End-winding Region Research Articles

Improved methods for stator end winding leakage inductance calculation

PurposeCalculating the stator end-winding leakage inductance, taking into account the rotor, is difficult due to the irregular shape of the end-winding. The end-winding leakage may distribute at the end of the active part and the fringing flux of the air gap. The fringing flux belongs to the main flux but goes into the end-winding region. Then, not all the magnetic flux occurring in the end region is the end-winding leakage flux. The purpose of this paper was to find a method to accurately separate the leakage from the total flux, taking into account the rotor.Design/methodology/approachIn this paper, two methods based on energy calculation are presented. Both methods require the assumption that the machine is symmetrical. The first method depends on the total leakage inductance and the machine’s active region length. The second method is based on the energy stored in the end region of the machine. In this case, removing the energy produced by the fringing flux of the air gap is necessary. The model should have a volume-closing fringing flux to remove the part of energy belonging to the end of the air gap.FindingsThe method presented in the paper does not require rotor removal. The values of the end-winding leakage inductance computed based on the proposed method were compared with values computed using the method with the removed rotor. The computations show that the proposed method is closest to the results from the method presented in the literature. Results obtained in the first method present that rotor influence on the value of end-winding leakage inductance exists. The model of the stator end-winding described in the paper is general. Therefore, the proposed methods are suitable for calculating the end-winding leakage inductance of other electric machines.Originality/valueThe method presented in the paper considers the rotor in end-winding leakage inductance calculation. It is not necessary to remove the rotor as in the similar method presented in the literature. The authors elaborated a parametric model with a volume-closing fringing flux to remove the part of energy belonging to the end of the air gap. The authors also elaborated their 3D model of the machine winding for calculations in Opera 3D.

Thermal Effects in the End-Winding Region of Electrical Machines

The main heat transfer mechanism in the end-winding region of electrical machines is convection. In order to increase the air motion, the rotor is equipped with a series of blades. Their geometry is reflected in the fanning factor, i.e., the ratio between the rotor peripheral speed and air velocity. An accurate calculation procedure for the fanning factor has not yet been given. Knowing its value is crucial for the determination of air velocity and heat transfer coefficient (HTC), as the latter describes the end-winding heat removal capability. In this study, the convective heat transfer phenomena between the end winding and air inside the end-winding region were analyzed, with the heat generated only in the end winding, mimicked with a custom designed coil, and air moved by the blades. The analysis was performed by experimental testing and computational fluid dynamics (CFD) modeling. Measurements data were used to build a reliable CFD model. Further on, CFD results were used to derive a generalized analytical equation for calculation of the end-winding HTC, related to blade geometry and rotor rotational speed. The developed analytical model significantly improves the quality of real-time lumped circuit thermal modeling of electrical machines and, thus, enriches this field of science.

Influence of the Shielding Winding on the Bearing Voltage in a Permanent Magnet Synchronous Machine

This article presents selected methods of limiting the bearing voltages of synchronous machines with permanent magnets supplied from power electronic converters. The authors analyzed methods based on the use of various shielding windings placed in slot wedges and mounted in the stator end-winding region. The values of the parasitic capacitances of the machine, on which the levels of bearing voltages depend, were determined using the finite element method. Three-dimensional simulation models were used for the calculations. The analysis of the influence of the shielding windings on the bearing voltage waveforms was conducted on the basis of circuit models with two- and three-level converters. The obtained calculation results indicate a high potential in limiting bearing voltages.

A Fast 3-D Winding Inductance Estimation Method for Air-Cored Resonant Induction Machines

The air-cored resonant induction machine removes the magnetic core, so the fields produced by the windings are truly 3-D in nature. The end-windings normally regarded as a nonactive and leakage source in conventional iron-cored machines now become an active part and contribute to the torque production. Therefore, the electromagnetic modeling can no longer be reduced to a 2-D analysis, and the 3-D inductance calculation becomes a key problem. The 3-D finite element analysis (FEA) can solve the 3-D magnetic field, but, first, the validity of its solution depends on the precision in geometry modeling. In particular, representing the end-winding region avoiding conductor clashing can be very complicated. Second, 3-D FEA solutions are computationally slow, and therefore inefficient as an “internal routine” of an optimization procedure. This article proposes a fast analytic 3-D winding inductance estimation method for air-cored resonant induction machines. The approach breaks down the real coils into straight conductors and represents them by single filaments located at their centers, then uses closed-form expressions derived from Neumann integrals to calculate the coil self and coil-to-coil mutual inductances, which are then collected into winding phase self and mutual inductances. All the independent coil-pair contributions are isolated, so as to eliminate redundant calculations. Good accuracy of the calculated results is confirmed by validation against both 3-D FEA and experimental results, including winding inductance breakdown and overall machine tested performance.

One-Dimensional Model for the Nonlinear Resistive Electric Field Control in Medium-Voltage Rotating Electrical Machines

This study provides an insight in the analytical estimation of the electric field along the surface of a stress grading system (SGS) in the end-winding region of an electrical machine. An analytical approach is derived for the field grading materials (FGMs) having power-law electric-field-dependent conductivity. Despite some limitations, the introduced model can be used for the preliminary analysis of SGS with specific geometric and dielectric parameters, both during sinus and pulsed voltage condition. The analytical considerations are verified with finite element simulations for 15 markedly different nonlinear FGMs, which were previously reported in the applications related to the medium voltage rotating electrical machines.

Raman distributed temperature sensing for end winding of high‐power generator

The temperature on the busbars of electric generators in the end-winding region needs to be monitored continuously. High temperature is associated with curvatures, seams, and poor ventilation. However, this solution has limitations, such as the number of measurement points. This article presents a reconstruction algorithm to estimate high-resolution signals, from readings of a distributed temperature system for monitoring high-power generator bars. The purpose of this work is to measure the temperature in the end-winding region with optical sensors based on Raman distributed temperature sensing (RDTS). The ability of RDTS equipment to perform a measurement is limited by its spatial resolution of 1 m. The proposed algorithm reduces spatial resolution through signal processing without changing the equipment hardware. Through the experimental results, it was possible to perform accurate temperature measurements for lengths up to 15 cm using the sensor element. With this method, the final winding of a generator bar of a 355 MW hydroelectric plant was instrumented in the laboratory. The results show that it is possible to monitor the temperature over this region, which has a length of 45 cm. Therefore, the proposed method has the potential for the use of RDTS systems for temperature acquisition of small, medium, and large electrical machines.

Stator End-Winding Thermal and Magnetic Sensor Arrays for Online Stator Inter-Turn Fault Detection

In this paper, two novel stator inter-turn fault sensing schemes, based on infrared (IR) thermopile sensor array (IRSA) and Hall-effect sensor array (HESA) are proposed. These circular sensing arrays are mounted along the inner wall of the stator's casing facing the end-winding region. This enables a direct measurement of temperature and magnetic flux distribution along the end-winding region in a non-contact way. Thus, the deviation in thermal and magnetic symmetry introduced by an inter-turn short circuit fault can be readily assessed. The proposed sensing schemes provides an intuitive and straight forward approach to inter-turn fault monitoring compared to the conventional methods, which depend on detecting fault induced secondary effects on external signals (motor currents, casing vibration, and temperature). The practicality and the diagnostic ability of the end-winding sensor array approaches in detecting the stator inter-turn faults is demonstrated using a 1.5 kW induction motor test rig. Compared to IRSA, HESA is found to be more versatile and with better early fault detection capability. Hence, an embedded online monitoring algorithm based on HESA is developed and demonstrated using the test rig.

A Rectangular End-Winding Model for Enhanced Circulating Current Prediction in AC Machines

The end-winding region is usually overlooked in the roebel design of large AC machines. However, saturated stator slots cause overhang parts to impact the circulating currents significantly. In fact, a precise knowledge of the winding overhang strand inductances is crucial when optimising the transpositions of large roebel bars, especially in the case of under-roebeling (having less than 360-transposition in the active part) where the goal is to compensate the winding overhang parasitic field with the slot-parasitic field. In this article, a rectangular inductance calculation model (R-ICM) is proposed. It results in a circuital lumped-element model (LEM) that takes the strand dimensions, the bar bending, as well as small-scale effects into account. Moreover, the work describes how to model finite current-carrying rectangular segments (straight and arced) from first principles. Finally, the methodology was demonstrated for two prototype specimens with different bending-shapes corresponding to the fundamental elements on a stator bar in the winding overhang of large electrical machines.

Analysis of air flow and heat transfer in a winding using porous medium approach

Abstract The efficient cooling of turbo-generators especially in the end-windings region directly affects the power output rating. Modeling the coolant flow passing through the stator end-winding of a high-powered generator, however, remains a challenge due to a large number of parts with irregular geometries as well as the intricacy of cooling flow paths. This paper focuses on a numerical investigation of flow and heat transfer in stator end-winding aiming at replacing the geometry of winding with a porous medium model. Using computational fluid dynamics analysis to examine the viscous and inertial contributions to the pressure drop of airflow in the stator end-winding region, a generalized porous medium model is developed for the real physical geometry of winding together with a correlation for interfacial Nusselt number. The results indicate that the inertial effect considerably prevails over the viscous effect, that is, viscous contribution becomes small and almost negligible. It is shown that not only the pressure drop characteristics match closely within both real and porous models, but also the heat transfer results agree as well which means that the replaced porous model can amply describe the macroscopic behavior of the winding.

Hybrid thermal model of a synchronous reluctance machine

This paper presents a hybrid thermal modeling methodology to analyze the temperature performance of radial flux electrical machines. For this purpose, the 2D finite element model of the active part of the machine is coupled with a lumped parameters thermal circuit of the end-winding region. A synchronous reluctance machine is used to validate the proposed approach. The results from the proposed method are compared with the experimental ones, which are obtained from a prototype machine. The computations show that the 2D FE model underestimates the temperature rise in the machine as it does not account for the power losses in the end-windings. The hybrid model accounts for these losses as well as for the heat dissipation in the end-winding region.

Thermal effects of stator potting in an axial-flux permanent magnet synchronous generator

Axial-flux machines often have certain problems with heat transfer as shrink fitting of the stator core in the housing is not an option, unlike in the case of radial-flux machines. In this paper, we study how potting of the stator affects the thermal behavior of a 100 kV A axial-flux generator. The axial-flux permanent magnet (PM) generator is of a one-rotor-two-stator type construction. A liquid cooling system is applied on the stator frame, and the potting material in the end-winding region thermally connects the end winding to the housing heat sink. The design principle of the cooling system is presented in detail. Simplified thermal models based on Computational Fluid Dynamics (CFD) are used to analyze the temperature distribution through the machine. The theoretical results are verified by measurements. For comparison, one stator of the prototype generator is potted with Ceramacast 675-N material while the other stator is not potted. In each stator there are 14 Pt-100 temperature sensors. As the temperature values between the potted and unpotted stator are compared, it is found that the temperatures differ from each other by approx. 10% at the end windings under load condition. The application of the potting material also provides the rotor cooling.

Numerical simulation of electromagnetic and mechanical phenomena in the end-winding region of three-phase induction machines*

The 3-D geometry of the motor end-region consisting of the end-winding together with the motor cross-section, housing and complementary construction parts is very complex, which makes the analytical computations of the electromagnetic phenomena related to the end-region very cumbersome and non accurate. Furthermore, owing to the complicated geometry, also the preparation of the numerical model is extremely time consuming and numerical simulation very computationally pretentious. The aim of this paper is to present the numerical approaches, which overcome these problems by introducing methods to simplify the modeling procedure of the machine end-winding and the consideration of the rotor current excitation. In this paper the use of the proposed methods is demonstrated by computing the induction motor end-winding leakage inductance, the computation of the eddy-current losses in the machine clamping-plates and by the calculation of the mechanical deformations of the synchronous generator end-winding under operating load conditions. Analysis of the time-variant magnetic field has been performed using T, Φ − Φ formulation for a 3-D time-harmonic finite element method (FEM).

Propagation of Partial Discharge Signals in Stator Windings of Turbine Generators

We studied the propagation of partial discharge pulses in a stator winding by means of measurements on a dismantled 35-MW generator and found that a stator winding acts as a transmission line. Therefore, a partial-discharge (PD) signal manifests itself at the generator terminals after a transit time that depends on the location of the discharge. Due to capacitive and inductive couplings in the end-winding region, a second propagation mode is present for higher frequencies. This "fast mode" manifests itself at the terminals without appreciable time delay. The capacitive and inductive couplings also cause crosstalk between the phases. As a consequence, a signal measured in one phase does not necessarily originate from a discharge in that phase. The amplitudes of the fast mode and, to a lesser extent, the slow mode (or transmission-line mode) are heavily damped when the discharge occurs further away from the measuring terminal. The consequence is that only discharges close to the measuring terminal can be observed. The propagation of a PD signal is not only influenced by the construction of the generator but also by its external connections.

Turbogenerator End-Winding Leakage Inductance Calculation Using a 3-D Analytical Approach Based on the Solution of Neumann Integrals

An analytical technique that can be effectively used for the calculation of the end-winding leakage inductance of a turbogenerator has been presented. It is based on a three-dimensional geometric model of the end-winding region in which each coil is modeled as a set of serially connected straight filaments. The calculation of the mutual inductance of the end coils is based on the multiple solutions of the Neumann integral. The method also accounts for the influence of stator core iron on the end-winding leakage inductance by using the method of images. The results of the calculations have been compared with the measured values of the leakage inductance for 247-MVA turbogenerator manufactured by KONCAR Generators and Motors Inc., Zagreb, Croatia. The principle of the end-winding leakage inductance calculation described herein can be effectively used for other types of machines and windings as well.

End-winding region configuration of an HTS transformer

Single-phase 14 kVA transformer model with Bi-2223 superconducting windings in a nonmetallic cryostat has been designed and fabricated. Rated voltage of the primary and the secondary winding is 400 V and 200 V, respectively. Considerable attention was paid to the minimization of the radial component of the magnetic field at the end of the winding, where this field component, perpendicular to the tape, reduces critical current and increases AC losses. Additional laminated ferromagnetic rings shaping the magnetic field around the winding edges are used to reduce the radial field component. The additional rings also eliminate stray field differences along winding circumference. A finite element method (software ANSYS) was used for optimization of the ring cross-section and their position with respect to the winding. The calculations show that the rings reduce the radial component of the magnetic field by about 50% and the critical current of the winding can be increased from 53 A to 65 A.

Partial discharges in HV machines; initial considerations for a PD specification

Partial discharge (PD) specifications exist for all types of electrical equipment except motors and generators. Whereas specifications essentially require that the equipment is discharge-free the stator conductor bar insulation of the motors and generators under consideration is micaceous and has excellent PD resistance. Consequently, the intention in a specification would be to permit a certain level of PD. It is therefore particularly important that the problem of overcoming the attenuation between the PD site and the measurement equipment at the winding terminals be solved. Within the general context of examining the feasibility of a PD specification, the problem of PD signal attenuation is addressed. The approach adopted was to seek a region of low attenuation by examining the whole of the possible range of PD measurement frequencies. The investigations described consist of experiments on a full-size 500 MW endwinding model and on two large high-voltage motor windings. Careful screening to reduce radiative pick-up from the calibration generator simulating a PD source and a direct earthing scheme enabled the essential elements of PD pulse transfer through a winding to be determined. The frequencies investigated ranged from kHz to GHz. Pulse transmission and frequency spectrum measurements were made. It is concluded that the PD pulse transmits essentially as a travelling wave, the high-frequency components being highly attenuated. No significant crosscoupling was apparent through the end-winding region. The windings acted as a low-pass filter, the cut-off frequency being dependent on the winding length, and being below 1 MHz. Consequently, it is concluded that it should be possible to measure PD, using equipment with a passband below the low-frequency cut-off, with low attentuation.

High-voltage stator insulation assessment by measurement of loss tangent and capacitance

The measurement of the capacitance and associated loss tangent over a range of voltages is a common method of assessing insulation condition. The author considers the use of such techniques for establishing aging trends and detecting abnormalities in high-voltage rotating plant stator insulation. Whereas the inherent accuracy of the technique, as determined by laboratory measurements, is good, measurements on site are shown to be subject to large variations. It is concluded that the variations below discharge inception voltage are mainly due to environmental effects in the endwinding region, whereas discharge-related properties vary because of the time dependence of the discharge process. It is shown that, in some circumstances, environmental variability can be reduced by phase-to-phase comparisons. >

End-Winding Leakage of High-Speed Alternators by Three-Dimensional Field Determination

The rapid increase in electric and magnetic loadings of electrical machines demands improved methods of predicting the end zone field distribution. This paper presents a numerical method for the determination of end zone fields and for the calculation of end-leakage reactance of high-speed alternators. The method takes account of all boundaries, simplified in regard to their geometries and magnetic nature. As a first step, the partial differential equations of the electromagnetic field in the different regions of the end-winding region of homopolar alternators are developed, based on the concept of the magnetic vector potential. These are transformed into finite difference equations, which are retained in a general form allowing for the nonlinearities of iron and the effect of current carrying regions. The theory of the energy method to evaluate the end-leakage reactance is explained. The difficulties of a numerical solution in three dimensions are presented. Then a mathematical model is set up taking the discrete nature of the windings into account. This model makes possible adequate consideration of the effects of the surrounding boundaries and also the effects of the air gap, slots, and of the short-pitched armature winding. An orthogonal lattice system is then fitted to the model. The boundary conditions in differential and difference forms are developed in terms of the magnetic vector potential. An iterative procedure consisting of successive point relaxation of the vector potentials is described.

The Solution of the Heat Flow Equations in Large Electrical Machines

To ensure that the materials used in the construction of a rotating electrical machine are utilized economically it is necessary to be able to predict the temperature distribution within the machine. A resistance network analogue representation of the stator core and windings is derived, based on the finite difference approximation to the heat flow equations. A solution of the analogue is achieved by matrix methods on a digital computer. The advantages of this particular analogue representation are that the effects of axial heat flow in the copper and changes in the air temperature in the radial air ducts are taken into account. The validity and accuracy of the analogue representation are checked by comparing the results with those obtained from detailed temperature measurements on a production machine. It is shown that the present standard methods of measuring winding temperature are inadequate for determining the actual copper temperature. Under certain circumstances high temperatures can be obtained in the endwinding region of a machine. These temperatures are undetected by the standard method of temperature measurement and are shown to be due to the low value of endwinding insulation thermal conductivity.