Effects of pulse-width-modulated supply voltage on eddy currents in the form-wound stator winding of a cage induction motor

The eddy currents of a form-wound multi-conductor stator winding because of the non-sinusoidal supply voltage in a cage induction motor are studied. The time and space dependence of the field, circuit variables and the motion of the rotor are modelled with the time-discretised finite-element analysis. A pulsewidth- modulated voltage is used to supply the motor. The eddy-current loss distribution of the stator bars and the total eddy-current losses are studied. The radial distance of the stator bars from the air gap is re-emphasised as a design parameter because of its effect on the losses and the hot spots. The means for minimising the losses and avoiding the local hot spots are studied.     

Time-stepping finite-element analysis of eddy currents in the form-wound stator winding of a cage induction motor supplied from a sinusoidal voltage source

The eddy-current effects of multi-conductor form-wound stator winding because of the fundamental and high-frequency magnetic flux in a cage induction motor are studied. The time dependence of the field and circuit variables and the motion of the rotor are modelled by the backward Euler time-stepping method. The motor was supplied from a sinusoidal voltage source. The series and parallel connected stator bars are strongly coupled with the circuit and field equations. The Newton-Raphson method is applied to solve the system of non-linear equations. The eddy-current loss distribution of the stator bars and the quantitative results of eddy-current losses are studied. The radial distance of the stator bars from the air gap has a remarkable effect on the losses and the hot spots. Methods to minimise the losses and to avoid the local hot spots are studied.     

Eddy-current loss in the rotor magnets of permanent-magnet brushless machines having a fractional number of slots per pole

We develop an analytical model for predicting the eddy-current loss in the rotor magnets of permanent-magnet brushless machines that have a fractional number of slots per pole, when either all the teeth or only alternate teeth are wound, and in which the unwound teeth may be narrower than the wound teeth. The model enables the magnetic field distribution in the air gap and magnet regions to be determined, by neglecting the eddy-current redistribution effect and assuming that the eddy currents are resistance limited. It can account for space-harmonic magnetomotive forces (MMFs) resulting from the winding distribution and time-harmonic MMFs due to nonsinusoidal phase currents, as well as for the effect of curvature and circumferential segmentation of the magnets. We have validated the model by finite-element analysis, and used it to investigate the eddy-current loss in the magnets of three surface-mounted magnet brushless motors that have similar slot and pole numbers, and employ identical rotors but different stators, when they are operated in brushless ac (BLAC) and dc (BLDC) modes. We show that the stator winding configuration, as well as the operational mode, significantly influence the resultant eddy-current loss.     

Time-Harmonic Induction-Machine Model Including Hysteresis and Eddy Currents in Steel Laminations

We have studied electromagnetic losses of a frequency-converter-fed cage-induction motor by using a numerical machine model that includes eddy-current and hysteresis phenomena in electrical steel sheets. We used the model to solve the two-dimensional (2-D) time-harmonic field and winding equations of a cage-induction machine, utilizing a finite-element method and phasor variables. We used complex reluctivity to couple the hysteresis and eddy currents in the sheets with the 2-D analysis. The model modifies the absolute value of the reluctivity according to a one-dimensional (1-D) eddy-current solution developed in the lamination thickness. To define the argument of the reluctivity, we applied both the 1-D field solution and measured hysteresis data. We compared computations of additional electromagnetic losses in a 37-kW test machine due to the higher harmonics of a frequency-converter supply with experimental results. The agreement is found to be reasonable.      

Steady-state finite-element solver for rotor eddy currents in permanent-magnet machines using a shooting-Newton/GMRES approach

This paper presents a two-dimensional steady-state finite-element solver, incorporating mechanical motion, that calculates eddy-current losses in the rotors of permanent-magnet machines. A shooting-Newton method is used to determine the periodic solution of the electromagnetics. Computation of the shooting-Newton Jacobian is avoided by using a generalized minimum residual (GMRES) linear solver. This method is more computationally efficient than performing transient analysis until convergence. The solver can be used to compare the rotor losses of different design choices for a high-speed permanent-magnet machine. Results show that rotor losses can be reduced significantly by laminating the rotor backiron, segmenting the permanent-magnet poles, increasing the number of stator slots, and closing the stator slots.     

AC Loss Evaluation of MgB2 Superconducting Windings Located in a Stator Core Slot with a Finite-Element Method

AC losses in stator windings of fully superconducting motors with an MgB₂ wire are numerically evaluated by means of a finite-element method using edge elements for a self-magnetic field. The physical properties of the MgB₂ wire for numerical calculations are obtained from the corresponding experiments with an existing wire. It is assumed that the voltage?Ccurrent characteristics of the MgB₂ wire are given by Bean??s critical-state model, in which the critical current density is independent of the local magnetic field. The influences of core slot size and turn number of windings on the AC losses are discussed quantitatively toward the optimum design of the stator winding with the MgB₂ wire.     

Effects of Armature Reaction on the Performance of a Claw Pole Motor With Soft Magnetic Composite Stator by Finite-Element Analysis

We investigated the effects of armature reaction on the performance of a three-phase three-stack claw pole motor with soft magnetic composite stator core by using three-dimensional finite-element analysis (FEA), which is an effective approach to accurately compute the parameters and performance such as the back electromotive force (EMF), core losses, and winding inductance at various saturation levels. The motor is rated as 500 W at 1800 rpm when the stator current is 4.1 A, driven by a sensorless brushless DC scheme. Because of the armature reaction, the back EMF produced by the rotor permanent magnets and the developed torque is reduced by about 3.3% at the rated load, and the core losses increase drastically by 41% from no-load to full-load. The winding inductance is computed with different loads at different rotor angles     

Analytical Modeling of a Permanent-Magnet Synchronous Machine in a Flywheel

We develop an analytical model for a radial-flux external-rotor permanent-magnet synchronous machine (PMSM) without slots in the stator iron and with a shielding cylinder. The machine is part of an energy storage flywheel, to be used as the peak-power unit in a hybrid electric passenger bus. To reduce the induced no-load losses due to the high rotational speed of the flywheel, the slots in the stator are made not of iron but of a nonmagnetic plastic material. This results in an air gap winding with a stator yoke consisting of stacked circular laminations. The analytical model includes the effect of the winding distribution on the field, the fact that it is in the air gap, and the effect of the eddy-current reaction field of the shielding cylinder. The two-dimensional magnetic field is solved in six defined machine layers and useful machine quantities are derived directly from it, leading to the machine voltage equation. We built a prototype flywheel machine. The locked-rotor machine resistance and inductance predicted by the analytical model was compared with the experimentally determined values. The values showed good agreement, thereby validating the analytical model of the machine.      

Modeling of Eddy-Current Loss of Electrical Machines and Transformers Operated by Pulsewidth-Modulated Inverters

Pulsewidth-modulated (PWM) inverters are used more and more to operate electrical machines and to interface renewable energy systems with the utility grid. However, there are abundant high-frequency harmonics in the output voltage of a PWM inverter, which increase the iron losses and result in derating of the machine or transformer connected to them. Predicting the iron losses caused by the PWM supply is critical for the design of electrical machines and transformers operated by PWM inverters. These losses are primarily attributed to eddy-current loss caused by the PWM supply. In this paper, after analyzing the harmonic components of PWM voltage, we derive the effects of different parameters of PWM switching on the eddy-current loss. We compare the iron losses modeled with the proposed analytical methods on a three-phase transformer, a dc motor, and an induction motor with the results of time-stepping finite-element analysis and experiments. We provide detailed equations for the prediction of iron losses. These equations can be directly applied in the design and control of PWM converters and electric motors to improve energy efficiency in electrical machines and transformers operated from PWM converters.      

Iron Loss Model for Permanent-Magnet Synchronous Motors

Iron losses in permanent-magnet synchronous machines form a larger portion of the total losses than in induction machines and, hence, more importance should be given to the iron losses. Previously, models have been presented for the calculations of these losses, but these models still rely on finite-element simulations to obtain correction factors, which are substantial, to apply to the theoretically derived formulas in order to obtain good agreement with the experimental data. This paper points out the source of this correction factor: the neglect of the excess eddy-current loss component. In many cases, this loss component dominates the total iron losses and needs to be incorporated in the theoretical considerations. The paper also provides a more complete model of iron loss, which greatly reduces the need for calculating the correction factors using the finite-element method (FEM). This more complete model reduces design time, especially when a number of candidate designs need to be analyzed. Otherwise, the calculation of the correction factors using FEM would be cumbersome, as the correction factors tend to be nonlinear.     

Fringing Field Formulas and Winding Loss Due to an Air Gap

The paper describes a simple treatment for the fringing fields of an air gap in the core of a magnetic component such as an inductor or a transformer. It verifies the derived analytical formulas for the fields by using numerical (finite-element) calculations. It then applies these formulas to the calculation of high-frequency eddy-current losses for two types of winding arrangements, both of which employ thin rectangular conductors. The rectangular conductors are commonly used in flex circuit windings, printed circuit windings, and thin-film windings. The two types of winding configurations are flat and barrel wound. Each behaves in a different way as a function of the position of the conductor.     

Field weakening for radial force reduction in brushless permanent-magnet DC motors

In brushless permanent-magnet dc (BLDC) machines, the attraction between the rotor permanent magnets and the stator iron causes radial stator forces that excite the stator structural response and radiate unwanted acoustic noise. In this paper, we develop an analytical model that predicts rotor torque and radial force ripple as functions of the stator currents. The model shows that field weakening of sinusoidally commutated BLDC machines can reduce radial forces but requires higher currents to maintain the desired torque. We confirmed the analytical results numerically on a BLDC motor using ANSYS finite-element analysis and found a 30% reduction in force ripple at no load.     

Bridge configured winding for polyphase self-bearing machines

The self-bearing or bearingless machine is an electromagnetic device that supports its own rotor by way of magnetic forces generated by windings on its stator. Various winding configurations have been used to accomplish the task of force production. This paper proposes a winding based on a bridge connection for polyphase self-bearing rotating electrical machines with advantages such as: 1) requiring only one power supply for torque production; 2) lateral forces are produced using auxiliary power supplies of relatively low current and voltage ratings; 3) relatively low power loss; and 4) preserving the flexibility for extensions to other polyphase machines. The bridge connection has been verified to exhibit the characteristics of a self-bearing motor via an electrically coupled finite-element analysis. A comparison of power loss with conventional winding schemes and general applications of such a proposed scheme are also presented.     

Application of the local radial point interpolation method to solve eddy-current problems

This paper introduces the meshless local radial point interpolation method to model eddy-current problems for the first time. The formulation is described and results are compared with those from the ordinary finite-element simulation and the analytical solution.     

Influence of High Temperature Superconducting Transformer Geometry on Leakage Magnetic Field

Leakage magnetic fields in high temperature superconducting (HTS) transformer windings reduce the critical current and increase the ac losses in HTS tapes. Moreover, because of the anisotropic properties of the HTS tapes, the influence of the radial component of the leakage field on critical current and ac losses is much stronger than that of the axial one. For these reasons, leakage magnetic fields must be carefully considered in HTS transformer design. In this paper, we report a study of the influence of the core structure and the winding configuration on the leakage field by the finite-element method (FEM), and offer some suggestions for reducing the maximal radial component of leakage field to make the HTS transformer more efficient.     

Temperature Rise Analysis of Switched Reluctance Motors Due to Electromagnetic Losses

We present a finite-element analysis of the temperature rise of switched reluctance motors (SRM) due to electromagnetic losses. We estimate the various components of electromagnetic losses, including core loss in the lamination as well as copper and eddy-current losses in windings, and then predict the temperature rise within the motor due to these losses. We present simulation results for an 8/6 SRM and discuss various aspects of thermal design of SRMs. To validate the procedure for the estimation of electromagnetic losses, we compare predicted and measured losses.      

A novel switched reluctance motor with C-core stators

This paper presents a novel switched reluctance motor (SRM) design in which the stator is simply formed from C-cores. Unlike conventional SRMs, the windings of the new motor can be individually wound into the stator cores without complex winding equipment. Because of the inherent axial field distribution, this type of SRM requires a three-dimensional (3-D) finite-element analysis (FEA) model for detailed flux analysis. This paper proposes an approximated two-dimensional FEA model to speed up computational time. In addition, since the proper current that ensures operation in the saturated region (to maximize torque and efficiency) is often hard to determine systemically, the paper proposes a simple method to determine the optimum operating current so that one can easily decide the rated current and also obtain the maximum motor efficiency. Finally, the paper compares some characteristics of a traditional SRM with those of the proposed SRM. The comparison shows that the proposed SRM performs well in terms of torque and efficiency, and provides a higher degree of flexibility in winding design.     

Finite-element analysis of the rotor/stator contact in a ring-type ultrasonic motor

A way to understand mechanical characteristics of an ultrasonic motor is presented. First, the vibration mode of a stator is calculated using a finite-element method (FEM) code. The path of the elliptic motion of the stator's teeth is obtained. The computed vibration mode at the surface of the stator is compared with that measured by an electrooptical displacement transducer. Next, the contact condition of the rotor/stator is calculated. The displacement and velocity of the rotor/stator, the distortion of the stick/slip area, the rotational speed of the rotor, and the friction loss of the motor are obtained. The calculated rotor displacement and torque-rotational speed curve correspond closely to the experimentally measured ones. The internal loss of the rotor/stator and the loss of the supporting felt are measured. The total loss of these losses and the calculated friction loss agree with the measured total loss. The calculated and the measured efficiency of the motor also agree.     

Comparison Between Finite-Element Analysis and Winding Function Theory for Inductances and Torque Calculation of a Synchronous Reluctance Machine

This paper compares the prediction of two independent methods for calculating electromagnetic torque and inductances of a synchronous reluctance machine under linear condition. One method is based on winding function analysis (WFA) and the other on finite-element analysis (FEA). Both methods take into account the rotor geometry, the stator slot effects and the stator winding connections. The simulation results obtained by the WFA are compared with the ones obtained by two-dimensional FEA. It is shown that the two methods give approximately the same results but require different computation times.     

High-Frequency Tunneling Magnetic Loss in Soft Ferrites

This paper considers high-frequency (200 kHz-1.0 MHz) losses in MnZn power ferrites and shows that none of the three well-known magnetic loss mechanisms (namely, hysteresis, classical eddy-current loss, and excess eddy-current loss) can account for the experimentally observed dependence of the loss on the frequency and flux density. In order to investigate the origin of this discrepancy, the electric field that is induced in the typical core when the material is driven at high frequencies and flux densities was estimated. The estimates show that these electric fields can be quite large. The paper presents experimental data on the electrical conductivity for such large electric fields, which shows a highly nonlinear behavior that can give rise to a modified eddy-current loss mechanism. By a simple curve fit to the nonlinear conductivity, the experimentally observed flux density dependence of the high-frequency loss, which previously could not be explained, can be reproduced by using this modified eddy-current loss mechanism. A modified ferrite structure can eliminate most of these extra losses by reducing the electric field generated at the grain boundaries due to high frequencies and flux densities