# Review of Magnetic Properties and Texture Evolution in Non-Oriented Electrical Steels
## 2 Magnetic Properties
### Magnetic Properties under AC Conditions  
As mentioned previously, core loss is one of the most important magnetic properties for application under AC conditions. Under AC conditions, some power is lost in the core of the device, transforming it to heat or noise. This energy loss is called core loss. It is commonly accepted that core loss can be separated into hysteresis loss (\(P_{h}\)), anomalous loss (\(P_{a}\)), and eddy current loss (\(P_{e}\)). \[P_{tot}=P_{a}+P_{e}+P_{h}, \tag{1}\]  
\(P_{h}\) is the energy loss that occurs during every cycle that the material undergoes an applied field change. In practice, hysteresis loss depends on the grain size, inclusions, precipitates, the presence of defects, the orientation, and the applied frequency. Figure 1: (**a**) Demands of core materials on an electric vehicle motor’s applications, reprinted/adapted with permission from [2]; and (**b**) Magnetic flux density B against the magnetizing force H (B-H) curve with some critical points. \(P_{e}\) represents the energy loss caused by the electrical current. This electrical current is induced by a change in the magnetic field. Eddy current depends on the chemical composition and geometry of the material. \(P_{e}\) is aided by increasing the material's resistivity which is controlled by higher contents of Si and Al and thinner steel laminations. As shown in Figure 2, the use of thin laminations leads to a decrease in the eddy current loss for applications in an electric motor. \(P_{a}\) is the energy loss present after the calculation of \(P_{e}\) and \(P_{h}\) (the eddy current and the hysteresis loss, respectively). Owing that it represents part of the energy loss that is not considered in the eddy current loss calculation in detail, the anomalous loss is also called the excess eddy current loss or excess loss [4]. The energy losses of \(P_{e}\), \(P_{a}\), and \(P_{h}\) may be expressed as follows [5]:  
\[P_{e}=\frac{\pi^{2}B_{max}^{2}t^{2}f^{2}}{6\rho D}, \tag{2}\]  
\[P_{a}=c_{1}\frac{\sqrt{d}}{\rho}t^{2}B_{max}^{2}f^{3/2} \tag{3}\]  
\[P_{h}=\frac{f}{D}\oint BdH \tag{4}\]  
where \(c_{1}\) is an experimentally determined constant, \(d\) is the material grain size, \(B_{max}\) is the peak magnetic induction, \(t\) is the lamination thickness, \(D\) is the material density, \(f\) is the working frequency, and \(\rho\) is the material resistivity. The Equation (3) about anomalous loss expression is not universally accepted. [PERSON] et al. [6] reported some different physical models on energy loss by expressing them in magnetic laminations under one- and two-dimensional fields. Other than that, there are also some works which compute energy losses based on the applications. [PERSON] [7] reported an algorithm to estimate the iron loss of power transformers from quantification of the contributions of the effect of joints, rotational and harmonic flux, stress, interlaminar flux, and core geometry. Taking into account the three energy losses that exert an influence on frequency, the \(P_{tot}\) total energy loss may be obtained as follows [5]:  
\[P_{tot}=k_{a}f^{3/2}+k_{e}f^{2}+k_{h}f, \tag{5}\]  
where \(k_{e}\), \(k_{a}\), and \(k_{h}\) are the parameters of the eddy current loss, the anomalous loss, and the hysteresis loss, respectively. As expressed in Equation (4), \(P_{e}\) and \(P_{a}\) are influenced most by the applied frequency. In practice, \(P_{e}\) has the largest contribution to \(P_{tot}\) when the applied frequency is higher than 400 Hz, just like the e-mobility [5]. Figure 2: **(a) Eddy current in the solid iron core. (b) Separating the iron core by thin laminations that are parallel to the field (to reduce the eddy currents, insulation layers were coated between laminations). In this figure, B is the magnetic field and I is the induced current. The direction of the arrow indicates the flow of the magnetic field. **  
There are new challenges presented by application under high frequency like e-mobility.