Transformer Windings Research Articles

Impact of one and two partial cooling ducts on temperature rise in transformer windings

We apply our quasi-1D model to the temperature rise in oil-filled transformer foil windings with two symmetric partial ducts. We compare the results with a two-dimensional FEM simulation. To compare the results to industrial tests we try to find a relationship between the effective values for heat transfer coefficients of different foil windings. Finally, we compare the effectiveness of adding one vs two partial cooling ducts to the winding.

A real-time solution method for three-dimensional steady temperature field of transformer windings based on mechanism-embedded cascade network

To enhance the computation efficiency and accuracy of three-dimensional steady temperature field of transformer windings, we propose a new non-invasive Reduced Order Model (ROM) based on a mechanism-embedded cascade network. Initially, a snapshot matrix is formed from the Full Order Model (FOM) and then combined with Proper Orthogonal Decomposition (POD) to extract key modal features that characterize the temperature field. Subsequently, a cascade network architecture, integrating Multilayer Perceptron (MLP) and Radial Basis Function Neural Network (RBFNN), is devised to swiftly map working condition parameters to modal coefficients. Additionally, the cascade network is embedded with condition sensitivity and modal contribution mechanisms to further enhance prediction accuracy. Finally, by linearly weighting the modes with predicted modal coefficients, a rapid reconstruction of the steady temperature field in transformer windings is achieved. Validation against Fluent software simulations and experimental measurements demonstrate a close agreement, with computational errors of less than 4K and an impressive single solution time of only 0.0087 s, which is 48760 times faster compared to Fluent software.

Transformer winding faults diagnosis using the transfer function of its high-frequency lumped equivalent model from the measured FRA data

The frequency response analysis (FRA) of the transformer is the data obtained in a wide frequency range that represents the transfer function (TF) that reflects the physical behavior of its coil. However, it can be considered one of the best tools for a better understanding of the electromagnetic characteristics of the winding. This article proposes the TF as a tool to locate and assess transformer winding failures. So, an autonomous algorithm has been developed to construct the TF in ‘s domain’ proposed in previous research. The TF has been determined from experimental measured FRA data from an isolated air-core winding, where the TF has been calculated for the axial defects (AD) realized on the winding discs. Besides, the diagnostic approach is based on the scaling factor (K) and the real zero (τ) of the TF that can be obtained from the measured equivalent capacitance, equivalent inductance, and the DC resistance of the winding in high and low-frequency ranges. However, the K, τ, and the slope of the equivalent inductance characteristics as a function of the winding defects degree have been used for locating and assessing the severity of the winding faults.

Diagnosis of Radial Deformation and Axial Displacement Faults in Power Transformer Windings using X-ray and Compton Backscatter Imaging

Continuous and uninterrupted transmission and distribution of electrical energy is highly dependent on the flawless operation of power transformers. Failure of these critical components can lead to network power interruptions and consequently have severe detrimental consequences. Therefore, timely detection and diagnosis of power transformer faults is crucial not only to prevent the escalation of faults but also to minimize repair and maintenance costs. Conventional methods for inspecting windings faults have limitations such as the need to take the transformer out of service, unreliable results, and the addition of auxiliary devices inside the transformer, such as dielectric windows. In contrast, the proposed method in this paper utilizes a Compton Backscatter Imaging (CBI) or X-Ray Transmission (XRT) device located outside the transformer, eliminating the need for any additional equipment. This enables online scanning of any number of transformers to assess their health status and identify the type, extent, and progression of potential internal faults. Experimental results demonstrate the feasibility of the proposed method for detecting radial deformation and axial displacement and disk space variations faults of varying magnitudes and locations in both high-voltage and low-voltage windings of power transformers.

PLC Based Transformer Protection from Over Voltage and Under Voltage

A PLC (Programmable Logic Controller) based transformer protection system is an electronic system designed to protect industrial transformers from various electrical faults and abnormalities. The system utilizes sensors to detect electrical parameters such as voltage, current, and temperature and uses a PLC to process the data and control the transformer's operation. The protection system can be programmed to detect faults such as overload, overvoltage, undervoltage, phase loss, phase reversal, and over-temperature conditions. Once a fault is detected, the PLC will automatically shut down the transformer to prevent further damage. The system provides reliable and accurate protection to the transformer, reducing the risk of costly downtime and repairs. Transformer protection from over and under voltages is a critical aspect of any transformer control system. Overvoltage can damage the transformer's insulation, bearings, and winding, while undervoltage can cause the transformer to stall or overheat. To protect the transformer from these conditions, various protection devices can be employed, including overload relays, circuit breakers, and voltage monitors. To protect against overvoltage, a voltage monitor can be installed, which will detect any voltage spikes or surges and trigger an alarm or shut down the transformer if the voltage exceeds a predetermined threshold. Similarly, an undervoltage relay can be used to protect the transformer from low voltage conditions. The undervoltage relay will monitor the voltage levels and shut down the transformer if the voltage drops below a certain level.. Key Words:-PLC (Programmable Logic Controller), SMPS, Voltage Controlled Relay, LED indicators, Transformer and Dimmer.

Derivation of transformer winding equivalent circuit by employing the transfer function obtained from frequency response analysis data

AbstractPrecisely interpreting frequency response analysis (FRA) curves is crucial when investigating mechanical malfunctions in power transformer windings (TWs). However, many conventional explanations of FRA features cannot be validated by an equivalent circuit (EC) that represents winding structures using resistance, inductance, and capacitance components in a ladder network. Incorrect interpretation can lead to misdiagnosis and confusion in asset management. Previous ECs are often proposed by analysing winding structures without rigorous verification compared to the corresponding FRA data. The specific EC is acquired using the transfer function (TF) derived from the measured FRA data. This allows for the establishment of the relationship between TW FRA curves, TF equations, and EC topologies. The precise interpretation of FRA curves can be achieved by closely observing the FRA curves created from TFs and ECs. The remarkable similarity between the measured and modelled FRA curves verifies the authenticity of the derived ECs. This significant achievement clarifies many misunderstandings regarding FRA and represents a substantial advancement in FRA technology.

Quasi-one-dimensional approach to heat transfer: General formulation and its application to transformer windings

A quasi-one-dimensional approach to conduction heat transfer with convective boundary conditions is developed for bodies of variable geometry. The novelty of the method is demonstrated on the windings in oil-filled distribution transformers with partial cooling ducts. We obtain analytical solution for the windings average temperature rise and tangential temperature distribution and find them in an excellent agreement with the FEM simulation, numerically confirming the validity of the reduction from 2D to 1D. When the quasi-one-dimensional approach is applied to calculation of temperature rise for the low and high voltage windings in industrial setting we obtain 1% and 5% discrepancy with the industrial tests respectively. Hence, the method offers reliable estimates of the temperature rise, and temperature distribution in a chosen direction, in bodies of variable geometry.

AC loss study on a 3-phase HTS 1 MVA transformer coupled with a three-limb iron core

High-temperature superconducting (HTS) technology provides an alternative approach to achieve compact transformers. Addressing AC loss in the HTS winding is crucial for HTS transformer applications. Most numerical AC loss studies on HTS transformers have neglected the influence of iron cores. This work carries out an AC loss study to explore the impact of an iron core on the HTS windings in a 3-phase HTS 1 MVA transformer coupled with it. AC loss simulations for the transformer winding both with and without the iron core are conducted by adopting the three-dimensional (3D) T-A homogenization method. When the iron core is incorporated, the saturation magnetic fields of iron materials, flux diverters (FDs) with different geometries, and variations in turn spacings in the LV winding composed of Roebel cables are considered to investigate their influence on the AC loss of the transformer winding. The inclusion of the iron core leads to a 1.2% increase in AC loss for the transformer winding while simulating at the rated current. We attribute this slight difference to the non-inductive winding structure of the transformer winding, where a strong magnetic field generated in the space between the LV and HV windings effectively shields the influence of the iron core.

A novel estimation methodology for multi-resonance equivalent inductance of transformer winding for inter-turn short-circuit fault detection

A novel, indirect measurement technique for estimating equivalent inductance associated with multi-resonance behavior of an isolated transformer winding is reported for both healthy and inter-turn short-circuit fault-condition. For healthy winding, the authors proposed measuring two unique admittance magnitude responses of the winding followed by utilizing their natural frequencies for estimating the said inductance. Here, the one response is for line-end excitation with neutral-end grounded and the other one is for two equal and opposite polarity excitations from two ends of the winding. For inter-turn shorting, driving-point admittance magnitude response with neutral-end open is also utilized. This inductance seems to be one important parameter for verifying the design constraint mainly for impulse behavior as well as for identifying inter-turn shorting of the winding. The proposed method was also verified by experimental measurements on two actual transformer windings; one of which incorporated an iron core within it. All pertinent analytical derivations and the associated results are also included in the paper.

Mathematical Model of a Nonlinear Power Transformer for Needs of Relay Protection

In this work, a mathematical model of a three-phase nonlinear transformer is suggested. The model enables simulating the transformer operation with allowance for its nonlinearity and covers needs of the relay protection. Our model has been developed on the basis of a mathematical model with phase coordinates, where differential equations are composed by the Kirchhoff’s phase-voltage law. Based on this model, we first compose a mathematical model for simulating steady-state operation modes of a transformer, taking into account the asymmetry and nonlinearity of its ferromagnetic core. In this model, the initial values of inductances and mutual inductances of loops are determined from the main phase inductance calculated by the experimentally found no-load current, and their current values are determined from the currents in windings and the magnetic fluxes in legs of the transformer core. The magnetic fluxes are calculated by the nodal-pair method. This improved mathematical model is verified through a comparison between the calculated harmonic components of the phase currents and the experimental results. The harmonic components are calculated with the use of Fourier expansion of the calculated phase currents. Their experimental values are determined with a spectrum analyzer. The calculated and experimental harmonic components of the currents of phase A during no-load and rated-load operation of the transformer are tabulated. The comparison of these results shows that the mathematical model of a three-phase transformer we suggest makes it possible to simulate currents in transformer windings under steady-state operation modes with accuracy acceptable for relay protection.

Optimized Design of New 24-pulse Rectifier

Compared with the conventional 24-pulse rectifier, the low-voltage winding of the rectifier transformer must be connected in the y and d modes, so that the voltage phase of the low-voltage side of the transformer is separated by 30° in sequence. This paper uses the phasor method to obtain a set of phase voltages that move towards 15° through the equivalent of three-phase voltages, so that the two sets of voltages produce a phase difference. Then, through decoupling and voltage reduction, the electrical quantity is converted into a signal quantity, the voltage level is reduced, and then the electrical quantity output is obtained to obtain the required voltage value. Finally, the required DC power is obtained through the rectification system. The effectiveness of the reverse model of this paper is verified by comparing the results and efficiency with the conventional 24-pulse rectifier.

Optimization of support vector machine for transformer core and winding looseness fault diagnosis based on improved grey wolf algorithm

To diagnose transformer core and winding looseness faults more timely and effectively, a complementary ensemble empirical mode decomposition (CEEMD) and improved grey wolf optimization-based support vector machine (IGWO-SVM) method for transformer core and winding looseness fault diagnosis are proposed. Firstly, the vibration signal is decomposed into multiple intrinsic mode functions (IMFs) through CEEMD. Secondly, the energy entropy of different IMFs is calculated, and the energy entropy of different states is formed into a feature dataset. Then, the improved GWO-optimized SVM model is used to classify and recognize the feature dataset. Finally, we establish an experimental platform for experimental verification. The results show that the proposed method can accurately and effectively diagnose transformer core and winding looseness faults, and has a high diagnostic accuracy, which is at least 3.5% higher than the existing optimal diagnostic models. The proposed method provides a theoretical reference for the development of transformer fault diagnosis strategies.

Thermal-flow characteristics analysis of a novel resilient capacity ceramic insulated winding dry type transformer

With the increasing demand for the resilient capacity of transformers in high-proportion renewable energy grids, the overload capacity of transformers and the thermal conductivity of winding insulation materials have been put forward as important requirements. In response to these requirements, a novel ceramic high temperature tolerance insulation winding is proposed in this paper and is applied in a ceramic insulated winding transformer. A combination of simulation and experimentation is used to analyze the thermal-flow characteristics of this transformer. The temperature and flow field distribution characteristics of transformers with both winding insulation methods (ceramic and Nomex paper) are compared. The internal mechanism of reflux near the iron core and high voltage winding under forced air cooling is clarified. A superior outside cooling condition is obtained. A prototype ceramic insulated winding transformer is developed and tested to verify the accuracy of the simulation model. The results show that the hotspot temperature of the ceramic insulated winding transformer under natural cooling is 10.7% lower than that of the Nomex paper insulated winding transformer. With forced air cooling of 2, 3, 4, 5, and 6 m/s applied at the bottom, the hotspot temperature of the ceramic insulated winding transformer is 11.4%, 10.5%, 9.7%, 14.0%, and 17.8% lower than that of the Nomex paper insulation winding transformer, respectively. Under forced air cooling, a reflux phenomenon is observed in both transformers in the vicinity of the iron core and high voltage winding due to the formation of adverse pressure gradient region and wall viscous force blocking. The strength of the reflux is affected by the magnitude of the forced air cooling flow velocity and the construction of the transformer. The optimal range of the external cooling flow velocity for the ceramic insulated winding transformer is 3–4 m/s. The errors between the simulated temperature and the measured temperature at the nine monitoring points of the prototype are all less than 5%, which verifies the effectiveness of the simulation model. The experimental and theoretical basis for the design and application of resilient capacity dry type transformers is provided by this research.

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.

Variational Mode Decomposition-Based Processing for Detection of Short-Circuited Turns in Transformers Using Vibration Signals and Machine Learning

Transformers are key elements in electrical systems. Although they are robust machines, different faults can appear due to their inherent operating conditions, e.g., the presence of different electrical and mechanical stresses. Among the different elements that compound a transformer, the winding is one of the most vulnerable parts, where the damage of turn-to-turn short circuits is one of the most studied faults since low-level damage (i.e., a low number of short-circuited turns—SCTs) can lead to the overall fault of the transformer; therefore, early fault detection has become a fundamental task. In this regard, this paper presents a machine learning-based method to diagnose SCTs in the transformer windings by using their vibrational response. In general, the vibration signals are firstly decomposed by means of the variational mode decomposition method, where a comparison with the empirical mode decomposition (EMD) method and the ensemble empirical mode decomposition (EEMD) method is also carried out. Then, entropy, energy, and kurtosis indices are obtained from each decomposition as fault indicators, where both the combination of features and the dimensionality reduction by using the principal component analysis (PCA) method are analyzed for the global effectiveness improvement and the computational burden reduction. Finally, a pattern recognition algorithm based on artificial neural networks (ANNs) is used for automatic fault detection. The obtained results show 100% effectiveness in detecting seven fault conditions, i.e., 0 (healthy), 5, 10, 15, 20, 25, and 30 SCTs.

Hybrid Analytical-FEM Approach for Power Transformer Transient Analysis

The paper describes a high-frequency model for transient calculation in transformer windings with segmentation on a turn level. The windings are represented by lumped RLC parameters given by the analytical approach, whereas the model is solved in the time domain. The accuracy of the analytical calculation is improved with correction factors obtained with a set of numerical calculations. The presented model is verified by measurements on the example of power transformer disc winding.

Strongly Coupled Circuit‐Magnetic‐Structural Effect on Winding Vibration Process of Power Transformer

Short‐circuit forces, which result in violent vibration of power transformer windings, are induced by the interaction between the short‐circuit currents and the leakage magnetic induction. During vibration, the rearrangements of disks affect the magnetic flux distribution, which leads to time‐varying equivalent reactance and further changes of currents and forces. When a short‐circuit accident occurs, these processes happen simultaneously and constantly. In this article, the influence of circuit parameters on short‐circuit currents is analyzed. The strongly coupled phenomenon between equivalent circuit, magnetic field and structural field is explicated, and the method to obtain vibration process with strongly coupled phenomenon considered is proposed. Then the strongly coupled effect on vibration process is investigated. The vibration process is characterized by the time‐varying currents, electromagnetic forces and displacements. The space coefficient is defined to represent the magnetic flux distribution. The changes of maximum value and its occurrence time of the characteristic parameters are obtained. The peak values of the short‐circuit forces and displacements increase and the waveforms change, which is caused by the distortions of leakage magnetic flux and the changes of spatial ampere‐turn balance during vibration. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Structural Deformation and Displacement of a Disc Winding Due to Standard Switching Impulse Voltage via Finite Element Method

Switching operations in a power system network can lead to transient overvoltage in the high voltage (HV) winding of distribution transformers that causes high-stress build-up. This paper presents the relationship between electromagnetic force due to a standard switching impulse (SSI) and mechanical deformation/displacement behaviours for a disc-type transformer. The analysis was carried out based on a three-dimensional (3D) modelling of a continuous HV disc winding configuration whereby it is subjected to the switching transient voltage and force excitations through the finite element method (FEM). The electric transient solver analysed the static and dynamic aspects of the electromagnetic forces associated with the variation of forces versus time. The transient structural solver evaluated the structural behaviours of the disc winding related to the axial height and radial width of the winding under electromagnetic forces. It is found that the positively dominant axial force generated in the winding with a magnitude of 8.7 N causes the top and bottom layers of disc winding to tilt and displace. In addition, the positive average radial force of 1.4 N causes the circumference of the winding to experience hoop tension and outwardly stretch.

Artificial neural network-based cooling capacity estimation of various radiator configurations for power transformers operated in ONAN mode

Power transformers submerged in oil are universally acknowledged as very useful elements in electrical power networks. A fraction of the electrical energy involved in the conversion from high to low voltages is lost as thermal energy, which is produced inside the transformer's windings and core. The effective dissipation of heat is of paramount significance and can be accomplished through the strategic installation of radiators on the tank. This study aims to examine the total cooling capacity of a radiator employed for cooling a power transformer operating in oil, natural air, and natural mode. The investigation is conducted by varying the design parameters, specifically the number of fins per radiator and the radiator length. The study also utilizes computational fluid dynamics results to achieve a substantial convergence with experimental findings. In the context of the verification study conducted for a specific study point, it was found that the simulation outcomes at a mass flow rate of 0.15 kg/s corresponded to about 7.4 % of the experimental results. Additionally, the cooling capacity value obtained was 7.2 %. In the context of machine learning, the performance of the numerical approach was assessed by employing the Bayesian regularization method. The evaluation revealed that the margin of deviation, mean squared error, and coefficient of determination (R2) metrics yielded values of −0.001 %, 1.32E-02, and 0.99930, respectively.

Direct single‐phase isolated improved gamma Z‐source AC–AC converter suitable for DVR application

AbstractA direct single‐phase isolated improved gamma Z‐source AC–AC converter is designed and manufactured in proposed paper. This converter contains an impedance source structure and its advantages. In general, these advantages are as follows. Firstly, the proposed structure has a wide range of output voltage as boost and buck as well as in‐phase or out‐of‐phase states. Secondly, the proposed converter is electrically isolated thanks to a high frequency transformer (HFT), which significantly reduces the volume of the structure; therefore, in applications such as dynamic voltage restorer (DVR), there is no need to install a coupling transformer with the grid frequency which is very bulky and full of losses. Furthermore, the HFT of the proposed converter is a three winding transformer which also acts as the inductance needed for impedance source network. In addition, the safe commutation method has been utilized, which reduces the voltage spikes on the power switches. Finally, the analysis and design of this converter has been done, and then confirmed by a small‐scale laboratory prototype.