Vibro-Acoustic Methods in the Condition Assessment of Power Transformers: A Survey <s> B. CORE/WINDINGS <s> There is an increasing interest in applying monitoring systems and on line diagnosis techniques to power transformers, as these are one of the most expensive and critical components of a power system. Detecting failures in an incipient stage can avoid major transformer damages, allowing important savings in investing, and giving time enough to plan transformer outages. In recent years, a great number of monitoring systems have been reported. Some of them, make use of models as a tool to assess transformer condition. In this paper the use of a vibration model to be applied to transformer monitoring is proposed. In the paper, a review of the basic theory of transformer vibration is performed and the results of an experimental set of tests carried out in order to establish the model basis are reported. <s> BIB001 </s> Vibro-Acoustic Methods in the Condition Assessment of Power Transformers: A Survey <s> B. CORE/WINDINGS <s> In this paper, a model developed for a transformer monitoring system to estimate transformer tank vibration is presented. The model calculates vibration on the transformer tank starting from some input variables that can be easily measured on the transformer. Tank vibration is also measured, showing a good concordance between estimated and measured values if the transformer is healthy. In case of a winding deformation winding vibration and, consequently, that of the tank, changes and a big difference between estimated and measured vibration appear. To estimate tank vibration, the model takes into account the main physical phenomena generating vibrations in the different transformer elements and how these vibrations are superposed and transmitted to the tank. The model has been tested experimentally on a test transformer fitted with internal and external accelerometers. A deformation has been provoked in the test transformer winding with the aim of testing the model's ability to detect it. The model has been also tested on several in-service grid transformers. The results of the experimental validation are shown in Part II of the paper. <s> BIB002 </s> Vibro-Acoustic Methods in the Condition Assessment of Power Transformers: A Survey <s> B. CORE/WINDINGS <s> In Part I of the paper, a tank vibration model was proposed as a method to detect the winding deformations in power transformers. This model is incorporated in a model-based monitoring system for power transformers. In this paper, the experimental verification of the proposed model that calculates vibration on the transformer tank is reported. The model was validated in a 1500-kVA experimental transformer constructed as a reduced scale model of a 60-MVA 220-kV unit. In order to load the test transformer, the opposition method described in IEC 60076-2 Standard was used allowing to vary the load and power factor over a wide range. Sensors to measure vibrations and temperature were installed in the test transformer. The model was validated under different test transformer operating conditions. In order to verify the model's ability to detect failures, a deformation was provoked in the test transformer winding. Model predictions were compared with the measured vibration in that situation. The model has also been applied to four (30-40 MVA) grid transformers. Some results of this field validation are presented in this paper. <s> BIB003 </s> Vibro-Acoustic Methods in the Condition Assessment of Power Transformers: A Survey <s> B. CORE/WINDINGS <s> A mathematical model for vibration analysis of the transformer core is developed in this study. Core vibration is principally caused by magnetostriction effect which is also a function of magnetisation. A simplified magnetisation model is introduced and compared with the J–A model in term of accuracy for the magnetic intensity within ±2500 A/m. As the magnetic properties are normally coupled with mechanical dependencies, the magnetostrictive characteristics are analysed based on establishment of the relationship between the strain and the stress. According to macroscopic thermodynamics and the law of energy conservation, a new model for magnetostriction effect is presented by expanding the Gibbs-free energy density in a polynomial form. In the cases where the magnetic field does not reach saturation, the quartic term and its above are neglected. The accuracy of the proposed magnetostrictive model is verified by comparing with the Sablik model. A mathematical expression for the equivalent magnetostrictive force is then derived, which is further utilised to calculate the core vibrations in the sinusoidal magnetic field. With the measurements previously available various numerical cases for core vibrations are evaluated and compared. <s> BIB004 </s> Vibro-Acoustic Methods in the Condition Assessment of Power Transformers: A Survey <s> B. CORE/WINDINGS <s> In this paper, a nonlinear N-L-N Hammerstein-Wiener model is used to build the vibration model of power transformer for the online monitoring of winding condition. The vibration mechanism for the identification of power transformer is presented first. Then the Hammerstein-Wiener model is introduced and ways to estimate the parameters of the model is illustrated explicitly. Validation over an in-service gird power transformer is done to verify the effectiveness of the model. The estimated results show good fitness with the measured data collected from the vibration monitoring system, which indicates its correctness of the proposed model. Moreover, compare to existing methods, the model presented in this paper gives a more comprehensive estimation including both linear and nonlinear information of the system which is beneficial for the online condition monitoring of power transformers. <s> BIB005 </s> Vibro-Acoustic Methods in the Condition Assessment of Power Transformers: A Survey <s> B. CORE/WINDINGS <s> This paper aims to construct an appropriate model to represent the nonlinear transformer vibration system, with electric applies as the system inputs and the vibration response on the transformer tank as the outputs. A single-input and single-output (SISO) Hammerstein-type model is developed for identifying the nonlinear transformer vibration system, when the observed vibration on the transformer tank is derived into two components contributed by the individual vibration sources. The nonlinear system is identified by the Fourier neural network, which consists of a nonlinear element and a linear dynamic block. The order determination method based on the Lipschitz criterion as well as the back-propagation algorithm for weights update are both presented. The Hammerstein-type Fourier neural networkbased model is tested on a transformer, giving promising results for prediction of the transformer vibration. <s> BIB006 </s> Vibro-Acoustic Methods in the Condition Assessment of Power Transformers: A Survey <s> B. CORE/WINDINGS <s> In this paper, a winding condition assessment model using vibration signals is presented, which can be used to diagnose power transformers online. The basic principle of this model is based on the correlation analysis of winding vibrations. In the model, the fundamental frequency vibration analysis is used to separate the winding vibration from the mixed signal. Then, a health parameter is proposed via principal component analysis. Another parameter is also proposed to detect the fault locations for suspected faulty transformers. In laboratory tests, the model is validated on a specifically designed 110-kV transformer. During the tests, man-made winding deformations are simulated to compare the vibrations under different conditions. The model has also been tested on several in-service power transformers. The preliminary study shows that the proposed model is feasible to assess the power transformer winding condition. <s> BIB007 </s> Vibro-Acoustic Methods in the Condition Assessment of Power Transformers: A Survey <s> B. CORE/WINDINGS <s> Abstract Health and usage monitoring (HUM) systems are critical for power transformers, and should provide accurate diagnostic information without delay. Diagnostic methodologies are the core of HUM systems. In this paper, we propose four complementary diagnostic techniques for power transformers based on vibrations that provide health metrics from different perspectives. During the field experiment, the vibrations of several in-service transformers under different conditions are collected, and the corresponding diagnostic results are obtained. Next, a health grade system is defined, and the suggested thresholds for each technique are also presented. The effectiveness of the health grade system is illustrated experimentally on three representative transformers. The consistency between the results of the proposed techniques and the actual condition of the test transformers show that the proposed techniques can distinguish transformers under different conditions. <s> BIB008 </s> Vibro-Acoustic Methods in the Condition Assessment of Power Transformers: A Survey <s> B. CORE/WINDINGS <s> Analyses of transformer electromagnetic vibration noise are presented in this study. A finite element model is established which combines transient electromagnetic field analysis, mechanical field analysis and acoustic analysis to calculate the sound pressure level of the radiated noise around the transformer. Transient electromagnetic field analysis is performed to get the Lorentz, reluctance magnetic forces and magnetostriction according to Maxwell theory and virtual displacement principle. Mutual influence of strain and magnetisation has been considered. The main frequency components of harmonic electromagnetic excitations are analysed by Fourier transformation so as to carry out the harmonic response analysis and obtain the nodes displacements of the windings and core. The noise distribution is further calculated by acoustic analysis based on the achieved vibration data. Comparison of calculated results and measured data verifies that the combined noise calculating model is applicable for transformer noise prediction. <s> BIB009 </s> Vibro-Acoustic Methods in the Condition Assessment of Power Transformers: A Survey <s> B. CORE/WINDINGS <s> Abstract The noise of electrical machines such as electric motors, power transformers and electrical inductors increasingly interested designers and manufacturers of several industries (automotive, rail, etc.). This interest concerns the reduction of noise caused by these machines in transportation vehicles for example, to provide better comfort to users. In this paper, the noise radiated by an electrical power transformer is predicted using an end-to-end multiphysics modelling solution. The modelling procedure is based on the chaining of three analysis methods. The first one simulates the electromagnetic problem which generates Maxwell forces on the magnetic core of the transformer from electrical excitation. These forces are considered as an input for the mechanical problem solved by the finite element method (FEM) to calculate the acceleration field on the structure. Finally, these accelerations are considered as in input for the acoustic model to compute the noise radiation using the Boundary Element Method (BEM). Two models of the ferromagnetic core are considered. The first is a bloc model where the different laminates are stuck and the second is a laminated model where a small sliding condition is introduced at interfaces between sheets of metal. Numerical results of the mechanical and acoustic models using a laminated core are compared with experimental data and show good agreements with measurements. <s> BIB010 </s> Vibro-Acoustic Methods in the Condition Assessment of Power Transformers: A Survey <s> B. CORE/WINDINGS <s> Large power transformers are an important component of the power system, because mainly they are the connecting points between generators, transmission system and distribution system. Although transformers are considered as electrical devices with high operation reliability, various faults can occur due to internal or external causes. Mechanical defects mainly are caused by electrodynamic forces and magnetostriction. It is relatively difficult to determine this type of faults directly; however technical condition can be evaluated through analysis of vibration pattern measured on transformer tank. This paper describes a model developed in COMSOL and Matlab software for estimation of elastic deformations of magnetic core caused by magnetostriction. The results are provided as a case study. <s> BIB011
Construction of a numerical model based on aforementioned spring damper concept was used to monitor tank vibrations in BIB002 , BIB003 , BIB001 . Basically, the used model was quite simple-it was constructed as the sum of the vibrations caused by the transformer core (proportional to applied voltage squared) and windings (proportional to load current squared). An additional variable was used to take into account temperature influence. The mathematical model is shown as (6) : where v tank,100 , i 50 , u 50 are the complex variables that represent the tank vibration model at 100 Hz frequency, transformer current and voltage fundamental frequency components, respectively. α, β, γ , δ are transformer geometry-specific complex parameters obtained from measurements. θ to is the temperature measured at the top of the oil. For other potential sources of vibrations, such as oil pumps and fans that don't work in continuous mode of operation, a different set of model parameters can be used in order to describe the system when such elements are turned on because they shift the dominant frequencies in the frequency spectrum of the recorded signal. The proposed model was experimentally validated on a real system in BIB003 . A deformation of the transformer winding lead to a significant increase in model error. Jing et al. BIB005 and Hong et al. BIB006 use standard Hammerstein-Wiener model type for nonlinear systems. These models are often used for systems where the inputoutput relationship can be decomposed into serial connection of static nonlinear input-output blocks and a dynamic linear block. Identification of the model parameters in BIB006 was done with a neural network. By using a neural network, it is possible to have less a priori knowledge of the system and that nonlinearity does not need to be predefined. Winding condition assessment based on principal component analysis was proposed in BIB008 and BIB007 using the mathematical model of transformer core/winding vibrations from BIB002 , BIB003 . Total vibration depends on the power factor between the fundamental voltage and current BIB008 , BIB007 , BIB001 , thus the currents and voltages must be treated as complex variables. In practice, if the power factor angle fluctuation is less than 0.02 radians, the transformer current is the only factor that contributes to the total winding variation. Therefore, two close samples of transformer vibrations can be used to separate the winding vibration from the total vibration. This principle is illustrated in Fig. 7 , where v total,i , v core,i , v winding,i are the total vibration signal, core and winding vibration signals of sample i, respectively. The winding vibration variation from sample i to sample i + 1 is denoted with v w and β is the phase angle between the total vibration signals i and i + 1. Winding vibration variation can then be expressed as (7): BIB009 BIB010 BIB004 BIB011 deal with the electromagnetic vibration noise analysis of core and windings of a power transformer using finite element modelling. Additionally, Hu et al. BIB009 and Bouayed et al. BIB010 combined electromagnetic field analysis with mechanical field analysis and acoustic analysis. FFT analysis of the electromagnetic forces has shown that the most prominent harmonics are again 100 and 200 Hz, respectively. Furthermore, the core magnetostriction depends only on the magnetic induction and that the frequency of core magnetostriction is twice as that of the magnetic induction, i.e. twice the fundamental grid frequency.