Analysis of the grain oriented electrical steel heterogeneities and their influence on the Epstein frame loss measurements

Abstract

The Epstein frame is a well-known standardized system used to characterize soft magnetic materials. The users of this device usually consider that all the strips of a same grade placed in the frame are homogeneous, and they do not take into account the potential impact of the heterogeneity of the sheets on the quality of the characteristics deduced from the measurements. The aim of this paper is to quantify the individual heterogeneity of Epstein samples of the same FeSi grade (BH curve, losses, permeability), and to analyze, by both experimental and numerical ways, if the layout of the sheets can impact the Epstein core losses.

Keywords

Grain oriented electrical steel epstein frame heterogeneity silicon iron iron losses

1. Introduction

The power electrical transformers market is currently changing with increasing environmental requirements coming from politics [1]. As a result, the steel manufacturers have to improve the knowledge of their products in order to reduce the transformer losses, especially the iron losses in the magnetic core. To do that, several devices for characterizing electrical steels exist: the Epstein frame [2–9] is the one studied in this paper.

Measures of magnetics properties can be obtained quickly with the Epstein frame as it is relatively easy to set up. However, the results may suffer from errors [10]. For instance, a method [11] based on cores with overlapped joints showed that the average length of the flux in a standardized Epstein frame can be very different from the standardized value of 0.94 m [12]. Then, grain size of grain oriented electrical steel (GOES) is huge, sometimes up to 50 mm, which is greater when compared to the Epstein samples width (30 mm). As a consequence, the shear cut technique, as other ones [13–17], can deteriorate the sample, and lead to a heterogeneity of internal magnetic properties even if samples have the same grade. In literature related to Epstein frame, the assumption is implicitly made that all samples have the same characteristics [10,11,18]. In fact, in the case of anisotropic sheets, the corners of the Epstein frame have a very high impact on the measured values due to the complex phenomena that take place inside [11]. The way the strips are handled can introduce stresses into the structure of the material, which can impact heterogeneity.

Taking into account all these aspects, the main goals of this academic paper are firstly to quantify the heterogeneity of magnetic properties for several materials, and secondly, to determine if this heterogeneity has an impact on the global characterization of the material.

2. Individual characterization of the Epstein samples

The first step before evaluating the impact of GOES samples heterogeneities on the Epstein frame results consists in characterizing the samples individually.

2.1. Device for the individual sample characterization

The individual characteristics of Epstein samples of 30 mm width were measured with a 60 mm width single sheet tester (SST) manufactured by Brockhaus, compliant with IEC standards related to this kind of devices [19]. The SST being wider than the measured strips, caution was taken in placing the strips. After demagnetization, the automated full sequence of measurement at 50 Hz is done, from 5 mT up to 1,9 T. The B(H) curve and iron losses (W/kg) are the minimum information required to evaluate the heterogeneity of all samples of one grade at a given frequency. Estimation of the source waveform accuracy is possible, with the DC offset and the waveform factor, which has to be kept close to 1.1107. The waveform factor k_f is computed from (1). $\begin{eqnarray}\displaystyle k_{f}=\frac{U_{\text{RMS}}}{U_{\text{ARV}}}=\frac{\frac{\hat{U} }{\sqrt{2}}}{\frac{2}{{\pi}}\hat{U} }. & & \displaystyle\end{eqnarray}$ (1) In (1), U_RMS, U_ARV and Û are respectively the root mean square, the average rectified value, and the crest value of the secondary voltage.

2.2. Results for 2 GOES grades

Two 0.27 mm thickness GOES FeSi materials provided by thyssenkrupp Electrical Steel (tkES) were tested: 28 strips of M95-27P and M110-M27 GOES grades. The main differences between these materials are shown in Table 1.

Table 1
Materials used in the experiments

Grade Mean specific losses (W/kg) at 1.7 T/50 Hz Mean maximum permeability of all sheets Flux density (T) for H = 800 A/m

M95-27P 0.941 40788 1.902

M110-27P 1.046 33532 1.870

Grade	Mean specific losses (W/kg) at 1.7 T/50 Hz	Mean maximum permeability of all sheets	Flux density (T) for H = 800 A/m
M95-27P	0.941	40788	1.902
M110-27P	1.046	33532	1.870

Differences measured between all samples of the same grade are shown in Fig. 1(a) for M95-27P grade, and in Fig. 1(b) for M110-27P grade. On the two figures, the average value is taken as the reference and the sheets are classified by their permeability, from the lowest to the highest.

Fig. 1.

Deviation of losses (at 1.0 and 1.7 T) and maximum permeability, compared to the mean value of all 28 samples, for M95-27P (a) and M110-27P (b) grades.

Several conclusions can be made from these results:

–

The differences measured between samples of both grades, for both losses or permeabilities, are quite important, and sometimes exceed 10%;

–

The samples with highest permeabilities are not always the ones with lowest losses, and vice versa. This is the case for the grade M95-27: the strip n°20 has the highest permeability, but the strip n°27 has the lowest losses;

–

Analyzing the losses also shows that samples with the highest/lowest losses at 1 T do not have the same rank at 1.7 T. Examples are given by samples 9 and 14 for grade M110-27P.

In conclusion, these differences between the characteristics of different strips of the same material may influence the material characterization, depending on random parameters that cannot be ignored.

3. Devices to evaluate the impact of samples heterogeneity

Once all the Epstein strips have been characterized separately, the following investigations are made to quantify experimentally and to analyze the impact of two parameters on the characterizations. The first parameter concerns the measurement protocol itself, i.e. the method of positioning vertically the samples in the coiled sheath. The second parameter concerns different possible distributions of the samples in the legs depending on their characteristics.

3.1. Epstein frame and measures

A normalized 250 mm × 250 mm Epstein frame is used. The primary and secondary windings are made of 700 turns. The core is magnetized through a NF4505 power amplifier. The sinusoidal voltage setpoint is given by an AWG2005 function generator. The experimental apparatus are shown in Fig. 2.

Fig. 2.

Scheme of the Epstein frame and all the related apparatus.

Measurements are made with a Yokogawa WT330 wattmeter. The measurement method is compliant with the recommendations of the NF EN 10252 and IEC 60404-2 [20] standards. Figure 2 shows a view of the experimental device. Also, even if the experiment conditions are the same (voltage applied for instance), some reproducibility errors, rarely higher than 1.5%, may appear after each disassembly and assembly of the core.

3.2. Influence of the sample position in the sheath

The goal of the first experimentation is to analyze if the samples, as their properties are not homogenous, are magnetized differently depending on the vertical position of the core. The layout of the samples is the same, but measurements are done for three heights in the core: low, middle and high position, as shown in Fig. 3. To change the position of the core, cork layers are added. This study is done only for M95-27P grade.

Fig. 3.

Schematic description of the three positions of the core.

3.3. Samples distribution

Then, several configurations were investigated depending on their loss values and their position in the frame.

Firstly, the core is kept in down position. In each limb, the samples with the lowest losses are placed in the middle of the limb, and are increasingly surrounded by the highest losses sheets;

Secondly, all the 28 samples are classified by their losses levels and grouped in four groups of samples of equivalent loss level. The samples of each group are dedicated to each limb of the Epstein frame.

Thirdly, it could be interesting to study the impact of the heterogeneity on a reduced core of 16 sheets (4 per leg), by selecting only those with the highest or the lowest losses.

4. Finite element model

A finite element model, inspired by [21] and [22], with all the 4 legs of the Epstein frame modeled, is proposed in Fig. 4. This model is performed with Altair Flux 2D software. The considered frame is unfolded to avoid a time consuming 3D model. That allows to model the overlapped joint, but the real path of the flux in the transverse direction is not taken into account. An air gap condition is applied to all lines representing the insulation in the corner areas. The power is given by a voltage source linked to the FE model by circuit coupling. The magnetic material is considered as non linear and isotropic. The model has 265240 nodes.

The Bertotti factors [23] are computed from the measured losses (W/kg) on the 500 × 500 mm SST, function of the peak flux density. Periodic boundary conditions are applied to the left and right sides of the model.

Fig. 4.

FE model of the unfolded Epstein frame (not at scale).

5. Results and discussion

5.1. Influence of the sample position in the sheath

The measurements of the losses (W/kg) depending on the core position are given for three global flux densities (1.0, 1.4 and 1.7 T) in Table 2. The differences of losses measured between positions are lower than 1%, which is in the same range than the errors due to reproducibility. Therefore, measurements performed with Epstein frame don not give posssibilities to conclude on a significant impact of the core position on the measured losses.

Table 2
Losses depending on the flux density and the core position

Flux density (T) Losses (W/kg) for each core position

Down Middle Top

1.0 0.264 0.264 0.266

1.4 0.510 0.506 0.503

1.7 0.787 0.787 0.783

Flux density (T)	Losses (W/kg) for each core position
1.0	0.264	0.264	0.266
1.4	0.510	0.506	0.503
1.7	0.787	0.787	0.783

5.2. Samples distribution in each leg in the frame

First, a loss measurement is done when the sheets are randomly placed in the core (case A). These values are compared with the following cases:

–
Case B: the sheets with lowest losses are placed in the middle of each leg, increasingly surrounded by sheets with highest losses;
–
Case C: the sheets with highest losses are placed in the middle of each leg, increasingly surrounded by sheets with lowest losses;
–
Case D: the 7 sheets with highest losses are placed in the same leg;
–
Case E: the 7 sheets with lowest permeabilities are placed in the same leg.

There are not clear differences of losses between the cases A, B and C, for both materials. This may be explained by the fact that each leg is made of both best and worst sheets of the considered grade. As a result, there is not a strong disequilibrium of the losses generated by each leg.

Table 3
Losses (W/kg) measured (“exp”) and computed with FE model (“simu”) in all cases A to E for M95-27P and M110-27P FeSi GO grades. B = 1.7 T

M95 (exp) M110 (exp) Differences with case A M95 (simu) Diff with case A

M95 M110

Case A 0.788 0.893 0.820

Case B 0.794 0.895 +0.76% +0.22% 0.818 −0.24%

Case C 0.794 0.895 +0.76% +0.22% 0.829 +1.10%

Case D 0.789 0.888 +0.13% −0.56% 0.816 −0.49%

Case E 0.772 0.877 −2.00% −1.78% 0.807 −1.58%

This disequilibrium may be observed in case E, where there are higher losses than in the preliminary case. The leg hosting all the sheets with lower permeabilities may saturate faster than the others, and create what can be called a “blockage” effect. Therefore, the three other legs will have a lower flux density within them, leading to lower losses generated.

The intent of the case D also was to create a “blockage” by putting all the sheets with highest losses in the same leg. But it has not so much losses differences compared to cases A, B and C. This could be explained by the fact that no real blockage is created in one leg, because the sheets with the highest losses are not always the ones with the lowest permeabilities.

For M95-27P grade, the simulations also shows a tendency of higher loss difference in case E, but not as evident as in the experimentation. Taking into account the simplified modelling, the results are acceptable as they give us the correct tendency, at least for the case E.

The numerical flux density distribution in the middle of each limb (along X axis) is shown in Fig. 5 for the case B, with all the best strips in the middle of each limb. The flux density distribution is coherent, as the higher flux densities are in the strips in the middle of each stack.

Fig. 5.
Magnetic flux density distribution in the middle of each limb in case B, from limb 1 (on the left) to limb 4 (right).

The flux density distribution of case E is given in Fig. 6. The limb n°1 hosts the 7 strips of lowest permeabilities, and the limb n°2 hosts the 7 following strips with the lowest permeabilities. As it can be seen in the distribution, the flux density is higher in these two limbs (n°1 and n°2), saturating faster than the other limbs. As the flux density is lower in limbs n°3 and n°4, the losses are lower, leading the whole core to generate lower global iron losses.

Fig. 6.
Magnetic flux density distribution in the middle of each limb in case E, from limb 1 (on the left) to limb 4 (right).

Finally, the specific volumic losses were invistigated in each of these two cases. For case B (Fig. 7) and case E (Fig. 8). The distributions are realistic, as in case B, the strips in the middle of each stack (along Y axis) hosts the strips with the lowest losses. In case E, the strips with the lowest permeabilities were placed in limb n°1, and the ones with the highest permeabilities in limb n°4. It can be seen that the 7 strips of the limb n°1 are generating the lowest losses.

Fig. 7.
Volumic power losses distribution in the middle of each limb in case B, from limb 1 (on the left) to limb 4 (right).

Fig. 8.
Volumic power losses distribution in the middle of each limb in case E, from limb 1 (on the left) to limb 4 (right).
5.3. Core reduced to 4 sheets per leg

	M95 (exp)	M110 (exp)	Differences with case A	M95 (simu)	Diff with case A
Case A	0.788	0.893			0.820
Case B	0.794	0.895	+0.76%	+0.22%	0.818	−0.24%
Case C	0.794	0.895	+0.76%	+0.22%	0.829	+1.10%
Case D	0.789	0.888	+0.13%	−0.56%	0.816	−0.49%
Case E	0.772	0.877	−2.00%	−1.78%	0.807	−1.58%

Two cores made of 16 sheets were built. They gather the 16 best or worst strips in terms of losses, randomly placed in the core. The experimental results are shown in Table 4, and the simulation results in Table 5 for M95-27P grade.

After analyzing of the percentages of difference between the two configurations of both grades, it can be concluded that the impact of the choice of the sheets is important for the grade characterization. If best or worst sheets of a specified grade are selected, the characterization of this grade can be modified. Results in Table 4 show quite important differences (13.2% or 8.6%) between the two experiments, for both grades. Simulations done for M95 grade confirm this tendency.

Table 4
Measured losses (W/kg) of reduced cores, grouped by losses levels

Grade 16 best sheets 16 worst sheets Differences worst VS best

M95-27P 0.787 0.854 +13.2%

M110-27P 0.873 0.987 +8.6%

Grade	16 best sheets	16 worst sheets	Differences worst VS best
M95-27P	0.787	0.854	+13.2%
M110-27P	0.873	0.987	+8.6%

Table 5

Simulation losses (W/kg) of reduced cores, sorted by losses levels

Grade	16 best sheets	16 worst sheets	Differences worst VS best
M95-27P	0.786	0.875	+11.32%

6. Conclusion

The heterogeneity of all the sheets of two FeSi grades were investigated, and differences can be quite important, both for losses or maximal permeabilities measured. The measured Epstein core losses are dependent of the sheets layout in the frame, especially if sheets with the lowest permeabilities are put together in the same leg. Also, the loss level is dependent of the sheets selected to perform experiments. Simulations gave quite accurate results compared to the experiments, even if the model has been simplified.

Footnotes

Acknowledgements

The authors are thankful to thyssenkrupp Electrical Steel for their financial and technical support in this project.

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Flux density (T)	Losses (W/kg) for each core position
	Down	Middle	Top
1.0	0.264	0.264	0.266
1.4	0.510	0.506	0.503
1.7	0.787	0.787	0.783

Analysis of the grain oriented electrical steel heterogeneities and their influence on the Epstein frame loss measurements

Abstract

Keywords

1. Introduction

2. Individual characterization of the Epstein samples

2.1. Device for the individual sample characterization

Table 1 Materials used in the experiments Grade Mean specific losses (W/kg) at 1.7 T/50 Hz Mean maximum permeability of all sheets Flux density (T) for H = 800 A/m M95-27P 0.941 40788 1.902 M110-27P 1.046 33532 1.870

3.1. Epstein frame and measures

4. Finite element model

5.1. Influence of the sample position in the sheath

Table 2 Losses depending on the flux density and the core position Flux density (T) Losses (W/kg) for each core position Down Middle Top 1.0 0.264 0.264 0.266 1.4 0.510 0.506 0.503 1.7 0.787 0.787 0.783

Table 4 Measured losses (W/kg) of reduced cores, grouped by losses levels Grade 16 best sheets 16 worst sheets Differences worst VS best M95-27P 0.787 0.854 +13.2% M110-27P 0.873 0.987 +8.6%

Footnotes

Acknowledgements

References

Table 1
Materials used in the experiments

Grade Mean specific losses (W/kg) at 1.7 T/50 Hz Mean maximum permeability of all sheets Flux density (T) for H = 800 A/m

M95-27P 0.941 40788 1.902

M110-27P 1.046 33532 1.870

Table 2
Losses depending on the flux density and the core position

Flux density (T) Losses (W/kg) for each core position

Down Middle Top

1.0 0.264 0.264 0.266

1.4 0.510 0.506 0.503

1.7 0.787 0.787 0.783

Table 4
Measured losses (W/kg) of reduced cores, grouped by losses levels

Grade 16 best sheets 16 worst sheets Differences worst VS best

M95-27P 0.787 0.854 +13.2%

M110-27P 0.873 0.987 +8.6%