Core Loss Calculation Research Articles

Methods for Determining Losses and Parameters of Cylindrical-Rotor Medium-Power Synchronous Generators

This paper presents the analytical and numerical application of a method to determine the parameters and power losses in the core of two medium-power synchronous generators. These generators are used as emergency power sources powered by diesel engines, gas engines, and gas turbines. They cover peak electricity demand but can also be used in traction drives. This article presents a new numerical method for determining losses in the generator core based on the use of a time-stepping solution using the FEM method and calculating these losses using analytical formulas. In calculating the losses for the FEM method, approximations of the loss characteristics of the sheet were used with a wide range of induction values and frequencies. This method is specific to the solution used and was adapted from the authors’ previous work on losses in induction machines. A one-phase winding with alternating voltage was supplied to determine the basic parameters in the form of synchronous reactance. Also, an important novelty is the introduction of a new method of determining the saturation state of the magnetic circuit, which significantly affects the machine parameters. The obtained results were used in analytical calculations and implemented in a computer program that allows for the calculation of electromagnetic parameters, operating characteristics, and core losses, taking into account additional losses, total losses, and efficiency, as well as machine parameters in unsteady operating states and the current characteristics of a three-phase symmetrical short circuit at the machine terminals. The calculations obtained were verified experimentally by measurements of real machines.

Research on loss characteristic of soft magnetic composites under nonsinusoidal excitations with DC bias field

Choosing a suitable core loss model and accurately predicting energy loss are crucial in designing magnetic devices with high efficiency based on soft magnetic composites (SMCs). In this work, FeSiAl and FeSi SMCs with a uniform insulating layer were fabricated by a phosphating process. The effects of excitation waveform and DC bias field on core loss have been investigated in depth. The results show that different remagnetization rates of SMC under ideal sinusoidal and square waves result in different core losses at the same frequency and flux density. The improved general Steinmetz equation and the modified Steinmetz equation were shown to be suitable for calculating core loss under square excitation waves without DC bias field. When the DC bias field is applied, the core loss of FeSiAl and FeSi SMCs was found to increase significantly due to the magnetization state gradually approaching saturation. Interestingly, the variation tendency of core loss can be accurately predicted using the waveform coefficient Steinmetz equation under square excitation conditions with a DC bias environment. This work not only provides deep insights into core loss under different excitation waveforms and DC bias fields but also determines the application scope of different core loss models.

Interactive and educational simulation tool for permanent magnet synchronous machines

PurposeThis paper aims to present an interactive design and simulation tool for permanent magnet synchronous machines based on the finite-element-method. The tool is intended for education and research on electrical machines.Design/methodology/approachA coupling between the software MATLAB and finite element method magnetics is used. Several functionalities are included as modular scripts and represented in the form of a graphical user interface. Included are fully parametrized motor models, automatic winding generations and the evaluation of torque waveforms, core losses and speed-torque-diagrams. A survey was conducted to determine how the motivation of students concerning the covered topics is influenced by using the tool.FindingsDue to its simplicity and the intuitive visualization of the results, the tool provides direct access to the topic of electrical machines without having to deal with separate scripts. The modular structure of the software allows simple extensions with new functions. Because students can directly contribute to the tool with their own work, their motivation for using and extending it increases.Originality/valueThe presented tool offers more functionalities compared to similar free software packages, e.g. the calculation of core losses and speed-torque diagrams. Also, it is designed in such a way that it can be easily understood and extended by students.

A comparative study of J–A and Preisach improved models for core loss calculation under DC bias

Power transformer is widely used in the power system with the rapid development of the power converters connected to the grid. When a transformer operates under DC bias conditions, its iron core loss increases significantly, causing local overheating and threatening the proper operation of the transformer. However, there are persistent difficulties in accurately assessing the core loss when the induction waveform is influenced by a DC bias. This paper first proposes improvements to the J–A and Preisach models to evaluate the core loss of the iron core under DC bias. Additionally, we incorporate the hysteresis models into the finite element method (FEM) by modifying the fundamental constitutive equations in the FEM model in order to perform a precise core loss/distribution calculation. To verify the accuracy of prediction, a transformer prototype with a laminated core is developed. The improved J–A-FEM and Preisach-FEM models were directly compared in terms of calculation accuracy, numerical implementation, and computational burden.

High-frequency loss modeling of nanocrystalline core considering nonuniform distribution of flux density

Nanocrystalline core is widely used in the design process of high-frequency transformers and inductors due to the attractive magnetic properties of nanocrystalline material. However, the flux density distribution is nonuniform in the core because the reluctance is closely related to its geometric shape. The nonuniformity of flux density distribution may cause huge calculation errors of core losses. In this paper, Finite Element Method (FEM) is used to justify taking into account nonuniform distribution of flux density during the process of core loss calculation. An improved loss separation equation considering nonuniform distribution of flux density is proposed, and the improved equation is verified through calculating and analyzing the losses of nanocrystalline cores with different wound thicknesses. Compared with the traditional loss separation equation, the accuracy is improved, and the average error of improved equation is confined in 10%.

Improved calculation of core losses of high-speed motors with two different permanent magnets considering higher order current harmonics

In high-speed permanent magnet synchronous motor drives, time harmonics in the current occur owing to the carrier frequency of the inverter, which affects the core losses among the electromagnetic losses. According to Steinmetz’s equation, the core loss depends on the frequency and magnetic flux density, with each term influenced by harmonic currents. Therefore, to accurately predict core loss, it is necessary to consider harmonic currents. This study presents the effects of differences in the resistance, inductance, switching frequency, and harmonic current on the core loss for two models with different PMs at the same output power. Core losses are significantly affected by harmonic current content and magnetic field behavior, making the analysis of harmonic components and magnetic field behavior essential. To achieve this, the stator core was divided into segments to examine the magnetic field behavior owing to harmonic currents in each region, thus facilitating a comprehensive analysis of the core losses. When the results were compared with the experimental data, it was observed that the analysis of harmonic currents significantly improved the accuracy compared to the analysis based solely on sinusoidal currents; in particular, the error rate reduced from 37.8% to 4.1%. Furthermore, it was confirmed that ferrite PMs resulted in smaller core losses owing to harmonic currents than rare-earth PMs. This finding suggests that ferrite PMs are a suitable alternative to high-speed permanent-magnet synchronous motors.

Reduced Order Model Coupling Frequency Domain Method for Calculation of Core Loss in SPM Machine Considering PWM Current Harmonics

Reduced Order Model Coupling Frequency Domain Method for Calculation of Core Loss in SPM Machine Considering PWM Current Harmonics

A core loss estimation method based on improved waveform coefficient Steinmetz equation for asymmetric triangular flux density waveform

Accurate estimation of high frequency magnetic core losses under non-sinusoidal excitations is critical to the design of solid-state transformers. This paper proposes a waveform transformation principle, termed the equal derivative transformation (EDT), for piecewise linear flux density waveforms. Under the same maximum flux density, an asymmetric triangular flux density wave can be transformed into a symmetric one with a different frequency in terms of the calculation of core losses, hence the introduction of the improved waveform coefficient Steinmetz equation (iWcSE). The magnetic characteristics of three different toroidal samples (nanocrystalline alloy FT-3KL, amorphous alloy 1K101, ferrite N87) under square excitation at different duty ratios and certain frequencies are measured. Core losses predicted by the model are in good agreement with the measurement.

Wideband loss separation model of nanocrystalline materials considering microscopic magnetization mechanism

The core loss directly determines the performance of high-frequency transformers. This paper presents an enhanced method for calculating core losses by integrating the LLG equation and Maxwell's diffusion equation. By the method, the losses caused by the rotation of the magnetic moment can be obtained. The loss attributed to domain wall displacement is derived from the total loss by subtracting losses due to magnetic moment rotation, further categorized into the hysteresis loss and the residual loss. The observation of the dynamic variation of nanocrystalline magnetic domains with applied excitation verifies the feasibility of the improved method. Finally, the causes of residual loss generation are also analyzed the model accuracy is verified by comparing the measured and modelled values and the traditional loss separation model.

Measurement and Calculation Techniques of Complex Permeability Applied to Mn-Zn Ferrites Based on Iterative Approximation Curve Fitting and Modified Equivalent Inductor Model

In many cases, power inductors are responsible for most of the power loss, volume, and cost if applied to high-frequency power electronics applications. It is desirable to optimize their design by the proper calculation of winding and core loss. It allows faster and cheaper commercial product release, which is the key to being successful in a highly competitive market. This is only possible if existing calculation techniques and technical data given by, e.g., core manufacturers, are verified and correct; otherwise, the inductor optimization process is less precise and requires several iterations to achieve good convergence. This paper addresses existing and proposes improved measurement and calculation techniques with regard to complex permeability, one of the key quantities that define inductor behavior in the frequency domain. This is done through impedance measurement and improved definition of the equivalent inductor model. Moreover, the proposed calculation techniques fulfill the need for the simple, accurate analytical methods required in commercial designs.

Non-Linear Material Model of Ferrite to Calculate Core Losses With Full Frequency and Excitation Scaling

A material model for ferrite is presented, enabling an accurate calculation of the core losses from 100 kHz to 1000 kHz with a single set of scalar parameters over a decade of excitation current. It is based on the modelling of different material effects such as quantum tunnelling conduction between ferrite grains and atomic level magnetisation. The implications of the satisfying results of this approach on core loss modelling techniques at high frequencies are discussed.

Analysis of Core Losses in Transformer Working at Static Var Compensator

This article presents the comparison of 3D and 2D finite element models of a power transformer designed for reactive power compensation stations. There is a lack of studies in the literature on internal electromagnetic phenomena in the active part of a transformer operated in these conditions. The results of numerical 2D and 3D calculations of no-load current and losses in the transformer core were obtained by using various methods and models. The impact of considering the hysteresis loop phenomenon on the calculation of core losses was investigated by using the Jiles–Atherton core losses model. The results obtained in the paper show that the model of the core must contain the areas representing the influence of overlappings on the no-load current and also on the flux density field in the core. The capacitive load of the transformer increases the flux density in the core limbs by several percent, so the power losses there must also increase accordingly. As a summary of the research, differences in the values of losses in each core element between the capacitive load and no-load conditions are presented. The results presented in this paper indicate that considering nonlinearity related to the magnetic hysteresis loop has a significant impact on the calculation of the core losses of power transformers.

Analysis of Core Loss Characteristics of Linear Phase-Shifting Transformer

Linear phase-shifting transformer, as a new type of phase-shifting transformer, has the advantages of shifting phase at any angle, good expansibility, and easy modularization compared with the traditional core column phase-shifting transformer. To calculate the output performance such as the efficiency of linear phase-shifting transformer, the loss of linear phase-shifting transformer should be studied. The loss of linear phase-shifting transformer includes copper loss and core loss. Among them, the core loss has an important impact on linear phase-shifting transformer performance parameters such as efficiency and temperature rise, but there is a lack of relevant research at present. In this paper, based on the traditional separation model of ferromagnetic materials, a calculation method for linear phase-shifting transformer core loss is proposed. In this method, the loss coefficient of the linear phase-shifting transformer iron loss model is calculated by the least square method based on the calculation and analysis of the magnetic field law of the core by the time-step finite element method, and the loss coefficient is further modified by considering the influence of local hysteresis loop, non-sinusoidal magnetic field, and harmonic magnetic field. The linear phase-shifting transformer model based on finite element field-road coupling simulation is established, a low-power experimental prototype is designed, and a multi-stack inverter system platform is built. The theoretical calculation is verified by simulation and experiment. Simulation and experimental results demonstrate the accuracy of the core loss calculation method presented in this paper.

The Influence of Cutting Technology on Magnetic Properties of Non-Oriented Electrical Steel—Review State of the Art

The global drive to reduce energy consumption poses new challenges for designers of electrical machines. Losses in the core are a significant part of losses, especially for machines operating at an increased rotational speed powered by PWM inverters. One of the important problems when calculating core losses is considering the effect of material degradation due to mechanical or laser cutting. To this aim, this paper analyzes and summarizes the knowledge about the sources of material property deterioration and ways of describing this phenomenon. The cited results of material tests indicate the lack of unequivocal relationships allowing us to estimate the degree of material damage and the resulting deterioration of material properties. The main task of this article is to present the state of knowledge on the possibility of taking into account the impact of cutting the core sheets of electric motors on core losses and their impact on the efficiency of the machine. This is a significant problem due to the need to design and manufacture energy-saving electric motors powered with a voltage of 20 to 350 Hz, whose magnetic cores are made of laminates. However, the performed analysis indicates the most important parameters of the cutting process, affecting the degree of material structure destruction. The method of the solution proposed by the authors for core punching and laser cutting, illustrated with a practical example, is also presented.

Thermal Analysis of a Flux-Switching Permanent Magnet Machine for Hybrid Electric Vehicles

This paper investigates the loss and thermal characteristics of a three-phase 10 kW flux-switching permanent magnet (FSPM) machine, which is used as an integrated starter generator (ISG) for hybrid electric vehicles (HEVs). In this paper, an improved method considering both DC-bias component and minor hysteresis loops in iron flux-density distribution is proposed to calculate core loss more precisely. Then, a lumped parameter thermal network (LPTN) model is constructed to predict transient thermal behavior of the FSPM machine, which takes into consideration various losses as heat sources determined from predictions and experiments. Meanwhile, a simplified one-dimensional (1D) steady heat conduction (1D-SHC) model with two heat sources in cylindrical coordinates is also proposed to predict the thermal behavior. To verify the two methods above, transient and steady thermal analyses of the FSPM machine were performed by computational fluid dynamics (CFD) based on the losses mentioned above. Finally, the predicted results from both LPTN and 1D-SHC were verified by the experiments on a prototyped FSPM machine.

Application analysis of self-bonded electrical steel sheet in high power density PMSM for all-electric aircraft

Driving motor for all-electric aircraft (AEA) needs high power density and high torque density, resulting in the magnetic load and electrical load of driving motor in a limit state. Therefore, it is important to analyze the accurate calculation of core loss and the technology of loss suppression. Firstly, B35A230 self-bonded electrical steel sheet is used as core, which can reduce core loss caused by machining process. Then the ratio-loss curves of B35A230 at different frequencies and different flux densities are measured by Epstein frame and ring sample method, and the increment of core loss after machining is obtained, and the influence of axial welding paths on stator core loss is analyzed. According to experimental results, Based on the classical stator core loss model, machining factors are considered to improve the accuracy of stator core loss, and a core loss model is adopted to improve accuracy, considering processing factor, alternating and rotating magnetization modes and harmonic magnetic field. Finally, an outer rotor SPMSM for AEA is designed and manufactured, and the no-load loss is tested experimentally, which verified that the self-bonded electrical steel sheet has certain advantages in high power density driving motor.

A Core Loss Calculation Method for DC/DC Power Converters Based on Sinusoidal Losses

Traditional predicted core loss models, such as the improved Steinmetz equations, cannot show the whole changing tendency of core losses in different topologies. In this article, a core loss prediction model is presented based on sinusoidal losses. The axis of flux density is divided into a number of slice pairs in a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> - <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P_h</i> plane, and the hysteresis loss density is given in each slice pairs. By summing hysteresis losses associated with the actual swings of flux density in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> - <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P_h</i> plane, total hysteresis losses can be calculated quantitatively. This empirical approach is available both in calculating hysteresis losses under the centered and noncentered minor hysteresis loops. The effect of duty cycles on the swings of flux density and dc bias are analyzed, and two terms of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dc</sub> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> ) and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k_Δ_B</i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> ) are identified to show their effects on hysteresis losses. Dynamic eddy current losses are mainly associated with exciting waveforms, which are indicated by introducing a term <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k_e</i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> ). Since the main features of power converters are characterized by three terms, the behaviors of core losses in various topologies can be described adequately. Experimental results from three typical power converters agree with theoretical analyses well.

Effect of core losses on thermal analysis of 3ɸ- Squirrel Cage Induction Motor using lumped parameter thermal model

The proposed Lumped Parameter Thermal Model (LPTM) is complex enough to predict temperatures in most parts of the 3ɸ- Squirrel Cage Induction Motor (3ɸ-SCIM), including the end winding and rotor surface temperatures. It is easily adaptable to a variety of frame sizes because it is formulated using dimensional information and constant thermal coefficients. The solution of linear differential equations adequately describes the thermal behavior of the 3ɸ-SCIM. The application of the thermal model on 15 kW 3ɸ-SCIM is discussed. The rise in temperature at different parts of motor is estimated considering copper loss, constant and variable core loss. The maximum flux density derived from Finite Element Method (FEM) analysis, used to calculate core loss at various loads of a 3ɸ-SCIM. Variable core loss causes deviation in temperature rise, from the results, it is observed that, the relative percentage error considering variable core loss to constant core loss is about 19 %.

Magnetothermal Coupling Analysis of Permanent Magnet Claw Pole Machine Using Combined 3D Magnetic and Thermal Network Method

The permanent magnet claw pole machine (PMCPM) is a special kind of transverse flux machine, different from conventional electrical machines the main magnetic flux path of PMCPM is 3D. Therefore, for accurate performance analysis,the 3D finite element method (FEM) is required to calculate both the electromagnetic characteristics and thermal distribution. However, it is time consuming especially when the coupling effect needs to be considered. In this paper, a combined 3D magnetic and thermal network method is proposed to obtain the performance of PMCPM. As the developed thermal network shares the same structure as the magnetic network, the calculated core loss can be regarded as the heat source in the thermal analysis easily, in which 3D rotational core loss is calculated as the 3D network is adopted. The proposed method holds the advantages of close magnetothermal coupling and fast calculating speed.For the calculation results verification, 3D FEM is used.

Improvement on Loss Separation Method for Core Loss Calculation Under High-Frequency Sinusoidal and Nonsinusoidal Excitation

The original loss separation formula introduced by Bertotti has long been utilized mainly for low-frequency sinusoidal applications. In this article, the traditional method is improved to fit into the core loss calculation under higher frequency sinusoidal and nonsinusoidal excitations, verified by the measured data of nanocrystalline material that is often used in medium-frequency transformers (MFTs). For high-frequency sinusoidal waveform, it is proposed that the exponent of the excess loss needs to be reidentified, and it is necessary to consider the skin effect for hysteresis and eddy current loss calculation under broader frequency scope. When the core is supplied with nonsinusoidal excitation (square and rectangular waveform), a new empirical method is derived based on the concept of effective frequency and the loss separation results, with which the estimation accuracy is greatly guaranteed compared to empirical methods originated from the Steinmetz equation such as improved generalized Steinmetz equation (iGSE). Due to clear separation of loss components, the new method has the potential to precisely predict losses for higher frequency applications.