## 4 Conventional Method for Studying Losses in Electrical Steels
The loss per cycle (\(P_{c}\)) at the magnetizing frequency (\(f\)) and peak flux density (\(B_{m}\)) is typically expressed as the total of static (DC) hysteresis loss (\(P_{h}\)), classical eddy current loss (\(P_{e}\)), and excess loss (\(P_{exc}\)), and it is written in forms such as  
\[Pc=P_{h}+Pe\big{(}\frac{d^{2}\pi^{2}B_{m}}{k\,\rho}\,f\big{)}+P\text{exc}(C_{ 3}\;B_{m}\,^{1.5}\,f^{0.5}) \tag{2}\]  
where \(d\) is the sheet thickness, \(\rho\) is the electrical resistivity, \(k\) is a magnetization waveform-dependent constant, and \(C_{3}\) is a material-dependent fitting parameter. \(P_{h}\) is determined through experimental observations as it is directly related to the region covered by the B-H loop when the magnetic field H is varied gradually. To obtain \(P_{h}\), Figure 6 displays the correlation relating the loss per cycle with frequency, allowing for extrapolation to zero. The process of slow and cyclic magnetization involves well-defined movements of domain walls [38]. Additionally, hysteresis loss is attributed to micro-eddy currents that manifest on a miniature level when the walls are released by chance from material hold down locations [39]. Figure 5: Total loss and its components for steels with different silicon content and processing conditions, keeping constant maximum induction (1.5 T), frequency (60 Hz), and thickness (0.5 mm), except for the grain-oriented material (0.35 mm) [29]. \(P_{e}\) is determined through classical Maxwell equations, assuming an extremely thin sheet with constant permeability and a time-varying, unidirectional alternating flux and magnetic field within its plane. Equation (2) typically employs a value of \(k=6\), which is valid only when the flux variation follows a sinusoidal pattern throughout the sheet. However, in practical situations, the assumptions underlying these calculations may be questionable due to factors such as varying permeability, non-sinusoidal flux density, and non-unidirectional local flux density. The origin of the phenomenon \(P_{exc}\) (excess loss) is still debated, and several attempts have been made to design and numerically adapt it to account for the discrepancy between the total measured loss and the combined losses of \(P_{h}\) and \(P_{e}\) at a particular given flow's density and frequency. Table 1 displays the normal distribution of loss factors in various types of electrical steels, where \(P_{h}\) is usually predominates at power frequency and drops with reducing thickness. On the other hand, the excess loss, illustrated in Figure 5, occurs due to variations in the magnetization processes caused by larger and more regularly distributed domains. Given that \(P_{exc}\) is frequently the minimum factor of NO steel, obtaining a reliable estimate of the total loss, as well as \(P_{h}\) and \(P_{e}\), is essential. Figure 7 outlines the factors influencing the loss factors. For instance, a large-grained thick steel with minimal residual \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Frequency (Hz)**} & **Material** & **Hysteresis Loss** & **Eddy Current** & **Excess Loss** \\  & **Specification** & **(\(P_{h}\))** & **Loss (\(P_{e}\))** & **(\(P_{exc}\))** \\ \hline \multirow{4}{*}{\(50\)} & Low silicon & 30–50 & 40–60 & 0–20 \\ \cline{2-5}  & High silicon & 55–75 & 20–30 & 10–20 \\ \cline{2-5}  & Thin high Si & 80–90 & 1–2 & 5–15 \\ \hline \multirow{4}{*}{\(100\)} & Low silicon & 20–30 & 50–70 & 10–20 \\ \cline{2-5}  & High silicon & 25–35 & 40–60 & 15–25 \\ \cline{2-5}  & Thin high Si & 80–90 & 1–2 & 5–15 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Valuable insights into the impact of silicon content on power loss components at frequencies of 50 Hz and 100 Hz. Figure 6: An illustration depicting the changes in traditional hysteresis, eddy current, and excess loss components with the magnetizing frequency in a typical commercial Grain-Oriented (GO) 3% silicon steel, measured at 1.32 T and 50 Hz [39]. stress and limited impurity-induced holding sites results in relatively minimal \(P_{h}\).