Article: Paper Introduction
Issue 5 For Those Planning to Start Analysis of Large Transformers Part 2
I, Takayuki Nishio from JSOL, am in charge of introducing the papers covered in this issue. Issue 3 introduced a paper about large transformers for those planning to start transformer analysis. As with the previous issue, this issue will introduce a large transformer textbook and a paper on stray loss analysis.
Images in this text are all self-created and have not been taken from papers or edited.
Large Transformer Textbook
This issue, I would like to introduce literature equivalent to a textbook on large transformers. I have only just started learning in earnest about transformer analysis, so a textbook comprehensively covering transformers is a necessary item, but there are not many such specialized textbooks that can be easily obtained from a bookstore nowadays.
 Tsuboshima, Shigehiko and Hata, Masahiro. "Zukai Henatsuki: Kiso kara oyo made (Illustrated transformers; From the basics to practical use)," Tokyo Denki University Press
This book is probably about the only one specializing in transformers that can be easily obtained. (There are, however, many books about transformers and rotating machines.) This book provides an easily understandable introduction of the composition of transformers (materials, main body structure and accessories) through to their basic properties, wiring, operation, testing and basic designing. I recommend this book for anybody about to start studying transformers from now. Anybody with an understanding of high school physics and AC phasors can get into reading it immediately.
 Hagino, Shozo. "Henatsuki no unten to shiken (Operating and testing transformers) (d-book Series)," Denkishoin
(He has also published another three books on transformers, but they have all sold out.)
This is an A4-sized, paperback textbook of about 20 pages, and is published as one of a series, with this particular publication dealing with transformers. Each book in the series sells for around 1,000 yen, which makes it a bargain, and the books are easy to assemble, making some publications in the series indispensable, depending on the topic.
 Japan Institute of Plant Maintenance, "Henatsuki no mentenansu (Transformer maintenance), (Electrical Equipment Maintenance Series)," Japan Institute of Plant Maintenance
It's not uncommon for large transformers to be used for more than 30 years, but a basic knowledge of maintenance practices is needed to make them last that long. Maintenance is that important. There are many technicians involved in maintenance and they need to share knowledge widely. This book provides easily understandable explanations of transformer standards and structure for starters, continues with the relationship between operations and lifespan, diagnoses coil lifespan and talks about conservation and inspections. An ideal introductory book for learning about conservation maintenance of transformers.
Paper Introduction: Stray Loss
In the March issue, we provided a comprehensive introduction of large transformer analysis papers based on the Finite Element Method (FEA) in relation to electromagnetic phenomena. To sum up magnoelectronic analysis of large transformers succinctly would be to say that there are a variety of fields concerned, each of which has its own degree of maturity in terms of analysis technologies.
In this issue I would like to discuss papers on stray loss analysis, which is moving forward in the field of electromagnetic analysis of large transformers.
Searching and Obtaining Papers
Stray loss has been a field of analysis study for a long time and there are many publications about the topic, but apart from the publicly available publications I obtained through places like the Internet, please understand that the papers mentioned below came from a service the company subscribes to.
To extract papers, first go to the IEEExplore website, search for "Power Transformer Stray Loss" and of the 125 papers that come up, extract those from JSOL's IEEE Magnetics division. At JSOL we also have joint research materials on rotating machines and stationary devices compiled with IEEJ's B Division and you can also extract items from there.
 Saito, Tatsu and Ioi, Akira. "Magnetic Field and Eddy Current Losses in Transformer Tank," The Institute of Electrical Engineers of Japan Journal, Vol. 96, No. 9, pp. 465-471, 1976
This is possibly the oldest paper to have sparked quantitative discussion on stray loss in Japan. The author actually produced an experiment on 150MVA-class test equipment (a main body and tank only), measured the magnetic flux density generated near the tank and compared the measurements with the analysis results. The analysis modeled the tank wall and by giving the actual measurements the magnetic field's strength as a boundary condition sought the magnetic flux density, magnetic flux and eddy current. As it was impossible to directly measure stray loss within the tank, several measurements were made of temperature distribution on the tank walls and then a comparison made of the tank wall temperature distribution calculations.
This paper was written in 1976, which was before electromagnetic field FEA, so uses the finite difference method as its method of analysis.
Fig. 1 Stray Loss Analysis Example of a Tank and its Interior
 Chen Yongbin, Yang Junyou, Yu Hainian, and Tang Renyuan. "Study on Eddy Current Losses and Shielding Measures in Large Power Transformer," IEEE Transactions on Magnetics, Vol. 30, No.5, 3068-3071, 1994
Stray loss analysis is needed on complicated structures so analysis models tend to become large scale. Analysis under the theme of stray loss therefore often involves papers dealing with ingenious ways to analyze while keeping the analysis scale at a controllable level.
This paper looks at a 360MVA large transformer and handles stray analysis, including the shield. It uses the tetrahedral edge element, finite element method popular at that time, and looks for the stray loss in the tank/shield, clamp, cover plate and cover. The test compares the impact the presence of a shield has on magnetic flux density and stray loss. The transformer geometry and characteristics differ from those mentioned on the transformer in 4) above, but in a case without a shield, the results resemble those in 4 in terms of iron core directional height and magnetic flux density distribution and have characteristics common with a three-leg core-type transformer. The paper shows the method of installing shields on the tank and caused significant changes in the tank's loss. Results showed placing the shield perpendicularly cause a reduction of over 60% compared to when the shield was horizontal, coming to the conclusion that the ideal location for installing a shield was in a perpendicular state inside the tank wall.
Fig. 2 Differences in Placement of Tank Shields
(Left: Perpendicular, Right: Horizontal)
 Kainuma, Kengo; Take, Tatsuo; Ito, Masayoshi; Tanaka, Motoo; Tsuboi, Hajime. "Eddy Current Analysis in the Tank of Three Phase Transformer," The Institute of Electrical Engineers of Japan materials, SA-00-18, RM-00-83
One reason why analysis models handling stray loss grew so large is because they are being required to have a mesh that considers eddy currents in structures.
This paper takes a 200MVA-class transformer and attempts to reduce model scale using the surface invertance method on the tank. As the surface invertance method has the feature of using a set target area as an invertance boundary, rendering exterior modeling of the boundary surface unnecessary, which enables use of a smaller-scale model. (Surface skin must be sufficiently thin, however, because the material properties are linear.) In this paper, heat analysis using stray loss as a heat source was conducted, thermaview used to collect actual results on tank temperature distribution and a comparison of the two made with the conclusion being that the analysis results were appropriate.
 Kurt Preis, Oszkar Biro, Gerhard Buchgraber, and Igor Ticar. "Thermal-Electromagnetic Coupling in the Finite-Element Simulation of Power Transformers," IEEE Transactions on Magnetics, Vol. 42, No.4, 999-1002, 2006
This paper also contains elements of methods to be employed to keep calculation costs controlled during a magnetic field-thermal coupled analysis. This paper looks at stray loss in a tank caused by low-pressure side bushing forming a large current and a two-way coupled analysis observing temperature change, electric and thermal conductivity and temperature dependency, as well as localized overheating in the tank. A two-way coupling analysis is problematic in terms of calculation costs on the magnetic field analysis side, but to keep these costs under control, an assumption that electrical conductivity temperature dependency will be steady is used and magnetic field analysis calculated anew in conjunction with updating the electrical conductivity, which limits the conductor generated by the eddy current and uses this for analysis. Integration of elements such as magnetic flux density in areas not calculated anew are assigned results from initially calculated areas as boundary conditions around the conductor.
 Marisa Rizzo, and Janusz Turowski. "Influence of Flux Collectors on Stray Losses in Transformers" IEEE Transactions. on Magnetics., Vol. 36, No.4, 1915-1918, 2000
In an attempt to control the side of a model in a complicated 3D geometry, analysis is carried out here using a three phase magnetic flux with a sum of zero. Generally with transformers, as the phases in a three phase magnetic flux are different, the three-leg iron core needs to be modeled in its entirety, but this paper takes the three phases of magnetic density as having a sum of zero and models not only the thickness direction iron core but also the 1/2 of the horizontal direction.
Fig. 3 Example of a Transformer 1/4 Model
 Takahashi, Norio; Nakau, Takaaki; Miyagi, Daisuke; Nogawa, Shuichi; Kuwata, Minoru. "3-D Eddy Current Analysis of Bevel Edge Core Reactor using Modeling Technique of Laminated Steel," The Institute of Electrical Engineers of Japan Journal, B Division, Vol. 128, No. 1, pp. 277-282, 2008.
Stray loss is evaluated by a short circuit test in the transformer, but at these times leakage flux seeps from the winding pattern into the laminated core, generating loss there. This loss is handled as stray loss because it was generated from leakage flux.
This paper is a discussion on the validity of laminated structure modeling including the homogenized method and actual measurements and is applied to analyzing stray loss in a transformer core. The authors modeled using a density model of four magnetic steel sheets only (the remainder underwent the homogenized method) and compared the results with results of all of the lamination under a density model and checked the validity of the models. They also confirmed the validity of modeling by comparing measurement results produced by actual machinery with analysis results obtained from applying this method.
Fig. 4 Comparing Magnetic Flux Distribution between a Homogenization Model and Density Lamination Model
 Hayashida, Hirokazu. "Study of local heating on by IPB connection box and around metallic parts of large power transformer by 3-D Magnetic field analysis," JMAG Users Conference 2010
We have customers give presentations on stray loss analysis at our Users Conference. When Fuji Electric Co. gave a presentation, they spoke about IPB connection boxes and not transformers, but this touched on analysis of localized overheating distribution within the box cause by leakage flux generated from the bus bar on the low pressure side. They showed an examination of improvements to the connection box. They also showed temperature evaluation accompanying a thermal conductivity analysis.
 Ruja, Costin. "Using JMAG and ANSYS for coupled thermal solution of a high current bus bar exit in GSU transformers," JMAG Users Conference 2012 in Germany
Taken from a presentation given at a Users Conference held in Germany and referring to an example of handling localized overheating in a connection box. A coupling analysis realized after referring to loss results obtained from a JMAG electromagnetic analysis and used in thermal fluid analysis software.
 Yingying Yao, Chang Seop Koh, Guangzheng Ni, and Dexin Xie. "3-D Nonlinear Transient Eddy Current Calculation of Online Power Transformer Under DC Bias," IEEE Transactions on Magnetics, Vol. 48, No.2, 739-742, 2012
In the transformer operation stage, power transmission occurs while passing through several transformers on its way from the power generator to ordinary homes or factories. Power transmission between transformers can witness DC bias seen as ground current being superposed over the transformer circuit due to the influence of geomagnetism or solar magnetic storms. DC components have nothing to do with the phase and can cause a shift in a three-phase current, which triggers oversaturation in the core and is the cause of adverse impact on stable power supply. Handling simulations of this phenomenon requires understanding of the non-linear transient problem and the analysis load becomes a significant issue.
Discusses the effects of an eddy current generated in structures influenced by the impact of DC current circulating through two, three-phase transformers connected by a 500kV transmission cable. Three-phase transformers are bunked with a single-phase transformer to model a single-phase 1/8th geometry as a finite element model. This paper seeks to find the eddy current of structures by assigning to a finite element model a current value derived from a circuit equation including a voltage source with a DC bias. There is a need to take into account the core saturation properties of the induced voltage appearing in the circuit equation and the authors do this by incorporating the circuit equation in a magnetic flux/current table obtained from static and frequency response analyses. The results of the analysis showed that imposing a DC bias on voltage not only shifted the current, but also sent the amplitude value skyrocketing. Remarkably, the results also showed that stray loss from the structure increased to the equivalent of double the value.
Fig. 5 Transformer Transmission Line Model Under DC Bias
This issue gave an introduction of papers with a focus on transformer stray loss.
Stray loss analysis has a tendency for model scales to grow large due to complicated structures or eddy current problems, which meant they went largely untouched until about a decade ago. But progress in mesh technology and accelerated solvers and hardware have drastically changed the situation. JMAG is now actively starting to tackle these large-scale issues, starting with transformers. To close, I can say we expect to make new technological breakthroughs due to what we see through analysis.