E.V. Bolovin, A.S. Glazyrin.

Department of Electric Drives and Equipment, National Research Tomsk Polytechnic University, Tomsk, Russia

Identification of the induction motor parameters by difference schemes

Abstract

In this paper a method for determining the induction motor parameters is developed based difference schemes.

Key words: induction motor, identification, difference schemes.

Introduction

The induction motors are widespread in industrial area due to they advantages such as simple design , reliability , durability , and low cost. Frequency converters are used in electric drive for increasing motor productivity and improving the static and dynamic operation. The frequency converters use the scalar and vector control Both control methods are dependent on a correct assessment of the induction motor parameters and are very sensitive to change . So, it’s necessary to continuously monitor changing parameters of the engine and determine the values of the parameter estimates with minimum error and quick.

Identification of the induction motor parameters

The induction motor was considered. Mathematical model of the induction motor with the well-known assumptions [1], may be written as follows:

(1)

here T₂ – rotor time constant;

R₁ - resistance of the stator winding , Ohm;

R'₂ - given to the stator rotor resistance , Ohm;

L₁=L_1σ+L_m - the equivalent inductance of the stator winding , H ;

L₂=L′_2σ +L_m - the equivalent inductance of the rotor winding , H ;

L_1σ - leakage inductance of the stator winding , H ;

L'_2σ - reduced to the stator leakage inductance of the rotor winding , H ;

L_m - resulting inductance due to the magnetic flux in the air gap of the machine , H ;

 - sinusoidal shape of the stator voltage component α axis orthogonal coordinate system fixed α, β, V;

- cosine shape component of the stator voltage axis orthogonal β fixed coordinate system α, β, V;

- peak value of the phase voltage of the stator winding , V;

U₁- phase voltage rms value of the stator winding, V ;

f₁ - the frequency of the stator voltage , Hz;

i_1α, i_1β - components of the stator current ( stator winding phase currents ) in the coordinate system α, β, A;

Ψ_2α, Ψ_2β - components of the rotor flux linkage in the system of coordinates α, β, Wb ;

М_с - the time of the static resistance of the motor shaft , including its own engine friction torque , N·m ;

 - scattering coefficient ;

J - moment of inertia , kg·m².

After numerous performances and replaced in the system (1) we obtain the equation (2):

          (2)

here

Given the interval Δt time sampling measurement system pass from the differential equation (DE ) to the system of difference equations (SDE ), written in matrix form with respect to the current and previous t_j-x·k=t_j-Δt·k moments of time at a constant guest parameters , where x=0, 1, 2,…5; k - the coefficient of delay time.

 (3)

where

- is the coupling matrix between the unknown parameters and external forcings,

- external influences matrix,

K=[K₁, K₂, K₃, K₄, K₅]^Т - the vector of unknown parameters.

In the above matrices - the components of the stator current (stator winding phase currents ) in the coordinate system α, β; - the first derivatives of the stator currents (phase stator winding currents ) in the coordinate system α, β; - second derivatives of the currents along the axis α; - voltage components a stator in the coordinate system α, β; - derivatives stator voltage in the coordinate system α, β by j, j-1·k, j-2·k,…, j-5·k steps, respectively.

We calculate the coefficients by solving a system of equations (3) by the method of least squares for finding estimates of the induction motor parameters:

After finding the coefficients define the parameter estimates AC-motor as follows:

Conclusion

The procedure of compilation the difference equations for identification the induction motor parameters is presented. This procedure can be used for adaptive control of electric drive

Bibliography

1. Cincirone, M., M. Pucci, G. Cincirone, and G. A. Capolino. A new experimental application of least-squares techniques for the estimation of the parameter of the induction motor // IEEE Trans. on Ind. Applications. Sep. 2003. Vol. 39, No. 5. С. 1247–1255.