A novel swarm intelligence assisted Euclidean distance based single detection index approach in transmission line relaying for fast decision making

Intelligent threshold value improves the speed and accuracy of any fault detector unit. But in the literature, any such traditional threshold selection mechanism is not available to implant in the fault detector unit of protective relay. This paper introduces a swarm intelligence-based threshold setting mechanism for fault detector. In this context, the Euclidean distance approach (EDA) with a single detection index is used for transmission network protection. The detection index function is formulated with fault parameters on a priority base. Further, the modified particle swarm optimization technique with adaptive inertia strategy is used to identify the optimal threshold value of detection index function. With swarm intelligence based optimal threshold, numerous cases are investigated on a test power system and obtained results show the efficacy of the method.

Global exponential stabilization of nonlinear systems via width time-dependent periodically intermittent smooth control

In this paper, the global exponential stability and stabilization problems for a class of nonlinear systems are investigated. Some sufficient conditions to guarantee global exponential stable and estimate the minimum admissible value of the control width are presented in virtue of time-dependent width Lyapunov functions. Furthermore, a periodically intermittent smooth controller with variant control width is introduced and theoretical analysis is provided. The smooth index function of periodically intermittent smooth control inputs is defined and the supremum (or least upper bound) of smooth index function set can be solved. On the basis of the analysis, the designed periodically intermittent smooth controller not only can globally exponentially stabilize the nonlinear systems, but also can control the exponential convergence rate of the nonlinear systems. Finally, numerical simulations are given to verify the obtained theoretical results.

Primality test and primes enumeration using odd numbers indexation

Odd numbers can be indexed by the map k(n)=(n-3)⁄2,n∈2N+3. We first propose a basic primality test using this index function that was first introduced in [8]. Input size of operations is reduced which improves computational time by a constant. We then apply similar techniques to Atkin’s prime-numbers sieve which uses modulus operations and finally to Pritchard’s wheel sieve, in both case yielding similar results.

A decomposition algorithm of Petri net utilizing index function

Recently, it is difficult to simulate, analyze and control a real knowledge-based system using the correspondence Petri net (PN) when there exist many current states. To overcome the state explosion problem of PN, an efficient decomposition algorithm is presented to divide a large-scale PN into a series of corresponding sub-PNs by keeping the consistency of dynamic properties. In this novel decomposition approach, an index function is defined to judge the subnet needs to be decomposed or not. Furthermore, an exhaustive analysis on the consistency of related dynamic properties is also discussed between the original PN and the corresponding sub-PNs. Finally, a case study is carried out to illustrate the feasibility and validity of the proposed approach.