Iron cores often operate under harmonic condition

resulting in biased minor loops inside the major loop

which makes it difficult to accurately predict the hysteresis loop. In this paper

an improved residual loss formula is introduced to achieve accurate simulation of quasi-static losses. Based on this

a calculation method of static hysteresis loops is proposed

and the calculation results are used to establish the static inverse Preisach model. First

a dynamic model is established based on the static model and the improved formula

which improves the simulation accuracy under sinusoidal excitation and the relationship between residual loss parameters and frequency is derived. Next

under harmonic excitation

the improved model is used to predict the major hysteresis loop. Combined with the dynamic Preisach model

the formula of residual loss parameters of the minor loop considering the influence of the offset component is derived. Then

the minor loop period is divided into loop period and transition period

and the time-dependent residual loss parameter is introduced. The sequence of local extreme points of the magnetic flux density is used for parameter identification

and a dynamic hysteresis prediction method is proposed considering biased minor loop under harmonic excitation. Finally

the feasibility and accuracy of the proposed method is verified by comparing the predicted loops with the measured ones.