In this work, the Simplified Multiscale Model (SMSM) is incorporated into the Energy-Based (EB) vector hysteresis model to represent anhysteretic material behavior. This approach enables the inclusion of effects such as mechanical stress, magnetostriction, material anisotropy, and crystallographic texture. By integrating the anhysteretic model into the EB framework, it becomes possible to account for dissipative effects while utilizing detailed material information. To solve the EB model in conjunction with the SMSM, two approaches are pursued: a numerical optimization of a free energy functional and an explicit approximate variant, known as the Vector Play Model (VPM). Both methods are compared in terms of computational performance, and the differences in results are demonstrated through the simulation of the cross-section of an electric machine. Furthermore, the local as well as global behavior is investigated.

Incorporating the magnetic core material in a lumped-element transformer model generally results in a nonlinear network with hysteresis. This network can be solved subsequently in time domain, yielding the transient response of the transformer. To directly obtain the steady-state solution, the method of harmonic balance is superior to such a transient analysis since it is a frequency domain approach capable of handling nonlinearities. For this reason, harmonic balance is derived theoretically and further applied to a dedicated single-phase transformer network based on a mutual and leakage flux approach. The nonlinear network element is represented by an energy-based dry-friction-like hysteresis model depicting the core material of the transformer. Finally, the results of harmonic balance are compared to measurements and the algorithm's efficiency is discussed.