Three-phase Transformer Core Research Articles

Имитационная модель силового трехфазного трансформатора бронестержневой конструкции с витым магнитопроводом

Background. One of the areas of industry digitalization is associated with the concept of digital twins, which allow simulating the operation of real devices in various modes. At present, simulation models of a three-phase rod-type transformer have been developed in the MatLab Simulink SimPowerSystem environment. The models can serve as the basis to design a digital twin of a real device. The problem is to find the most universal method for mathematical description of a transformer of unspecified design to develop its simulation model. The purpose of this study is to develop a simulation model of a three-phase shell-type transformer core with a twisted magnetic circuit and to study this model when the transformer is operating in steady and transient modes. Materials and methods. The authors have applied the methods to model electrical circuits based on the theory of ordinary differential equations, a simulation method using the MatLab Simulink SimPowerSystem software package. Results. The structural futures of the transformers with shell-core design and the main assumptions when developing the simulation model have been assessed. A system of nonlinear equations has been developed to find the flows and MMF generated by the windings of the device. A simulation model of a three-phase shell-core transformer with a twisted magnetic core has been developed. It is based on the obtained equations using the Algebraic Constraint block with the Solver function in MatLab Simulink SimPowerSystem. The results of simulation of dynamic processes in the transformer in various modes are presented. Conclusions. The results of the study can be used to design power transformers in engineering companies and under production conditions. It is also possible to use the developed models in case of power transformer operation to analyze the static and dynamic modes of operation of sections of electrical networks.

Detection and Classification of Lamination Faults in a 15 kVA Three-Phase Transformer Core Using SVM, KNN and DT Algorithms

This paper deals with the detection and classification of two types of lamination faults (i.e., edge burr and lamination insulation faults) in a three-phase transformer core. Previous experimental results are exploited, which are obtained by employing a 15 kVA transformer under healthy and faulty conditions. Different test conditions are considered such as the flux density, number of the affected laminations and fault location. Indeed, the current signals are used where four features (Average, Fundamental, THD and STD) are extracted. Elaborating A total of 328 samples, these features are utilized as input vectors to train and test classification models based on SVM, KNN and DT algorithms. Based on the selected features, the results confirm that the transformer current can be used for the detection of lamination faults. An accuracy rate of more than 84% is obtained using three different classifiers. Such findings provide a promising step toward fault detection and classification in electrical transformers, helping to prevent the system and avoid other related issues such as the increase of power loss and temperature.

On the Effects of Lamination Artificial Faults in a 15 kVA Three-Phase Transformer Core

Cutting and punching of the steel used in power transformer core may cause edge burrs. This, along with the degradation of the lamination insulation, can lead to interlaminar short circuits. Analysing these faults helps understanding their effect on the transformer reliability and performance. In this light, the actual paper aims to experimentally simulate and analyse both faults using a 15 kVA three phase power transformer. Effects produced from both selected faults are experimentally investigated in this paper where different scenarios are considered such as the area of the affected regions and the number of short-circuited laminations. Various flux densities are considered ranging from 0.5 to 1.8 T. Of interest, the current at no load is recorded and the test is repeated for any given scenario. The obtained results are presented and discussed to study the effect of each fault on the transformer performance. Overall, the transformer current increases with the number of short-circuits between laminations for both faults. This increase is related to the flux density, which is dependent and sensitive to the short circuit location. Such findings represent a good indication of the severity of short circuits relative to their position in the transformer core, and can be exploited to discuss the power losses in the transformer core.

Improved Flux-Controlled VFCV Strategy for Eliminating and Measuring the Residual Flux of Three-Phase Transformers

The residual flux (RF) in three-phase transformers can dramatically increase the inrush current when the transformer is energized. The RF can also severely interfere with diagnostic tests, such as the frequency-response analysis (FRA) test. However, there is no effective method to fully eliminate the RF in the core of a three-phase transformer. Additionally, there are few relevant experimental reports on methods to accurately measure the RF in the magnetic core of a three-phase transformer; this measurement is important for evaluating the demagnetization results and phase-controlled switching strategies. Hence, this paper proposes an improved flux-controlled variable frequency-constant voltage (VFCV) strategy combined with core flux equalization to simultaneously eliminate and measure the RF of a three-phase transformer core by applying a low-power electronic device. The effectiveness and accuracy of the proposed strategy are validated by the simulation and experimental tests of a 10 kV distribution transformer and a 500 kV delta-connection three-phase separating transformer. The results reveal that the RF can be eliminated to less than 1% of the knee point flux and that the measurement is fairly accurate.

Numerical and Experimental Determination of Local Building Factors of a Three-Phase Transformer Core Package

The analyses of flux distributions and losses in transformer cores need highest expenditure if performed in experimental ways. This paper presents a novel combined methodology for the evaluation of local and global loss building factors BF. As a first step, the local patterns of the dynamic induction vector B(t) were calculated, by means of a novel numerical “magnetic anisotropic circuit calculation (MACC) methodology. The latter considers the core materials non-linear permeability functions in rolling direction and transverse direction, as well as non-linear effects of overlaps in corners and T-joints. In a second step, the calculated induction patterns were exactly simulated on the hexagonal Vienna rotational single sheet tester and the corresponding local losses p were measured electrodynamically. Finally, the values p were allocated to the corresponding core positions, taking into account the entire core geometry. BF of the core was estimated from the total of loss values weighted to the corresponding volume portions. The method was applied for a three-phase core of highly grain-oriented material, magnetized with BNOM = 1.7 T. The procedure shows the local distributions of losses, yielding also information on those of eddy currents and rotational magnetization (RM). As an example, the T-joint, as the area of highest RM, yields a local loss increase of about 50%. Apart from RM, the local induction variations-including waveform distortions, caused mainly by circulating magnetization-prove to have a high impact on losses, locally yielding 50% as well. These highly convincing results indicate that the complicated sensor studies of cores can partly be replaced by: 1) numerical modeling of induction distributions and 2) subsequent allocations of loss values as detected by RSST simulations.

3D-Printed Detector Band for Magnetic Off-Plane Flux Measurements in Laminated Machine Cores.

Laminated soft magnetic cores of transformers, rotating machines etc. may exhibit complex 3D flux distributions with pronounced normal fluxes (off-plane fluxes), perpendicular to the plane of magnetization. As recent research activities have shown, detections of off-plane fluxes tend to be essential for the optimization of core performances aiming at a reduction of core losses and of audible noise. Conventional sensors for off-plane flux measurements tend to be either of high thickness, influencing the measured fluxes significantly, or require laborious preparations. In the current work, thin novel detector bands for effective and simple off-plane flux detections in laminated machine cores were manufactured. They are printed in an automatic way by an in-house developed 3D/2D assembler. The latter enables a unique combination of conductive and non-conductive materials. The detector bands were effectively tested in the interior of a two-package, three-phase model transformer core. They proved to be mechanically resilient, even for strong clamping of the core.

Interlaminar Magnetic Flux Assessment of a Transformer Core Measured by an Extra-Thin Printed Foil Detector

Transformer cores represent complex 3-D magnetization systems with balancing off-plane fluxes, normal to magnetization plane. Therefore, for optimizations of core performance, not only the information about the local induction distributions in the plane, but also perpendicular to it is highly essential. The conventional sensors for detections of off-plane inductions $B_{Z}$ ( ${t}$ ) are either of very high thicknesses, causing significant air gaps between laminations, or require extremely laborious preparations and are not reusable. In this paper, we developed an extra-thin ( $\approx 50~\mu \text{m}$ ), reusable foil detector with handles for easy and precise insertion and positioning in the interior of a laminated core. The detector was assembled by a low-cost 3-D printer, equipped with a micro-dispersing system for printing of conductive ink, controlled by in-house developed software. The manufactured foil sensor, due to its high mechanical stability, enables detections of off-plane flux at many different locations within an entire core. The detector was effectively tested in a three-phase model transformer core, stacked from three packages of different width. The results prove the important role of sensor thickness for precise detection of off-plane induction. Peak induction $B_{Z}$ increases in a strong non-linear way with increasing nominal magnetization $B_{\mathrm{ NOM}}$ . Maxima of $B_{Z}$ arise close to border regions of packages. $B_{Z}$ ceases for $B_{\mathrm{ NOM}} T, favoring low level of audible noise.

Elimination of Residual Flux in Transformers by the Application of an Alternating Polarity DC Voltage Source

The purpose of core demagnetization is twofold: 1) to reduce the inrush currents when transformers are energized; and 2) to make sure that the frequency-response analysis (FRA) tests are consistent to avoid false diagnoses of damage during transportation. The significance of demagnetizing is presented on field measurements of an 80 MVA unit with FRA measurements. A new demagnetizer device with an alternating polarity dc voltage source is prototyped. Experimental verification of this prototype is presented for the demagnetization of transformers. A nearly complete demagnetization was observed in the laboratory for a small single-phase isolation transformer. The method proposed in this paper is applied to three-phase transformers with different core configurations and connections. Topologically correct modeling and numerical simulations confirm the full demagnetization of all branches of three-phase (three- and five-limb) transformer cores. Inrush current measurements and FRA plots before and after demagnetization confirm the effectiveness of the process.

Magnetostrictive vibrations model of a three-phase transformer core and the contribution of the fifth harmonic in the grid voltage

The effect of the fifth harmonic in the grid voltage (with fundamental frequency of 50 Hz) on the vibrations of a three-phase transformer core is computed, since such harmonic has the largest contribution in the European grid voltage. The computational method is a two-dimensional (2D) finite element technique. The modal vibrations under various magnetisations (viz with different fifth harmonic components) are compared with those obtained under a purely sinusoidal magnetisation and showed that the variations for the 100 Hz harmonic of the vibrations are small. However, the 200 Hz harmonic showed a significant increase when a fifth harmonic was present on the applied voltage. In fact, the presence of a fundamental component with 50 Hz frequency and a fifth harmonic on the magnetisation signal generates a 200 Hz harmonic on the magnetostriction strains (and the magnetic forces), and thus this harmonic increases significantly.

Effect of Artificial Burrs on Local Power Loss in a Three-Phase Transformer Core

The increase in losses due to burrs occurring on cut edges of electrical steel laminations in transformer cores is difficult to quantify. Artificial burrs were applied to a 350 kVA, three-phase, five packet, transformer core. Total core loss, flux density distribution and local loss near the burrs were measured. Burrs applied to a portion of a packet of laminations in one limb caused the flux distribution to become more nonuniform than normal throughout the whole core. Local losses increased significantly outside the burr region. The loss increased to over 1000 W/kg in the severely burred region at 1.8 T, 50 Hz. Measured flux distribution data was used in simplified eddy current calculations to predict the total and localized losses. The predicted and measured localised losses in the burred regions followed similar trends but did not agree well in magnitude probably due to the errors caused by the simplifications and assumptions which were necessary in the eddy current analysis.

Improved Transformer Noise Behavior by Optimized Laser Domain Refinement at ThyssenKrupp Electrical Steel

The present paper shows the impact of different laser domain refinement variants for grain oriented electrical steel on the noise of three-phase transformer cores. The impact is evaluated as well by calculated noise on basis of magnetostriction measurements of the electrical steel sheets as by measured noise of transformer core models built from these GO electrical steel sheets. The industrially relevant process of laser domain refinement is reviewed with respect to the influence of different process parameters on the later materials and transformer performance. Contrary to the usually admitted statement, it is demonstrated, that (a) the use of optimum laser domain refinement conditions will not increase the noise level of the transformer cores compared to the non DR status and (b) the use of magnetostriction data for judging about later transformer noise is resulting in only rough indications, but not the final behavior of the real cores.

Mixed Si-Fe Wound Cores Five Legged Transformer: Losses and Flux Distribution Analysis

This paper proposes a three-phase five legged wound transformer core constructed of two high permeability Si-Fe wound cores and two conventional Si-Fe wound cores. The two large internal wound cores are manufactured of high permeability, grain-oriented electrical steel. The two small outer wound cores are manufactured of conventional, grain-oriented electrical steel. The specific arrangement is based on experimental evidence concerning the peak flux density non-uniformity of the typical three-phase five legged wound trans former core, constructed of the high magnetization grain-oriented steel. Since the peak flux density of the two outer cores is lower than the two internal cores, low cost, low permeability, conventional grain-oriented electrical steel can be used for the outer cores. Losses, excitation currents, flux waveforms, and their harmonics contents are presented in this paper. A comparison of the mixed three-phase transformer core and the typical one is also carried out.

Rotational Magnetization in Transformer Cores—A Review

Usually, rotational magnetization (RM) is associated with rotating machine cores. However, in more restricted ways, it also arises in three-phase transformer cores. Modern designs of T-joint yield detours of flux, as a source of RM in the T-joint, the middle limb ends, as well as in the yokes. Simulation of RM is possible by means of so-called rotational single sheet testers which should consider the large grains of highly grain oriented materials. Their high effective anisotropy yields induction patterns of rhombic or lancet-like type with maximum values of axis ratio a up to 0.5, and very high angular velocity round the materials hard directions. Compared to elliptic RM-as arising in non-oriented materials-the corresponding losses are lower due to restricted induction in the hard direction. But they show strong increase with (i) rising a and (ii) rising angular velocity of the induction vector. The magnetostrictive strain shows a pronounced (negative) maximum in the rolling direction with values up to 10 ppm, the transverse direction and normal direction exhibiting positive maxima of lower extent. With respect to industrial relevance, significant RM effects are restricted to the vicinities of T-joints. They represent the location of maximum core loss and also of maximum magnetostrictive strain as a source of audible core noise.

Effect of Artificial Burrs on the Total Power Loss of a Three-Phase Transformer Core

Burrs occurring on electrical steel laminations are likely to increase the losses of transformer cores; however, it is still difficult to quantify this effect. Artificial burrs were applied to a three-phase distribution transformer core in a controlled manner. When large burrs, short circuiting 66 laminations together, were applied to the core, total loss at 1.8 T rose by almost 100%. From eddy current analysis, localized losses were estimated to increase to 1500 W/kg at 1.8 T for 66 laminations electrically connected by burrs. Additionally, various burr locations were investigated and it was found that it does not matter whether the burrs placed on one limb are located opposite each other, forming a rectangular affected region, or are shifted, forming a skewed shape. For burrs affecting a low number of laminations the calculated and measured losses agreed whereas, for large burr regions, calculated values were higher due to the approximations made.

Magneto-Mechanical Resonance in a Model 3-Phase 3-Limb Transformer Core Under Sinusoidal and PWM Voltage Excitation

This investigation presents the measurement results of acoustic noise and vibration of a model three-phase three-limb transformer core under sinusoidal and PWM voltage excitation for assigned value of modulation index with switching frequency from 1 kHz to 3 kHz at no-load condition. Results show that the acoustic noise decreased around 2 (dBA) with increasing switching frequency. However, magneto-mechanical resonance phenomenon was observed at 3 kHz vibration frequency, which could cause excess acoustic noise under some excited conditions.

Normal Flux Distribution in a Three-Phase Transformer Core Under Sinusoidal and PWM Excitation

Transformer no-load loss and noise have been reduced considerably because of improved core material and improved core design. The variation of normal or interlaminar flux distribution (z direction) in a three-phase transformer core has been measured under pulse width modulation (PWM) excitation (no-load) with switching frequencies in the range of 1-3 kHz. The planar eddy current loss and attractive interlaminar force were analyzed for selected values of modulation index and magnetization condition (frequency 50 Hz; induction 1.5 T). Results showed significant reduction of the planar eddy current component and attractive interlaminar force for low modulation index with increasing switching frequency

Magnetic Linkage between Other Leg Windings of a Three-Phase Three-Leg Core-Type Transformer

In this paper, the view of the magnetic linkage between other leg windings of a three-phase three-leg core-type transformer core is clarified. In a three-phase three-leg core-type transformer, even if the geomagnetically induced current of a quasi- direct current by the magnetic storm flows in, the asymmetrical DC magnetization of the core is not carried out at all. In a zigzag-Y connection transformer, it can restrict to a three-phase three-leg core transformer, and single-phase load can be taken between the terminal of a secondary Y connection, and a neutral point.

Improvement of T-joint part constructions in three-phase transformer cores by using direct loss analysis with E&S model

This paper presents the effects of the joint method in the T-joint of three-phase transformer cores on iron losses. The effects of joints on the decrease of core loss have been analyzed by using FEM with E&S model, considering the hysteresis of vector magnetic properties. As a result, we can improve the T-joint part constructions to reduce iron losses in the three-phase transformer cores.

Relevance of multidirectional magnetostriction for the noise generation of transformer cores

As well known, T-joint regions of three-phase transformer cores tend to show rotational magnetisation (RM) patterns which yield distinct increases of magnetostriction. The present work was focused on the question whether these local phenomena exhibit practical relevance for the core's global magnetostriction-caused strain. A main effect was found for the yoke's horizontal direction, RM causing about 80% increase of total strain in the T-joint region and 40% for the total yoke.

Measurement of Local Magnetic Flux in the T-Joint Model of a Three-Phase Stacked Transformer Core

Local magnetic flux in the T-joint model of three-phase stacked transformers was examined by a stylus probe method. The distribution of the rotational loss in the T-joint part was determined by two-dimensional SST measurement. The deterioration of the iron loss in the form of the iron loss in the T-joint model to the iron loss in the material was calculated. The deterioration caused by the rotational flux decreased as the excitation magnetic flux density increased, whereas the deterioration caused by the distortion of the wave form of the local magnetic flux increased. Therefore the penetration of the magnetic flux into the limb and the yoke was determined to be the major cause of the increase in the iron loss of transformers at higher inductions.