This paper reports on performances of high permeability grain oriented electrical steel when used in association with power electronic switching devices. Loss measurement results obtained from the Epstein test, using sinusoidal or various PWM voltages in medium frequency range, show that for both studied thicknesses (HGO 0.23mm and HGO 0.18mm), comparing performances at a fixed induction level between the various situations may not be the most convenient method. The effect of magnetic domain refinement has been investigated. After having shown the interest of lowering the thickness, an alternative way of looking at losses is proposed that may help to design the magnetic core when it comes to the matter of reducing size in considering frequency and magnetization levels.

## I. INTRODUCTION

Recently developed thin high permeability grain oriented electrical steels are of interest for medium frequency applications. The standard 60404-8-8 defines the performance measured under classical sinusoidal waveforms. Nowadays when power electronic is involved, rectangular voltages are applied to the windings placed around the cores instead of classical sinusoidal voltages. As a GOES (Grain Oriented Electrical Steel) producer thyssenkrupp Electrical Steel is interested in the changes of material behavior than can be induced when using such waveforms. Influence of the lamination thickness or of the magnetic domain refinement process appear also of interest when considering those power electronic voltages. Therefore a series of investigations was performed, the results of which are reported in this paper. Measurements were done by applying respectively sinusoidal voltages up to 4 kHz and various PWM like waveforms (two level or three level) in the same range of fundamental frequencies with high order rank harmonic of the carrier triangle signal. High permeability GO grades of nominal thickness 0.23mm and 0.18mm, magnetic domain refined and non-magnetic domain refined have been considered. The obtained results have been used to compare sinus effect and PWM effect. They highlight the magnitude of the differences that can be expected. Efficiency of the various grades are commented. The results show that thin 0,18mm GOES is suitable for new power electronic transformers associated to converters using wide band gap components. These results also raise the question about the parameters to be taken into account when comparing various waveforms effects and therefore which ones have to be considered when sizing a magnetic core.

## II. EXPERIMENTAL

The reported analysis is based on measurement performed on thyssenkrupp Electrical Steel high permeability GO grades powercore^{®} H18 and powercore^{®} H085-23L.^{1} Both are magnetic domain refined by laser scribing. The measurement was performed with a Brockhaus MPG200D setup at L2EP laboratory (Lille 1 University) on Epstein test samples for various frequencies and wave shapes. Due to investigation into the medium frequency range, an Epstein frame according to the IEC 60404-10 standard has been used although SST frame is more convenient to assess laser magnetic domain refined grades. The number of Epstein strips was adjusted to the frequency range in order to keep as much as possible a good control of the secondary waveform and avoid amplifier saturation effects. The desired voltage wave shape was monitored at the secondary winding of the Epstein frame thanks to an analogue feedback.

In order to assess the effect of magnetic domain refinement on the loss performance variation with frequency, annealed and non-annealed Epstein samples of the same grade were compared. The non-annealed samples were shear cut out of band width into Epstein samples. For this purpose and to minimize induced stress and burrs, a shear equipped with a set of two new blades was used. One set each of respectively HGO18L and HGO23L Epstein sample was annealed to restore a non-refined domain structure. (denoted HGO18 & HGO23 respectively).

Before comparing the effect of various complex waveforms among the 4 generated sample conditions, the behavior under sinusoidal secondary voltage at 50 Hz was checked for eventual anomalies induced by shear cutting. Apart from the sinusoidal case for establishing a known reference at various frequencies up to 4 kHz, Epstein samples have been submitted to sine-triangle made PWM voltages of two families: two level and three level as summarized on Figure 1. PWM was generated by comparison between sine and triangle signals. Frequency of the carrier signal and its relative amplitude to the sinusoidal wave shape were adjustable. The chosen ratio for the amplitudes of the respective triangle and sinusoidal signal was two. The resulting signal was then amplified to the desired voltage with the amplifier of the MPG200D complying with high slew rates. Measurements were made for 1000 samples per period. Fundamental frequencies where imposed up to 4kHz and the triangle shaped carrier signal (CS) frequency was set to correspond to a harmonic rank up to 400. Those CS were corresponding either to an even or odd numbers of a fraction of the fundamental frequency. The trial matrix is represented in Table I. As can be seen, all conditions offered by the table were not experienced partly due to limitations of the bench, partly for simplification.

On overall 140 series of measurements were performed. It had the target to collect a wide spectrum of parameters in order to identify influences of voltage waveforms, frequencies and grade. Each series corresponds to a range of induction levels differing with the condition of waveform and frequencies. All the measurements did not give satisfactory results. Many of them had to be rejected in order to perform a clean comparison between relevant measurement conditions. The rejection was made on the basis of the quality of the secondary wave shape or on the existence non negligible of DC levels.

The PWM results hereafter reported stand for waveforms of 1 kHz, 2 kHz and 4 kHz fundamental frequencies. Those values correspond to the ones used in inverters or that can be used in power electronic transformers with existing off-the-shelf components. Here they are considered as representative for establishing a relevant comparison between the measured performances of the studied HGO grades.

## III. PERFORMANCES UNDER SINUSOIDAL MAGNETIC POLARIZATION

These measurements were performed in order to verify that the measuring bench and samples lead to consistent results for known conditions according to thickness and laser effect. 50 Hz measurement results obtained on the 4 series of Epstein samples are reported on Figure 2. For each grade, the magnetic domain refined material is clearly better than the corresponding annealed one. This means that the chosen samples are representative of the hierarchy between a magnetic domain refined and a non-magnetic domain refined grade of the same thickness. The hierarchy between HGO18 and HGO23 is respected as well.

For 4000 Hz it can be seen on Figure 3 that HGO23 and HGO18 still differentiate from each other on the full induction range. The graph shows also that there is no longer any differentiation due to magnetic domain refinement. This effect of the laser magnetic domain refinement is decreasing with increasing frequency. The beneficial effect of thickness on specific losses passing from HGO23 to HGO18 is clearly shown. This is directly induced by the decrease of eddy currents contribution which becomes more significant than the effect of domain spacing on the losses.

## IV. PERFORMANCES UNDER PWM VOLTAGES

### A. Variation of losses with peak magnetic polarization

The reported trends are related to 1kHz and 2 kHz fundamental frequencies. To report on a relevant comparison the peak magnetic polarization levels at which the losses have been measured are limited to 0,8T. The carrier signal frequency of the PWM voltage has been set in order to correspond to the 10^{th} harmonic rank. The graphs showing the trends for each of the fundamental frequencies can be seen on Figure 4–5. Much information are already given by these trends.

At 1 kHz and 2kHz and 0.8T of the sinusoidal case, the losses are respectively around 20 W/kg and 60 W/kg; the loss levels generated by the PWM signals are significantly higher at the same induction value. The two level case (red) leads systematically to much higher losses than the three level case (blue). This trend is even more pronounced in the case of a 2kHz fundamental frequency compared to 1 kHz one.

Here the stress relief annealing thermal cycle gives an advantage to the loss compared to the non-annealed magnetic domain refined case. This means that the displacement of magnetic domains originally facilitated by the laser scribing (decrease of excess loss component according the classical breakdown of losses) generates less contribution to loss compared to eddy current losses. For such medium fundamental frequency levels, the field as well as the magnetization are not homogeneously distributed across the thickness of the lamination. Due to eddy current effect, the outer surface of the lamination is more magnetized that the inner part. The steady wall movement of a wall crossing the strip thickness that can be described as the one phenomenon of magnetization taking place at 50 Hz is no longer a valid representation at such frequencies. The wall movements may take place in quite a complex structure in relation to the field distribution. The mechanism involved in the decrease of losses has to be further investigated in detail.

The conclusion of these results is that for a magnetic circuit fed by converters using PWM waveforms at medium frequencies, the high permeability GOES of thickness 0.18mm which underwent a stress relief annealing thermal cycle is the preferable solution for low losses among the presented results. It is better to involve a three level voltage feeding of the circuit (known also as full bridge switching) compared to a two level voltage feeding (known also as half bridge feeding).^{2} The loss levels obtained with PWM are nevertheless much higher than what is provided with the use of a sinusoidal waveform for the same peak magnetic polarization value. This is easily understood by looking at the hysteresis cycles generated by such systems. It is now well established that the sub cycles generated inside the principal one, contributes to the loss increase as shown on Figure 6

Some convertor topologies like Dual Active Bridge have been reported^{3} to be efficient in lowering the losses compared to sinusoidal voltage at the same peak magnetic polarization value. This was measured for a core built with a powercore^{®} H18 used inside a solid state transformer for the purpose of DC to DC voltage conversion. The PWM waveforms, whose effect is reported here would not then provide the same advantage compared to a 3 level dual active bridge voltage.

### B. Alternative way of considering losses for downsizing the magnetic core

Let’s consider a converter dedicated for example at DC to DC voltage conversion which is operated under fixed voltage conditions V1 and V2 as described^{4} on figure 7. This converter uses a magnetic core for galvanic insulation between converter input and output. What matters in comparing the performance of the system included its core is the power that can be transmitted for a certain rated voltage. This voltage has to be considered first. In terms of shrinking the core size, the one immediate way to do it is to increase the frequency. Therefore this parameter is to be included in the analysis as well. Referring to the previous section, peak magnetic polarization does not bear frequency information; it is only related to the voltage in a simple way in the sinusoidal case. It may be that peak magnetic polarization is not the criterion on which a relevant comparison should be led in order to optimize size and losses. Therefore an alternative way of comparing between them the various experimental conditions that are more related to voltage, frequency and size of the core has been investigated. This is illustrated in the following figures where the losses are plotted versus the applied voltage per unit area of the cross section to be magnetized.

If core size is to be reduced by use of a medium frequency voltage system, the core has to cope with the same input and output voltages whatever is the associated power electronic. To glean information about the size that can be reached by applying one or another switching strategy, it then comes to light that the efficient voltage (Urms) per square meter of cross section of the core (A) is a suitable parameter. This transformation we applied to the former analyzed data and the results are reported on Figure 8 – 9. The comparison was made also in the sinusoidal cases as illustrated on Figure 10 – 11.

This way of comparing losses on the basis of Urms/A variation does not change the hierarchy between the effect of magnetic domain refinement, thickness and stress relief annealing thermal cycle. HGO18 annealed samples have still the best performances in all cases. What changes is that the PWM signal shows an advantage in terms of losses compared to the sinusoidal case. For the same ratio Urms/A, the three level voltage shows less deviation of the losses compared to two level case. Contrary to the Jpeak analysis, the increase in frequency does not influence specific losses so much. This analysis would show that PWM is not detrimental for core losses. Again the HGO18 is the best grade to reduce losses level.

A glance at 4kHz performances with a carrier frequency of 5 (limit of trial matrix) illustrated on figure 12 shows no strong improvement or are even worse compared to the previous reported trend. This means that there would be a set of optimum frequency values (fundamental and carrier) above which improvement would no longer be possible.

## V. CONCLUSION

The trial matrix used for the reported analysis provides rich information which would deserve to be investigated in more depth. This would help at having more precise indications about some trends for designers; for example, loss variation with carrier frequencies and fundamental frequencies. This work is expected to be performed at a later date. Firstly, all these results enabled to show that the classical qualification of a material using the traditional analysis of losses vs peak magnetic polarization Jpeak is not always the relevant one. It is particularly the case when comparison is made involving non sinusoidal voltages in the medium frequency range with the aim of optimizing the magnetic core size. The reported results show that an analysis using the Urms per unit cross section (U/A) may help to identify the best optimum situation. Using this approach indicates that PWM voltages may lower losses compared to sinusoidal voltages for the same values of U/A. Again designers would take benefit in comparing magnetic performances like magnetizing current or losses plotted function of the ratio (RMS voltage per unit core cross section) to choose the best solution for the PWM fed converters.

The other part of the study was dedicated to determine the influence of the thickness of high permeability GOES grades and also the influence of the magnetic domain refinement for medium frequency range. The results show that the lowest thickness grade bearing no laser scribing effect, PowerCore^{®} H18, is the best candidate for obtaining lower losses. Magnetic domain refinement which is efficient at 50Hz appears no longer of use in improving the losses for the medium frequency range.