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This paper aims to propose and establish a set of new benchmark models to investigate and confidently validate the modeling and prediction of total stray-field loss inside magnetic and non-magnetic components under harmonics-direct current (HDC) hybrid excitations. As a new member-set (P21^e) of the testing electromagnetic analysis methods Problem 21 Family, the focus is on efficient analysis methods and accurate material property modeling under complex excitations.

This P21^e-based benchmarking covers the design of new benchmark models with magnetic flux compensation, the establishment of a new benchmark measurement system with HDC hybrid excitation, the formulation of the testing program (such as defined Cases I–V) and the measurement and prediction of material properties under HDC hybrid excitations, to test electromagnetic analysis methods and finite element (FE) computation models and investigate the electromagnetic behavior of typical magnetic and electromagnetic shields in electrical equipment.

The updated Problem 21 Family (V.2021) can now be used to investigate and validate the total power loss and the different shielding performance of magnetic and electromagnetic shields under various HDC hybrid excitations, including the different spatial distributions of the same excitation parameters. The new member-set (P21^e) with magnetic flux compensation can experimentally determine the total power loss inside the load-component, which helps to validate the numerical modeling and simulation with confidence. The additional iron loss inside the laminated sheets caused by the magnetic flux normal to the laminations must be correctly modeled and predicted during the design and analysis. It is also observed that the magnetic properties (B27R090) measured in the rolling and transverse directions with different direct current (DC) biasing magnetic field are quite different from each other.

The future benchmarking target is to study the effects of stronger HDC hybrid excitations on the internal loss behavior and the microstructure of magnetic load components.

This paper proposes a new extension of Problem 21 Family (1993–2021) with the upgraded excitation, involving multi-harmonics and DC bias. The alternating current (AC) and DC excitation can be applied at the two sides of the model’s load-component to avoid the adverse impact on the AC and DC power supply and investigate the effect of different AC and DC hybrid patterns on the total loss inside the load-component. The overall effectiveness of numerical modeling and simulation is highlighted and achieved via combining the efficient electromagnetic analysis methods and solvers, the reliable material property modeling and prediction under complex excitations and the precise FE computation model using partition processing. The outcome of this project will be beneficial to large-scale and high-performance numerical modeling.

This paper aims to investigate an efficient approach to model the electromagnetic behaviors and predict stray-field loss inside the magnetic steel plate under 3D harmonic magnetization conditions so as to effectively prevent the structural components from local overheating and insulation damage in electromagnetic devices.

An experimental setup is applied to measure all the magnetic properties of magnetic steel plate under harmonic excitations with different frequencies and phase angles. The measurement and numerical simulation are carried out based on the updated TEAM Problem 21 Model B+ (P210-B+), under the 3D harmonic magnetization conditions. An improved method to evaluate the stray-field loss is proposed, and harmonic flux distribution in the structural components is analyzed.

The influence of the harmonic order and phase angle on the stray-field loss in magnetic steel components are noteworthy. Based on the engineering-oriented benchmark models, the variations of stray-field losses and magnetic field distribution inside the magnetic components under harmonic magnetization conditions are presented and analyzed in detail.

The capacity of the multi-function harmonic source, used in this work, was not large enough, which limits the magnetization level. Up to now, further improvements to increase the harmonic source capacity and investigations of the electromagnetic behaviors of magnetic steel components under multi-harmonic and DC-AC hybrid excitations are in progress.

To accurately predict the stray-field loss in magnetic steel plate, the improved method based on the combination of magnetic measurement and numerical simulation is proposed. The effects of the frequency and phase angle on the stray-field loss are analyzed.

The purpose of the paper is to give a review of TEAM Problem 21, focus on its extended progress in engineering-oriented developments, and report the new benchmarking activity undertaken by the authors.

Testing electromagnetic analysis methods; verify computation models; detail the field behavior of typical magnetic structure; benefit to large-scale numerical modeling.

The calculated results of power loss and magnetic flux for all the member models agree well with the measured ones. The updated Problem 21 Family can now be used to model the saturation effect in the magnetic plate or the lamination by increasing the exciting currents. The new member model P21d-M allows further detailed examination of the electromagnetic behavior inside laminated sheets. The variation of both the iron loss and the magnetic flux with the excitation patterns and magnetic property data can be investigated inside the laminated sheets and the magnetic plate.

In order to model the possible saturation level of magnetic steel using Ar-V-Ar or T-Ω solvers, the exciting currents are increased from 10 to 50 A. In order to model the iron loss and magnetic flux densities inside the laminated sheets, a very simplified model, P21d-M of Problem 21 Family as shown in Figure 2, has been proposed.

The purpose of this paper is to investigate the effects of the related factors on the mean path length of the Epstein frame and propose a weighted method based on the different specific losses to decide the actual mean path length of the Epstein frame.

Two Epstein frames of different dimensions (i.e. standard 25 cm and revised 17.5 cm Epstein frame) are used in experiments, and two kinds of the mean path lengths, lm1 and lm2, are defined based on the different specific iron losses produced at the middle part of the limb and the rest of the whole frame, respectively.

The mean magnetic path varies with many factors such as peak flux density, excitation frequency, permeability as well as the anisotropy of the material under test.

The results play an important role in designing the transformer core and the building factor.

The purpose of this paper is to present a simple method to analyze the iron loss in the laminated core of power and distribution transformers.

This paper presents a practical method to calculate the no-load loss in the transformer cores. Considering the non-uniformity of the magnetic flux density in the corner areas of the Epstein frames will affect the measurement precision of the Wt-B curves then further affect the core loss calculation in FEM, a dual-Epstein frame method is used to measure the Wt-B curves with the Epstein sample stripes cutting by different angles to the rolling direction. A 2D FEM that considers the type of joints of the core and eddy current effect in the laminations is used to analyze the core loss with multi-angle Wt-B curves.

The impact of lamination thickness, size of gaps and type of joint of the core are considered. Considering the no-load testing conditions, harmonics in the exciting currents are taken into account.

Harmonic wave of magnetic flux density in the transformer core is calculated and the core loss in the joint region is calculated by the loss curve measured with dual-Epstein frame. It makes the calculation result of transformer core loss more exactly.

This paper aims to introduce the decomposed harmonic balance finite element method (HBFEM) to decrease the memory requirement in large‐scale computation of the DC‐biasing magnetic field. Harmonic analysis of the flux density and flux distribution was carried out to investigate the DC biased problem in a laminated core model (LCM).

Based on the DC bias test on a LCM, the decomposed HBFEM is applied to accurately calculate the DC‐biasing magnetic field. External electric circuits are coupled with the magnetic field in the harmonic domain. The reluctivity matrix is decomposed and the block Gauss‐Seidel algorithm solves each harmonic solution of magnetic field and exciting current sequentially.

The calculated exciting currents and flux density are compared with that obtained from measurement and time domain finite element analysis, respectively, which demonstrates consistency. The DC bias leads to the significant saturation of the magnetic core and serious distortion of the exciting current. The flux density varies nonlinearly with DC bias excitation.

The harmonic balance method is only applicable in solving the steady state magnetic field. Future improvements in the method are necessary in order to manage the hysteresis effects in magnetic material.

The proposed method to solve the DC biased problem significantly reduces the memory requirement compared to the conventional HBFEM. The decomposed harmonic balance equations are solved efficiently by the block Gauss‐Seidel algorithm combined with the relaxation iterative scheme. An investigation on DC bias phenomena is carried out through the harmonic solution of the magnetic field. The decomposed HBFEM can also be applied to solve 3‐D DC‐biasing magnetic field and eddy current nonlinear problems in a practical power transformer.

Coulomb's earth pressure theory is widely used in foundation pit supporting structure and retaining wall design, and Rupture angle is one of the key parameters in determining the failure surface location and the foundation pit influence scope. But there is no explicit formula of rupture angle or some wrong in existing formula. This paper, according to the limit equilibrium condition of slide wedge, obtained the analytical expression of Rupture angle which is the most simplified form in the current information. Through the numerical test this simplified solution is consistent with coulomb theory. The conclusion of this paper has some reference value in engineering application of coulomb theory.

This paper aims to explore the impact of business environment on high-quality economic development (HQED) and clarify the role of technological innovation and government intervention in this relationship.

Based on China’s provincial panel data from 2010 to 2019, this paper adopts the system generalized method of moments to empirically analyze the influential mechanism and heterogeneity of the business environment on HQED. Furthermore, the authors construct a dynamic panel threshold model to test the threshold effect of government intervention.

The results indicate that optimizing the business environment can significantly promote HQED, technological innovation plays a partial mediating role in the impact of business environment on HQED, mainly by enhancing the intensity of innovation input and increasing innovation output to facilitate HQED. Government intervention can regulate the impact of business environment on HQED, and there is a double threshold effect, and it possesses an inverted U-shaped feature of first promoting and then inhibiting.

This paper examines the influence path of business environment on HQED from the perspective of technological innovation and government intervention, filling the gap in the study of provincial business environment. Moreover, the conclusions furnish a theoretical basis for optimizing the business environment and facilitating the HQED in China.

The purpose of this paper is to study the controller design of flexible manipulator. Flexible manipulator system is a nonlinear, strong coupling, time-varying system, which is introduced elastodynamics in the study and complicated to control. However, due to the flexible manipulator, system has a significant advantage in response speed, control accuracy and load weight ratio to attract a lot of researchers.

Since the order of flexible manipulator system is high, designing controller process will be complex, and have a large amount of calculation, but this paper will use the dynamic surface control method to solve this problem.

Dynamic surface control method as a controller design method which can effectively solve the problem with the system contains nonlinear and reduced design complexity.

The authors assume that the dynamic parameters of flexible manipulator system are unknown, and use Radial Basis Function neural network to approach the unknown system, combined with the dynamic surface control method to design the controller.

The authors present a location selection model for the field hospital to build after a possible earthquake in Ankara, Turkey using the VIKOR method.

Companies or governments that make location selection decisions to improve their performance in new investment decisions for different service industries. On the other hand, disasters, especially earthquakes, force the governments to evaluate their existing potentialities and develop action plans to improve their middle and long-term preparations. This paper proposes a VIKOR method-based location selection model for the field hospital to build after a possible earthquake. Also, the authors present a methodology using the VIKOR method that how government agencies take action for the field hospital's location selection process via VIKOR methodology.

The modeling and application results show that the field hospital's location selection decision-making process improves considerably using the VIKOR model. This paper shows that the proposed VIKOR-based model can rank alternatives suitability at various criteria targeting to minimize the possible earthquake's impact and obtains a single overall ranking score to select the best alternative.

The study does not consider the uncertain nature of the field hospital selection problem. The application part is restricted to the Ankara case. But the proposed model can easily extend for different locations in the world.

This paper presents the multi-criteria decision-making (MCDM) framework study of the establishment of field hospitals and demonstrates its importance when criteria diversity is restricted.