Contingency analysis (CA) is a well-known function in power system planning and operation. In accordance with CA results, the operator dispenses information regarding static security of (overloads and/or voltage outside tolerable limits). However, classic remedial action schemes cannot distinguish safe operating regimes from potentially dangerous ones terms (in)stability. fact, instability cons...

‎in this paper we try to extend geometric concepts in the context of operator valued tensors‎. ‎to this end‎, ‎we aim to replace the field of scalars $ mathbb{r} $ by self-adjoint elements of a commutative $ c^star $-algebra‎, ‎and reach an appropriate generalization of geometrical concepts on manifolds‎. ‎first‎, ‎we put forward the concept of operator-valued tensors and extend semi-riemannian...