Comparison of Rotor Flux and EMF based MRAS for Rotor Speed Estimation in Sensor-less Direct Vector Controlled Induction Motor Drives

(1)

Varun. Puli

, IJRIT 130 International Journal of Research in Information

Technology (IJRIT)

www.ijrit.com www.ijrit.com www.ijrit.com

www.ijrit.com ISSN 2001-5569

Comparison of Rotor Flux and EMF based MRAS for Rotor Speed Estimation in Sensor-less Direct Vector Controlled

Induction Motor Drives

Varun. Puli¹, Mr.A.Venkadesan²

1Student, Department of Electrical and Electronics Engineering, SRM University Chennai, Tamil Nadu, India

[email protected]

2 Assistant Professor, Department of Electrical and Electronics Engineering, SRM University Chennai, Tamil Nadu, India

[email protected]

Abstract

This paper compares two types of MRAS based speed estimators for sensor-less direct vector controlled IM drives.

Model Reference Adaptive System (MRAS) based techniques are one of the popular methods to estimate the rotor speed due to its simplicity. The performance of MRAS scheme depends on the sate variables used for speed estimation.

Hence, in this paper, MRAS scheme with rotor flux and e.m.f as state variable are used for rotor speed estimation. Two types of MRAS schemes are designed based on rotor flux and e.m.f. The performance of rotor flux based MRAS (RF- MRAS) and e.m.f based MRAS (EMF-MRAS) are investigated extensively for various operating conditions. Their performance is compared in terms of mean square error. The suitable MRAS scheme is identified for senor-less direct vector controlled IM drives.

Keywords: Induction-motor (IM) drive, model reference adaptive system (MRAS), Speed estimator, flux based MRAS and EMF based MRAS.

1. Introduction

Advances in digital technology have made the vector control realizable by industries for high performance variable speed control applications. The vector control is classified into two types. They are direct and indirect vector controlled IM drives. The direct vector control is most popularly used in industries. In particular, sensor-less direct vector control is an emerging area. The speed sensor which is expensive, fragile, requires extra attention from failures under hostile environment and needs special enclosures and cabling is not needed for sensor-less direct vector control of Induction Motor (IM) drives. This leads to cheaper and more reliable control. Various on-line speed estimation methods are proposed in the literature.

They are state synthesis equation, Model Reference Adaptive System (MRAS), Observed based techniques.

MRAS scheme offer simpler implementation and require less computational effort compared to other methods and therefore the most popular strategies used for sensor-less control [11]-[13]. The performance of MRAS scheme depends on the state variables used for speed estimation.

In this paper, two types of MRAS methods using flux and e.m.f as state variables are designed and validated through simulation. The performance of these two methods are analysed extensively and

(2)

131 IJRIT

compared in terms of Mean Square Error (MSE). The suitable method for speedestimation for induction motor drive is identified.

Section 2 deals with sensor-less direct vector controlled IM drives. Section 3 deals with MRAS based speed estimation using rotor flux and e.m.f based techniques. Performance comparison of rotor flux and e.m.f MRAS speed estimators is presented in Section 4. The conclusions are drawn in section 5.

2. Sensor-less Direct Vector Controlled IM Drives

The speed sensor-less vector control of induction motor drive presented is direct rotor flux field oriented control. Fig. 1 shows the overall block diagram of the speed-sensor-less drive system of an induction motor. Generally through a PI controller, the speed error signal is processed and the torque command is generated. It is combined with the flux command corresponding to the flux error to generate the common reference to control the motor current. The reference is used to produce the PWM pulses to trigger the voltage source inverter and control the current and frequency applied to the IM drive. The performance of sensor-less vector controlled IM drive to a large extent depends on the accuracy of speed estimation. There are many speed estimation schemes available in the literature. Out of which, MRAS scheme is most popularly used for speed estimation because of its simplicity and hence chosen in this paper. The MRAS schemes are dealt in the section 2.

Fig. 1. Sensor-less Vector Controlled IM Drive showing the Speed Estimator

3. MRAS Estimators

The MRAS technique was first proposed in [2] followed by [3] which consists of a reference model (which determines the desired states) and adjustable model (which generates the estimated values of the states).

The error between these two states is fed to an adaptation mechanism which can be a PI controller to generate an estimated value of the rotor speed. This is used to adjust the adaptive model. This process continues till the error between two outputs tends to zero.

The MRAS with the rotor flux as state variable is called Rotor Flux based MRAS (RF-MRAS). The MRAS with the e.m.f as state variable is called e.m.f based MRAS (EMF-MRAS). These two MRAS techniques are discussed briefly in below.

3.1

Rotor Flux based MRAS (RF-MRAS) Speed Estimation

The schematic representation of Rotor Flux based MRAS is shown in Fig. 2. In Rotor Flux based MRAS (RF-MRAS) speed estimator, the state variable used is the rotor flux. The reference model is constructed by

ωr

C PWM

Inverter

ia

ic va

vc IM

Rotor Flux Oriented Controller

Speed Estimator

PWM-a

PWM- PWM-

r,ref ω

Solid State IM Drive Systems

r,est ωωω ω

Input

ψref

r,est ω ωω ω

(3)

132 IJRIT

voltage model equations because it is independent of rotor speed. This model calculates the rotor flux vector from the machine stator voltages and current signals. The current model flux equations are used as the adaptive model because it is dependent on rotor speed. For adaptive model, fluxes are calculated from the input stator currents if rotor speed is known. The equations defining the reference model are given in (1) and (2) and the equations for adaptive model of induction machine are given in (3) and (4) respectively.

Fig. 2 Block diagram of rotor flux based MRAS

The voltage model equations of the induction motor is given as

] )

(

[

_dr _s _qs _s _qs

m s r

qr

v R i dt L i

L

L σ

ψ = ∫ − −

(1)

] )

(

[

_dr _s _ds _s _ds

m s r

dr

v R i dt L i

L

L σ

ψ = ∫ − −

(2)

Where,

r s

m

L L

L

²

1 − σ =

The current model equations of the induction motor is given as

_qs

r m dr r qr r

qr

i

T L T

dt

d ψ = 1 ψ + ω ψ +

(3)

ds r m qr r dr r

dr

i

T L T

dt

d ψ = ¹ ψ + ω ψ +

(4)

PI controller is used as the adaptive mechanism.

3.1 EMF based MRAS (EMF-MRAS) Speed Estimation

The schematic representation of e.m.f based MRAS is shown in Fig. 3. In EMF-MRAS speed estimator, the state variable used is back e.m.f. The equations for reference model are presented in (5) and (6). The equations for adaptive model are shown in (7) and (8).

Reference Model

idq

Adaptive Mechanism (PI-Controller) vdq

Adaptive Model

sqr Ψ

' s Ψdr

' sqr Ψ ,

r est ω

ξ

s Ψdr

(4)

133 IJRIT

Fig. 3 Block diagram of EMF based MRAS

The reference model equations of the induction motor are given as

)

( dt

L di i R v

e

_md^s

=

_ds

−

_s _ds

+

_s ^ds (5)

)

( dt

L di i R v

e

_mq^s

=

_qs

−

_s _qs

+

_s ^qs (6)

The adaptive model equations are given as

1 1 )

(

2

ds r md r mq r r m

md

i

i T i T

L

e = L − ω − +

(7)

1 1 )

(

2

qs r mq r md r r m

mq

i

i T i T

L

e = L − ω − +

(8)

Where, _ds

r md r mq r

md

i

i T i T

dt

di 1 1

+

−

= ω

_qs

r mq r md r

mq

i

i T i T

dt

di 1 1

+

−

= ω

4. Performance Comparison of Rotor Flux and EMF MARS Speed Estimators

The Performance of flux and EMF based MRAS methods are analysed for various operating conditions extensively for rotor speed estimation. Sample results for the major test conditions are presented in the following sections. The operating conditions are explained in terms of operating frequency & load instead of speed & load for convenience.

4.1 Test 1- Change in frequency from 50Hz to -50Hz under 0% loaded condition

In this test condition, the motor is initially operated with the frequency of 50 Hz and the frequency is gradually changed to -50 Hz under 0% loaded condition. Fig. 4 shows the performance of RF-MRAS and EMF-MRAS for ramp change in frequency. From the results obtained, it is observed that the RF-MRAS shows superior steady state and transient response as compared to EMF-MRAS.

4.2 Test 2- Change in frequency from 50Hz to -50Hz under 100% loaded condition

This test condition examines the frequency change capability of MRAS schemes. In this operating condition, the motor is initially operated with the frequency of 50 Hz and the frequency is gradually changed to -50 Hz under 100% loaded condition. Fig. 5 shows the performance of RF-MRAS and EMF-

Reference Model

idq

Adaptive Mechanism (PI-Controller) vdq

Adaptive Model

e

^sqr

e

^'sdr

e

^'sqr ,

r est ω

ξ

e

^s_dr

(5)

134 IJRIT

MRAS. From the results obtained, it is again observed that the RF-MRAS shows superior steady state and transient response as compared to EMF-MRAS.

4.3 Test 3- Rated frequency with step change in load torque from 0% to 100%

The test condition 3 examines the performance of both the MRAS schemes for load torque disturbance under rated frequency. The motor is initially operated at rated frequency under 0% loaded condition and 100% step change in load torque is given at 2sec. The performance of RF-MRAS and EMF-MRAS is shown in Fig. 6. From the results obtained, it is observed that the speed estimated from the RF-MRAS closely tracks the actual with lesser error and settles faster with the actual as compared to speed estimated from the EMF-MRAS. The transient response is also observed to be good for RF-MRAS as compared to EMF-MRAS.

4.4 Test 4- Rated frequency with step change in load torque from 100% to 50%

The test condition 4 also examines the performance of both the MRAS schemes for load torque disturbance under rated frequency. The motor is initially operated at rated frequency under 100% loaded condition and the torque is reduced to 50% at 2sec. Fig. 7 shows the performance of RF-MRAS and EMF-MRAS. From the results obtained, it is observed that the speed estimated from the RF-MRAS closely tracks the actual with lesser error and settles faster with the actual as compared to speed estimated from the EMF-MRAS. In this test also, the transient response is found to be good for RF-MRAS as compared to EMF-MRAS.

(a)

(b)

Fig. 4 Actual and estimated speed for Test condition 1: (a) RF-MRAS (b) EMF-MRAS

(6)

135 IJRIT

(a)

(b)

(a)

(b)

(7)

136 IJRIT

(a)

(b)

Table 1

Performance Comparison of RF-MRAS and EMF-MRAS in terms of Mean Square Error (MSE)

Types

Mean Square Error Test Condition

1

Test Condition 2

Test Condition 3

Test Condition 4 RF-MRAS 5.3228×10^-4 2.659×10^-4 2.5965×10^-4 6.8246×10^-5

EMF-

MRAS 0.0154 0.0111 0.1442 0.0347

The performance of RF-MRAS and EMF-MRAS is compared in terms of Mean Square Error (MSE). The results obtained is consolidated and presented in Table I. Means Square Error is given by

∑

=

−

=

ⁿ

i

Estimated Actual

MSE n

1

)

2

1 (

Where n is total number of data over a period.

From Table 1, it is observed that Mean Square Error of flux based MRAS is lesser than the EMF based MRAS for all the operating conditions. Hence, it can be concluded that the Flux based MRAS method is found to be more suitable for speed estimation in sensor-less direct vector controlled IM drives.

5. Conclusion

This paper identifies a suitable MRAS scheme for sensor-less direct vector controlled IM drives. Two types of MRAS methods based on rotor flux (RF-MRAS) and e.m.f (EMF-MRAS) as state variables are designed

(8)

137 IJRIT

for rotor speed estimation. The performance of RF-MRAS and EMF-MRAS are tested extensively for various operating conditions. Both the MRAS schemes is compared in terms of MSE. From the investigations, it is found that RF-MRAS shows better MSE as compared to EMF-MRAS. Hence, flux based MRAS method is found to be more suitable for sensor-less direct vector controlled IM drives.

6. Appendix

Table 2

Electrical And Mechanical parameters of the IM

Parameters Values

Rated Power 1.1 KW

Rated voltage 415 V

Rated current 2.7 A

Type 3 Phase

Frequency 50Hz

Number of poles 4

Stator Resistance (R_s) 6.03Ω Rotor Resistance (R_r) 6.085Ω Magnetizing Inductance (L_m) 0.4893H Stator Inductance (L_s) 0.5192H Rotor Inductance (L_r) 0.5192H

Inertia (J_tot) 0.01178Kgm²

Friction (B) 0.0027 Kgm²/s

Rated Torque (T) 7.5Nm

References

[1] M. Ta-Cao, Y. Hori and T. Uchida, “MRAS-based speed sensorless control for induction motor drives using instantaneous reactive power”, IEEE-IES conference rcord, pp. 1717-1422. 2001.

[2]S. Tamai, H. Sugimoto, M.Yano, “Speed-sensorless vector control of induction motor with model reference adaptive system”, Conf. Record of the 1985 IEEE-IAS Annual Meeting, pp. 613-620, 1985.

[3] C. Shauder, “Adaptive speed identification for vector control of induction motor without rotational transducers”, IEEE Trans. Ind. Application, Vol. 28, No. 5, pp. 1054-1061, sept./oct. 1992.

[4] A. Venkadesan, S. Himavathi and A. Muthuramalingam, “A Robust RF-MRAS based Speed Estimator using Neural Network as a Reference Model for Sensor-less Vector Controlled IM Drives”, ISSN Control Theory and Informatics, Vol. 2, No.3, pp.2225-0492, 2012.

[5] P. C. Krause, O. Wasynczuk, S. D. Sudhoff, “Analysis of electric machinery and drive system” IEEE press, 2002.

[6] Ms. M. Nandhini Gayathri, Dr. S. Himavathi and Dr. R. Sankaran, “Comparison of Rotor Flux and Reactive Power based MRAS Rotor Resistance Estimators for Vector Controlled Induction Motor Drive”, IEEE-International Conference On Advances In Engineering, Science And Management (ICAESM-2012) March 30, 31, 2012.

[7] Dr. Dhiya Ali AL-Nimma and Salam Ibrahim Khather, “Modelling and simulation of a speed sensorless vector controlled induction motor drive system”, CCECE, pp. 978-1-4244-9789-8/11, 2011.

(9)

138 IJRIT

[8] M. Rashed and A. F. Sronach “A Stable Back-EMF MRAS-based sensorless low-speed induction motor drive insensitive to stator resistance variation”, IEEE Proc.-Electr. Power Appl., Vol. 151, No. 6, November 2004.

[9] Mokhtar Zerikat and Soufyane Chekroun and Abdelkader Mechernene, “A Robust MRAS-Sensorless Scheme Based Rotor and Stator Resistances Estimation of a Direct Vector Controlled Induction Motor Drive”, IEEE, pp. 978-1-4577-0914-2/11, 2011.

[10] Bimal K. Bose, “Modern Power Electronics and AC Drives”, Prentice-Hall, Pvt.Ltd., India 2005.

[11]Shady M.Gadoue, Damian Giaouris and John W. Finch, “Sensorless Control of Induction Motor Drives at Very Low and Zero Speeds Using Neural Network Flux Observers”, IEEE Transactions on Industrial Electronics, Vol. 56, No 8, pp.3029-3039, August 2009.

[12] V. Vasic and S. Vukosavic uder, “Robust MRAS-based algorithm for stator resistance and rotor speed identification”, IEEE Power Eng. Rev., vol. 21, no. 11, pp. 39–41, Nov. 2001.

[13] Colin Schauder, “Adaptive Speed Identification for Vector Control of Induction Motors without Rotational Transducers”, IEEE Transactions on Industry Applications, Vol. 28, No.5, pp.1054-1061, September/October 1992.

[14] P. Vas, “Sensorless Vector and Direct Torque Control”, NewYork:Oxford Univ. Press, 1998.

[15] S.Maiti, C. Chakraborty, Y.Hori and M.C. Ta, “Model reference adaptive controller-based rotor resistance and speed estimation techniques for vector controlled induction motor drive utilizing reactive power”, IEEE Transactions on Industrial Electronics, Vol.55, No.2, pp. 594-601,Feb. 2008.

[16] P.Vas, Sensorless Vector and Direct Torque Control, New York: Oxford University Press, 1998.