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.      

Theoretical prediction and experimental verification of light-load instability in a 11-kW open-loop induction motor drive

This paper presents the small-signal stability analysis of an 11-kW open-loop inverter-fed induction motor drive, including the effect of inverter dead-time. The analysis is carried out using an improved small-signal model of the drive that has been reported in literature recently, and is used to demonstrate small-signal instability in a higher-power-level motor. Through small-signal stability analysis, the region of oscillatory behaviour is identified on the voltage versus frequency plane (V–f plane), considering no-load. These predictions using the improved model are also compared against predictions of a standard model of an inverter-fed induction motor including dead-time effect. The oscillatory behaviour of the 11-kW motor drive is also studied through extensive time-domain numerical simulations and actual measurements over wide ranges of operating conditions. Both the simulation and experimental results confirm the validity of the predictions by the improved analytical model. Further, these results establish that the analysis is valid for both sine-triangle pulse-width modulation (PWM) and conventional space vector PWM.     

Space-vector-based PWM switching strategies for a three-level dual-inverter-fed open-end winding induction motor drive and their comparative evaluation

Two space-vector-based pulse-width-modulated (PWM) strategies are proposed for a dual two-level inverter-fed open-end winding induction motor drive. Neither of these PWM strategies require sector identification or lookup tables. These PWM strategies require only instantaneous phase reference voltages. Also, a simple model is suggested to compute the motor phase currents for this drive, and this model is validated through experimentation. The inverter losses are estimated for this drive system with these PWM strategies using an existing thermal model. The simulation studies suggest that one of these two PWM strategies is better than the other, as it causes lower losses in the inverters.     

Application of Wind Energy Conversion Systemsfor the Production of Electrical Energy at the Northeast of Brazil

The stead-state analysis of wind energy conversion system, consisting on windmill, synchronous generator, transmission line and induction motor driving a centrifugal pump is developed. The performance of the system operating at variable speed with a flux control is examined using mathematical models and digital simulation. The control scheme is proposed and tested in a laboratory and test center to compare field results with simulation results.     

Thermal analysis of induction motors using 3D finite element method

Abstract

To design a reliable and economical induction motor, it is necessary to be able to predict accurately the temperature distribution within the motor. In this paper, a 3D thermal model of an induction motor is presented. Except for providing a more accurate representation of the problem, the proposed model can also reduce computer memory and time. The finite element method (FEM) is used to analyze the three dimensional (3D) heat flow equation which describes the thermal model. Galerkin's procedure is used to derive the element equations and first order tetrahedral elements are used to discretize the field region. Galerkin's time‐stepping scheme is employed to treat time differential terms. Values of surface heat transfer coefficients are obtained from the empirical formula and heat losses are revised by the factory test. Application of the proposed method to the analysis of a 9,000 HP induction motor yields temperature distribution very close to the experimental data.     

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.     

Additional losses in induction machines under synchronous no-load conditions

The paper examines factors and parameters that affect the additional losses produced in the rotor cage of an induction motor during a no-load test at synchronous speed. The analysis uses a numerical approach based on a finite-element step-by-step procedure, taking into account the rotor movement. Iron losses are evaluated according to the loss separation theory. Additional losses are computed on the basis of predictions of high-frequency phenomena induced in the rotor cage. The model has been validated by comparison with experiments performed on a specific laboratory setup, consisting of a stator that can be equipped with two different rotors. The numerical approach was used to investigate the role of different parameters (supply conditions, geometrical dimensions, material properties) affecting the additional losses.     

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.      

Multi-criteria-based design approach of multi-phase permanent magnet low-speed synchronous machines

A design methodology dedicated to multi-phase permanent magnet synchronous machines (PMSMs) supplied by pulse width modulation voltage source inverters (PWM VSIs) is presented. First, opportunities for increasing torque density using the harmonics are considered. The specific constraints caused by the PWM supply of multi-phase machines are also taken into account during the design phase. All the defined constraints are expressed in a simple manner by using a multi-machine modelling of the multi-phase machines. This multi-machine design is then applied to meet the specifications of a marine propeller: verifying simultaneously four design constraints, an initial 60-pole three-phase machine is converted into a 58-pole five-phase machine without changing the geometry and the active volume (iron, copper and magnet). First, a specific fractional-slot winding, which yields to good characteristics for PWM supply and winding factors, is chosen. Then, using this winding, the magnet layer is designed to improve the flux focussing. According to analytical and numerical calculations, the five-phase machine provides a higher torque (about 15%) and less pulsating torque (71% lower) than the initial three-phase machine with the same copper losses.     

Comparison of the ${mbi A}^{*}{-}{mbi A}$ and ${mbi T}, Phi{-}Phi$ Formulations for the 2-D Analysis of Solid-Rotor Induction Machines

We present two eddy-current field potential formulations to solve rotating electrical machine problems by applying the finite-element method (FEM) using the motional ${mbi A}^{*}{-}{mbi A}$-potential formulation and the motional ${mbi T}, {bf Phi}{-}{bf Phi}$-potential formulation. We use the single-phase and three-phase solid-rotor induction motors of Problem No. 30a of TEAM Workshops to compare the potential formulations. We have solved both problems in the time domain and the frequency domain.      

Dispersion free analysis of acoustic problems using the alpha finite element method

The classical finite element method (FEM) fails to provide accurate results to the Helmholtz equation with large wave numbers due to the well-known “pollution error” caused by the numerical dispersion, i.e. the numerical wave number is always smaller than the exact one. This dispersion error is essentially rooted at the “overly-stiff” feature of the FEM model. In this paper, an alpha finite element method (α-FEM) is then formulated for the acoustic problems by combining the “smaller wave number” model of FEM and the “larger wave number” model of NS-FEM through a scaling factor ${a\in [0,1]}The classical finite element method (FEM) fails to provide accurate results to the Helmholtz equation with large wave numbers due to the well-known “pollution error” caused by the numerical dispersion, i.e. the numerical wave number is always smaller than the exact one. This dispersion error is essentially rooted at the “overly-stiff” feature of the FEM model. In this paper, an alpha finite element method (α-FEM) is then formulated for the acoustic problems by combining the “smaller wave number” model of FEM and the “larger wave number” model of NS-FEM through a scaling factor a ? [0,1]{a\in [0,1]} . The motivation for this combined approach is essentially from the features of “overly-stiff” FEM model and “overly-soft” NS-FEM model, and accurate solutions can be obtained by tuning the α-FEM model. A technique is proposed to determine a particular alpha with which the α-FEM model can possess a very “close-to-exact” stiffness, which can effectively reduce the dispersion error leading to dispersion free solutions for acoustic problems. Theoretical and numerical studies shall demonstrate the excellent properties of the present α-FEM.     

Minimization and identification of conducted emission bearing current in variable speed induction motor drives using PWM inverter

The recent increase in the use of speed control of ac induction motor for variable speed drive using pulse width modulation (PWM) inverter is due to the advent of modern power electronic devices and introduction of microprocessors. There are many advantages of using ac induction motor for speed control applications in process and aerospace industries, but due to fast switching of the modern power electronic devices, the parasitic coupling produces undesirable effects. The undesirable effects include radiated and conducted electromagnetic interference (EMI) which adversely affect nearby computers, electronic/electrical instruments and give rise to the flow of bearing current in the induction motor. Due to the flow of bearing current in the induction motor, electrical discharge machining takes place in the inner race of the bearing which reduces the life of the bearing. In high power converters and inverters, the conducted and radiated emissions become a major concern. In this paper, identification of bearing current due to conducted emission, the measurement of bearing current in a modified induction motor and to minimize the bearing current are discussed. The standard current probe, the standard line impedance stabilization network (LISN)), the electronics interface circuits are used to measure high frequency common mode current, bearing current and to minimize the conducted noise from the system. The LISN will prevent the EMI noise entering the system from the supply source by conductive methods, at the same time prevents the EMI generated if any due to PWM, fast switching in the system, will not be allowed to enter the supply line. For comparing the results with Federal Communications Commission (FCC) and Special Committee on Radio Interference (CISPR) standards, the graphs are plotted with frequency Vs, line voltage in dBμ V, common mode voltage in dBμ V and the bearing current in dBμ A with out and with minimizing circuits.     

Identification of magnetic parameters by inverse analysis coupled with finite-element modeling

We present a new approach for identification of the material electromagnetic parameters that are involved in electrothermal process simulations. We use inverse analysis techniques coupled with an induction heating finite-element model (FEM) and software developed in our laboratory. We describe here the direct induction heating FEM, the physical formulations, and the iterative identification procedure, and then present numerical tests and results.     

Investigation of very fast transient overvoltage distribution in taper winding of tesla transformer

In order to study the very fast transient overvoltage (VFTO) distribution in the taper winding of a tesla transformer under high-frequency steep-fronted voltage surge, we built a distributed line model based on multiconductor transmission line (MTL) theory. We used a new hybrid algorithm combining finite-element-method (FEM) and interpolation formulas to quickly evaluate the induction coefficient matrix K by utilizing some characteristics of the taper structure. The turn-to-ground and interturn voltage distributions can be obtained by solving the telegraphist's equations in the frequency domain. We measured the voltage distribution inside the taper winding to find some ways to weaken the voltage oscillations. Here, we compare the results with numerical values.     

Apparatus for Optical Study of Atomic Hydrogen on the Surface of Liquid Helium

Spin-polarized atomic hydrogen adsorbed on the surface of liquid helium is the most promising candidate for the observation of quantum degeneracy in a two-dimensional Base gas. In this article we describe our experimental apparatus which is being used to realize this goal. The apparatus employs a system of superconducting and iron magnets to supply electron and proton spin-polarized hydrogen to a cold cell (T 0.1K) at sufficient flux to compensate recombination losses and attain the regime of two-dimensional quantum degeneracy. The gas in the cell is probed using light resonant with the Lyman- atomic transition.     

A New Structure for Permanent-Magnet-Biased Axial Hybrid Magnetic Bearings

We propose a new structure for a permanent-magnet-biased axial hybrid magnetic bearing. Starting with the inner air gap and the outer air gap of conventional axial magnetic bearings, we first construct a novel air gap between the permanent magnet and the outer housing, which we call the second air gap, separating the bias flux paths from the control flux paths. As a result, the control flux paths will have lower reluctance, and the power loss of the axial magnetic bearing will be lower. Next, we modeled this axial hybrid magnetic bearing and analyzed it using the equivalent magnetic circuit method, 2-D finite element method (FEM), and 3-D FEM. We have designed and assembled an axial hybrid magnetic bearing prototype for a reaction flywheel system with angular momentum of 15 $hbox{N}!cdot!hbox{m}!cdot!hbox{s}$ at a speed of 5000 r/min. The theoretical analysis and the prototype experiments show such advantages as simple structure, good force current and force displacement, and high operating reliability.      

Modeling Magnet Length In 2-D Finite-Element Analysis of Electric Machines

Two-dimensional finite-element-method (2-D FEM) calculations are widely used in electric machine modeling instead of three-dimensional calculations because of their faster calculation time and simplicity. However, the 2-D calculations ignore end effects, causing a large error in calculating eddy currents in permanent magnets of synchronous machines. In this paper, we develop three analytical models and one curve-fitting model based on numerical calculations. The models improve the eddy-current loss calculation accuracy in 2-D FEM. The method adjusts the resistivity of a magnet material according to magnet dimensions. The adjustment takes into account the resistivity, the temperature dependence, and anisotropy of the resistivity of rare-earth magnet materials. We compare the models against FEM calculations in two and three dimensions and show that all the models improve the eddy-current loss calculation accuracy significantly, especially when the time-harmonic caused eddy-current losses in permanent magnets are considered.      

Direct Modeling of Motional Eddy Currents in Highly Saturated Solid Conductors by the Magnetic Equivalent Circuit Method

Motional eddy currents are induced in conductors due to a localized $vec{v}timesvec{B}$ electric field. Direct modeling of this term by finite-element-based analysis may lead to nonphysical oscillations. In this paper, two modified magnetic equivalent circuit (MEC) methods to calculate motional eddy currents in highly saturated moving solid conductors are presented. The comparison between the results of the proposed methods with the finite-element method (FEM) proves high accuracy of the proposed methods in a wide velocity range for highly saturated solid conductors. The mesh sensitivity analysis shows the higher stability of the calculations of the proposed methods, compared with FEM, as no numerical oscillations occur.      

A hybrid method of analysis of low-speed linear induction motors

A current-excited low-speed solid-iron secondary single-sided linear induction motor (SLIM) with aluminum reaction rail is considered, A hybrid method of analysis consisting of field analysis in conjunction with the multilayer transfer-matrix concept with adjustment of secondary iron permeability to match the tangential magnetizing field in each layer is developed. It is shown that this method gives valuable information on permeability and flux penetration in secondary iron. Computed thrusts are in good agreement with test results.     

Inverted and Forward Preisach Models for Numerical Analysis of Electromagnetic Field Problems

This paper discusses the use of the inverted ($B$-based) Preisach model and its incorporation into the finite-element method (FEM). First, the$B$-based Preisach model is studied thoroughly along with the forward ($H$-based) Preisach model, highlighting the advantages and disadvantages of both models. The study confirms that, in addition to the main purpose of the$B$-based model—to compute the magnetic field$H$directly—the$B$-based model can overcome the congruency problem. Thus, the$B$-based model proves to be more accurate than the$H$-based model. Second, the paper suggests that incorporating the$B$-based Preisach model into FEM models results in relatively accurate, computationally efficient simulations. The method has been validated by simulating hysteresis torque in a high-speed induction motor, and a comparative investigation of the effectiveness, accuracy, and efficiency of the models has been conducted.