# Core Losses

The core losses are a bulk term used to include the losses due to the different effects happening inside a ferromagnetic core when an alternating magnetic field runs through it. In the literature these effects are usually listed as three: hysteresis losses, eddy current losses, and excess eddy current losses.

When a magnetic field (H field) is applied to a ferromagnetic material, some of its grains change the orientation and align themselves to the applied field, creating a magnetic flux inside the material. If the magnetic field strength is increased, more grains will align with the direction of the field, incrementing the magnetic flux. This conversion ratio is called the material permeability, and it is not constant: as the magnetic field increases more and more, less and less grains are left to align, and the conversion gain, the permeability, decreases; until a point of saturation is reached in which a non-negligible increment of magnetic field strength produces a negligible increment in the magnetic flux.

If now, after applying a given magnetic field strength, we reverse the direction of the field, some of the already aligned grains will realign with the new direction, but less quantity than before for the same increment of field: some of the grains that were aligned for a given increasing value of H field, will remain unchanged for the same decreasing value of H field. If the H field is now decreased constantly, the ratio of alignment of grains, the permeability, will be similar to the previous iteration, but the net number of turns grains will be lesser than in the previous iteration for the same absolute H field value.

This process will repeat iteratively, and in each loop the number grains that were aligned as we got further from zero magnetic flux will be greater than the number align on the way back when the magnetic flux approaches zero; producing a hysteresis effect and drawing a closed loop, if we were to draw a graph with the magnetic field strength on one axis and the magnetic flux on the other axis.

This extra energy needed to align the extra grains on the way back to zero is lost in material resistance and dissipated as heat. The total amount of energy can be obtained by calculating the area surrounded by the hysteresis loop and is fundamentally independent of the frequency of the field switching; although for some materials the permeability might be influenced by this switching frequency.

Finally, the losses due to hysteresis effect can be obtained by integrating the product of the energy and the frequency over the whole volume of the magnetic material subjected to the magnetic field.

A side effect of the magnetic field circulating through the magnetic material is that, due to the fact that the magnetic materials do not have an infinite resistivity, electrical eddy currents will be induced along the core volume. The boundaries between the grains that realize the ferromagnetic material have a capacitance effect, so at low switching frequencies these induced eddy currents will circulate only inside the grains, which restricts the losses produced by them (eddy current losses are proportional to the area in which they circulate). These losses inside the grains are called excess eddy current losses, and are heavily dependent on the grain size of the ferromagnetic material, its resistivity, and the switching frequency.

As we increase the switching frequency of the magnetic field, the frequency of the induced eddy currents also increases, and the capacitance effects of the grain boundaries start preventing their circulation. Longer eddy currents start appearing through the whole dimension of the magnetic core, ignoring the grains, and generating increasing resistance losses, and therefore heat. These losses are called bulk eddy current losses, or just eddy current losses, and depend heavily on the cross section of the magnetic core, the frequency, and the resistivity of the material. The problem with the latter is that, for ferromagnetic cores, the resistivity is not a fixed value depending only on the temperature (as happens for diamagnetic materials, e.g., copper) but its resistivity depends also on the frequency and magnetic flux in the material, making it really difficult to properly estimate.

The total sum of these losses is what is generally called core losses, though as has been explained it includes really different effects. In order to make an estimation of these total losses, Charles Proteus Steinmetz, in the 19th century, proposed an analytical equation that consists of an exponential curve fit to empirical data measured for each material, resulting in a series of power coefficients that scale the effects of the magnetic flux density, frequency and temperature in total core losses, abstracting them from the physical effects and just using measured data.

The biggest problem with Steinmetz approach is that these measurements and curve fits are usually done in small cores, where the eddy currents are negligible. But as the core sizes grow, the eddy currents losses start gaining a weight that Steinmetz’s model cannot predict.

Steinmetz developed his equation for the then only existing sinusoidal magnetic field, but as electronics developed, the magnetizing currents, and therefore the magnetic fields and fluxes, became triangular in nature, with varying duty cycles.

To account for the effect of these triangular waveforms, many models derived from Steinmetz were proposed, being the most extended the Improved Generalized Steinmetz Equation (iGSE) [1]. This method tries to break down the magnetic flux waveform into small chunks, and then scaling with the switching frequency, which highly improves the accuracy for non-sinusoidal waveforms.

The current analytical model implemented in our platform is the iGSE with a very fine resolution, although other models are being implemented that take into account the losses of both eddy currents [2].

Additionally, these models are used to generate a dataset, that, by being mixed and trained with the measured data taken in our laboratory by means of the TPT method [3], produces an AI model able to improve any analytical data. Refer to the leakage inductance section for more information.

[1] K. Venkatachalam, C. R. Sullivan, T. Abdallah and H. Tacca, "Accurate prediction of ferrite core loss with non-sinusoidal waveforms using only Steinmetz parameters," 2002 IEEE Workshop on Computers in Power Electronics, 2002. Proceedings., 2002, pp. 36-41, doi: 10.1109/CIPE.2002.1196712.).

[2] W. A. Roshen, "A Practical, Accurate and Very General Core Loss Model for Nonsinusoidal Waveforms," in IEEE Transactions on Power Electronics, vol. 22, no. 1, pp. 30-40, Jan. 2007, doi: 10.1109/TPEL.2006.886608.

[3] Triple Pulse Test (TPT) for Characterizing Power Loss in Magnetic Components in Analogous to Double Pulse Test (DPT) for Power Electronics Devices," IECON 2020 The 46th Annual Conference of the IEEE Industrial Electronics Society, 2020, pp. 4717-4724, doi: 10.1109/IECON43393.2020.9255039.