TEAM Workshop Problem No. 21
An Electrical Engineering Model for Loss Evaluation

Z. Cheng, S. Gao and D. Zhang
Baoding Transformer Works, Baoding 071056, China

Abstract

This paper proposes a 3-D engineering-oriented eddy current loss model taking into acount of nonlinearity but not of hysteresis of materials.


1. Some idea on the engineering modelling

In electrical engineering the evaluation of power losses in steel parts of electric machinery is difficult to solve exactly by either experiment or analysis [7]. Engineers, however, devote themselves to confirm the engineering usefulness of various practical analysis techniques used in CAD, on the other hand, many TEAMed (tested by TEAM) codes [2-6] provide yhe useful tools.

The aim of this modelling is to:
1) calculate the distribution of 3-D eddy current in steel, magnetic flux density at specified points, and eddy current losses in steel plate taking into account of non-linearity but not of hysteresis in various analysis techniques;
2) check the engineering usefulness of 3-D eddy current codes and various approach to find some engineering solving methods to be used in aided analysis of products.


2. Description of the model

The design of this model is based on some typical engineering power loss problem as show in Fig. 1. It consists of two air-core coils with same number of turns and the same dimensions in which the exciting currents flow in opposite directions as show in Fig. 1; a steel plate of 10 mm thick is placed vertically near the coils.

The key points of this model are that the eddy currents flow three dimensionally in steel plate, the penetration depth is so smaller that the meshes in steel region have to be enough fine, and the power losses are stored in both the coils and the steel plate, therefore, it is difficult to pick out the losses of the steel plate from total power losses, the appropriate measurement techniques to find the losses generated only in steel plate is needed.




3. Data for Eddy Current Modelling

  1. dimensions of exciting coils have been shown in Fig. 1;
  2. size of the steel plate is 10 x 360 x 520 (mm) without hole;
  3. number of turns of each coil is 300, coil consisting of 10 layers was winded continuously;
  4. amplitude of a.c. exciting current of 50 Hz is SQRT(2) x 12.0 or SQRT(2) x 20.0 ampere;
  5. conductivity of steel plate is 6.78E+6 S/M;
  6. B-H curve of steel plate shown in Fig. 2;
  7. specified points for calculation and measurement of flux density have been shown in Fig. 3 and listed in table 1;
  8. specified points of calculation of eddy current have been shown Fig. 4 and listed in table 2.


No. B(T) H(A/m)
1 0.00 0.0
2 0.10 554.8
3 0.20 705.6
4 0.30 760.0
5 0.40 878.6
6 0.50 1140.6
7 0.60 1396.9
8 0.70 1660.9
9 0.80 1914.8
10 0.90 2212.0
11 1.00 2570.0
12 1.10 3000.0
13 1.20 3525.5
14 1.30 4145.0
15 1.40 4946.5
16 1.50 6058.2
17 1.60 9190.2
18 1.70 11427.0
19 1.71 11849.0
20 1.72 12307.0
21 1.73 12807.0
22 1.74 13361.0
23 1.75 13987.5
24 1.76 14720.0
25 1.77 15630.5
26 1.78 16948.5
27 1.785 19480.0





















Authors thank Prof. T. Nakata of Okayama University in Japan [8] and Mr. Q. Hu of Baoding Transformer Works in China for nice comments to design the model.



Table 1 - Flux density |B| [T] in the air

Table 2 - Average eddy currents J [A/m2]


References

  1. O. C. Zienkiewicz: "The Finite Element Method, (3rd edition)", New York, NY: McGraw-Hill, 1977.
  2. T. Nakata, N. Takahashi, K. Fujiwara and Y. Okada: "Improvements of the T-Omega Method for 3-D Eddy Current Analysis", IEEE Trans. on Magnetics, Vol. Mag-24, (1988), pp. 94-97.
  3. C. W. Trowbridge: "Electromagnetic Computing: The Way Ahead", IEEE Trans. on Magnetics, Vol. Mag-24, (1988), pp. 8-13.
  4. O. Biro and K. Preis: "Finite Element Analysis of 3-D Eddy Currents" , IEEE Trans. on Magnetics, Vol. Mag-26, 2, (1990), pp.418-423.
  5. D. Rodger and J. F. Eastham: "A Formulation for Low Frequency Eddy Current Solutions", IEEE Trans. on Magnetics, Vol. Mag-19, (1983), pp. 2443-2446.
  6. A. Bossavit and J. C. Verite: "The Trifou Code: Solving the 3D Eddy Currents Problem by Using h as State Variable", IEEE Trans. on Magnetics, Vol. Mag-19, (1983), pp.2465-2470.
  7. Z. Cheng, S. Gao and J. Wang: "Engineering Solutions of Engineering Field Problems in Transformers", 3-D Electromagnetic Field Analysis, edited by T. Nakata), (1989), pp. 151-154.
  8. Private Communications, 1990.