# Hysteresis Loops and Simulation

The iron core, laminated by grain-oriented silicon steel (30Q140), is used to carry out experiments according to the electric schematic diagram in Figure 5.42. The laminated core is entwined by two coils (both 312 turns). The exciting coil is fed by alternating voltage (50 Hz). The power analyzer is used to measure the magnetizing current *i* in the exciting coil and the no-load induced voltage *U*_{ac} in the search coil. The measured data are manipulated by Equations (5-64) and (5-65) to obtain hysteresis loops under sinusoidal magnetization:

where *ф* is the total flux in the laminated core, N_{co}ii is the number of turns of the coil, *S* is the cross-sectional area of the core, and *L* is the mean length of the magnetic circuit.

Figure 5.42 Laminated core model and electric schematic diagram

## A. Hysteresis Loops Under Sinusoidal Excitation

The measured hysteresis loops of the laminated core under sinusoidal magnetization are shown in Figure 5.43(a).

According to Equations (5-62), (5-64) and (5-65), the hysteresis model based on *B *and *H* can be established by:

where B_{acm} is the magnitude of alternating flux density, and the consuming function H_{2 }can be approximated simply by H_{ob}^cos(mt), which is similar to its counterpart in

Figure 5.43 Simulated and measured hysteresis loop under sinusoidal magnetization. (a) Symmetrical hysteresis loops. (b) Simulated and measured results

Equation (5-63). The consuming coefficient *H _{ob}* can be obtained from the measured data in Figure 5.43(a).

Consequently, the presented model in Equation (5-66) can finally be used to simulate the hysteresis loops under sinusoidal magnetization. The simulation and measurement are compared in Figure 5.43(b).