Analyzing system trajectory from the perspective of individual machines provides a distinctive angle to analyze the transient stability of power systems. This two-paper series propose a direct-time-domain method that is based on the individualmachine equal area criterion. In the first paper, by examining the mapping between the trajectory and power-vs-angle curve of an individual machine, the s...

Abstract Given any n points in the plane, not all on same line, there exist two non-collinear triples such that ratio of areas triangles they determine, differs from 1 by at most $$O(\log n/n^2)$$ O ( log n / 2 </mm...

We consider the set of triangles in the plane with rational sides and a given area A. We show there are infinitely many such triangles for each possible area A. We also show that infinitely many such triangles may be constructed from a given one, all sharing a side of the original triangle, unless the original is equilateral. There are three families of triangles (including the isosceles ones) ...

Superconductor fault current limiter (SFCL) is an effective device to suppress high fault currents. This paper presents a comparative study of resistive and inductive fault current limiters from transient stability point of view.  Appropriate location and type of the limiters in a HV substation is selected by a qualitative approach based on the equal area criterion. Study system is simulated by...

There are many situations in which it is desirable to derive reliable estimators for small geographical areas or small subpopulations, from existing survey data. The basic random e ects model and corresponding small area predictors for small area estimation is introduced. There are also many situations in which it is necessary to have the total of the small area predictors equal to the total of...