Core Window Research Articles

Axial vibration characteristics analysis of transformer windings based on magnetic‐structural coupling correction model

AbstractDue to the strong coupling effect between the internal magnetic field and the structural field of the transformer, the magnetic‐structural coupling should be considered in axial vibration process of the winding short‐circuit impact. A 110 kV transformer is taken as the research object. Firstly, the vibration modal characteristics of the transformer are calculated using the classical axial vibration model, and the spatial distribution of the leakage magnetic flux density of the iron core window is obtained based on the image method, which is used as the basis for calculating the excitation electromagnetic force. With the consideration of the non‐linear mechanical characteristic of the pad, the dynamic stiffness equation is analysed and established and the magnetic‐structural coupling correction model is constructed. Finally, the winding vibration amplitudes obtained respectively by the classical model, the magnetic‐structural coupling model, and the magnetic‐structural coupling correction model considering the dynamic stiffness are compared. The results show that, compared with the classical model, the vibration amplitude increment with the magnetic‐structural coupling correction model is less. The dynamic stiffness will hinder the vibration intensification. The magnetic‐structural coupling correction model can provide a more accurate calculation scheme for the winding vibration characteristic analysis.

Enhanced thermal modeling of three-phase dry-type transformers

This work presents an enhanced thermal modeling for dry-type three-phase transformers, addressing the heat exchange mechanisms through conduction, radiation, and convection. Additionally, an equivalent thermal network is proposed to analyze the thermal behavior of these transformers. The thermal model includes several improvements, such as the differentiated representation of the core and windings through different nodes, and the consideration of primary and secondary windings as distinct nodes. Furthermore, the effects of convection and radiation in the inner areas of the core windows are accounted for, providing higher accuracy to the model. This modeling allows for a detailed analysis of the transformer under unbalanced load conditions, considering the complete geometry of the equipment. The results demonstrated that even with just a 5% load imbalance, there was a change in the hot spot temperature (HST). Moreover, the evaluation of temperatures in the coils, both internal and external to the core windows, revealed variations of up to 7 °C in the analyzed load unbalance scenarios. The study also highlighted that the phase of the harmonic component has an impact on the final equipment temperature. Additionally, the overvoltage and overload analyses showed that voltage has a greater impact on increasing the average core temperature, while overload mainly affects the winding temperature. Another relevant finding is that the internal coils near the core windows are most vulnerable to temperature rise when subjected to overload.

Analytical Double-2D Frequency-Dependent Leakage Inductance Model for Litz-Wired High-Frequency Transformer

Accurate and fast calculation of frequency-dependent leakage inductance is critical for the optimization of the high-frequency transformer with Litz wire winding. The analytical method is widely used due to its high computation speed. However, its computation accuracy is limited due to the following factors. i) One-dimensional (1D) or two-dimensional magnetic field model (2D) has unsatisfying accuracy for the transformer with a rotationally asymmetric structure. ii) The skin and proximity effect factors based on the multilayer foil winding are inaccurate for the Litz wire winding in the calculation of frequency-dependent magnetic energy. This paper proposes a double-2D frequency-dependent leakage inductance model for the transformer with Litz wire winding. It uses the image method to calculate the 2D leakage magnetic field inside and outside the core window, respectively, which considers the rotationally asymmetric structure in leakage inductance calculation. The round conductor model is proposed for the frequency-dependent magnetic energy calculation. The single strand in a Litz wire is taken as the basic modeling object of the round conductor model, which is more detailed than the multilayer foil winding model for the Litz wire winding. The comparison between the experiment, FEM, state-of-the-art models and the proposed model is conducted for eight transformers with E-core, U-core, round or rectangular Litz wire winding. The proposed model shows satisfying computation accuracy in the whole frequency band. And the computational speed of the proposed model is 100 times that of the FEM.

Optimization design of insulation structure of multiwinding high-frequency transformer based on response surface method

PurposeThe purpose of this paper is to study the insulation structure optimization method of multiwinding high-frequency transformer (HFT).Design/methodology/approachThis paper takes 100 kW, 10 kHz multiwinding HFT as the research object. First, the distribution of electric field strength within the core window of multiwinding HFT with different winding configurations is simulated by the electrostatic field finite element method. The symmetrical hybrid winding structure with minimum electric field strength is selected as the insulation design. To reduce the electric field strength at the end region of the winding, the electrostatic ring and angle ring are designed based on the response surface method.FindingsThe optimal results show that the maximum electric field strength can be reduced by 15.4%, and the low voltage stress can be achieved.Originality/valueThe above research provides guidance and basis for the optimal design of insulation structure of multiwinding HFT.

Influence of Core's window height on leakage reactance of power transformers

To examine leakage reactance, different analytical methods are often used. This paper addresses one of the major problems which is practically encountered during the leakage reactance evaluation. The selection of the core's window height is also an essential factor for the leakage reactance calculation that should be carefully considered during the manufacturing of the transformer. The window's height of the core is not considered in the analytical methods yet, which results in the difference between the experimental and analytical methods, affecting the transformer's overall design. This paper presents six different three-dimensional (3-D) finite element transformer models for calculating leakage reactance under the various heights of the window. The influence of the height of the window is revealed, this effect is never considered in analytical techniques. To examine the finite element method precision, two 0.25 MVA transformer prototypes were manufactured with different heights of cores, and the same windings were used for both prototypes. The highest leakage reactance was obtained in the transformer, where the window height was minimum. On the contrary, leakage reactance decreased significantly with the increase in the core's window height.

Improved Winding Losses Calculation Based on Bessel Functions

In this paper, an approach combining semi-empirical equations and the method of images is proposed for round conductor layer windings with un-gapped core. The new equation for proximity effect can convert the constant field strength from the magneto-motive force (MMF) across the core window into a frequency dependent uniform background magnetic field strength, which can take partly the interaction between conductors into account. Geometric factors are introduced by fitting the finite element method (FEM) results to improve the accuracy. The method of images is used to calculate the field strength in order to counteract the impact of 2D edge effect. The new method is compared with the 2D FEM, analytical methods, and is also validated by measurements with EE core transformers. The proposed method shows good accuracy (<10% error) compared to 2D FEM for both high and low porosity factor windings. Therefore, it can handle more winding configurations than other 1D analytical methods.

Electromagnetic and Mechanical Characteristics of Transformer under Multiple Short‐Circuit Impacts

The short‐circuit withstand capability of the transformer is crucial to the reliability of power systems. Research on the short‐circuit characteristics of windings is the basis for improving the stability of power transformers. Although many studies focus on electromagnetic force and cumulative deformation of two‐winding transformers, there is a lack of careful comparison of the electromagnetic and mechanical characteristics of three‐winding transformers, as well as the cumulative effect of stress, displacement and strain. In this paper, the model is established to study temporal response and spatial distribution of the electromagnetic and mechanical properties under short‐circuit impacts. The results show that the short‐circuit effects on medium and low‐voltage windings are more severe than on high‐voltage windings. The first current peak will lead to the greatest threat. Second, the influences of iron core and pre‐stress on short‐circuit characteristics are investigated. The characteristics of windings differ between inside and outside the iron core window, which is pronounced for high‐voltage winding. Besides, the greater pre‐stress is not better for the stability of windings. Finally, it is found that the residual stress and displacement continue to accumulate and the plastic strain appears under multiple short‐circuit impacts. This work is helpful for the analysis of short‐circuit withstand capability of transformers. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

Application of Expert Adjustable Fuzzy Control Algorithm in Temperature Control System of Injection Machines.

The stability and accuracy of temperature control of the injection molding machine is one of the keys to determine the quality and appearance of plastic parts. Due to the temperature control system of water-cooled injection molding machine has the characteristics of coupling, nonlinearity, and hysteresis, the traditional proportion-integral-derivative (PID) method to control the barrel temperature of injection molding machine will yield temperature overshoot and oscillation, affecting the product and appearance quality. In order to improve the effect of barrel temperature control, in this paper, an expert adjustable fuzzy control strategy (EAFCA) is designed to optimize the barrel temperature control system through the combination of expert control, fuzzy control, and PID control. The expert control rules are designed according to the barrel temperature deviation e and its change rate ec. The expert rules are used to adjust the mapping range of the fuzzy universe in real time for the input and output variables of the fuzzy controller and finally to realize the accurate adjustment of the PID controller parameters. In terms of control systems, the distributed control system (DCS) monitoring system of injection molding machine is designed with Siemens CPU315-2PN/DP and industrial computer as the hardware core and Step7 and windows control center (WinCC) as the software platform to complete the tool plastic production monitoring system. The DCS improves the operability, data management convenience, and plastic production efficiency of the injection molding machine monitoring system. The Simulink simulation and field test show that the EAFCA method can increase the adjustment speed by approximately 34 s and reduce the overshoot by nearly 3.1%, which significantly improves the stability and accuracy of the barrel temperature and improves the quality of plastic parts.

A Novel Semi-Analytical Method for Foil Winding Losses Calculation Considering Edge Effect in Medium Frequency Transformers

The design of the medium-frequency transformer (MFT) attracts increasing academic attention in recent years, in which the accuracy of the calculation method serves as the pivotal foundation. The existing 1-D based theoretical method generally fails to precisely estimate the foil winding losses under a significant 2-D edge effect. The 2-D semi-empirical methods are merely suitable for limited parameters and structures, and the pre-processing is cumbersome. The finite-element method (FEM) is accurate, yet its high computational cost makes it hard to apply in the MFT designing process. Regarding these issues, a novel 2-D semi-analytical method is proposed in this article with strict theoretical basis and sufficient generality. The foil region is divided into several rectangular elements with uniformly or linearly distributed current density, and one layer of images is placed around the magnetic core window. By deriving the basic electromagnetic relations between those rectangular elements, algebraic equations are formed with current density of the elements being the unknowns. Through the method, the whole problem turns into the process of solving algebraic equations, where all of the coefficients are obtained analytically. The new approach can achieve significantly high accuracy with acceptable computation cost, and it could suitably fit into the MFT designing process.

An Accurate Analytical Method for Leakage Inductance Calculation of Shell-Type Transformers With Rectangular Windings

This paper presents an accurate analytical method for calculating the leakage inductance of shell-type E-core transformers with rectangular windings. For this purpose, first, an expression for calculating the leakage inductance per unit length inside the core window considering the core walls as the flux-normal boundary condition is derived. Then, a new accurate method for determining the Mean Length of Turns (MLT) based on the total stored energy is presented. The MLT is needed for the leakage inductance calculation using 2-D methods. By dividing the MLT into three partial lengths and calculating the corresponding leakage inductances using three different core window arrangements, the effect of core structure on the total leakage inductance is considered. The method is verified by 3-D FEM simulations as well as the leakage inductance measurements on two different fabricated transformer prototypes. The superiority of the method is also confirmed by comparisons with the previous analytical approaches. The proposed method enables the leakage inductance calculation with an error less than 1%, compared to the 3-D FEM results. Using the presented method, the leakage inductance calculations can be performed rapidly and accurately in the design stage without the need for time-consuming 3-D FEM simulations.

Design and Control Features of Switched-Reluctance Motor with Minimization Torque Pulsation

Permanent magnet motors are often used as electric drives in middle and low power vehicles due to their high density of power and torque. Neodymium magnets increase its cost, therefore, alternative motors made from cheaper materials are actively sought. One of the most perspective candidates are switched reluctance motors (SRM) which may be designed with ferrite or steel materials. Despite their simple design, low production cost, excellent speed and torque characteristics, simple power distribution between motor sections, high operational reliability, they are not widely used because of insufficient torque and power density and complex electric drive. These problems may be reduced with choosing proper structure of SRM and its drive that provides a constant predefined torque. In the paper an efficient structure of the SRM is proposed and the relationship between the stator and rotor poles for high efficiency is suggested. For determining current shape in stator poles of SRM that provide constant torque electromagnetic processes in SRM are analyzed. As result of analysis a criterion of SRM efficiency base of relationship between acceleration and braking forces is proposed. High efficiency of SRM operation is possible when the brake force Fbr tends to zero i.e. near rotor pole in direction of movement. Such condition has to be achievable permanently during the rotor rotation. For SRM structure with n rotor poles andn+1 stator poles one stator. Such feature allows to achieve high efficiency if simultaneously operates only one predefined pole. Based on such considerations, the total magnetic flow may be split to accelerated flow, brake flow and leakage flow in proportion reversed to magnetic resistance of accelerate, brake and leakage contours. As close the rotor pole to the stator pole as less the relation of braking force to accelerating force. With increasing the rotor poles number, the minimum value of distance is decreased and subsequently the SRM efficiency too. So, SRM efficiency is increased with number of poles. The high-frequency principle of magnetic flux formation is used to minimize torque ripples. A general algorithm for the development of a SRM with the proposed structure are presented. The algorithm consists of following steps: determining the number of poles according to the requirements of SRM efficiency; calculation the stator pole dimensions according to the criterion of providing the necessary force (the rotor pole is the same); check the placement of the stator winding in the core window; correction of the number of poles, if necessary; determining the number of turns of the winding according to the desired current of the converter. The proposed algorithm allows to calculate SRM structure and poles parameters for predefined torque and motor dimensions.

Design Aspects of Core Components of Stabilizer Transformer of given Power Rating

There are wide ranges of transformers for voltage stabilizer. The autotransformers used in the voltage stabilizers are designed and constructed under design specifications of standard assumptions. In this work, core components of autotransformer are designed using power rating as only input parameter, nevertheless, taking into consideration of standard assumptions. The bounded area of the flux of magnetic field forms basis for core area of electromagnetic induction of transformer. The core area of the electromagnetic induction and window area of transformer for housing copper windings, thus, have linkage with power rating and e.m.f equation of the transformer. Accordingly, we establish a relationship, in the form of equation, between core area and window area. The product of core area and window is equated to the numerical value of the product that has been determined from the power rating and standard assumptions of other design parameters. With the help of proportional relationship, standard as well as from aspect of desired look of the transformer, between length and breadth of the core area and similarly for window area, the dimensions of the core components of the transformer are designed. The designed parameters are tested for feasibility and a transformer under the designed parameters is constructed to validate the experimental result with the theoretical values of the parameters of the transformer. This design is used to determine accurate dimensions of core components of transformer of desired power rating and desired look. This design aspect minimizes waste of core material in fabrication of core components and help in proper lamination of components such as E &amp; I of the transformer.

Optimization of CT windowing for diagnosing invasiveness of adenocarcinoma presenting as sub-solid nodules

PurposeTo evaluate the optimal window setting to diagnose the invasiveness of lung adenocarcinoma in sub-solid nodules (SSNs). MethodsWe retrospectively included 437 SSNs and randomly divided them 3:1 into a training group (327) and a testing group (110). The presence of a solid component was regarded as indicator of invasiveness. At fixed window level (WL) of 35 Hounsfield Units (HU), two readers adjusted the window width (WW) in the training group and recorded once a solid component appeared or disappeared on CT images acquired at 120 kVp. The optimal WW cut-off value to differentiate between invasive and pre-invasive lesions, based on the receiver operating characteristic (ROC) curve, was defined as “core” WW. The diagnostic performances of the mediastinal window setting (WW/WL, 350/35 HU) and core window setting were then compared in the testing group. ResultsOf the 437 SSNs, 88 were pre-invasive [17 atypical adenomatous hyperplasia (AAH) and 71 adenocarcinoma in situ (AIS)], 349 were invasive [233 minimally invasive adenocarcinoma (MIA), 116 invasive adenocarcinoma (IA)]. In training group, the core WW of 1175 HU was the optimal cut-off to detect solid components of SSNs (AUC:0.79). In testing group, the sensitivity, specificity, positive, negative predictive value, and diagnostic accuracy for SSN invasiveness were 49.4%, 90.5%, 95.7%, 29.7%, and 57.3% for mediastinal window setting, and 87.6%, 76.2%, 91.6%, 76.2%, and 85.5% for core window setting. ConclusionAt 120 kVp, core window setting (WW/WL, 1175/35 HU) outperformed the traditional mediastinal window setting to diagnose the invasiveness of SSNs.

A Novel Magnetic Equivalent Circuit Model for the Corner of Inductor Core

The accurate calculation of inductance is the most basic problem of inductor design. Based on finite element method (FEM) analysis of the flux density distribution in the corner of the core, a local corner magnetic equivalent circuit (MEC) model is proposed for a core-type inductor. In this model, the corner is divided into three parallel branches, and the joint part of the corner and the core limb are divided into two branches, one of which is continuously divided into three branches. In addition, a flux leakage branch of the core window inner corner is modeled. These branches form a local corner MEC by series and parallel to describe the flux distribution of the corner. The calculation results show that, in the local corner MEC model, the core flux density distribution is consistent with the FEM simulation. The maximum relative error of the inductance is less than 6% and the average relative error is less than 4% compared to the physical prototype measured data with the range of current from 20 A to 1000 A, which shows that the local corner MEC model has a high accuracy inductance calculation.

An Improved Stray Capacitance Model for Inductors

This paper proposes an improved analytical stray capacitance model for inductors. It considers the capacitances between the winding and the central limb, side limb, and yoke of the core. The latter two account for a significant proportion of the total capacitance with the increase of the core window utilization factor. The potential of the floating core/shield is derived analytically, which enables the model to apply not only for the grounded core/shield, but also for the floating core/shield cases. On the basis of the improved model, an analytical optimization method for the stray capacitance in inductors is proposed. Moreover, a global Pareto optimization is carried out to identify the tradeoffs between the stray capacitance and ac resistance in the winding design. Finally, the analysis and design are verified by finite element method simulations and experimental results on a 100-kHz dual active bridge converter.

Modeling and Design of Contactless Sliprings for Rotary Applications

Contactless sliprings (CS) based on inductive power transfer (IPT) offer a safe and reliable power transfer solution for rotary applications. An accurate reluctance model for CS is presented in this paper along with the associated parameters identification, considering the partially linking effect of the magnetic flux. Aiming to obtain higher coupling coefficient and lighter weight, a design optimization for CS is also proposed by defining a new design parameter “ ζ .” Both simulations and experimental measurements are presented to verify the effectiveness of the proposed modeling method. The maximum errors (between the identified results and the measured results) of the mutual inductance, the leakage inductance, and the coupling coefficient are 8.72%, 7.12%, and 5.98%, respectively, when the gap is less than the core window width. Comparative studies among different modeling methods are carried out, which testify that the proposed method has the highest accuracy. Finally, a 1.5 kW IPT system employing the designed CS is fabricated for verification.

Attenuation Changes in ASPECTS Regions: A Surrogate for CT Perfusion-based Ischemic Core in Acute Ischemic Stroke.

Background Recent studies have proven the effectiveness of thrombectomy up to 24 hours after stroke onset for patients with specific criteria at advanced CT or MRI. Clinical implementation of treatment in this extended time window remains a challenge, as many stroke centers do not routinely use advanced imaging. Purpose To determine whether automated cerebral x-ray attenuation measurements at noncontrast CT provide information on the presence of CT perfusion-defined ischemic core as applied in late time windows for thrombectomy. Materials and Methods In this retrospective study, patients with middle cerebral artery stroke due to proximal occlusion from 2009 to 2017 were included. All patients underwent noncontrast CT and CT perfusion. Automated software was used to calculate relative Hounsfield unit (rHU) values for Alberta Stroke Program Early CT Score (ASPECTS) regions on noncontrast CT images as the ratio of x-ray attenuation between ischemic versus non-ischemic hemispheres. Sensitivity, specificity, and diagnostic performance of rHU and composite rHU-ASPECTS, a score incorporating rHU from all regions, were analyzed for the classification of regional ischemic core and late time window thrombectomy criteria at CT perfusion. Results Data in a total of 200 patients were evaluated (105 women [mean age, 74 years ± 14 {standard deviation}] and 95 men [mean age, 76 years ± 14]). There were 121 patients in the validation cohort and 79 patients in the independent test cohort. Compared among all examined regions, rHU values yielded the best classification of ischemic core for the caudate nucleus, the lentiform nucleus, and the insula (with areas under the receiver operating characteristic curve [AUCs] ranging from 0.70 to 0.77; P < .001 for each). The composite rHU-ASPECTS score allowed classification of CT perfusion imaging selection criteria of ischemic core sizes of less than 70 mL and target mismatch of greater than 1.8 with AUCs of 0.80 (P = .001; 75% sensitivity and 83% specificity) in the test cohort and 0.74 (P < .001; 58% sensitivity and 82% specificity) in the validation cohort. Conclusion Noncontrast CT x-ray attenuation measurements identify Alberta Stroke Program Early CT Score regions classified as ischemic core at CT perfusion. This approach may serve as a selection criteria surrogate for thrombectomy in late time windows. © RSNA, 2019 Online supplemental material is available for this article.

Determination of the necessary inductor core dimensions for switching electrical energy converters

Each developer of switching electrical energy converters, sooner or later, faces the need to select or develop an inductor. However, currently, the method of choosing an inductor core for switching converters is very ambiguous, fragmented and confused. In the article, formulas are obtained that allow determining the minimum-necessary product of the core cross-sectional area by the core window cross- sectional area for the inductors of the most common switching converters circuits: buck, boost, buck-boost and fly-buck. In addition, the best mode of core operation, from the energy point of view, in which the maximum converters power density is provided both in the transmission and recuperation modes, is analyzed in the article. The article is intended for a wide range of electronics developers, including for specialists engaged in research of switching electrical energy converters.

Modelling of a Hall Effect-Based Current Sensor with an Open Core Magnetic Concentrator.

The present paper deals with the modelling of a Hall effect current sensor with open core magnetic concentrator. 3D magnetic field modelling is carried out using the finite element method (FEM) and Comsol Multiphysics software. Two rectangular core constructions are considered. Different geometric parameters of the magnetic concentrator are varied and their influence on the sensor characteristic is studied, with the aim of reducing the dependence on the output signal on the distance to the conductor. Of the studied parameters, core window length leads to the most significant change in the sensor characteristic. Future work can include the optimization of the sensor construction.

Tracking Algorithm with Adaptive Bandwidth of Kernel Function for UAV Autonomous Aerial Refueling

The use of machine vision to track the receiver aircraft’s receptacle is one of the key steps in automated aerial refueling. Traditional Meanshift tracking algorithm’s kernel bandwidth is fixed, when the target size changes, it will produce with the bias even with the loss of the situation. Aiming at this problem, this paper proposes a kernel bandwidth adaptive algorithm based on corner matching. First, use backward tracking method to amend the core window center. Then according to the Harris algorithm to detect the corner, use small-scale approach for the two points between frames to match and regression analysis, namely determine the update parameters of nuclear window width. Experiments show that the algorithm can track the target accurately when the size of tracking target change, and the kernel window width can be better suited to the target size.