Winding Model Research Articles

Analysis and estimation of power losses in high-power, high-frequency transformers for isolated DC/DC converters

The paper presents an in-depth analysis of the power losses in the windings and the cores of two different transformers as applied to a phase-shifted full bridge (PSFB) converter at the power level of 20–25 kW and the switching frequency of 50 kHz. The main difference in the construction of the considered devices was the method of winding realization as well as the shape and material of the cores. The influence of the winding geometry on the conduction losses was analyzed, and the losses in the cores were analytically estimated, taking into account the operating conditions of these elements in the full-bridge system with phase-shift modulation. Original resistive models of windings made of cooper sheets are presented. The obtained results were verified by experimental tests carried out in an isolated full-bridge DC/DC converter.

Study on the tribological performance at the interface between a steel wire rope and groove during a twisting process

In actual use, a steel wire rope is often stretched and twisted around a groove, increasing the risks of contact fatigue, friction and wear at the rope-groove interface under a long-term service condition. With the consideration of influence factors such as the nonlinear contact and wear between the rope and groove, the tribological performance at the rope-groove interface during a twisting process is analyzed in this study. A winding rope-groove model is first established in order to obtain the contact and sliding solutions at the interface between the rope and groove, which are then used as the load conditions of a simplified local model that is built for wear solution using a modified Archard's wear theory. Based on the finite element simulation software ABAQUS, the ALE adaptive mesh technology and UMESHMOTION subroutine secondary development are adopted to analyze the evolutions of wear topography and contact behavior between the rope and the groove. The results show that the twisting movement of the steel wire rope around the groove causes an interfacial wear between them. The wear scars occur on the outside wire of the steel wire rope and the bottom area of the groove, and the wear scar on the groove is smaller but deeper. A ring-shaped region of stress concentration happens near the edge of wear region. As the wear process proceeds, the depths and dimensions of the wear scars increase, while the contact pressure decreases. The contact performance and wear change dramatically at the beginning of wear process and tend to be stable subsequently. An increment of lay angle of the outside wire aggravates the wear and contact between the steel wire rope and the groove.

Winding Response under Difference Effective Inductance for Single Phase High Voltage Transformer

Early studies of transformer winding parameters were focused on the determination via its physical dimensions and empirical formulas. In most cases it is divided into several parts namely coil section pairs, coils distance, disc coils diameter and thickness of insulation. Maxwell’s equations are often the solution to the problem, which satisfy related boundary conditions between conductors for mutual inductance and capacitor equations. Such solutions often led to errors and hence its mathematical model. To counter the problem, it was suggested that such approximations must be conducted with experimental model windings at the same time. Frequency domain measurements and time domain measurements can be conducted to effectively determine these parameters. This in turn will investigate the behaviour of transformer winding electromagnetic transient at high frequency. From theoretical point of view, predominantly capacitive winding model often considered to represent its behaviour at high frequency and will give the results of its initial distribution. Under this consideration, a single phase plain winding is considered for investigation. A single rectangular wave was considered to represent infinitive impinge incident wave, injected at one end of transformer winding and the measured response signals of the wavetail were considered for measurement. The experimental response and modelling results were compared and proved to have high agreement between the two.

Homogenization of foil windings with globally supported polynomial shape functions

In conventional finite element simulations, foil windings with thin foils and with a large number of turns require many mesh elements. This renders models quickly computationally infeasible. This paper uses a homogenized foil winding model and approximates the voltage distribution in the foil winding domain by globally supported polynomials. This way, the small-scale structure in the foil winding domain does not have to be resolved by the finite element mesh. The method is validated successfully for a stand-alone foil winding example and for a pot inductor example. Moreover, a transformer equipped with a foil winding at its primary side is simulated using a field-circuit coupled model.

A Magnetic-Geared Machine With Improved Magnetic Circuit Symmetry for Hybrid Electric Vehicle Applications

Magnetic-geared machine (MGM) has been widely investigated as the power split device for hybrid electric vehicles with the inherently high-integration of multi-mechanical ports. It is revealed that the magnetic circuits of armature winding in MGM are essentially asymmetrical for different phases under the magnetic field modulation effect. This inevitably results in unbalanced phase back electromotive force (EMF) waveforms, severe torque ripples, acoustic noise, and difficulty for precise control. To alleviate the asymmetry problem, a generic winding design model is presented for MGMs in this paper, which allows for consideration of all potential winding configurations. Firstly, a novel back EMF harmonic factor is proposed to account for both the harmonic content and asymmetric level in MGM. The genetic algorithm (GA) is further employed to optimize the winding in terms of minimizing the back EMF harmonic factor, armature magnetomotive force harmonic contents, and phase winding resistance. The proposed winding layout exhibits superior filtering capability for three-phase asymmetric magnetic field harmonics. As compared with the conventional integral-slot distributed winding, the MGM with the proposed winding exhibits improved back EMF waveform symmetry, suppressed torque ripple, and reduced core losses. Finally, an experimental prototype is manufactured to validate the effectiveness of asymmetric magnetic field suppression for MGMs. The results show the investigated winding design method is an effective solution to the asymmetric issue of MGMs, paving the way to research opportunities for further improvements.

Online Detection and Classification of Interturn and Groundwall Insulation Aging Based on Broadband Common-Mode Impedance Spectrum

Online condition monitoring for stator insulation is important for reliable operation of electrical machines. Recent studies show that the method based on common-mode (CM) impedance spectrum is effective in online monitoring of the overall insulation ageing condition. However, it is difficult to detect the inter-turn ageing condition since the groundwall insulation ageing has the similar impact on the monitoring results. In this paper, the relationship between the change in the common-mode impedance spectrum and the stator winding insulation ageing is studied based on the per-turn-unit broadband CM stator winding model. The dataset of impedance spectrum for different insulation ageing conditions is built using this model. Multiple points in the impedance spectrum are used to detect the change in the inter-turn and groundwall insulation parameters separately. The online experiment results prove the validity of the proposed method. The proposed method can detect the insulation ageing condition with the error about 6%. There is no other method which can quantify the ageing degree of inter-turn insulation in the presence of groundwall insulation ageing. Compared with the black-box data-driven methods, the proposed method is based on a model with clear physical meaning, which makes the results more reliable.

Toward unique electrical ladder network model synthesis of a transformer winding high-frequency modeling using K-means and metaheuristic-based method

PurposeAlthough, numerous optimization algorithms have been devoted to construct an electrical ladder network model (ELNM), they suffer from some frail points such as insufficient accuracy as well as the majority of them are unconstrained, which result in optimal solutions that violate certain security operational constraints. For this purpose, this paper aims to propose a flexible-constraint coyote optimization algorithm; the novelty lies in these points: penalty function is introduced in the objective function to discard any unfeasible solution, an advanced constraint handling technique and empirical relationship between the physical estimated parameters and their natural frequencies.Design/methodology/approachFrequency response analysis (FRA) is very significant for transformer winding diagnosis. Interpreting results of a transformer winding FRA is quite challenging. This paper proposes a new methodology to synthesize a nearly unique ELNM physically and electrically coupled for power transformer winding, basing on K-means and metaheuristic algorithm. To this end, the K-means method is used to cluster the setting of control variables, including the self-mutual inductances/capacitances, and the resistances parameters. Afterward, metaheuristic algorithm is applied to determine the cluster centers with high precision and efficiency.FindingsFRA is performed on a power transformer winding model. Basing on the proposed methodology, the prior knowledge in selecting the initial guess and search space is avoided and the global solution is ensured. The performance of the abovementioned methodology is compared using evaluation expressions to verify its feasibility and accuracy.Originality/valueThe proposed method could be generalized for diagnosis of faults in power transformer winding.

Application of Dynamic Detailed Thermal Hydraulic Model on a Transformer with zig-zag winding scale model

Application of Dynamic Detailed Thermal Hydraulic Model on a Transformer with zig-zag winding scale model

Simulation calculation of fluid field- thermal field of oil-immersed transformer and optimization of winding structure parameters

The optimization method of winding structure parameters of oil-immersed transformer is proposed to reduce the hot spot temperature of transformer and the metal conductor consumption based on the coupling calculation method of electromagnetic-fluid-thermal. Firstly, according to the electrical and structural parameters of the oil-immersed transformer, a 3D simulation model is established by using finite element software, and the distribution of the thermal field and the fluid field around the transformer as well as the fluid field and thermal field of the low-voltage winding are obtained. In order to accurately reflect the temperature rise distribution characteristics of the low-voltage winding, a 2D model of the low-voltage winding of the transformer was established considering the calculation efficiency and accuracy, and the thermal field and fluid field distribution of the two low-voltage winding models were compared and analyzed. The temperature error was less than 5.98?, which verified the accuracy of the equivalent model. On this basis, the hot spot temperature of low voltage winding under different structural parameters is obtained by combining the Latin hypercube experiment design and thermal field simulation method, and the response surface model of winding hot spot temperature and structural parameters is established. Taking the hot spot temperature of low voltage winding and the amount of metal conductor as optimization objectives, combined with the response surface model, the optimal solution set of Pareto is obtained by using NSGS-? optimization algorithm, and two kinds of optimal design results are obtained on the Pareto front surface. The results show that the hot spot temperature is reduced by 4.16% and the metal conductor consumption is reduced by 13.79% in scheme 1; the hot spot temperature is reduced by 0.51% and the metal conductor consumption is reduced by 28.46% in scheme 2. The research results have important guiding significance for the optimization of oil-immersed transformer.

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.

Analytical Thermal Model of Slot for Electric Propulsion Motor in Electric Aircraft

Accurate prediction of temperature is critical for evaluating electric propulsion motor performance. This paper presents an analytical thermal model of slot for the prediction of temperature. According to the heat transfer in the slot, the shortcomings of the traditional winding model are pointed out. This paper adopts a more advanced layered model. The number of layers is calculated analytically. Based on Laplace's equation and Poisson's equation, the thermal resistance and temperature rise of each layer are analytically calculated. The layered windings and insulation are equivalent to a heat-generating entity whose thermal resistance and temperature rise are equal to those of the layered slot. The equivalent thermal conductivity of heat-generating entity can be obtained. The slot is equivalent to a heat-generating entity through the analytical method, which reduces the computational complexity of the simulation. The experiments are employed to validate the accuracy of the proposed model.

Design and optimisation of oil injection pipe cooling structure for permanent magnet synchronous motors in hybrid electric vehicles

AbstractIn recent years, with the continuous improvement of motor power density, oil cooling technology has been widely used in permanent magnet synchronous motors (PMSMs) for electric vehicles (EVs) as an efficient cooling method. A PMSM with a rated capacity of 53kW for hybrid electric vehicles (HEVs) is designed, and the motor is cooled by the oil injection pipe. In order to improve the heat dissipation efficiency of the end winding, the number of injection pipes and the structure of the nozzle are optimised, and a novel nozzle structure is proposed. By using the moving particle solution (MPS) method to simulate the fluid flow, the optimal cooling structure of the motor is determined. In addition, different from the equivalent winding model in the traditional temperature field simulation, a hairpin winding model that can more realistically reflect the geometry of the end winding is established. On this basis, the temperature field of the motor is simulated. It is verified that the cooling structure designed can effectively improve the thermal performance of the end winding.

High-Speed Design with Separated Tapering for Reducing Cogging Torque and Torque Ripple of a 3 kW Dry Vacuum Pump Motor for the ETCH Process

This paper proposes a design method to reduce cogging torque and torque ripple in the concentrated winding of IPMSMs (Interior Permanent Magnet Synchronous Motors) used in motors for the semiconductor ETCH process. IPMSMs can utilize reluctance torque through the difference in inductance between the d axis and q axis, but they are at a disadvantage in terms of reducing cogging torque while tapering the rotor and stator to reduce torque ripple. In addition, the existing single tapering can push the permanent magnets into the rotor. If the rotor’s permanent magnets are embedded, the magnetic reluctance will increase, and the overall performance of the motor will decrease. However, an optimum design method was derived in which the magnets do not move during rotor tapering. This geometric design is an optimum design method that reduces cogging torque and torque ripple. This paper compares and analyzes four models, the concentrated winding model, distributed winding model, conventional tapering model, and separated tapering model, using 2D and 3D finite element analysis (FEA).

A peak time shifting phenomenon in transformer axial short‐circuit electromagnetic force due to the coupling of electromagnetic‐axial vibration

AbstractAccurately calculating axial electromagnetic force is essential to analyse transformer winding axial stability. Prior research has mainly focused on the effect of winding structure on static axial electromagnetic force and studying vibration by substituting the static force in a time‐varying function. However, the coupling effect between axial electromagnetic force and winding vibration has not been addressed, and no calculation method for the axial electromagnetic force that considers both winding meso‐structures and vibration coupling effects has been proposed. Previously the authors presented an electromagnetic force calculation model that considers winding structure characteristics, and an iterative algorithm for magnetic‐structure coupling calculation. Currently, the winding vibration model was first proposed and the dynamic calculation method was formulated. By applying the method to a typical 110kV transformer, the spatial‐temporal distribution of winding axial short‐circuit electromagnetic force was obtained. It was found that the peak value of the axial short‐circuit electromagnetic force of some windings appears at the second or third peak moment of the short‐circuit current, which is called as peak time shift phenomenon. Further stress analysis indicates that existing evaluation methods may overestimate the short‐circuit resistance of windings by only considering short‐circuit electromagnetic force under maximum peak of short‐circuit current.

Semi-Analytical AC Resistance Prediction Model for Litz Wire Winding in High-Frequency Transformer

Semi-Analytical AC Resistance Prediction Model for Litz Wire Winding in High-Frequency Transformer

An equivalent winding thermal model considering fill factor and void ratio for multiphysics coupling analysis of permanent magnet linear motors

Accurately clarifying thermal characteristics and acquiring thermal limits of permanent magnet linear motors (PMLMs) is significant for system safety, which is often evaluated by computational thermal analysis. However, conventional thermal analysis methods are faced with the contradiction between the complexity of modeling and the accuracy of computation. To fix the problem, a new two-way multiphysics coupling method is developed by proposing an improved equivalent homogeneous winding thermal model. The energy consumption distribution is used as the heat source for thermal field calculation, and the material properties are determined by temperature in the electromagnetic field. To further reduce the complexity of winding region modeling and ensure the accuracy of calculation, an improved equivalent homogeneous winding thermal model is established by considering the fill factor and void ratio. The new coupling method is verified by temperature rise experiments on a single winding sample and a PMLM prototype. The error between the simulation and experiment of the single winding sample is less than 3 %, which indicates the high accuracy of the improved equivalent model. Meanwhile, the low error (less than 6 %) on the PMLM case indicates the high accuracy of the new multiphysics coupling method. Then, the temperature distribution of PMLM is analyzed, and the effect of the fill factor and void ratio on the temperature rise of PMLM is studied with the effect of the void ratio on the limiting temperature and continuous working time of PMLM discussed. It is demonstrated that both fill factor and void ratio affect the temperature rise of winding, and thus impact the temperature rise of the PMLM. The continuous working time decreases rapidly with the increase of the void ratio, and this effect will be more significant with a higher effective current. The results can provide references for improving the precision of temperature estimation and selecting a reasonable current density. This also demonstrates the high accuracy and efficiency of the new coupling method.

Thrust Bandwidth Modeling and Optimization of PMSLM Based on Analytic Kernel-Embedded Elastic-Net Regression

To improve the bandwidth and thrust performance of permanent magnet synchronous linear motor (PMSLM), from the perspective of motor structure design, this paper proposes a high-accuracy and fast-calculation inductance model of centralized winding based on analytic kernel-embedded Elastic-Net regression (AKER) to establish a comprehensive analytical model of PMSLM performance. A stochastic fractal search (SFS) algorithm is introduced to optimize the comprehensive performances of PMSLM. First, Neumann's formula of integral is used to establish the equivalent inductance analytical model (EIAM) for the three-phase winding of PMSLM, and the analytic kernel is constructed based on the EIAM. In combination with the finite element simulation samples of inductance, the analytical kernel is embedded into the Elastic-Net regression to establish the inductance model of high efficiency, namely AKER, and compared with the finite element mode (FEM), EIAM and other advanced methods, the superiority of AKER is verified from the accuracy and time cost. Then, based on the proposed AKER inductance model, the current and voltage equations of PMSLM are decoupled in the two-phase rotating coordinate system to establish the comprehensive analysis model of the PMSLM performance. Based on the comprehensive model, the optimization function of PMSLM is constructed, and the SFS algorithm is introduced to solve the function iteratively. Finally, the effectiveness of the proposed modeling and optimization method is verified by FEM-based control simulation and prototype experiment respectively.

A Mechanical-Electromagnetic Coupling Model of Transformer Windings and its Application in the Vibration-Based Condition Monitoring

Winding vibration leads to the oscillation of coils position and further affects winding's nonlinear stiffness as well as electromagnetic forces (EMFs). This paper establishes a winding Mechanical-Electromagnetic Coupling Model (MECM) where the coupling between stiffness coefficient and vibration, magnetic field and vibration are considered, and deploy it in the vibration-based condition monitoring. In this model, EMFs are obtained through the superposition of leakage magnetic field generated by each coil. A novel numerical analysis method is further proposed, which is capable of calculating the vibration response containing nonlinearity and electromechanical coupling, and the accuracy of the method is verified in experiments. Then, the numerical analysis method is used to quantitatively analyze the effects of Nonlinearity and ElectroMechanical Coupling (NEMC) on the vibration characteristics. The study demonstrates the law that NEMC intensity increases with vibration, and the NEMC is obvious especially under mechanical fault. To extract the vibration patterns, Nonlinearity-ElectroMechanical Coupling Coefficient (NEMCC) with amplifying NEMC effects is proposed to monitor the winding mechanical condition. The analytical method predicts the variation trend of the winding looseness condition curve, and laboratory experiments prove that the Mean Absolute Percentage Error (MAPE) is able to successfully identify different degrees of winding looseness faults. Compared with the short-circuit impedance (SCI) method, the MAPE value based on NEMCC has a stronger detection capability and higher sensitivity for winding mechanical faults. This paper lays a foundation for the numerical solution of vibration response and pave a way for winding mechanical condition monitoring.

Precise Electrical Machine Stator Winding Modeling for Thermal Analysis of Efficient Cooling Concepts

<div>The current development of electric and hybrid electric vehicles has drawn more attention toward the development of electrical machines with high power densities. Though highly efficient, these machines heat up significantly during operation. By design, state-of-the-art water jacket cooling concepts remove the heat mainly through high internal thermal resistances of the electrical machine. The resulting maximum temperatures in the end winding region limit the achievable machine power output. In this study, alternative cooling concepts are presented, which efficiently use the existing heat conduction paths of an electric machine. For this purpose, two modeling methods for the stator windings were developed: a high-resolution approach that considers each individual wire and an abstract approach that uses zones of constant anisotropic thermal conductivity to specify the heat flow in the windings. Both models were used in conjugate heat transfer simulations of a long-term thermal test of the electrical machine integrated in the BMW i3. For both models the validation showed a very good agreement of simulated and measured temperatures. An evaluation of both methods showed the abstract approach to be more efficient than other simulation methods used in the current R&D. Its application for alternative cooling concepts revealed the necessary heat transfer coefficients at different fluid temperatures for a sole convective cooling of the end windings. However, it could be found that a homogeneous temperature distribution in the stator of the machine can only be achieved if a combination of water jacket cooling and convective end winding cooling is used.</div>

Novel Technique for Location Identification and Estimation of Extent of Turn-to-Turn Fault in Transformer Winding

This paper presents a novel technique for diagnosing a turn-to-turn fault at the incipient level inside the power transformer winding using frequency response analysis (FRA). Utilizing lower frequency region of FRA in case of pre-fault and post fault conditions of transformer windings, the proposed technique determines the deviation in equivalent inductances. Based on the deviation, a location factor (<i>lf</i>) is derived, which indicates location of fault, by calculating accuracy factor (<i>x</i>) corresponding to each section of the winding. Thereafter, the extent of turn-to-turn fault and number of faulted turns are determined based on the accuracy factor of the faulted disk. The performance of the proposed technique has been validated through a simulation model as well as from two different laboratory-developed winding models and 400 kVA real filed transformer. The results designate that the developed technique is proficient to estimate location of turn-to-turn fault even when number of faulted turns are lower than 5&#x0025; of the total turns. Its response remains immune against winding configurations and lead error encountered during measurement. Eventually, a comparative assessment of the proposed approach with various other approaches indicates its eminence in terms of turn-to-turn fault localization and estimation of fault extent and faulted turns.