Hybrid fuzzy Monte Carlo technique for reliability assessment in transmission power systems

This paper proposes a new methodology to reduce the probability of occurring states that cause load curtailment, while minimizing the involved costs to achieve that reduction. The methodology is supported by a hybrid method based on Fuzzy Set and Monte Carlo Simulation to catch both randomness and fuzziness of component outage parameters of transmission power system. The novelty of this research work consists in proposing two fundamentals approaches: 1) a global steady approach which deals with building the model of a faulted transmission power system aiming at minimizing the unavailability corresponding to each faulted component in transmission power system. This, results in the minimal global cost investment for the faulted components in a system states sample of the transmission network; 2) a dynamic iterative approach that checks individually the investment’s effect on the transmission network. A case study using the Reliability Test System (RTS) 1996 IEEE 24 Buses is presented to illustrate in detail the application of the proposed methodology.

Arc exchange systems and renormalization

We exhibit the construction of stable arc exchange systems from the stable laminations of hyperbolic diffeomorphisms. We prove a one-to-one correspondence between (i) Lipshitz conjugacy classes of C(1+H) stable arc exchange systems that are C(1+H) fixed points of renormalization and (ii) Lipshitz conjugacy classes of C(1+H) diffeomorphisms f with hyperbolic basic sets Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. Let HD(s)(Lambda) and HD(u)(Lambda) be, respectively, the Hausdorff dimension of the stable and unstable leaves intersected with the hyperbolic basic set L. If HD(u)(Lambda) = 1, then the Lipschitz conjugacy is, in fact, a C(1+H) conjugacy in (i) and (ii). We prove that if the stable arc exchange system is a C(1+HDs+alpha) fixed point of renormalization with bounded geometry, then the stable arc exchange system is smooth conjugate to an affine stable arc exchange system.