Fault induction dynamic model, suitable for computer simulation: Simulation results and experimental validation

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Abstract

The study of induction motor behavior under not normal conditions and the ability to detect and predict these conditions has been an area of increasing interest. Early detection and diagnosis of incipient faults are desirable for interactive evaluation over the running condition, product quality guarantee, and improved operational efficiency of induction motors. The main difficulty in this task is the lack of accurate analytical models to describe a faulty motor. This paper proposes a dynamic model to analyze electrical and mechanical faults in induction machines and includes net asymmetries and load conditions. The model permits to analyze the interactions between different faults in order to detect possible false alarms. Simulations and experimental results were performed to confirm the validity of the model.

Introduction

Induction motors are commonly used electrical drives because they are rugged, mechanically simple, adaptable to a wide variety of operation conditions and simple to control. Motors are often exposed to different loading and environmental conditions. These conditions acting together with the natural aging of the motor may lead to many failures [1]. Hence, monitoring the motor condition is crucial to detect any fault in early stage to eliminate the hazards of severe motor faults [2]. Generally, squirrel-cage induction motor faults are categorized into electrical and mechanical faults [3]. Electrical faults are divided into rotor and stator faults.

The stator inter-turn short circuit is one of the most common motor failure and represents 36% of failures that occur in induction motor [4], [5], [6], [7].

Broken rotor bars can be a serious problem when induction motor have to perform hard duty cycles. Broken bars do not initially cause a motor to fail, but they can impair motor performance and cause serious mechanical damage to the stator windings if left undetected [8]. For these reasons much research has been devoted to this topic in the last years [9], [10], [11], [12], [13], [14], [15].

Static eccentricity is characterized by a rotation axis displacement which can be caused by misalignment of the mounted bearings, the bearing plates or stator ovality. Since the rotor is not centered within the stator bore, the field distribution in the air gap is no longer symmetrical. The nonuniform air gap increases the radial force of electromagnetic origin, which acts in the direction of minimum air gap. However, static eccentricity may also cause dynamic eccentricity. Dynamic eccentricity means that the rotor is rotating on the stator bore axis but not on its own axis. This kind of eccentricity may be caused by a bent shaft, mechanical resonances, bearing wear or movement, or even static eccentricity [16].

The ultimate goal in fault diagnosis is the development of a diagnostic technique, which is able to detect any fault in the motor with a minimum knowledge about its parameters and constructional data. An efficient diagnostic technique should be noninvasive and requires only the acquisition of signals that are readily available in the motor control center [17].

Typical questions are: how to detect a starting fault, how to distinguish a deterioration fault from a harmless construction asymmetry, which are the physical quantities that best indicate a fault and how to measure them, and how should the signals be measured and processed to get the most reliable diagnosis [18]? However, to perform reliable and accurate diagnosis of the motor faults an understanding of the cause and the effect of motor faults and performances is required. Then, a good start of any reliable diagnosis method is an understanding of the machine electric, magnetic and mechanical behaviors in a healthy and under fault conditions. There are two main issues associated with the detection of induction machine faults. The first issue is the modeling of the induction motor under fault condition, in the lack of comprehensive field fault data-bases [19]. The second issue is to develop complete fault model in order to avoid false positives when diagnosing, and a special attention must be given to the presence of net asymmetries and load conditions.

Modeling of induction motors with internal faults is the first step in the design of the fault detection systems. Several machine models with broken bar or models with stator short-circuited or models with mechanical faults were proposed in the literature [13], [20], [21], [22], [23], [24]. But, those models are not complete. Moreover, to obtain fault signatures the models must permit the simulating of all kinds of faults and include net asymmetries and load conditions, in order to analyze the situation of false positive. Therefore simpler complete models are needed in order to allow several simulations conditions to determine the effects produced by the faults.

The purpose of this paper is to present a dynamic model suitable for computer simulation of induction machines in a healthy state and with general asymmetries, that could be analyzed simultaneously. The asymmetries can be: power systems unbalance, stator inter-turn short circuit, rotor broken bars and mechanical faults (unbalance, misalignment and mechanical looseness). The proposed model is based on the classical fourth order transient model for symmetrical induction machines. An experimental setup was built up to test the induction machine with asymmetric stator and rotor. Several case studies of rotor and stator asymmetries were performed and also simulated in order to validate the model.

The organization of the paper is as follows. In Section 2 the model of voltage unbalance is proposed. Section 3 briefly describes the symmetric model. In Section 4 the mechanical fault model is analyzed. The inter-turn short circuit model is proposed in Section 5. Section 6 presents a rotor asymmetry model. In Section 7 all models are integrated and the results of simulation and experimental tests are shown in Section 8. Finally, conclusions are drawn in Section 9.

Section snippets

Voltage unbalance

Voltage unbalance is regarded as a power quality problem of significant concern at the electricity distribution level. A high level of voltage unbalance can produce serious impacts on induction motors. It rises the current unbalance which leads to excessive stator and rotor losses and also leads to torque pulsations. The last one brings out vibrations and mechanical stresses [25]. Hence it is very important to detect a high level of unbalance. Voltage unbalance is characterized by the

Symmetric model

The voltage equations to describe the induction machines are established in [26]. Some of the machine inductances are functions of the rotor speed, whereupon the coefficients of the differential equations (voltage equations) which describe the behavior of these machines are time-varying except when the rotor is stalled. A change of variables described by Eq. (5) is often used to reduce the complexity of these differential equations. Therefore, the voltage (v), the flux (λ) and the current (i)

Mechanical fault model

The occurrence of motor mechanical faults (unbalance, misalignment and mechanical looseness) results changes in the air-gap space harmonics distribution, which leads to a sideband currents in the current spectrum that can be written asfmec=f1±kmec1-spwhere f is the stator supply frequency, kmec=1,2,3 is the order number, and s represents the motor slip. The slip is defined ass=w-wrw

The interaction of those harmonics with the mainly sinusoidal supply voltage causes specific harmonics in the

Stator fault model

In the following, a model of an induction motor, including an inter-turn short circuit is derived. The mathematical representation is similar to the one presented in [28] that the variables are considered in a stationary reference frame. In this work, the model is more complete because the transformation refers a frame of reference which rotates at an arbitrary angular velocity.

The leakage inductance of the shorted turns is assumed as μLls , where μ denotes the fraction of shorted turns. The

Rotor fault model

The method proposed by [24] to model rotor asymmetries is used for a machine with only one pair of poles. In this work it is developed for a machine with n pair of poles. The complex vector rotor current, Eq. (15) or Eqs. (26), (27), is computed from the symmetric model in rotor fixed reference frame as in the following equation:ir1ir2.irn=Tdq-1idriqr.0The Tdq transformation matrix is generated by a simple algorithm.Tdq=kbcosθcosθ-p22πncosθ-p24πncosθ-p2n-1n2πsenθsenθ-p22πnsenθ-p24πnsenθ-p2n-1n

Dynamic model

Fig. 1 shows the flowchart of the computer program that is suitable for computer simulation of induction machines in a healthy state and with general asymmetries: power systems unbalance, stator inter-turn short circuit, rotor broken bars and mechanical faults. The parameters tend and h are the total simulation and integration time, values in seconds.

Description of the test

To validate the proposed method, simulation of different squirrel cage induction machine were carried out. The simulations presented here refer to a motor with the following nominal parameters: 3 CV, 220 V, 60 Hz, 1710 rpm, four poles. It is the motor of the test bech. Monte Carlo method was used to simulate random conditions: motor load, different rotor broken bar, degree of mechanical load or fault, numbers of turns short-circuited, degree of voltage supply unbalance and mismatched sensors.

Fig. 2

Conclusion

The paper proposed a novel dynamic induction machine model, that accounts for both mechanical and electrical faults in induction machines. The model allowed several simulations in different conditions and outstanding effects produced by the faults. A convenient selection of the state-space variable set enables description of the machine with a very simple set of equations. A state-space representation of the dynamic equations is presented, suitable for digital simulation. Then by thoroughly

Acknowledgments

The authors gratefully acknowledge financial support by Fapemig, CNPQ and CAPES and for purchasing the required instruments and equipments. We also thank Càssia Nunes for reading and providing valuable comments regarding English structure.

Lane Maria Rabelo Baccarini received the B.Eng. degree in Electrical Engineering with class honorus from Faculdade de Engenharia Elétrica de São João del Rei, nowadays recognized as (Federal University of São João del Rei). She received the UFSJ, M.Sc. degree in Electrical Engineering from Federal University of Itajubá (UNIFEI). She is currently a Professor of Electrical Engineering at Federal University of São João del-Rei (UFSJ). She has been teaching electrical machines since 1990. She

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    Lane Maria Rabelo Baccarini received the B.Eng. degree in Electrical Engineering with class honorus from Faculdade de Engenharia Elétrica de São João del Rei, nowadays recognized as (Federal University of São João del Rei). She received the UFSJ, M.Sc. degree in Electrical Engineering from Federal University of Itajubá (UNIFEI). She is currently a Professor of Electrical Engineering at Federal University of São João del-Rei (UFSJ). She has been teaching electrical machines since 1990. She received the Ph.D. degree from the Electrical Engineering at Federal University of Minas Gerais (UFMG). Her work named Fault Detection in Electrical Machines was supervised by Professors Walmir Matos Caminhas, Benjamim Rodrigues de Menezes and Homero Nogueira Guimarães. Dr. Lane's main research interests include machine learning techniques, and drives control and diagnosis in electrical machines.

    Benjamim Rodrigues de Menezes is a Professor at the Department of Electronics Engineering at Federal University of Minas Gerais. He received the B.S. degree in Electrical Engineering from the Federal University of Minas Gerais, Brazil, in 1977. He received the M.S. degree in Electrical Engineering from the Federal University of Rio de Janeiro, Brazil, in 1980 and the D.E. degree in Electrical Engineering from the Institut National Polytechnique of Lorraine, France, in 1985. His areas of interest are intelligent control, fault diagnosis of dynamical systems and reliability engineering.

    Walmir Matos Caminhas received the Ph.D. degree in Electrical Engineering from University of Campinas, Sao Paulo, Brazil, in 1997. Currently, he is an Adjunct Professor at the Department of Electrical Engineering, Federal University of Minas Gerais, Belo Horizonte, Brazil. His research interests include computational intelligence and control of electrical drives.

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