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This paper provides a series of new results in both steady-state accuracy and frequency-domain analyses for two Laguerre-based approximators to the Grünwald-Letnikov difference. In a comparative study, the Laguerre-based approximators are found superior to the classical Tustin- and Al-Alaoui-based approximators, which is illustrated in simulation examples.

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Accurate prediction of power loss distribution within an electrical device is highly desirable as it allows thermal behavior to be evaluated at the early design stage. Three-dimensional (3-D) and two-dimensional (2-D) finite element analysis (FEA) is applied to calculate dc and ac copper losses in the armature winding at high-frequency sinusoidal currents. The main goal of this paper is showing the end-winding effect on copper losses. Copper losses at high frequency are dominated by the skin and proximity effects. A time-varying current has a tendency to concentrate near the surfaces of conductors, and if the frequency is very high, the current is restricted to a very thin layer near the conductor surface. This phenomenon of nonuniform distribution of time-varying currents in conductors is known as the skin effect. The term proximity effect refers to the influence of alternating current in one conductor on the current distribution in another, nearby conductor. To evaluate the ac copper loss within the analyzed machine a simplified approach is adopted using one segment of stator core. To demonstrate an enhanced copper loss due to ac operation, the dc and ac resistances are calculated. The resistances ratio ac to dc is strongly dependent on frequency, temperature, shape of slot and size of slot opening.