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Modeling of Structural Deformation in Transformers Using EMWorks

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Problem Description 

In this application note, EMS is used to study both electromagnetic and structural behavior of a high-power transformer. Both AC Magnetic and structural solvers of EMS are used to compute the magnetic and structural results. The impact of the magnetic shunts utilized to protect the outer tank is investigated in this analysis.

CAD model of the studied transformer
Fig. 1. CAD Model of the Studied Transformer 

The electro-structural analysis performed using EMS coupled to the structural module provides valuable magnetic and structural..  For example, it provides  3D plots of magnetic field, current distribution, loss density, force density, mechanical displacement and stress results.  It also computes  lamped quantities such as  inductance, resistance, voltage, current, rigid body force , and losses including core loss, eddy loss, hysteresis loss, and winding loss.  

Electromagnetic Results 

The simulation is performed under short circuit conditions. AC Magnetic solver of EMS is used to generate the electromagnetic solution. Results of the magnetic field in the transformer core are shown in Figure 2. 

Magnetic field results, a) full model- fringe plot, b) cross section view – fringe plot, c) full model- streamline plot
Fig. 2. Magnetic Field Results, a) Full Model - Fringe Plot, b) Cross Section View – Fringe Plot, c) Full Model - Streamline Plot  

The eddy current results in the outer tank are illustrated in Figures 3a), 3b) and 3c). These results show the difference in the induced eddy currents in the tank- with and without- the magnetic shunts. It can be observed that these magnetic plates protect the tank by reducing the eddy currents and the electromagnetic forces. Figure 4 contains a plot of the eddy currents distribution in the magnetic shields.  

 Eddy currents results in the tank, a) without magnetic shunts, b) with magnetic shunts (hidden), c) streamline plot of the eddy currents
Fig. 3. Eddy Currents Results in the Tank, a) Without Magnetic Shunts, b) With Magnetic Shunts (Hidden), c) Streamline Plot of the Eddy Currents 
Eddy currents in the magnetic plates
Fig. 4. Eddy Currents in the Magnetic Plates 

Table 1 summarises the force results of the transformer under different conditions. It shows that the force in the tank is reduced when the magnetic shunts are added. However, the shunts do not have much impact on the force in the windings. 

  Force Results (N)
  Without Magnetic Shunts With Magnetic Shunts
Tank 21.32 8.12
Transformer Core 367 368
Magnetic shunts 0 28
Primary winding 1 1452 1432
Primary winding 2 1972 1993
Primary winding 3 2134 2116
Secondary winding 1 534 530
Secondary winding 2 54 54
Secondary winding 3 899 895

Table 1. Force Results in the Different Parts of the Transformer 

Structural Results  

In addition to the results above, the coupling to the linear static solver, which comes with EMS, generates the following structural results: structural displacement, mechanical stress, strain, reaction force, and safety factor. 

Figures 5a) and 5b) contain, respectively, plots of the mechanical displacement and stress in the transformer core. The maximum displacement is around 15nm in the outer limbs while the stress reaches a maximum value of 6e4 N/m2. These mechanical deformations are caused mainly by the magnetostriction  forces in the core.  

 mechanical displacement results- scale x1M, b) mechanical stress - scale x1M
Fig. 5. a) Mechanical Displacement Results - Scale x 1M, b) Mechanical Stress - Scale x 1M 

The circulating currents, especially in case of a short circuit, produce high Lorentz force in the transformer’ windings. These forces generate deformation in the windings. Figures 6a) and 6b) show, respectively, the mechanical displacement and strain in the transformer’ windings. The maximum displacement is around 33 micrometers.  It is interesting to note that the highest displacement is reached in the inner coils which belong to the low voltage side of the transformer.  

The outer coils have a displacement of 19 to 21 micrometers. However the forces generated on the outer coils are higher (Table1) than on the inner coils, but the displacement is larger in the inner coils. This can be explained by the difference in the size of the coils. The primary windings (outer windings) are bigger than the secondary coils which can give them more rigidity and strength. It can be seen also that the displacement in the primary and secondary windings has different directions. 

mechanical displacement in the coils - scale x800, b) strain in the coils- scale x800
Fig. 6. a) Mechanical Displacement in the Coils - Scale x 800, b) Strain in the Coils- Scale x 800  

Figure 7a) and 7b) illustrate the displacement results in the transformer tank, respectively, without and with magnetic shunts. It can be observed that the displacement in the tank is around 41 micrometers in the absence of the magnetic shunts. This displacement is estimated by 6 micrometers when the magnetic shunts are used. As mentioned above the magnetic shunts help to decrease the magnetic force in the outer tank, consequently the mechanical stress and deformation.  

Animation plot of the displacement results is shown in Figure 8. 

 Mechanical displacement in the tank, a) without magnetic shunts – scale x2000, b) with magnetic shunts – scale x5000
Fig. 7. Mechanical Displacement in the Tank, a) Without Magnetic Shunts – Scale x 2000, b) With Magnetic Shunts – Scale x 5000 
Animation of the mechanical displacement in the transformer tank
Fig. 8. Animation of the Mechanical Displacement in the Transformer Tank (Without Magnetic Shielding) – Scale x 2000 

The mechanical displacement in the magnetic shunts is plotted in Figure 9. The magnetic plates deformation is mainly in the range of 2 to 5.6 micrometers.   

Mechanical displacement in the magnetic shunts – scale x10000
Fig. 9. Mechanical Displacement in the Magnetic Shunts – Scale x 10000 

The mechanical stress results in the tank of the transformer are shown in Figure 10. These results confirm the impact of the magnetic shunts. They play an important role in shielding and preventing larger mechanical displacement in the outer tank. This can reduce the vibration and noise caused by the deformations.  

Mechanical stress in the tank, a) without magnetic shunts- scale x5000, b) with magnetic shunts  - scale x5000
Fig. 10. Mechanical Stress in the Tank, a) Without Magnetic Shunts- Scale x 5000, b) With Magnetic Shunts  - Scale x 5000 


In this application, EMS coupled to the structural solver was used to study the mechanical behavior of a high voltage transformer. Both magnetic and structural quantities were computed under different conditions. The effect of magnetic plates in protecting the transformer tank was investigated and found to be effective. 


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