Actual Winding Research Articles

Generalized Analytical Expression for Natural Frequencies of a Single Isolated Air-Core Inhomogeneous Transformer Winding

Given a completely inhomogeneous, fully-coupled, $N$ -section ladder network in which elements of each section are distinct from the others, there exists no closed-form solution which connects the ladder network elements to its natural frequencies. Instead of the present practice of comparing individual natural frequencies, finding such a generalized solution would not only permit quantification of deviations between two frequency responses (FRA) but also provides a generic platform for its interpretation. Presently, interpretation of FRA is mostly empirical and difficult to generalize. Although pioneering contributions by Bewley et al. , Abetti and Maginniss, Heller and Veverka, and many others, were made towards developing analytical solutions, they were essentially suitable for a homogeneous winding. For any formulation to become suitable for FRA interpretation (corresponding to a pre and postdamage condition), it must obviously be applicable to an inhomogeneous winding structure. Pursuing this motivation, this paper presents complete details of derivation of analytical expressions that aims to correlate natural frequencies (and their deviations as well) of the ladder network to its basic inductances and capacitances. For this, both short-circuit and open-circuit natural frequencies are examined. Finally, the analytical solution is extended from the discrete-domain to the continuous-domain (transformer winding). Recently, authors have shown practical usefulness of this derived formula for localization and severity assessment of radial/axial displacements in an actual single-isolated continuous-disk transformer winding.

Localization of Radial Deformation and Its Extent in Power Transformer HV Winding Using Stationary UWB Antennas

In this paper, three monitoring stages of detection, localization, and extent determination of radial deformation in power transformer winding using stationary ultra-wideband antennas, are investigated. For this purpose, two types of radial deformation are implemented on the actual transformer high-voltage winding. The first type is a modeled bulgy mechanical deformation, which its extent and reversibility may be changed and it can occur in different positions. The second type is an actual radial deformation applied to the winding. Hyperboloid method and 2-D locus of the winding are adopted in the localization stage. To perform a precise analysis of the received signals, matched filter technique is employed. The extent of the deformation is also determined by magnitude Euclidean distance index. The experimental results prove the effectiveness of the proposed method.

Diagnosing axial displacement in an actual, single, isolated transformer winding: Experimental results

Localization and severity assessment of an axial displacement occurring in an actual transformer winding is reported. Axial displacements considered in this paper are still in their initial or incipient stages of development and so assumed to be physically confined between two consecutive double-disks. It is needless to emphasize that early detection of such a winding condition is crucial. In a recent paper, authors derived a generalized analytical formula that linked the harmonic sum of squares of short-circuit natural frequencies of the winding to the basic winding parameters, viz., capacitances and inductances (taken on a per double-disk basis). This formula was successfully used to localize a radial displacement. Proceeding further, it is now shown, how the same expression can be used to localize and assess severity of an actual axial displacement. A procedure is developed for this purpose. Its philosophy is explained, and thereafter, it is verified by experiments on a single, actual, isolated, continuous-disk transformer winding. The results seem to be promising.

Localization of Radial Displacement in an Actual Isolated Transformer Winding—An Analytical Approach

In this paper, a novel analytical method is developed to locate and assess the severity of a true radial displacement (confined to 1 or 2 disk pairs) in an actual continuous-disk transformer winding. An analytical solution becomes possible mainly due to a simple manipulation of the system matrix, that is, to consider sum of the inverse squares of natural frequencies, instead of just the natural frequencies. This leads to an elegant expression that connects displacement location and its severity to changes in natural frequencies. For its implementation, short-circuit natural frequencies and variation of inductance as a function of winding length are the required inputs. Details of the derivation and experimental results are reported. In summary, it emerges that incipient and true radial displacements in an actual continuous-disk transformer winding can be localized with reasonable accuracy and a qualitative assessment of its severity is also possible.

Measurement and analysis of transient overvoltage distribution in transformer windings based on reduced-scale model

Non-uniform voltage distribution under transient voltage is a primary cause of breakdown of the major insulation of power transformers. Actual power transformer winding has no tap, and is unable to directly measure impulse voltage distribution. Research on the measurement of impulse voltage distribution is important and practical in engineering. According to the relationship between physical quantities, the present study established a simplified shrinkage ratio criterion. Then, the researchers designed a similar ratio 1/20, typed 10kVA 220V/2400V, tapped transformer reduced-scale model, and used the finite element simulation software to simulate the reduced-scale and the original model of the electromagnetic field. Finally, a test platform was built to measure nanosecond pulse voltage and lightning impulse voltage distribution in transformer winding. The researchers also studied the nanosecond pulse width and lightning wave tail time affecting the winding voltage distribution.

Localization and estimation of severity of a discrete and localized mechanical damage in transformer windings: Analytical approach

Mechanical damages in transformer windings during its nascent stages are usually confined to small portions of the winding and can therefore be assumed as localized and discrete in nature. Early detection of the first such event followed by its localization and severity assessment is desirable. Previous researchers have attempted this task by trying to capture correlations that exist between the deviations in measured frequency responses (using indices) and the known types of damage. But, experience reveals that this method lacks generalizability, thus limiting its use. This, perhaps, can be attributed to the lack of a theoretical basis to adequately capture the complex interactions between damages and the frequency response. With this motivation, this paper develops an analytical method (which is obviously generic) for localizing a discrete damage and estimating its severity. During the initial stages of development, the damage can be treated as a localized shunt capacitance change occurring at any arbitrary position in the winding. The analytical formulation is based on equating the coefficients of the driving-point impedance of the ladder network with one of its series/shunt capacitances arbitrarily changed to the respective coefficients of the rational function constructed from measured frequency response of the winding in the presence of a discrete damage. Experiments on an actual continuous-disk winding show that the results are promising.

Experimental Studies on Monitoring and Metering of Radial Deformations on Transformer HV Winding Using Image Processing and UWB Transceivers

In this paper, a novel method based on image processing is proposed for detecting the presence and location of mechanical deformations on an actual power transformer winding. A vertical imaging setup is used to obtain a two-dimensional (2-D) image of the transformer winding using synthetic aperture radar (SAR) imaging method and Kirchhoff migration algorithm. The main goal of the image processing method is to detect the location of the radial deformation on the transformer high-voltage (HV) winding. Two different deformations are applied on the winding under the test in this paper. The first one is a modeled bulgy mechanical deformation and the second one is an actual concave buckling made on the actual transformer HV winding. The experimental results for different cases show the effectiveness of the proposed method to detect the presence and location of the deformation on the transformer winding.

Alternating-gradient canted cosine theta superconducting magnets for future compact proton gantries

We present a design of superconducting magnets, optimized for application in a gantry for proton therapy. We have introduced a new magnet design concept, called an alternating-gradient canted cosine theta (AG-CCT) concept, which is compatible with an achromatic layout. This layout allows a large momentum acceptance. The 15 cm radius of the bore aperture enables the application of pencil beam scanning in front of the SC-magnet. The optical and dynamic performance of a gantry based on these magnets has been analyzed using the fields derived (via Biot-Savart law) from the actual windings of the AG-CCT combined with the full equations of motion. The results show that with appropriate higher order correction, a large 3D volume can be rapidly scanned with little beam shape distortion. A very big advantage is that all this can be done while keeping the AG-CCT fields fixed. This reduces the need for fast field ramping of the superconducting magnets between the successive beam energies used for the scanning in depth and it is important for medical application since this reduces the technical risk (e.g., a quench) associated with fast field changes in superconducting magnets. For proton gantries the corresponding superconducting magnet system holds promise of dramatic reduction in weight. For heavier ion gantries there may furthermore be a significant reduction in size.

A critical review of the definition of FRA resonance frequency of transformers as per IEEE Std C57.149-2012

The explanation of resonance given in IEEE Std C57.149-2012 to define resonance during frequency response analysis (FRA) measurements on transformers implicitly uses the conditions prevalent during resonance in a series R–L–C circuit. This dependence is evident from the two assertions made in the definition, viz., resulting in zero net reactive impedance, and, accompanied by a zero value appearing in the phase angle of the frequency response function. These two conditions are satisfied (at resonance) only in a series R–L–C circuit and certainly not in a transformer, as has been assumed in the Standard. This can be proved by considering a ladder-network model. Circuit analysis of this ladder network reveals the origin of this fallacy and proves that, at resonance, neither is the ladder network purely resistive and nor is the phase angle (between input voltage and input current) always zero. Also, during FRA measurements, it is often seen that phase angle does not traverse the conventional cyclic path from +90° to −90° (or vice versa) at all resonant frequencies. This peculiar feature can also be explained using pole-zero maps. Simple derivations, simulations and experimental results on an actual winding are presented. In summary, authors believe that this study dispels existing misconceptions about definition of FRA resonance and provides material for its correction in IEEE Std C57.149-2012.

Improved Power Transformer Winding Deformation Fault Diagnosis Method

according to analysing the generation principle of transformer winding deformation and its impact on the vibration signal, and make a large number of trial, it can be found in addition to the fundamental frequency component that can reflect the failure, the new characteristic frequency which conclude 50Hz frequency component and some of its harmonic components, the harmonic components of the fundamental frequency can also reflect the failure. Transformer winding deformation fault diagnosis method is proposed based on the relationship between the characteristic frequency, it can not only diagnose whether the failure inside the transformer windings, but also determine the type of fault. In order to verify the proposed method, deformation fault is set to the actual transformer winding. After de-noising, discounted processing, the acquisition monitoring points of vibration signal is used by the proposed method, and the actual transformer is diagnosed, The diagnostic result is same with actual failure. It is shown that the proposed diagnostic method is accurate and feasible.

Study on Mechanical State Diagnosis of Power Transformer Winding Based on Vibration Method

This paper uses the vibration method to diagnose the mechanical state of transformer winding,directed against the fact that the accuracy of the mechanical fault diagnosis in transformer winding is not high. It collects the load test vibration signal of transformer winding in normal and abnormal state, analyzes the vibration signals in different states, and use the vibration frequency and load current matching to judge the winding condition. By setting the different faults to the actual transformer winding of S11-M-500/35 type, it uses the vibration method to do the diagnosis analysis. And the research content is of great significance for the promotion and application of vibration analysis method.

Computer and full-scale models of magnets with a single-layer quasi-force-free winding and evaluations of the possibility of using such magnets in inductive energy stores

Results of numerical modeling and experiments, which confirm the possibility of greatly decreasing the mechanical stresses in the equilibrated magnet winding compared with the usually implemented winding, are presented. An increase in the specific energy capacity of the inductive energy store is pointed out in case of using such winding in it. The possibilities of correction upon the violation of the equilibrium in the actual magnet winding because of the deviation of its configuration from the calculated one are shown.

Interleaved winding and suppression of natural frequencies

Ideally, it is desirable to design and manufacture a transformer winding that can render all its internal resonances non-excitable. This study examines the effectiveness of an interleaved winding in achieving this goal. While investigating its effectiveness, it led to the establishment of a much desired theoretical basis that reinforces the reasons put forward in the literature to explain internal insulation failures observed in interleaved windings used in extra high voltage (EHV) transformers. Numerical calculations along with experimental verification on actual transformer windings are presented. This study reveals that most of the natural frequencies that are normally non-excitable in the line and neutral current responses of an interleaved winding have been rendered excitable in the disk-to-disk voltages, thus, providing favourable conditions for insulation overstress because of resonant overvoltages. Prevalence of such a condition is an inherent characteristic of interleaved windings.

Sub-Cooled Liquid Nitrogen Test System for Cooling HTS Synchronous Motor

A 400 kW radial-axial flux type experimental HTS synchronous motor is designed. There are twelve armature coils using HTS wires in the motor. They are accommodated in the cooling vessels made of FRP material, and twelve cooling vessels are enclosed in the vacuum vessel. In order to cool the HTS coils of the motor, a sub-cooled liquid nitrogen cryogenic system is presented. The operation temperature is below 70 K. This system consists of vacuum system, liquid nitrogen dewar, data acquisition system and a cold box with liquid nitrogen pump, G-M cryorefrigerator, cryogenic valve and a heater inside. The heater can present the heat of the HTS coils. In this paper, the design and the composition of this test cooling system are presented. When liquid nitrogen is injected into the vessel and the cryorefrigerator is operating, the cool down curve of the test system is obtained. After adding heat to the system, the capacity curve of the system is presented in this paper. The results proved that this sub-cooled liquid nitrogen system can be used for cooling the actual armature windings in the HTS motor.

Active Shim Design of a 7 T Highly Homogeneous Superconducting Magnet for Lanzhou Penning Trap

Lanzhou Penning Trap (LPT) is now being developed for precise mass measurements in Institute of Modern Physics (IMP). Homogeneity of magnetic field in LPT was about 3 ppm when without active shimming, while the required value is less than 0.5 ppm. Linear programming algorithm was employed to design a 9-coil cylindrical shim set for main magnet in LPT. First, mesh on the cylinder and current paths are expressed by connectings between the grid nodes. Then current paths are calculated to compensate the high order components of magnet field through linear programming algorithm optimization. The resulting designs are relatively sparse and can be readily constructed. The method has good flexibility, which can uses current paths on any given surface to generate any order shim field and set allowable errors separately over different arbitrary regions of interest (ROI). Software simulation is used to evaluate the influence on field due to bend corners and limited current density for actual windings.

Electromagnetic waves from partial discharges in windings and their detection by patch antenna

The electromagnetic (EM) radiation accompanying partial discharges (PDs) in enameled-wire winding is analyzed assuming the Gaussian currents in the basic PD model. A simplified procedure is proposed to evaluate the response of patch antenna or microstrip antenna to the EM wave based on the transient circuit calculus. Analyses on the twisted pair specimen show that EM radiation from the wire currents contribute to patch antenna output much more than that from the PD itself. The analytical results are verified by an experiment on the twisted pair. It is confirmed that the patch-antenna sensor is potentially capable of detecting PDs in actual motor winding.

Fault diagnosis of actual large-power high-voltage windings using transfer function method

Fault diagnosis of actual large-power high-voltage windings using transfer function method The transfer function (TF) method is presently a well-known method used to detect various types of winding damage in power transformers. Although abundant research has been done on this subject using laboratory windings as test objects, it is hard to find one, whose test objects are actual large-power transformer windings. Hence, a 400 kV disc winding consisting of 86 discs is used in this paper to study turn-to-turn short circuit with the help of the TF method. To evaluate the effects of this type of fault on TF curves, some mathematical comparison algorithms are used in this research.

Localisation of discrete change in a transformer winding: a network-function-loci approach

An entirely different approach for localisation of winding deformation based on terminal measurements is presented. Within the context of this study, winding deformation means, a discrete and specific change externally imposed at a particular position on the winding. The proposed method is based on pre-computing and plotting the complex network-function loci [e.g. driving-point impedance (DPI)] at a selected frequency, for a meaningful range of values for each element (increasing and decreasing) of the ladder network which represents the winding. This loci diagram is called the nomogram. After introducing a discrete change, amplitude and phase of DPI are measured. By plotting this single measurement on the nomogram, it is possible to estimate the location and identify the extent of change. In contrast to the existing approach, the proposed method is fast, non-iterative and yields reasonably good localisation. Experimental results for actual transformer windings (interleaved and continuous disc) are presented.

A New Method for Detection and Evaluation of Winding Mechanical Faults in Transformer through Transfer Function Measurements

1 Abstract—Transfer function (TF) is an acknowledged method for power transformer mechanical faults detection. However the past published works mostly discovered how to specify the faults levels and paid less attention to detection of the type of faults using comparison of TFs. whereas, it seems important for most of the applications to specify the type of fault without opening the unit. This paper presents a new method based on vector fitting (VF) to compare the TFs and specify the type, level and location of the fault. For development of the method, and its verification the required measurements are carried out on four model transformers; under intact condition, and under different fault conditions (axial displacement, radial deformation, disc space variation and short circuit of winding) and the TFs are determined. Employing VF, the coefficients of TFs are determined with the required accuracy. Using those coefficients, a new index is introduced to specify the type, level and location of the fault in the winding. Convincingly good results were obtained. Therefore it is believed that this finding could be helpful in fault diagnosis in actual power transformer windings.

Direct-phase-variable model of a synchronous reluctance motor including all slot and winding harmonics

A detailed model in direct-phase variables of a synchronous reluctance motor operating at mains voltage and frequency is presented. The model includes the stator and rotor slot openings, the actual winding layout and the reluctance rotor geometry. Hence, all mmf and permeance harmonics are taken into account. It is seen that non-negligible harmonics introduced by slots are present in the inductances computed by the winding function procedure. These harmonics are usually ignored in d– q models. The machine performance is simulated in the stator reference frame to depict the difference between this new direct-phase model including all harmonics and the conventional rotor reference frame d– q model. Saturation is included by using a polynomial fitting the variation of d-axis inductance with stator current obtained by finite-element software FEMAG DC®. The detailed phase-variable model can yield torque pulsations comparable to those obtained from finite elements while the d– q model cannot.