Vibro-Acoustic Methods in the Condition Assessment of Power Transformers: A Survey <s> II. CAUSES OF TRANSFORMER VIBRATIONS <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> BIB001 </s> Vibro-Acoustic Methods in the Condition Assessment of Power Transformers: A Survey <s> II. CAUSES OF TRANSFORMER VIBRATIONS <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> BIB002
Main cause of transformer core vibrations is magnetostrictiona property of ferromagnetic material to change its shape under the influence of a magnetic field. Magnetostrictive stress vs. magnetic induction curve of iron can be approximated with a quadratic formula (Fig. 2) since the magnetostrictive stress is proportional to the square of the magnetic induction  BIB001 BIB002 . Thus, it also correlated to the square of the applied voltage. On the other hand, current through the transformer windings induces axial, radial and combined Lorentz forces which try 83916 VOLUME 7, 2019 FIGURE 2. Iron magnetostriction as a function of induction-taken from BIB001 . to compress and stretch the windings, respectively  BIB001 BIB002 . Lorentz forces are proportional to the square of the current. Voltages and currents are mutually dependent and since they cause transformer core and windings vibrations, respectively, bulk of the works in this field treat the problem of diagnosing these two vibrations simultaneously. Transformer core and windings vibrations propagate through the transformer oil and reach the transformer housing which will also, in turn, start vibrating. The viscosity of transformer oil as well as any rigid structures (reflection) affect the propagation of vibrations towards the chassis. Therefore, all these issues must be taken into account when choosing the appropriate sensors and points for sensor placement to perform the measurements. Motion of the OLTC contacts will cause vibrations that can be sensed on the OLTC housing. Ageing of the contacts or early occurrence of a defect (deformation) cause changes in the vibration pattern. Therefore, by analysing these signals it is possible to establish a diagnostic method which can be used to evaluate the condition of the OLTC contacts, without disassembling its chamber. It is possible to detect faults in the OLTC tap selector and the diverter switch by means of vibration measurements.