rated line current of 10.8 A.

7) Stator resistance Rs = 1.3 .8) Rotor resistanceRr = 3.35 .9) Magnetizing inductance L0 = 0.1035 H.

10) Stator leakage factor s = 0.3159 H.11) Rotor leakage factor r = 0.3159 H.

12) Filter inductance Lf = 2.7 mH.13) Filter capacitance Cf = 47 F.


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REFERENCES

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Suvajit Mukherjee received the B.E. degree inelectrical engineering from Bengal Engineering Col-lege, Shibpur, India, in 2001, and the M.E. degreein electrical engineering from Jadavpur University,Calcutta, India, in 2004. He is currently workingtoward the Ph.D. degree at the Indian Institute ofTechnology, Kharagpur, West Bengal, India.

Since 2004, he has been in the Department of

Electrical Engineering, Indian Institute of Technol-ogy, as a Research Scholar. His fields of researchinterests are multilevel converters, control of high-

power drives, and sensorless control of ac motors.

Gautam Poddar received the B.E. degree in elec-trical engineering from Bengal Engineering College,

Calcutta University, West Bengal, India, in 1992, theM.Tech. degree in electrical engineering from IndianInstitute of Technology, Kharagpur, West Bengal,India, in 1994, and the Ph.D. degree in electri-cal engineering from Indian Institute of Science,Bangalore, India, in 2002.

From 1995 to 2004, he was with the Power Elec-tronics Group, Electronics Research and Develop-ment Centre, India,where he wasworkingin thefield

of power electronics and drives. Since 2004, he has been in the Departmentof Electrical Engineering, Indian Institute of Technology, as an AssistantProfessor. His fields of research interest are control of high-power drives,sensorless control of ac motor, and active power filters.

Dr. Poddar was the recipient of the Indian National Academy of EngineersYoung Engineers Award 2003.

Fast Control of Filter for Sensor Less Vector Control SQIM Drive With Sinusoidal Motor Voltage

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Transcript of Fast Control of Filter for Sensor Less Vector Control SQIM Drive With Sinusoidal Motor Voltage