Modeling of high-precision piecewise variable coefficient two-term iron loss model and iron loss calculation

Background Iron loss substantially influences the efficiency and performance of electrical machines, but conventional two-term models with fixed coefficients often fail to capture excess loss, skin effects, minor hysteresis loops, and harmonic contributions across wide frequency and flux-density ranges. Objective This study develops a high-accuracy piecewise variable-coefficient two-term iron-loss model to improve prediction accuracy and enable reliable frequency extrapolation under varying operating conditions. Methods Using iron-loss test data from silicon-steel sheets, the model augments the conventional two-term formulation by adding an extra term to represent excess loss and by treating hysteresis, eddy-current and correction coefficients as piecewise functions of flux density and frequency. An enhanced skin-effect coefficient that accounts for the nonlinear permeability of silicon steel is integrated into the eddy-current term. Coefficients are identified from measured data. During motor iron-loss calculations, minor hysteresis loops and harmonic content are considered. The model is applied to an external-rotor consequent-pole PMSM (ERCP-PMSM) at rated conditions. Results Validation against experimental measurements shows substantially improved agreement compared with conventional fixed-coefficient models: the proposed model maintains high prediction accuracy when frequency and flux density vary widely and provides more reliable extrapolation to higher frequencies and large flux densities. Conclusions The proposed piecewise variable-coefficient two-term model effectively overcomes limitations of traditional models, yielding accurate iron-loss predictions across broad operating conditions and supporting reliable application in electromagnetic design and optimization of electrical machines such as the ERCP-PMSM.