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Application of BEMF-MRAS with Kalman filter in sensorless control of induction motor drive

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Abstract

This paper describes an induction motor speed estimation using the observer with back electromotive force-based model reference adaptive system and Kalman filter. In the first part of the paper, there is a mathematical description of the rotor speed observer. The second part of the paper includes Kalman filter that is used for the filtration of measured stator currents and obtaining their time derivatives. The third part contains a description of the laboratory workplace with the induction motor drive and active load unit that was used for an experimental verification of the rotor speed observer. The last section of the paper shows experimental results that were obtained for different changes in the induction motor speed. The experimental results confirmed expected dynamic properties of the induction motor drive with sensorless control.

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Abbreviations

\(\mathbf{u}_\mathrm{S}^{S}\) :

Stator voltage vector in [\(\alpha ,\beta \)] stator coordinate system

\(\mathbf{e}_\mathrm{m}^{S}\) :

Back electromotive force vector in [\(\alpha ,\beta \)] stator coordinate system

\(\mathbf{i}_\mathrm{m}^{S}\) :

Magnetizing current vector in [\(\alpha , \beta \)] stator coordinate system

\(\mathbf{i}_\mathrm{S}^{S}\) :

Stator current vector in [\(\alpha ,\beta \)] stator coordinate system

\(\mathbf{i}_\mathrm{S}^{F}\) :

Stator current vector in [x, y] rotating field coordinate system

\(i_{{\mathrm{S}x}}\) :

Magnetizing component of the stator current vector in [x, y] rotating field coordinate system

\(i_{{\mathrm{S}y}}\) :

Torque component of the stator current vector in rotating [x, y] field coordinate system

\(i_{{\mathrm{Sxref}}}\) :

Reference magnetizing current component

\({\varvec{\Psi }}_\mathrm{R}^{S}\) :

Rotor flux vector in [\(\alpha , \beta \)] stator coordinate system

\(\varPsi _{{\mathrm{Rref}}}\) :

Reference rotor flux

\(\varPsi _\mathrm{R\_{\mathrm{est}}}\) :

Estimated rotor flux

\(\varPsi _{{\mathrm{RN}}}\) :

Nominal rotor flux

\(L_\mathrm{m}\) :

Magnetizing inductance

\(L_\mathrm{R}\) :

Rotor inductance

\(L_\mathrm{S }\) :

Stator inductance

\(R_\mathrm{R}\) :

Rotor phase resistance

\(R_\mathrm{S}\) :

Stator phase resistance

\(\sigma \) :

Total leakage constant

\(T_\mathrm{R}\) :

Rotor time constant

\(\omega _\mathrm{m}\) :

Real rotor angular speed

\(\omega _\mathrm{m\_{{est}}}\) :

Estimated rotor angular speed

\(\omega _{{\mathrm{ref}}}\) :

Reference rotor angular speed

\(\omega _{{\mathrm{mN}}}\) :

Nominal rotor angular speed

\(\gamma \) :

Orienting angle

P :

Covariance matrix of state vector

Q :

Covariance matrix of system noise vector

R :

Covariance matrix of measurement noise vector

K :

Kalman gain

\(\hat{}\) :

Estimated quantity

\(\tilde{}\) :

Predicted quantity

x(t):

Measured quantity

\(\dot{x}(t)\) :

Time derivative of the measured quantity

x :

State vector

\({\hat{\mathbf{x}}}\) :

Estimated state vector

\({\tilde{\mathbf{x}}}\) :

Predicted state vector

FC:

Frequency converter

PWM:

Pulse width modulation

IS:

Incremental sensor

BEMF-MRAS:

Speed estimation block using BEMF-MRAS

IM:

Induction motor

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Acknowledgements

This paper was supported by the projects: Center for Intelligent Drives and Advanced Machine Control (CIDAM) project, Reg. No. TE02000103 funded by the Technology Agency of the Czech Republic and Project Reg. No. SP2017/104 funded by the Student Grant Competition of VSB-Technical University of Ostrava.

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Authors and Affiliations

  1. Department of Electronics, VSB – Technical University of Ostrava, 17. listopadu 15/2172, 708 33, Ostrava-Poruba, Czech Republic

    Pavel Brandstetter, Marek Dobrovsky & Martin Kuchar

  2. Department of Automation, Ton Duc Thang University Ho Chi Minh City, 19 Nguyen Huu Tho Street Tan Phong Ward, District 7, Ho Chi Minh City, Vietnam

    Chau Si Thien Dong & Hau Huu Vo

Authors
  1. Pavel Brandstetter
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  2. Marek Dobrovsky
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  3. Martin Kuchar
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  4. Chau Si Thien Dong
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  5. Hau Huu Vo
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Correspondence to Pavel Brandstetter.

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Brandstetter, P., Dobrovsky, M., Kuchar, M. et al. Application of BEMF-MRAS with Kalman filter in sensorless control of induction motor drive. Electr Eng 99, 1151–1160 (2017). https://doi.org/10.1007/s00202-017-0613-4

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