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This paper models and simulates a salient-pole synchronous generator using a modified winding function theory and more precise stator and rotor winding distribution with dynamic eccentricity between the stator and rotor. Air-gap permeance is also computed more accurately compared to currently available methods. Inductances with this method are comp...
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... distribution of the air-gap and the excitation of the rotor into (1). In [11], a linear rise of mmf of the air-gap across the stator slots has been considered and the first three terms of its Fourier series has been used. In this paper, the mmf rise is taken as shown in Fig. 5. The stator winding of a typical synchronous machine is shown in Fig. 6, with its specifications given in Table I [9]. Fig. 7 shows the turn functions of stator phases winding. Fig. 8 presents a similar function for the excitation winding. ...
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... One possible approach to derive a fully analytical model is to use the winding function (WF) theory. WF theory was successfully used for modeling of synchronous machines but damper winding was not of particular interest for those researches [18][19][20], or it was modeled considering dq reference frame without interest for currents in individual bars [6]. Electric machine models based on the WF theory are well known and widely used in the field of cage induction machines, especially when it is necessary to capture design-related phenomena like different number of rotor bars in the simulation [21][22][23]. ...
The original dynamic model of the grid-connected synchronous round-rotor generator, also known as synchronous turbo-generator (STG) is presented in the paper. The model is based on the Winding Function (WF) theory and as such it is derived in the natural frame of reference. Depending on the presence or absence of a cage damper winding on the rotor two independent models are derived. The strength and the importance of the derived models lie in the fact that it is possible to consider the real spatial distribution of all the windings in the machine, including the damper winding. The time-dependent currents in all the windings, including the currents in all the bars of the damper cage winding, are the output of the model. In addition, the model execution time on a mid-range computer is a few tens of seconds, which is incomparably faster than the execution time of models based on the Time Stepping Finite Element (TSFE) method, which is measured in days. On the other hand, the results obtained with a completely different and independent TSFE model fully confirm the validity of the results obtained with the proposed WF model.
... [10,11] using the winding function method for modelling and simulation. The SPSG has been simulated in Ref. [12] under variable DE severities. In Ref. [13], the effect of the stator tooth magnetic saturation has been used to model a synchronous machine with DE fault. ...
... Except for the first and the last integrals, the other integrals in equation (12) are independent of θ and are solved as follows: ...
Here, a dynamic analytical model is provided for salient pole synchronous generators (SPSGs) under different eccentricity faults. A useful technique is developed first to describe the rotor position‐dependent non‐uniform air gap distribution by a proper function in the healthy state, which includes the stator slotting effect. Then, the exact air gap function is used along with the modified winding function theory to extract non‐integral equations for computing the SPSG various inductances that are playing critical role during analytical modelling and simulation of the machine. Afterword, the air gap function and the inductance equations are modified to include all types of the eccentricity fault. A 3 kW SPSG is simulated and then tested in laboratory under the healthy and the mixed eccentricity (ME) conditions. There are good accordance between the simulation and corresponding experimental results; they show that some harmonic components are introduced in the rotor and the stator currents due to the ME fault whose frequencies are integer multiples of the rotor speed frequency and whose amplitudes increase by increasing the fault severity. The load level change also affects the amplitudes of the harmonics.
... 28, N 1, A , 2021 165 -179 está propensa a sufrir tanto fallas externas como internas, siendo que estas últimas pueden ocurrir tanto en el rotor como en el estator de la máquina. Las principales fallas que pueden presentarse en estas máquinas son: [1,2,3] Fallas en rodamientos.(40-50 %) Fallas en aislamiento del estator. ...
... Inicialmente, para un conjunto de entradas separables linealmente, denotado como S = (x 1 ; y 1 ); . . . ; (x n ; y n ), se puede definir un hiperplano de separación como una función lineal de la forma indicada en la ecuación (2). ...
Dado que la máquina sincrónica en su funcionamiento como generador constituye un elemento vital en los sistemas eléctricos de potencia, el desarrollo de programas y técnicas de mantenimiento predictivo, a fin de identificar y solucionar problemas en la máquina antes de que se produzcan daños irreversibles en la misma es prioridad. A continuación se establece una metodología para detectar fallas incipientes en rodamientos de un generador sincrónico de prueba a través de máquinas de vectores de soporte (SVM por sus siglas en inglés). Se presenta el análisis de las corrientes de fase, utilizando métodos variados para la reducción de los datos y algoritmos de aprendizaje automático basados en las máquinas de vectores de soporte como elemento clasificador de datos; a fin de obtener un modelo que sea capaz de discriminar la condición de una máquina, en cuanto a fallas mecánicas se refiere. El entrenamiento de las máquinas de vectores de soporte para obtener los criterios de clasificación se ejecutó utilizando los comandos para SVM de MatLab, las funciones que brinda este software permitieron: el entrenamiento, la optimización y la posterior validación de los clasificadores. Los resultados obtenidos demostraron que el método aplicado basado en la SVM posee una buena capacidad de reconocimiento de fallas presentadas en los diferentes componentes del rodamiento, para distintas condiciones de operación.
... This section presents the dynamic equations of three phase salient pole synchronous machine applied in computer simulation. The electrical and electromechanical behaviour of most synchronous machines can be predicted from the dynamic equations that describe the three phase salient pole synchronous machine [23][24][25]. A summary of the dynamic equations for the synchronous machine in the rotor qdo reference frame with all the rotor quantities referred to the stator is lucidly elaborated in references [26][27][28]. ...
The effects of a varied d.c excitation voltage on the speed and power output of two selected synchronous machines were analyzed in this paper through computer simulations. The steady state equations for a cylindrical rotor and salient pole synchronous machines were derived and simulated at different values of quadrature axis reactance. A varied excitation voltage values were also considered while a significant increase in the value of power output for the salient pole machine was obtained after simulation. The cylindrical rotor machine remained unaffected by the variation in the quadrature axis reactance. The dynamic equations for a salient pole machine were also modeled and simulated with simplified algorithms using embedded MATLAB Function block in ideal motor operating condition and under a three phase to ground fault. The simulation results showed an increase in real power and reactive power values at an increased excitation voltage. A rapid drop in speed and torque value was observed during a three phase to ground fault and was restored after six seconds. All Simulation results were achieved in MATLAB/Simulink software.
... Since creating the air-gap eccentricity fault and analysis of the SG behavior is destructive and costly, some model-based fault detection methods have been introduced [10,17]. The winding function method and the Finite element method (FEM) are alternative approaches that can be used to model eccentricity in SGs [8,[18][19][20][21]. Tabatabaei et al. [18] employed a modified winding function to present a model for SGs with dynamic eccentricity. ...
... The winding function method and the Finite element method (FEM) are alternative approaches that can be used to model eccentricity in SGs [8,[18][19][20][21]. Tabatabaei et al. [18] employed a modified winding function to present a model for SGs with dynamic eccentricity. Iamamura et al. [19] used the FEM to study the model of SGs in the presence of static and dynamic eccentricity faults. ...
... The static air-gap eccentricity fault occurs when the rotation axis of the rotor does not coincide with the stator of the symmetry axis, and dynamic air-gap eccentricity happens when the axis symmetry is displaced [18]. The dynamic and static airgap eccentricity are shown in Fig. 2. If both static and dynamic air-gap eccentricities occur simultaneously, it is called mixed eccentricity [10]. ...
Air-gap eccentricity fault causes rotor-stator rub and consequently damage to Synchronous Generators (SGs). In this paper, a fault diagnosis approach to diagnose the eccentricity fault for SGs is presented. In this approach, the state matrix eigenvalues based on the subspace identification are estimated, and those are used for fault diagnosis. Two dq models of SGs in faulty and healthy conditions are employed to present the theoretical foundation of the method. As the main advantage, the introduced fault diagnosis method is working properly for either linear or nonlinear loads of SGs. The stator and field currents and voltages, and rotor rotational speed are required signals in the introduced approach. The method is validated using experimental data of SGs in Iran-Safir (ER24) diesel-electric locomotives.
... A model-based fault detection methodology has been used to diagnose air-gap eccentricity and inter-turn short circuits in the SG [11,12]. In [13] and [14], a model for an SG with dynamic eccentricity fault using modified winding function theory has been presented. Faiz et al. [11] have introduced a method based on the winding function to calculate the self-inductance of stator and rotor, the mutual inductance of the two phases of the stator, and mutual inductance of the rotor and stator under static and dynamic eccentricities. ...
... In the dynamic eccentricity, the rotation axis of the rotor coincides with the stator axis of symmetry, but the rotor axis symmetry is displaced. In the mixed eccentricity, static and dynamic eccentricities are occurred simultaneously [14]. Therefore, eccentricity faults lead to change in the maximum and minimum length of the air gap. ...
In this paper, an online model-based fault detection approach based on residual analysis in synchronous generators (SGs) is presented. Two types of faults are studied in this paper: (i) reduction of the cross-sectional area of windings wires in SGs, and (ii) air-gap eccentricity. The residual vector based on the equivalent circuit (EC) parameters or state-space model of the SG is employed for fault detection. The introduced fault detection approach employs the stator and field currents and voltages, and rotor rotational speed. The main advantage of the presented method is able to be used for linear and nonlinear loads in the presence of uncertainty in EC parameters. The effectiveness of the proposed method is shown using the experimental data of five SGs in diesel-electric locomotives.
... Some scholars have investigated rotor eccentricity. Tabatabaei et al. 13 used a modified winding function theory to simulate a salient-pole synchronous generator and obtained stator and rotor winding distribution with dynamic eccentricity between the stator and rotor. Zhu et al. 14 adopted a nonlinear finite element method to calculate the no-load branch voltage waveform of a synchronous generator with an eccentric rotor and skewed stator slots. ...
To determine the effect of rotor eccentricity on the vibration of multistage pumps, a five-stage centrifugal pump with vaned diffusers was selected to experimentally measure the vibration characteristics under both stable condition and unstable condition due to the rotor eccentricity. The results show that the rotor eccentricity results in an irregular orbit of the rotor axis, which is diffused outward. As the flow rate increases, the peak amplitude of the rotor axis’ orbit first decreases and then increases, and the peak amplitude at the design flow rate is minimized. The main vibration frequencies of rotor axis’ orbit are the axis passing frequency and a secondary high frequency. After rotor eccentricity occurs, all monitoring point vibrations increase by different degrees, the increments of axial vibration are particularly obvious, and the characteristic frequencies of the pump increase.
... It will benefit the fast magnetic field calculation and the study of noise characteristics [5,6]. In [7][8][9], the magnetic field of rotor eccentric induction motor, synchronous reluctance motors, etc. are calculated using the winding function method analytically. However, since the tangential magnetic field is neglected, the winding function method cannot satisfy the calculation accuracy of SPMSM. ...
... Therefore, early-stage detection of machine fault can avoid costly damages to the machine and economic loss. Detecting eccentricity fault is mostly based on methodologies relying on analysing stator current [3][4][5]. In that approach, the Fourier transform is applied to the phase current, and the harmonic components of the phase current are assigned as an index to detect eccentricity fault. ...
Abstract Although synchronous generators are robust and long‐lasting equipment of power plants, consistent electricity production depends on their health conditions. Static and dynamic eccentricity faults are among the prevalent faults that may have a costly effect. Although several methods have been proposed in the literature to detect static and dynamic eccentricity faults in salient pole synchronous generators (SPSGs), they are non‐sensitive to a low degree of failure and require a predefined threshold to recognise the fault occurrence that may vary based on machine configuration. This article presents a detailed magnetic analysis of the SPSGs with static and dynamic eccentricity faults by focusing on the external magnetic field. The external magnetic field was measured using two search coils installed on the backside of the stator yoke. Also, advanced signal processing tools based on wavelet entropy were used to analyse the induced electromotive force (emf) in search coils to extract the fault index. The proposed index required no threshold to recognise the starting point of fault occurrence and was sensitive to a low degree of fault. It was also non‐sensitive to load variation and noise that may induce a false alarm.
... Lipo gave a full explanation of conventional WFT (CWFT) for ideal electric machines without considering the effect of slots and magnetic saturation [2]. CWFT has been used to calculate the inductances under healthy and rotor eccentricity conditions for cage-rotor induction motors (CRIM) [3][4][5] and for synchronous machines [6][7]. The influence of optimal rotor bar number on the performance of CRIMs was also validated by CWFT [8]. ...
... This saturated air-gap function was then improved by Ojaghi and Faiz through accurate finding the zero-crossing air-gap flux density [14][15][16]. Recently, the third harmonic saturation factor has been also considered in saturated air-gap function in addition to the fundamental one [17].The fluctuation of air-gap length in synchronous machines due to rotor saliency and magnetic saturation was better modeled in [18] than [6][7] using modified WFT. One of the first attempts to consider the effects of slots and salient poles on the inverse air-gap function was done in [19] using the straight lines and circular arc segments for flux lines inside air-gap region. ...
An improved winding function theory (IWFT) is presented in this paper, which can be also used to calculate the self and mutual inductances of large air-gap electric machines, while accurately considers the air-gap length function and the magnetic saturation in iron parts, simultaneously. In IWFT, the radial length of flux path in different points inside air-gap is calculated using the conformal mappings (CMs). The total air-gap length is the resultant of air-gap length at differential elements in radial direction. A modified inverse air-gap function is then presented for a typical cage rotor induction motor (CRIM) and a typical surface permanent magnet synchronous motor (SPMSM), which considers the real paths of flux lines in slotted air-gap. The high accuracy of these modified inverse air-gap functions are verified through comparing with the corresponding results obtained through finite element method (FEM). To consider the magnetic saturation, a virtual winding function as a 2-D function is introduced in this paper, which can consider the magneto-motive force (MMF) drops in iron parts of stator and rotor obtained through magnetic equivalent circuit (MEC) model. By using IWFT, dependent on the structure of relevant motor, a 2-D or 3-D lookup table is pre-calculated and stored for self/mutual inductances and their derivatives, and they are then used to model the running condition of CRIM and SPMSM under different loading conditions. Finally, the accuracy of IWFT results are verified by comparing with the corresponding results obtained through FEM.
