Modelling of Magnetostriction of Transformer Magnetic Core For

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) algorithm carries out this approximation [8]. Figure 2: First case of magnetic core anisotropy These results from Matlab subsection allow determining whether magnetostriction is the cause of these vibration epicentres. The input parameters of the proposed magnetostriction 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, secondary 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 and yokes are not considered; of transformer magnetic core. • Interwinding insulation is not considered; The difference in resulting magnetic field for this lay- • The model functions as an enclosed magnetic sys- out of anisotropy shows ∆ = 0.7119% absolute change. The tem – magnetic field does not exist outside ofit. model obtains this result by comparing the values of magnetic induction in all positions within the Matlab subsec- The result of this magnetostriction model is a visuali- tion three-dimensional model matrix. Equation (1) shows sation of calculated elastic deformation values within the this calculation, magnetic core of the transformer. ∑︀n abs(Bbase.n−Bani.n) i B · 100% ∆ =1 base.n = n (1)

4 Research on Magnetic Core where Bbase – RMS value of magnetic induction with Anisotropy of Proposed Model isotropic magnetic core; Bani – RMS value of magnetic induction with anisotropic magnetic core; The created three-dimensional model in COMSOL soft- n – total amount of positions in the Matlab subsection of ware consists of domains for the magnetic core that are the model. isotropic. Therefore, it is necessary to verify, whether However, for the second case of magnetic anisotropy, anisotropy would have relative influence on the results of the difference of magnetic field was ∆ = 11.90%. This is because the intersections of domains with different direc- 806 Ë J. Marks and S. Vitolina

Figure 5: Result for visualisation of vibration diagnostics data on the transformer tank surface, µm

5 Case Study

As case study, the authors chose 5-legged large power transformer [10] with primary voltage – 13.8 kV, secondary voltage – 137 kV,primary and secondary rated power – 200 MVA for this paper. For this large power transformer vibration measurement results on tank surface are available in the study [11]. Continued research after a year showed that Figure 4: a) segment of created FEM mesh in COMSOL software; b) resulting instantaneous values of magnetic induction in magnetic the values of vibration velocity exceed the given limit of 20 core mm/s 2.5 times. However, the values of vibration displacement and acceleration did not exceed limits that indicate necessity for in depth analysis. tions of anisotropy shifted from the corners of magnetic ∘ This magnetostriction model uses a method proposed core towards the rods and had 90 cut angle between rod by author in [12] for visualization and approximation of vi- and yoke domains (see Figure 3). bration results for areas of transformer tank surface where Therefore, for this anisotropy type of magnetic core, vibration sensors were not installed (see Figure 5). If this the magnetic field is more concentrated near the inner cor- visualisation displays vibration amplitudes that exceed ners where rods and the yoke connect and there is a wind- the given limits, the model begins the simulation since ing around the rod. Figure 4 shows this result, where both otherwise there is no necessity to calculate possible me- the a) FEM mesh and b) instantaneous values of magnetic chanical faults. induction are visualised. Such approximation allows determining the possible Increased instantaneous values of magnetic induction vibration epicentre regions and their intensity. However, are visualised in red tones (see Figure 4 b)). These posi- it is not possible to distinguish between vibrations caused tions are the closest segments of the magnetic core to the by the magnetic core and vibrations caused by transformer windings due to the geometry of the magnetic core. Fur- windings since the output of the visualisation is the re- thermore, the rapidly changing direction of the anisotropy sult of a surface not a three-dimensional model. Therefore, of magnetic permeability contributes to this result since there is a necessity for further diagnostics of the magnetic the magnetic field has least resistance in the region. core, which the magnetostriction model carries out. When taken in consideration that the program cal- The first subsection of the magnetostriction model for culates this difference by using absolute values, the total case study has the following results. Overall, from the cal- magnetic field experiences these differences as a change culations, magnetic core has 12779 positions, primary and in placement of the highest magnetic induction values not secondary windings have 4167 positions and transformer an overall increase or decrease. Therefore, the conclusion oil has 14181 positions, where the instantaneous values of is that isotropic magnetic core is suitable for this magne- magnetic induction were calculated using COMSOL soft- tostriction model. ware. Figure 6 shows a cross-section of instantaneous values of magnetic induction from these results. Modelling of magnetostriction of transformer magnetic core Ë 807

sibility of other mechanical faults such as insufficient mechanical bracing of some parts of magnetic core. The authors plan to implement this magnetostriction model as a separate section of a more extensive diagnostics methodology of power transformers with the modelling of the electrodynamic force influence on the transformer windings.

References

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