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Toroidal inductors are present in many different industrial applications, thus, still receive researchers' attention. AC winding loss in these inductors have become a major issue in the design process, since switching frequency is being continuously increased in power electronic converters. Finite element analysis software or analytical models such as Dowell's are the main existing alternatives for their calculation. However, the first one employs too much time if different designs are to be evaluated and the second one lacks accuracy when applied to toroidal inductor windings. Looking for an alternative that overcomes these drawbacks, this paper proposes an accurate, easy-to-use analytical model, specifically formulated for calculating high-frequency winding loss in round-wire toroidal inductors.

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Toroidal inductors are present in many different industrial applications, thus, still receive researchers' attention. AC winding loss in these inductors have become a major issue in the design process, since switching frequency is being continuously increased in power electronic converters. Finite element analysis software or analytical models such as Dowell's are the main existing alternatives for their calculation. However, the first one employs too much time if different designs are to be evaluated and the second one lacks accuracy when applied to toroidal inductor windings. Looking for an alternative that overcomes these drawbacks, this paper proposes an accurate, easy-to-use analytical model, specifically formulated for calculating high-frequency winding loss in round-wire toroidal inductors.

Inductors are cornerstone components in power electronics converters. Since winding loss is the dominant loss mechanism in these components, its accurate measurement is fundamental for the validation of the inductor's operation and design. The techniques for the winding resistance Rw measurement in power inductors can be classified into two groups, indirect and direct. Both techniques use coupled inductors to separate winding and core power losses. If coupled inductors with non-zero winding mutual resistances Rw,m are used, invalid results are obtained with these techniques. Understanding the meaning of Rw,m in coupled inductors is complex. In this paper, the impact of Rw,m on the inductor Rw measurement techniques is demonstrated and practical guidelines for the design of the zero Rw,m coupled inductors are given. Particularly, the location of the auxiliary winding for the direct technique is investigated. In order to compare the Rw measurement techniques and to validate the coupled inductor's Rw,m impact, two different inductors are built and tested. The results are compared with the values for Rw calculated by FEA simulation. It is found that only the direct technique with an auxiliary winding carefully designed and located following the guidelines given in this paper makes the accurate measurement of Rw in power inductors possible.

Wide-area disturbances are power outages occurring over large geographical regions that dramatically affect the power system reliability. Protection systems play an important role in the sequence of events of wide area disturbances. A detailed analysis of the disturbance reports published by NERC during 1988 to 1996 concluded that double contingencies (N-2) have contributed significantly to the wide spread of the initial disturbance. Nearly to 70% of N-2 contingencies are caused by relay mis-operations, particularly those due to hidden failures.Hidden failures in protection systems are defined as "a permanent defect that will cause a relay or a relay system to incorrectly and inappropriately remove a circuit element(s) as a direct consequence of another switching event [1]." The most peculiar and dangerous characteristic of relay mis-operations caused by hidden failures is the fact that their effects appear when the power system is under stressed conditions, such as during or immediately after faults, under-voltages, overloads, or as a consequence of another switching event. In addition, the local effect of hidden failures is also a factor since the circuits tripped by hidden failures constitute the second contingency, which is coupled to the first contingency.It will be convenient at this time to include a list of elements necessary to have a hidden failure:

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