Idealized Two-Axis Model of Induction Machines under Rotor Fault

Rodyukov,; Медведев, С. Б.

doi:10.1109/iciea.2006.257199

Cited by 6 publications

(2 citation statements)

References 6 publications

(7 reference statements)

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“…vii. Models which approximate the effect of rotor bar breakage with the variations of equivalent resistance [41][42][43][44][45][46][47][48][49][50][51][52][53] ;…”

Section: Introductionmentioning

confidence: 99%

“…All the important approaches proposed in the literature for the modeling of SCIMs with faulty rotor can be classified into the following eight categories: Models which impose symmetry restrictions on the distribution of bar breakages along rotor periphery 13–17 ; Models which introduce the effect of one broken rotor bar by injecting a current in the damaged bar 18,19 ; Models which are based on the magnetically coupled equivalent circuit approach 12,20–30 ; Models which utilize the classical multiphase distributed winding approach 31–34 ; Models which exploit the complex space‐vector approach and the multi‐phase symmetrical component theory 35–37 ; Models which are effective but are less widely adopted 38–40 ; Models which approximate the effect of rotor bar breakage with the variations of equivalent resistance 41–53 ; Models which rely on the detailed solutions of the magnetic fields in machines 54–65 …”

Section: Introductionmentioning

confidence: 99%

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An analytical model for squirrel cage induction machine with broken rotor bars derived based on the multiple coupled circuit theory and the winding function approach

Guo

Zhang

et al. 2021

Circuit Theory & Apps

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In this paper, a squirrel cage induction machine (SCIM) with broken rotor bars is modeled by using the multiple coupled circuit theory and the winding function approach. This analytical model includes all the spatial harmonic components of air gap magnetomotive force and is applicable to the study of transient machine behaviors. Equivalent circuits that are consistent with the topologies of healthy and faulty cage rotors are developed. The equivalent circuit for the healthy rotor of a SCIM having an integer number of rotor bars per pole is simplified further by exploiting the symmetry of the winding functions of the stator. In the equivalent circuit for a healthy rotor, inserting an independent current source in the bar that breaks in the damaged rotor, whose current

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“…vii. Models which approximate the effect of rotor bar breakage with the variations of equivalent resistance [41][42][43][44][45][46][47][48][49][50][51][52][53] ;…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An analytical model for squirrel cage induction machine with broken rotor bars derived based on the multiple coupled circuit theory and the winding function approach

Guo

Zhang

et al. 2021

Circuit Theory & Apps

View full text Add to dashboard Cite

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On-Line Estimation of All Electrical Parameters in Induction Machines subject to Stator Fault

Stocks

Medvedev

2007

2007 IEEE International Conference on Control Applications

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Abstract-Identification of all the electrical parameters of Induction Machines (IMs) is a prerequisite for successful modelbased control and/or fault detection. Most of the existing identification methods of symmetrical IMs are, strictly speaking, valid only at stationary conditions, which limitation results in either poor dynamics excitation or gross approximation errors, depending on the working conditions of the motor.In this paper, the topic of identification of all electrical parameters of faulty IMs is addressed for the first time. A method for on-line observer-based estimation of all electrical parameters of IMs with faulty stator is presented aiming primarily at fault tolerant control and fault detection. The approach does not rely on any assumptions regarding the rotor angular speed and/or acceleration.-mutual inductances εA, εS, εr -electrical parameters µA, µ -goodness factors KA, KS -normalization factorsFor the variables,· denotes a normalized (dimensionless) variable and subscripts α and β refers to the corresponding axis in a two-axis system, respectively.For both the variables and parameters, capital letter subscript A refers to stator axis A in a conventional three-axis system. Similarly, subscript S refers to stator axis B or C. In the same manner, a small letter subscript r refers to rotor axis a, b or c. The units used for the variables and parameters are SI-units throughout the paper.Bold capital letters stand for matrices, whereas small and capital letters denote respectively scalars and vectors. Identity and zero matrices of appropriate dimension (mostly 2 × 2) are denoted as I and 0. The unitary matrixis frequently used in the sequel. The complex conjugate transpose of a matrix is denoted by · H and · * means complex conjugate of a scalar. The determinant of a matrix is denoted by | · |. The transition matrix of matrix A is denoted by Φ A (t, t 0 ).

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Guaranteed Convergence Rate for Linear-Quadratic Optimal Time-varying Observers

Stocks

Medvedev

2006

Proceedings of the 45th IEEE Conference on Decision and Control

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Abstract-A well-known method by Anderson and Moore for optimal quadratic feedback design with guaranteed convergence rate for linear time-invariant systems is generalized to linear complex-valued time-varying systems and convergence rates. The resulting method is applied to observer design and illustrated by solving the problem of flux estimation in induction machines. A pre-assigned time-varying convergence rate is shown to improve the observer's transients in comparison with a constant one. The suggested design technique can be readily utilized for nonlinear state-affine systems. I. BACKGROUNDConsider a linear time-invariant systeṁwhereis a controllable pair and A, B, C are real matrices of suitable dimensions. The problem of optimal quadratic control of (1) with a prescribed degree of stability was first solved in [1] and later presented in book format in [2].LetP be the stationary solution (i. e.P = lim t→−∞ P(t, t 0 )) of the Riccati equationwith the boundary condition P(t 0 , t 0 ). Then the constant feedback gain control lawwhere R > 0, (G, A) is an observable pair and α is a nonnegative constant. Besides, the closed-loop state vector governed byẋapproaches zero at least as fast as e − 1 2 αt . Since α can be chosen freely and beforehand, the latter property is referred to as prescribed degree of stability.Generalizing the method of Anderson-Moore to a timevarying case, Linear-Quadratic (LQ) optimality of the design † Systems and Interaction, Luleå University of Technology, SE-971 87 Luleå, SWEDEN, e-mail: Stocks@ltu.se ‡ Information Technology, Uppsala University, SE-75105 Uppsala, SWE-DEN, e-mail: Alexander.Medvedev@it.uu.se is usually sacrificed for the sake of simplicity. In [3], the stabilization ofẋwith the transition matrix Φ A (t, t 0 ) being the unique solution toΦis considered assuming that the controllability gramianis non-singular and bounded from above. Then, for any α > 0, the control law A (t + τ, t)x(t) whereand β ∈ [ 1 2 , ∞) stabilizes (2) with a prescribed degree of stability of at least where P is the solution to the Lyapunov equationAny vector norm · of the estimation error e =x − x satisfies e(t) ≤ ke − 1 2 αt , t ≥ 0 and some constant k, whose value depends only on the initial conditions and u. It worth to notice here that the actual upper bound provided in [4] relates to the convergence of a Lyapunov function and does not take into account the fact that the estimation error norm converges as a square root of it, thus necessitating the factor 1 2 in the exponential. The observer exists when, for some t 0 , u satisfies the "persistency" property

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Idealized Two-Axis Model of Induction Machines under Rotor Fault

Cited by 6 publications

References 6 publications

An analytical model for squirrel cage induction machine with broken rotor bars derived based on the multiple coupled circuit theory and the winding function approach

An analytical model for squirrel cage induction machine with broken rotor bars derived based on the multiple coupled circuit theory and the winding function approach

On-Line Estimation of All Electrical Parameters in Induction Machines subject to Stator Fault

Guaranteed Convergence Rate for Linear-Quadratic Optimal Time-varying Observers

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