Open Phys. 2017; 15:803–808 Research Article Janis Marks* and Sandra Vitolina Modelling of magnetostriction of transformer magnetic core for vibration analysis https://doi.org/10.1515/phys-2017-0094 In Latvian power system, there are three different vari- Received Nov 02, 2017; accepted Nov 12, 2017 ants of performing mechanical diagnostics of large power transformers: in no-load operation mode, at 50% and at Abstract: Magnetostriction is a phenomenon occurring in 100% of full rated power. The sensors do not save har- transformer core in normal operation mode. Yet in time, monic analysis; they obtain and save the total values of it can cause the delamination of magnetic core resulting vibrations. If within the received data, there are vibration in higher level of vibrations that are measured on the values that exceed the provided limits: displacement – 100 surface of transformer tank during diagnostic tests. The µm, velocity – 20 mm/s, acceleration – 10 m/s2, more de- aim of this paper is to create a model for evaluating elas- tailed analysis is required. tic deformations in magnetic core that can be used for With this diagnosis methodology, it is possible to ob- power transformers with intensive vibrations in order to tain robust information about the power transformer and eliminate magnetostriction as a their cause. Description of discover, if a relatively large mechanical defect has oc- the developed model in Matlab and COMSOL software is curred. However, there are no following actions and pro- provided including restrictions concerning geometry and cedures advised in the case of increased vibration values. properties of materials, and the results of performed re- Therefore, there is a necessity for a different diagnostic search on magnetic core anisotropy are provided. As a case approach of large power transformer mechanical fault de- study modelling of magnetostriction for 5-legged 200 MVA tection to improve result accuracy and reliability. The aim power transformer with the rated voltage of 13.8/137kV is of this paper is to develop a simulation model for trans- conducted, based on which comparative analysis of vibra- formers with high vibration level to determine if magne- tion levels and elastic deformations is performed. tostriction process is the cause for such vibrations. Au- Keywords: magnetostriction, magnetic cores, computer thors have presented the results of this simulation model modeling and simulation, vibration measurement, mag- at international symposium [2]. netoelectric devices PACS: 07.05.Tp; 07.10.-h; 75.80.+q; 85.70.-w; 85.80.Jm 2 Magnetostriction in Magnetic Core 1 Introduction Magnetostriction is a property of ferromagnetic materials The mechanical condition of windings and magnetic core that changes their geometric dimensions when exposed to of power transformers can be determined by using vi- magnetic field [3]. It is because these ferromagnetic mate- bration diagnostics. This process is performed for loaded rials are composed of small magnetic domains that have transformer or in a no-load operating mode by placing their unique magnetic orientation, placement and size. vibration accelerometers on the surface of power trans- Generally, magnetic orientation is random through- former tank [1]. out the ferromagnetic material, when there is no magnetic field passing through. Figure 1 a) shows this situation. The color coding corresponds to a correlation with an upward direction. However, when an external magnetic field passes *Corresponding Author: Janis Marks: Department of Electrical through, the magnetic domains react to it and partially re- Machines and Devices, Riga Technical University, Riga, Latvia; Email: [email protected] arrange their sizes [4]. With this process, the domains with Sandra Vitolina: Department of Electrical Machines and Devices, matching magnetic orientation with the external magnetic Riga Technical University, Riga, Latvia Open Access. © 2017 J. Marks and S. Vitolina, published by De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License 804 Ë J. Marks and S. Vitolina Figure 1: a) ferromagnetic material magnetic domain individual orientation with no external magnetic field; b) magnetostriction process in ferromagnetic material domains; c) resulting outcome of magnetostriction process in ferromagnetic material domains field grow larger by changing the materials magnetic ori- 3 Magnetostriction Model entation on their individual surfaces. Thus, the magnetic domains, with individual magnetic orientation pointing Description against the external magnetic field become smaller [4]. This process is visualised in Figure 1 b), where areas color In order to determine these elastic deformations, it is nec- coded in grey, represent the fractions of the non-aligning essary to know characteristics of the magnetic field inside magnetic domains with the external magnetic field that magnetic core and magnetostriction curve of it. In this pa- will change their individual magnetic orientation and sep- per, magnetostriction curve is used as a function L = f(B) arate from their original magnetic domains. Afterwards, that expresses the elastic deformation, depending on mag- these grey regions will join their more aligned neighbour- netic induction [6]. This magnetostriction curve differs for ing magnetic domains. each material since the magnetic domains in multiple fer- The result of this process is visualised in Figure 1 c). romagnetic materials can have varying sizes and can resist The magnetic domains have changed their original shape. to external magnetic field differently. Due to this, the shape of the entire ferromagnetic body has Since the model uses two software programs, it has changed as well. two distinct subsections: In the case of large power transformers, magnetic core • The first consists of a three-dimensional model cre- is made of sheet steel, which creates a complex three- ated in COMSOL software to calculate magnetic in- dimensional system consisting of a ferromagnetic mate- duction values within the magnetic core, windings rial since the largest part of magnetic flux concentrates and the surrounding area; there [5]. This causes elastic deformations and vibrations • The second is also a three-dimensional model cre- of the magnetic core that have a sinusoidal form since the ated in Matlab software for the calculation of elastic externally caused magnetic field is also sinusoidal. This deformations. process over a period can cause delamination since the elastic deformations are continuous throughout the oper- The first subsection in COMSOL begins with the cre- ating period of power transformer. Furthermore, the vibra- ation of model geometry and the assignment of a material tion amplitudes may increase since this process can slowly to every created domain. Windings are made of copper, reduce the mechanical resistance of the transformer mag- magnetic core from steel but the surrounding area from netic core. transformer oil. Each material used in the model has de- fined physical characteristics and parameters. Afterwards, it is necessary to generate a finite element mesh. Then the program calculates the values of magnetic induction in all the coordinates of finite element mesh intersections within a given time intervals in a provided duration of time. A built-in calculation system carries out the computations, which contains Maxwell equations [7]. Modelling of magnetostriction of transformer magnetic core Ë 805 Afterwards, the model exports obtained results to MS Excel in the form of a table and then imports in Matlab where RMS values of magnetic induction are calculated. The program creates a three-dimensional matrix that rep- resents the geometrical structure of transformer model. Within it, it is assumed that every element is 1 cm3. The model uses approximation to obtain the RMS values of magnetic induction where they are unknown. A modified three-dimensional nearest neighbour problem (NNP) algo- rithm carries out this approximation [8]. Figure 2: First case of magnetic core anisotropy These results from Matlab subsection allow determin- ing whether magnetostriction is the cause of these vibra- tion epicentres. The input parameters of the proposed magnetostric- tion model have the following aspects: • The geometric dimensions of transformer tank, windings and magnetic core; • The materials for different parts and their physical characteristics; • Frequency of the voltage, primary voltage, sec- Figure 3: Second case of magnetic core anisotropy ondary voltage, primary winding rated current, sec- ondary winding rated current and the transforma- tion coefficient; the magnetostriction model since it is present in magnetic • No-load operation mode; cores of actual large power transformers [9]. • Magnetostriction curve function L = f(B) of magnetic As verification, two types of magnetic core anisotropy core material. are used. Figures 2 and 3 show their layout. The arrows display the direction in magnetic core rods The simulation model has the following restrictions: and yokes with lesser magnetic permeability. The first case • The magnetic core consists of 10 steel sheets. Each of magnetic core anisotropy has a characteristic that the of them is 60 mm thick; anisotropy direction aligns with the direction of the trans- • The bracings of magnetic core are not considered; former magnetic field. The intersections of the different • The terminals of primary and secondary windings domains are located at the corners between rods