Article: Paper Introduction
Issue 3 For Those Planning to Start Analysis of Large Transformers
I will be introducing some papers for you in this issue. I have been working on analysis technology for large transformers since last year. Here, I will present materials that will serve as a reference for people who, like me, are just getting started with analysis of large transformers, focusing on electromagnetic field analysis using the finite element method (FEM). Of course, the materials chosen here represent my perspective only, and I hope you will be understanding toward any seeming biases that I may have been unable to avoid.
What Should I Read First?
Large transformers, like other electric machines, have been around for more than a generation, and a wide variety of papers and other materials have accordingly been produced. The general trends can be found by looking at these, but there is such a large number that it is very difficult to know which to read first. I personally am interested in history, so I have chosen to take a long view of large transformers within the history of technology. Technological history is not a good way of learning about technical issues in detail, but I think it is a good approach for getting a broad overview of large transformers in general.
Here, I would draw your attention to Reference . The author has been involved in the development of large transformers at a large manufacturer for many years, and he discusses technological changes in large transformers over time from the standpoints of reliability, higher capacity, higher voltage, environmental issues, and accessory parts. He includes his own experiences such as an insulation breakdown incident when conducting the first 500kV test transmission in this country, and I think he makes it easy to read even for people who are not familiar with the field. It should be useful for gaining and systematizing basic knowledge.
I think this is an interesting way of seeing how the history of technology has led to today's technology, almost like watching a documentary film with its glimpses of human drama as opposed to a textbook full of specialist terminology and technical descriptions that may sometimes leave you staring blank-faced.
Materials on Large Transformer Analysis Using FEA
The purpose of a transformer is to provide a transformation ratio for its application, and large transformers are those that handle tens of kV on their high-voltage side, tens of kA on their low-voltage side, and electrical power in the hundreds of MVA. Because of this, electromagnetic phenomena such as leakage flux, loss, magnetostriction and electrostriction vibration, and others, all caused by the high electric field and large current at this scale lead to technical problems.
I will introduce some materials dealing with these problems in sections for: loss analysis; electric field analysis; magnetostriction and electrostriction vibration analysis; and transient phenomena and electromagnetic force analysis.
1. Loss Analysis
One of the most promising uses for electromagnetic field FEM is the analysis of stray loss caused by leakage flux in large transformers (Fig. 1).
The large current produced on the low-voltage side generates leakage flux and stray loss inside the tank. The stray loss does not only have one fixed value, but can cause localized heat generation in the tank. Understanding and suppressing this stray loss is a design issue.
For stray loss analysis, it is necessary to include not only the core and coils, but also surrounding structural parts such as the tank and clamps, so the analysis model inevitably grows in scale. The issue becomes, at this point, what scale of analysis is possible?
In Reference , a 3-phase transformer is represented in a full model with around 11.5 million elements including the tank, shield, and clamps, and analyzed using a region partitioning method on the frequency region. Also, a thermal conduction analysis of heat caused by loss in the tank is carried out and compared with measured temperatures at the tank surface.
Stray loss analysis of a full transformer model focusing on local heat production can also be seen in Reference . By running an FEA analysis on a nominal 240 MVA 3-phase transformer and comparing the loss density in various parts tank, upper and lower clamps, cover plate (side plate) it is found that stray loss is largest in the cover plate near the core.
As solving speed increases thanks to the spread of 64-bit machines and parallel processing technology, it is now becoming possible to run analysis at around the 10-million-element level at our own companies or our customers' companies. In the future, it is likely that even larger-scale electromagnetic field FEM will become possible.
Local heat generation is not only caused by stray loss in parts around the core, but also by iron loss in the core itself. Step lap construction, which has been increasingly employed since the 1980s, contributes to a reduction in iron loss, but at the same time it has led to problems with local heat generation at joints. It is unfeasible to directly reproduce the core in step lap construction because the analysis model becomes too large, but, because it is localized heat generation, an argument can be made for partial models focusing on joints.
In Reference , attention is given to step lap construction and overlap construction, and the local loss distribution in each is compared. A homogenization method of equivalent values is proposed from magnetic properties measurement, this is applied to transformer models, and iron loss values for each construction are compared.
Fig. 1 Stray loss analysis of the tank and its interior
2. Electric Field Analysis
Adequate insulation measures are necessary on the high-voltage side because accidents in transformers are often caused by local insulation breakdown phenomena. It seems that evaluation using partial models focusing on transformer legs is common for evaluating insulation using electric field analysis, due to how localized and detailed the phenomena are (Fig. 2).
In Reference , attention is given to one leg of a 3-phase transformer, and the electric potential and electric field distribution are compared using steady state analysis by creating separate models for: the leg and coil adjacent to the tank wall; and the leg and coil adjacent to the next phase. Where electric field is expected to be high the area around the pressboard and the start of the coil winding modeling is done at the single-strand level (and changed to a bulk coil model partway through), and then differences in the electric field distribution in each region are compared. No clear difference is found between the two in this paper, but it is interesting to see what points designers pay attention to when using simulation to install insulation measures.
Reference  points out the importance of instantaneous electric field generation under drive and material nonlinear properties. An electric field analysis of the area near the pressboard, using the pulse waveform, is carried out by solving continuity and Poisson equations in the time domain. Nonlinear properties of physical values are accurately handled in analyses of the time domain. The conductivity's dependence on the electric field is compared from the electric load distribution and electric field distribution in the analysis results. It is found that materials with nonlinear properties have a higher instantaneous electric field peak value than linear materials.
Fig. 2 Electric field analysis of pressboard
3. Magnetostriction and Vibration Analysis
Power generation facilities and substations generally have to be established a certain distance away from living environments, but with new residential areas being developed, borders between the two are frequently coming closer. There has been a lot of talk about the effects on the human body of the magnetic field generated by transmission lines, etc., but at this time no causal relationship has been established. Rather, there has been a greater demand for reduction of the more directly felt problem of low-frequency noise produced by substations, and more work has been done on vibration reduction and sound dampening in the transformers inside them.
Vibration phenomena produced in transformers are thought to be mainly due to magnetostriction and electromagnetic force, but quantitative evaluation using measurement by analysis has not been carried out much yet. In particular, because the force caused by magnetostriction is not actually measured but rather estimated as an equivalent value from the amount of deformation, there is said to be room for disagreement about the applicability of that estimation. At present it is only at the stage of research including modeling, but it is now possible to find papers in which attempts are made to apply this to magnetostriction phenomena in transformers (Fig. 3).
In Reference , magnetostriction-magnetic flux density measurement results for the L and C directions of directional magnetic steel sheet are applied in a magnetic field analysis of a transformer core, and the amount of deformation and nodal force are calculated from the magnetic flux density distribution.
Reference  turns to the hysteresis properties (multivalent properties) of core magnetization properties and emphasizes differences by comparing them with the univalent properties of the past.
Fig. 3 Magnetic flux density and Mises stress in high harmonic components
4. Transient Phenomena and Electromagnetic Force Analysis
Excessive forces can be generated in the coils of large transformers from Lorentz force, and instantaneous geometry changes from this force are so large that they can be seen with the naked eye. Especially for transient phenomena, distortion harmonics other than the drive frequency can be generated due to nonlinearity in material properties. For this reason, it is expected that cases dealing with transient phenomena will be more common in future studies using analysis (Fig. 4).
In Reference , a formalization of magnetic field analysis in the time domain is applied to an analysis with an assumed short circuit in a transformer, and the Lorentz force distribution generated in the coils on the high-voltage side and the low-voltage side are evaluated along the direction of the leg. Further, the leakage flux from the shield and magnetic bypass plate and the reduction in stray loss due to this are confirmed.
Reference  handles transient phenomena using a formalization of magnetic field analysis in the time domain and tries verifying it with Team Problem 21C and applying it to a 380 MVA single-phase transformer test machine
Fig. 4 Coil Lorentz force distribution analysis
This article has introduced some materials that you may find useful in starting to use JMAG for analysis of large transformers. By also looking at the materials referenced by the papers introduced here, you can gain even more knowledge about large transformer analysis. I truly hope that the resources presented here will prove helpful for anyone planning to start electromagnetic field analysis of large transformers.
 Koji Fujiwara, Yoshifumi Takakura, Yasuhito Takahashi, et. al., "Iron Loss Analysis of the Wound-Core Transformer Considering Core Joint Configuration" The Institute of Electrical Engineers of Japan Research Materials SA, Static Machines Research Society 2011(63), 43-48, (2011)
 Gang Liu, Lin Li, Feng Ji, Wenping Li, Youliang Sun, Bo Li, and Jinzhong Li "Analysis of Transient Electric Field and Charge Density of Converter Transformer Under Polarity Reversal Voltage" IEEE Tran. on Magn., vol. 48, no. 2, 275-278 (2012)
 Wataru Kitagawa, Yoshiyuki Ishihara, et. al., "Analysis of Structural Deformation and Vibration of a Transformer Core by using Magnetic Property of Magnetostriction," The Transactions of the Institute of Electrical Engineers of Japan. B, A Publication of Power and Energy Society SA-06 76-9453-58 (2006)
 Tom Hilgert, Lieven Vandevelde, and Jan Melkebeek, "Comparison of Magnetostriction Models for Use in Calculations of Vibrations in Magnetic Cores" IEEE Tran. on Magn., vol. 44, no.6, 874-877 (2008)
 S. L. Ho, Y. Li, H. C. Wong, S. H. Wang, and R. Y. Tang "Numerical Simulation of Transient Force and Eddy Current Loss in a 720-MVA Power Transformer" IEEE Tran. on Magn., vol. 40, no.2, 687-690, (2004)