Winding Function Approach Research Articles

State-space model for induction motors with static eccentricity faults

This work proposes a novel state-space model for eccentric induction motors, allowing the use of modern control theory to diagnose the eccentricity faults and to mitigate their effects. The proposed model is derived from the inductance-based multiple coupled circuit model. Instead of actual stator windings and rotor bars placed in slots, equivalent ideally distributed stator and rotor windings are considered in the motor modelling. The self and mutual inductances that incorporate the effects of static eccentricity in motors are evaluated using the modified winding function approach. Moreover, the rotor quantities are referred to the stator side to reduce the number of characteristic inductances. An eccentricity-oriented coordinate transformation is implemented to decouple the flux linkages in the new coordinate system and to reduce the system complexity further. Hereafter, stator currents and rotor fluxes are selected as system states, forming a fourth-order state-space model for the electromagnetic system of an eccentric motor. The proposed model is validated through comparisons with the reference data sourced from both the experiments and the finite element method. The potential of the proposed model for static eccentricity fault diagnosis purposes is explored.

CUSUM based Fault Detection of Stator Winding Short Circuits in Doubly-Fed Induction Generator based Wind Energy Conversion Systems

This paper investigates the detection of short-circuit faults in the stator winding of a Wind Energy Conversion System (WECS) based on a Doubly-Fed Induction Generator (DFIG). The Cumulative Sum (CUSUM) algorithm is used to detect the change in the stator negative-sequence current magnitude which is used as the fault residual. The grid voltage unbalance is considered along with the fault position and its severity to evaluate the effect on the residual. The generator is modeled using the winding-function approach. Simulation results are presented for a 15 kW system operated, under a power control strategy, at rated conditions. It is shown that the fault-detection method is able to detect the fault rapidly and is not influenced by the grid voltage unbalance within normal limits.

Modelling and Analysis of Inter-Turn Short-Circuit Fault of PM Machines With Parallel-Connected Coils

This paper presents a general analytical fault model in a compact matrix form for surface-mounted permanent magnet (SPM) machines with parallel-connected coils, which is useful to study the machine performance under the inter-turn short circuit (ITSC) fault. To simplify the fault model, the multiphase Clarke transformation has been proposed. In the model, the branch currents rather than the phase currents are employed as state variables to describe machine behaviours under fault. Additionally, self- and mutual-inductances are obtained by winding function approach (WFA) plus slot permeance method. The proposed analytical fault model is applied to a 3 kW 96-slot 32-pole SPM machine and validated by time-stepping FE simulations. A small scale 12-slot 4-pole SPM machine prototype has also been built to further validate the accuracy of the proposed fault model.

Design advantages and analysis of a novel five-phase doubly-fed induction generator

PurposeThe purpose of this paper is to provide an analysis of the performance of a new five-phase doubly fed induction generator (DFIG).Design/methodology/approachThis paper presents the results of a research work related to five-phase DFIG framing, including the development of an analytical model, FEM analysis as well as the results of laboratory tests of the prototype. The proposed behavioral level analytical model is based on the winding function approach. The developed DFIG model was used at the design stage to simulate the generator’s no-load and load state. Then, the results of the FEM analysis were shown and compared with the results of laboratory tests of selected DFIG operating states.FindingsThe paper provides the results of analytical and FEM simulation and measurement tests of the new five-phase dual-feed induction generator. The use of the MATLAB Simscape modeling language allows for easy and quick implementation of the model. Design assumptions and analytical model-based analysis have been verified using FEM analysis and measurements performed on the prototype. The results of the presented research validate the design process as well as show the five-phase winding design advantage over the three-phase solution regarding the control winding power quality.Research limitations/implicationsThe main disadvantage of the winding function approach-based model development is the simplification regarding omitting the tangential airgap flux density component. However, this fault only applies to large airgap machines and is insignificant in induction machines. The results of the DFIG analyses were limited to the basic operating states of the generator, i.e. the no-load state, the inductive and resistive load.Practical implicationsThe novel DFIG with five phase rotor control winding can operate as a regular three-phase machine in an electric power generation system and allows for improved control winding power quality of the proposed electrical energy generation system. This increase in power quality is due to the rotor control windings inverter-based PWM supply voltage, which operates with a wider per-phase supply voltage range than a three-phase system. This phenomenon was quantified using control winding current harmonic analysis.Originality/valueThe paper provides the results of analytical and FEM simulation and measurement tests of the new five-phase dual-feed induction generator.

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

In‐depth investigation of inter‐turn short‐circuit faults of surface‐mounted permanent magnet machines with series‐parallel coil connections

AbstractA general analytical model is developed in a concise block matrix form for surface‐mounted permanent magnet (SPM) machines with series‐parallel coil connections under inter‐turn short circuit (ITSC) fault. In the model, branch currents are used as state variables and inductances of different series‐parallel coil connections are calculated using an analytical method, namely winding function approach (WFA) together with slot permeance method. Based on the characteristics of the calculated inductances and the developed fault model, the multiphase Clarke transformation has been proposed to simplify the fault model. In the process of model simplification, the healthy machine model using branch currents as state variables have been proven to be equivalent to that using 3‐phase currents as state variables. The proposed fault models of a 3kW 96‐slot 32‐pole SPM machine with different series‐parallel coil connections have been built in Matlab/Simulink and validated by time‐stepping 2D FE simulations. Simulation results show that different series‐parallel coil connections have little influence on the amplitude of the ITSC current. Finally, a small scale 24‐slot 8‐pole SPM machine prototype has been built to further validate the accuracy of the proposed fault model.

Improved Configuration Proposal for Axial Reluctance Resolver Using 3-D Magnetic Equivalent Circuit Model and Winding Function Approach

Resolver is a position sensor that is widely employed in motor servo systems under harsh working conditions. In this article, a novel axial flux resolver with a fractional-slot sinusoidal distributed winding configuration is developed, which has the advantages of a simple structure and convenient mass production. Sinusoidal distribution winding expands the optional range of pole–slot combinations, and its harmonic suppression capability is proposed and verified by the winding function approach (WFA). Furthermore, the magnetic equivalent circuit (MEC) model is formulated to analyze the impact of structural parameters on the induced voltage envelope, through which the optimal parameters on the resolver are developed. In terms of computation time and accuracy, the results of the MEC model under healthy and eccentric conditions are compared with the finite-element method (FEM). In addition, the antiaxial offset capability of the half-wave resolver is illustrated and verified. The effectiveness and superiority of the proposed resolver are illustrated and verified based on numerical simulations and experimental tests.

Scaling Effect On Inter-Turn Short-Circuit Fault of PM Machines for Wind Power Application

This paper proposes a general analytical model of surface-mounted permanent magnet (SPM) machines with series-connected coils under inter-turn short circuit (ITSC) fault. One prominent feature of this fault model is that the air-gap and slot-leakage components of inductances under fault are calculated separately, and the influences of pole number and spatial distribution of coils have been considered in the calculations. In the model, the winding function approach (WFA) is used to calculate the air-gap inductance components by considering all space harmonics whilst slot-leakage inductance components are obtained by using slot permeance method. The proposed fault model built in Matlab/Simulink is validated by time stepping FE simulations for a 3 kW 96-slot 32-pole SPM machine. The fault model has acceptable accuracy and is suitable for the fast evaluation of fault performance of SPM machines and its accuracy considering core saturation can be improved using FE-based results. Other power ratings (0.5 MW and 3 MW) have also been investigated to study the scaling effect on machine fault-tolerant capability. A 12-slot 4-pole small scale prototype has been built to validate the developed fault models.

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.

Efficient index for detecting the stator winding interturn fault in six-phase squirrel-cage induction motors

Multi-phase electrical machines have recently drawn growing attention, among which; six-phase squirrel-cage induction motors (6PIMs) have gained a considerable share. 6PIMs are main candidates to be utilized in hybrid vehicles, electrical trains, ships, submarines, etc. Incipient fault diagnosis is an essential technology, which enables preventing serious damages to the machines and catastrophic interruption of them. The stator winding interturn fault is among the main incipient faults. Although, numerous studies have dealt with this fault in three-phase induction motors, there is a few studies concerning the 6PIMs. In this paper, the winding function approach is utilized to model, simulate and analyse the performance of the 6PIM with interturn fault in a stator phase winding. After examining the simulation results, an analytical method is followed to extract efficient graphic and quantitative indices for detecting the stator interturn fault and for evaluating its severity. The indices require sampling the stator phase currents only in one fundamental period, enable identifying the faulty stator phase, show good sensitivity to the fault severity and are almost insensitive to the load torque change. The stator voltage unbalance cannot mislead the fault detection method based on the indices. Various simulation and corresponding experimental test results confirm these merits.

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).

Advances in Fault Diagnostics and Post‐Fault Operation of Electrical Drives

Advances in Fault Diagnostics and Post‐Fault Operation of Electrical Drives

Modeling and simulation of a 3-ф induction motor based on two types of WFA

This paper has been proposed to simulate the transient model of 3-Ф cage rotor induction motor based on winding function approach (WFA). According to this method the motor is assumed to be consist of an electrical circuits on both stator and rotor. The magneto motive forces (MMF) that have been generated by these circuits play a role for coupling them together. Then mutual and self-inductances will be easily computed using WFA. Two types of WFA have been used to build and simulate the model of the induction motor. In the one part type, it’s assumed that the coupling MMF between stator and rotor have a non-sinusoidal shapes according to the actual windings distribution over the motor slots. While in second part type the generated MMF in are assumed to have sinusoidal waveform. The suggested models may be used to simulate the dynamic as well as steady state performance of a faulty and non-faulty motor. A simulation of the suggested models that consists of m-rotor bars and n-stator phases multiple coupled circuit-based has been performed using matlab m.file and the results of the motor current have been proved in its nonlinear way by using WFA.

Eccentricity fault detection in brushless doubly fed induction machines

A new fault diagnosis method for detecting the rotor eccentricity faults including static, dynamic and mixed eccentricity is proposed for brushless doubly-fed induction machines (BDFIMs). BDFIMs are attractive alternatives for the conventional doubly-fed induction generator (DFIG) for offshore wind power generation; therefore, paying attention to their fault detection is essential. Existing fault detection methods for conventional induction machines cannot be directly applied to the BDFIM due to its special rotor structure and stator winding configurations as well as complex magnetic field patterns. This article proposes a novel fault detection method based on motor current signal analysis to determine stator current harmonics, induced by the nested-loop rotor slot harmonics (NRSHs), as fault indices. The analysis is performed under healthy conditions and with different types of rotor eccentricity. Finally, a sensitivity analysis is carried out to confirm the practicability of the proposed technique with various fault intensities and load conditions. Analytical winding function approach, finite element analysis and experimental tests on a prototype D180 BDFIM are used in this study to validate the proposed fault detection technique.

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

SummaryIn 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 is the negative of the current through the same bar, and replacing all the voltage sources in the rest of the bars with short circuits result in an equivalent circuit that can be employed to solve for the deviations in rotor mesh currents caused by bar breakage. A simulation is carried out in MATLAB/Simulink for a 2.2 kW, three‐phase, four‐pole SCIM with 28 rotor bars and a laboratory test rig is built. The effectiveness of the proposed model was validated by the good agreement of the simulation results with the experimental data.

A Steady-State Equivalent Circuit of TSCAOI Configured Induction Generator for Renewable Energy Conversion Systems

3-phase cage induction machines, operated in two series-connected and one-isolated (TSCAOI) winding configuration, have been proposed to generate standalone single-phase electricity at variable speeds for renewable energy conversion systems. However, the steady-state behaviour and performance of this particular generator are not yet to be theoretically investigated. This paper therefore presents the first theoretical investigation based on the steady-state equivalent circuit model for standalone TSCAOI configured generators. Moreover, this paper is the first to adopt the winding function approach to derive a dynamic mathematical model for TSCAOI configured generators. This approach not only eliminates the cumbersome mathematical manipulation required in all previous papers related to TSCAOI configured generators but also provides a visual insight into the resulting winding distribution of the machine. In order to investigate the load and excitation characteristics pertinently, the dynamic model is transformed into two different equivalent circuit models by appropriate selected transformation matrix. Using these two models, this paper identified the impacts of system parameters on the load and excitation characteristics, as well as on the level of voltage unbalance. Experimental results of a prototype generator under various operating conditions are presented, together with simulated results, to demonstrate the accuracy of the proposed investigations.

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 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.

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.