End-winding Leakage Inductance Research Articles

Analytical Estimation of End-Winding Leakage Inductance of Stator Winding of Electric Machines

Analytical Estimation of End-Winding Leakage Inductance of Stator Winding of Electric Machines

Electrical Machine Winding Performance Optimization by Multi-Objective Particle Swarm Algorithm

The present work aims to optimize the magnetomotive force and the end-winding leakage inductance from a discrete distribution of conductors in electrical machines through multi-objective particle swarm heuristics. From the development of an application capable of generating the conductor distribution for different machine configurations (single or poly-phase, single or double layer, integral or fractional slots, full or shortened pitch, with the presence of empty slots, etc.) the curves of magnetomotive force and the end-winding leakage inductance associated with the winding are computed. Taking as an optimal winding the one that presents, simultaneously, less harmonic distortion of the magnetomotive force and less leakage inductance, optimization by multi-objective particle swarm was used to obtain the optimal electrical machine configuration and the results are presented.

Simulation of the Circulating Bearing Currents for Different Stator Designs of Electric Traction Machines

Pulse–width modulated inverters are commonly used to control electrical drives, generating a common mode voltage and current with high–frequency components that excite the parasitic capacitances within electric machines, such as permanent magnet synchronous machines or induction machines. This results in different types of bearing currents that can shorten the service life of electric machines. One significant type of inverter–induced bearing currents are high–frequency circulating bearing currents. In this context, this work employs finite element analysis and time-domain simulations to determine the common mode current and circulating bearing current for various permanent magnet synchronous machine designs based on the traction machines of commercial electric vehicles with a focus on the stator. The results suggest that the ratio between the circulating bearing current and common mode current is much smaller in permanent magnet synchronous machines for traction applications than previously established in conventional induction machines, with values below 10% for all analyzed designs. A further increase in the robustness of such electric machines to the detrimental effects caused by the inverter supply could be achieved by reducing the parasitic winding–to–stator capacitance or by increasing the stator endwinding leakage inductance.

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.

Investigation of Analytical Models for Surface-Mounted Permanent Magnet Motor Using Voltage Source Inverter

This article analyzed and compared the complex permeance model (CPM) and nonlinear analytical model (NAM) for surface-mounted permanent magnet (SPM) motor using a voltage source inverter (VSI). For linear CPM, the slotting effect is represented using the improved complex permeance function that describes the real slot shape rather than infinitely deep slot. NAM is extended from CPM and it replaces the magnetic potential drop of stator iron by the equivalent virtual current in the slot-opening and tooth-tip to account for the nonlinearity effect. The nonlinear inductance of SPM motor including the main phase inductance, slot leakage inductance, tooth-tip leakage inductance, and end winding leakage inductance is calculated using the frozen permeability method, which is the key to solve the electric circuit with VSI. The instantaneous back electromotive force (EMF) is calculated from the nonlinear back EMF coefficient and the back EMF neglecting iron nonlinearity. The electromagnetic torque obtained from motor model is used in the mechanical model and then the rotational speed and rotor position are obtained for the electric circuit model. Hence, the iterative solving process for the motor system is established to calculate the transient performance of SPM motor using VSI. Compared with CPM, NAM can greatly improve the calculation accuracy, which is also validated by both finite-element model and experiment. Besides, the proposed NAM is computationally efficient, which is useful for both motor design and motor control.

Numerical simulation of a squirrel cage motor including magnetic wedges and radial vents

This work is a proposal of a finite element model to obtain the electromagnetic performance of a squirrel cage motor considering the magnetic wedges and radial vents. To analyze the electromagnetic performance at the design stage, without the need to build a prototype, the paper proposes a simple two dimensions finite element model, which includes components as magnetic wedges used to hold the windings in the stator slots, radial vents in the core, which are part of motor cooling system, and edge effects to improve the model. The stator and rotor cores are modeled with an equivalent homogeneous permeability, obtained from the combination of the radial air vents of rotor and stator and the magnetic core material. The permeability of magnetic wedges is also considered. Edge effects considered are the end winding leakage inductance, representing the leakage flux in the end coils of the stator, and an equivalent impedance between rotor bars due to conductivity and leakage flux in the rings of the squirrel cage. The results obtained are compared with experimental tests performed in steady state to validate the model. Furthermore, no-load, and blocked-rotor tests are simulated to estimate the equivalent circuit parameters and draw the typical induction motor torque-speed curve, which is compared with the obtained curve by means of Thevenin’s theorem. With this proposed model, the results are close to the ones obtained experimentally. The implementation of a 3D model is complex, and the computational cost can be much higher, compared to the 2D model developed here.

Computation of Leakage Inductance of End Coils in Electrical Machines Considering Core Effects

A new analytical method is presented for computing the leakage inductance of the single-end coils of electrical machines, based on the solution of Maxwell’s equations, which considers core eddy currents. Maxwell’s equations are solved in general form in two regions: inside and outside the core, employing appropriate boundary conditions and an iteration scheme. Asymptotic methods are effectively employed for the analytical calculation of Green’s functions in both the regions. Analytical results are compared with 3-D finite-element computations. The comparison shows a close correspondence between the analytical and numerical results. Our formula is the basis for further computations of the end-winding leakage inductance of rotating electric machines.

Parameters evaluation of a permanent magnet synchronous generator with modular stator

This paper presents the evaluation of the parameters of a surface-mounted permanent magnet synchronous generator designed for wind generation in urban areas, and manufactured in a ring shaped around the turbine with modular stator. In the project, the analytical subdomain method and finite element analysis provides the inductances, both in two dimensions, and compared with experimental results in order to quantify the end winding leakage inductance. The analytic and numeric results indicate a reduction of inductances with increases of slots per winding phase. The experimental measurement allows identify the end winding leakage inductance that, due to the unconventional dimension proportions, is approximately 30% of total.

Research of Mathematical Model of the Twelve-Phase Linear Induction Motor with Double-Sided Long Stators

Based on the requirement of high-power linear propulsion system, a novel twelve-phase linear induction motor (LIM) with double-sided long stators was designed, and the winding construction of twelve-phase LIM was presented in this paper. On the basis of this, the mathematical model of ABC coordinates for this novel motor was derived, and the rule of the asymmetry of end-winding leakage inductance of the twelve-phase LIM with double-sided long stators, which is determined by the relative space position of the each phase end-winding in the motor, and then this rule was compared with the law of the asymmetry of end-winding leakage inductance of the multi-phase rotating motor. Simulation model of the motor was established, and the electromagnetic properties of the motor is calculated.

Influence of constructional turbo-generator end region design on end winding inductances

Influence of constructional turbo-generator end region design on end winding inductancesThe paper introduces a comprehensive investigation in end winding inductances of large two-pole turbo-generators. With the aid of an analytic-numeric approach, where Neumann's formula is applied, the influence of geometric characteristics of double-layer stator end windings with involute shape is analysed. This parameter study results in approximation formulas for the stator self and mutual inductances at strand level as well as for the common used end winding leakage inductance. In order to consider field affecting components as pressure plate, flux shield, rotor shaft and rotor retaining ring, finite elements models for two machines (250 MVA and 1150 MVA) are created and computed. The results are integrated in the developed approximation formulas. Finally the simulation results of machine 1 are compared to the data of two different measurements. All approaches introduced in this paper show good correlation. The high speed of the analytic-numeric calculation is combined with the accuracy and opportunity to consider field affecting components within the extensive finite element computation successfully.

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).

Calculation and Analysis of Stator End-Winding Leakage Inductance of an Induction Machine

This paper proposes an improved method for calculating the value of and for analyzing the frequency-dependence of the stator end-winding leakage inductance of an induction machine. The method was based on the stored magnetic energy, which was calculated by a 3-D time-harmonic finite element analysis. In this method, there were no rotary parts in the model of the simulated machine. The results of the analysis show that the stator end-winding is capable of influencing the end of the active region of the machine whereas the influence on the central part of the active region is small. In addition, the phenomenon that the stator end-winding leakage inductance, as well as the magnetic energy in the machine, relates to the frequency of the stator current is explored.

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.