Modified Winding Function Approach Research Articles

Direct-Indirect PWM vector controlled of the dual-star asynchronous motor based on a modified winding function approach using the current controller for a six-phase inverter

Direct-Indirect PWM vector controlled of the dual-star asynchronous motor based on a modified winding function approach using the current controller for a six-phase inverter

Improved Analytical Analysis of Novel Integrated Variable Reluctance Resolver for Compact Machine Topology

Variable reluctance resolvers (VRRs) have been widely used for rotor position detection in harsh working conditions. However, conventional installation of VRRs inevitably occupies the axial space of machine systems, and may weaken the reliability of rotor position detection encountering shock and vibration. In this article, a novel VRR structure with inner stator is investigated, which is radially integrated inside a permanent magnet synchronous machine (PMSM) to construct compact machine topology. The hybrid machine topology is first discussed, and detailed electromagnetic design is carried out. Improved analytical analysis on air gap flux density distribution and inductance evaluation of the integrated VRR is derived based on modified winding function approach, and testified by finite element analysis. A prototype is manufactured from an existing 2.2 kW PMSM, and experiments are conducted to validate the effectiveness of proposed machine topology.

An Exact Solution to the Modified Winding Function for Eccentric Permanent Magnet Synchronous Machines

The Winding Function Approach has been used since 1965 to describe the inductance behavior of small air-gap electrical machines, and several works have contributed to its formulation in the presence of mechanical faults, such as eccentricity, leading to the Modified Winding Function Approach (MWFA). In order to use the MWFA, an integral over a full rotation period needs to be computed. Nevertheless, this typically requires the performance of numerical integration, and thus it is affected by integration error, requires relatively high computational effort and, at the same time, it does not easily allow for performance of the analysis of the inductance harmonics. In this work, an exact analytical solution to the MWFA equation is provided in a form that allows to highlight the harmonic content of the inductances. After a thorough mathematical derivation of the solution, a numerical investigation is proposed for verification purposes.

Extension of Winding Function Theory for Modeling and Diagnosis of Partial Demagnetization Fault in PMSM Drive

This paper proposes the development of a new mathematical model dedicated to the diagnostic of the partial Demagnetization Fault (DF) in Permanent Magnet Synchronous Motor (PMSM). To do this, an extension of the Modified Winding Function Approach (MWFA) is proposed to accurately take into account the air gap asymmetry caused by the Demagnetization Fault (DF) in the PMSM inductances calculation. The calculated inductances are then used in the magnetically coupled electrical circuit model to simulate the PMSM behavior in the different operating modes. Finally, a diagnostic method based on the stator current spectral analysis is used to highlight the PMSM stator current spectral content in the various operating modes (with and without Demagnetization Fault).

A novel methodology for fault size estimation of ball bearings using stator current signal

Bearing fault diagnosis that utilizes motor current has shown great potential for industrial application. For estimating fault sizes, this paper develop an electromechanical-magnetic coupling computational model of induction motor (IM) based on modified winding function approach (MWFA) in order to extract the fault-excited harmonic components and amplitudes in stator current. A new evaluating indicator FHD (Fault-excited Harmonic Distortion) is then proposed to describe the specific relation between fault sizes and severity of fault-excited harmonic distortion. The statistical results show that there is a fixed functional relation curve between FHD and fault sizes in different IM. Finally, an experimental IM with a known size built-in faulted bearing is investigated. The 1 mm artificial damage on outer raceway is recognized by calculating FHD (0.5636 in average) value and comparing with the simulated relation curve. The results validate the accuracy and robustness of the proposed approach in fault size estimation.

A model-based method for bearing fault detection using motor current

Existing bearing fault diagnosis approaches utilize signal processing techniques in combination with vibration measurements. The common vibration measurement method, using accelerometer, has disadvantages such as position-constrains, high costs and external interferences. Meanwhile, the commonly used modelling methods of motor are not able to analyse both mechanic and electromagnetism simultaneously. For detecting the fault-related frequencies in motor current, a mathematical model is developed in this paper based on modified winding function approach (MWFA). The simulation results show that the fault-related characteristic frequencies can be exactly found in the spectrum results of motor current. The proposed method is proven to be feasible.

A Proposed Approach for Separation between Short Circuit Fault, Magnetic Saturation Phenomenon and Supply Unbalance in Permanent Magnet Synchronous Motor

This paper proposes a new approach for discrimination between short circuit fault, magnetic saturation phenomenon and supply voltage unbalance in permanent magnet synchronous motor. This proposed approach is based on tracking the simultaneous position in the polar coordinates of the amplitude and phase angle of the voltage and current indicator FFT signals of the harmonics characterizing the three phenomena. The voltage indicator set using three supply voltages to check the status of the power source. In the same way, the current indicator defined using three line currents to discriminate between the short circuit fault and the magnetic saturation phenomenon. To highlight the effectiveness and the capability of this approach, a series of simulations are performed on signals obtained from a permanent magnet synchronous motor mathematical model. This model is based on a 2D-extension of the modified winding function approach.

Stator Inter-Turn Short-Circuit and Eccentricity Faults Detection in Permanents Magnets Synchronous Motors Using Line Current Spectrum Analysis

Stator inter-turn short-circuit and Eccentricity faults are among the most common types of faults encountered in permanent magnet synchronous motors. This paper proposes a new method for the diagnosis of these types of faults based on the motor current signature analysis. A mathematical model based on the modified winding function approach has been developed to model the healthy PMSM, considering the effect of the magnetic saturation phenomenon and in the presence of inter-turns short-circuits and eccentricity faults. In order to highlight the interest of the model employed and the efficiency of the spectral analysis technique of the stator current, a series of simulations are performed in the different operation modes (Healthy and faulty operation modes).

Induction Motor Faults Diagnosis when Considering Bars Skew and Saturation Effects

The objective of the work presented in this paper is the diagnosis of the three-phase induction machine with secondary effects such as the rotor bars skewing and the saturation phenomenon. To enable reliable diagnosis of an induction machine, a mathematical model is required to simulate the machine behavior. Among the existing mathematical models, the approach of the winding function is the most promising because it takes into account the actual distribution of the windings in the stator slots. Nevertheless, the major drawback of this model is the non-consideration of the skewing effect of the bars and the non-linear evolution of the FMM between the ends of the slots. The aim of this paper is to use the modified winding function approach (MWFA) with 2D extension to take into account the rotor bars skewing and saturation effects in the presence of faults such as the rotor broken bars, the short-circuit between stator turns and the eccentricity. A series of simulations is conducted to study the spectral contents of the stator current of the induction squirrel cage motor in the various operating cases.

A Proposed Technique for Discrimination between Saturation Phenomenon and Short-Circuit Faults in Induction Motor

This paper proposes a new technique of discrimination between the two signatures related to the magnetic saturation phenomenon (MSP) and the inter-turn short-circuit (ITSC) fault in a three-phase induction motor (IM). This technique is based on the exploitation of the amplitude and the phase angle of a new harmonic characterizing both phenomenons obtained from the characteristics of the Hilbert transform. In addition, and in order to simplify the interpretation and analysis of the various modes of operation covered in this paper, a new graphical tool based on a triangular representation is proposed. This graphical representation depending on the position and the orientation of the triangle makes it possible to display in a simple and clear manner the existence of the ITSC fault and its discrimination with respect to the MSP phenomenon. To assess the performance of this new technique, some simulation works are performed on signals obtained from a mathematical model of the IM based on the calculation of the inductances by the modified winding function approach (MWFA).

Eccentricity fault diagnosis in three‐phase‐wound‐rotor induction machine using numerical discrete modeling method

SummaryIn recent years, several papers have dealt with eccentricity fault diagnosis considering the cage‐induction machine while wound machine type has not been studied as a case. In this paper, eccentricity fault is studied based on the current/torque signature considering modified winding function approach (MWFA). A novel discrete model is introduced, and eccentricity fault is evaluated in both static and dynamic cases. To reach this aim, a numerical model is presented for slot openings, distributed windings and air‐gap, thereby computing the machine's inductances using MWFA. Power spectral density (PSD) of stator's current and machine's vibration are analyzed for static and dynamic eccentricity diagnosis and the finite element method (FEM) is utilized to precisely verify the proposed method. Mathematical‐based model with consideration of both slot openings and non‐sinusoidal winding function effects are the advantages of the proposed method over the previous researches in this field. Moreover, proposed method, which is based on mathematical modeling, could be easily applied to other types of electrical machines, and this feature is regarded as another key point of this paper. Copyright © 2016 John Wiley & Sons, Ltd.

A Model for Analyzing a Five-Phase Fractional-Slot Permanent Magnet Tubular Linear Motor with Modified Winding Function Approach

This paper presents a model for analyzing a five-phase fractional-slot permanent magnet tubular linear motor (FSPMTLM) with the modified winding function approach (MWFA). MWFA is a fast modeling method and it gives deep insight into the calculations of the following parameters: air-gap magnetic field, inductances, flux linkages, and detent force, which are essential in modeling the motor. First, using a magnetic circuit model, the air-gap magnetic density is computed from stator magnetomotive force (MMF), flux barrier, and mover geometry. Second, the inductances, flux linkages, and detent force are analytically calculated using modified winding function and the air-gap magnetic density. Finally, a model has been established with the five-phase Park transformation and simulated. The calculations of detent force reveal that the end-effect force is the main component of the detent force. This is also proven by finite element analysis on the motor. The accuracy of the model is validated by comparing with the results obtained using semianalytical method (SAM) and measurements to analyze the motor’s transient characteristics. In addition, the proposed method requires less computation time.

On-line fault diagnostics in operating three-phase induction motors by the active and reactive currents

Motor current stator analysis (MCSA) are usually used to detect the broken bars. In several industrial applications, like cement industry, the motor is subjected to load torque variations of low frequencies, which have effects similar to rotor faults in the current spectrum and result of diagnostic procedure may be ambigues. In this paper, we present a study based on the application of the instantaneous active and reactive courant signature analyses for discriminating broken rotor bars from mechanical load oscillation effects in operating three-phase squirrel cage induction motors. This method is attractive because it does not need to interrupt the operating system in its application and allows the user to “see” the diagnosis information in the same way as in the well-known MCSA, i.e., as sidebands next to the fundamental current component. This technique has been first tested through the simulation of induction motors using a mathematical model based on the modified winding-function approach (MWFA). Then, experimental results are presented in order to demonstrate the capability of the proposed tool for discriminating between a motor with broken rotor bars from a motor driven by an oscillating load.

Analysis and Control of Multiphase Permanent-Magnet Bearingless Motor With a Single Set of Half-Coiled Winding

In this paper, a multiphase bearingless motor (MBLM) with a single set of half-coiled winding is proposed, with advantages such as simpler construction and capability of fault-tolerant operation, comparing with the traditional BLM with dual groups of three-phase windings. The magnetomotive force distribution of the half-coiled winding is analyzed. Then, the winding configuration of a five-phase permanent-magnet bearingless motor is introduced, and the inductance of the MBLM is deduced by the modified winding function approach and verified by finite-element analysis. Furthermore, the control system is proposed based on the derived voltage model, torque model, and suspension force model, considering rotor eccentricity. Finally, static and dynamic experiments are provided on a prototype motor to verify the validity of the analysis.

A Fast Inductance Computation Devoted to the Modeling of Healthy, Eccentric, and Saturated Induction Motors

This work deals with a detailed method for the calculation of induction motor inductances based on the convolution theorem. The integral form leading to the inductance expressions is derived from the 2D modified winding function approach, which takes into account the space harmonics, slot skewing, and radial and axial air-gap eccentricities. As first applications, a model is presented that allows teeth saturation to be taken into account by the corresponding air-gap permeance variation. Next, the idea is adapted to the rotor eccentricity modeling. It is shown that appropriate arrangements make it possible to use the convolution theorem for fast calculation of the inductances. The proposed method proves to be competitive compared to the conventional techniques of integration and even those employing equivalent analytical expressions. To demonstrate the effectiveness of the new proposed methodology, simulation tests based on the multiple coupled circuit model, experimental spectra, as well as time processing verification on a personal computer, are provided.

Identification of spectral components in the line current of eccentric salient pole machines using a binomial series‐based inverse air‐gap function

Current literature does not provide any generalised method for specific permeance - magneto-motive force-based approach to predict all possible harmonic components in the air-gap flux and line current of an eccentric salient-pole machine. This study provides an elegant solution to express specific permeance of an eccentric reluctance synchronous machine as a summation of constant coefficient co-sinusoidal terms. Binomial series expansion has been used to achieve this. The analysis has been validated by matching the presence of the predicted harmonic components in the stator line current by coupled magnetic circuit simulation based on modified winding function approach and experimental results. It is also shown that the effect of sensor errors, machine asymmetry, supply harmonics etc. can be minimised by residual estimation to vastly improve detection sensitivity under all load conditions. Thereafter, a procedure to identify fault type and severity has been presented.

Modelling and simulation of faults in synchronous generators for robust numerical protection

When an internal fault occurs in a synchronous generator, the symmetry between the parallel paths of the winding is broken and different currents flow in them, due to unsymmetrical magnetic linkage between the stator windings. The aim of this paper is to present a simulation model to investigate the effect of internal fault on the parallel path currents of a large synchronous generator using direct phase quantities. This model is based on a modified winding function approach where the machine inductances are calculated directly from the machine winding distribution using machine electrical parameters instead of the geometrical ones. The simulation results for different cases of internal faults in salient-pole and non-salient-pole synchronous machines have been obtained. Salient-pole synchronous generator has wave winding distribution while the non-salient-pole generator has lap winding arrangement. Due to different stator winding arrangements, the two machines have been simulated individually. By using the simulated fault data, a suitable numerical protection scheme for synchronous generators can be developed.

A Novel Technique for the Computation of Inductances of Salient Pole Machines under Different Eccentricity Conditions

In this article, comprehensive analytical equations are developed to compute time-varying inductances of salient pole machines with any eccentricity type and degree in a unified technique. For this purpose, the inverse air-gap function of the eccentric salient pole machine has been defined, and its indefinite integral has then been determined. The derived analytical expressions, unlike the previous proposals, take into account all the harmonics of the inverse of the air-gap function without any development in Fourier series. The presented method eliminates the need for inexact analytical equations, numerical differentiations, and huge lookup tables, which are common in the modified winding function approach. Theoretical fundamentals and experimental results that validate the proposed technique are presented.

A Detailed Analytical Model of a Salient-Pole Synchronous Generator Under Dynamic Eccentricity Fault

In this paper, a new detailed analytical model of a salient-pole synchronous generator (SPSG) under dynamic eccentricity (DE) is presented which is capable of accounting for the effects of magnetic saturation, rotor pole shoe saliency, and space distribution of stator phases and rotor winding. A real form of rotor pole shoes is taken into account in the proposed SPSG air-gap function distribution. Saturation effects incorporate into the air-gap function of SPSG as a simple proposed analytic equation that varies by the generator load and operating condition. Furthermore, variation of the resulted air-gap distribution of SPSG in the presence of DE fault is then computed precisely and the inverse air-gap function calculated using Fourier series in order to compute time varying self- and mutual-inductances of stator phases and rotor winding via the modified winding function approach (MWFA). The computed inductances are used for simulation of SPSG and studying the frequency spectrum of stator line current in the presence of DE fault. It is shown that the results of proposed model are closer to the finite-element (FE) computation results compared to the available analytic models.

Development and Validation of a Comprehensive Synchronous Machine Model for a Real-Time Environment

A comprehensive model of a salient-pole synchronous machine is developed for a real-time environment. By obtaining the effective specific permeance of the machine from simple experimental measurements and the exact geometry of the rotor pole arc, a model is developed that includes the exact distribution of windings and operating-point-dependent saturation. This model offers a superior simulated response of the machine for fault transients, as well as for steady-state harmonic behavior, and is suitable for the closed-loop testing of relays and controls. The inductances of the machine are computed using the modified winding function approach and validated using finite-element analysis. Finally, the performance of the model is validated under healthy and faulted conditions by comparison with tests on an actual machine.