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It is hard for traditional current protection to solve problems of distribution networks with highly penetrative DGs. The fault information required by the most protection methods cannot be provided by the poor infrastructure of distribution networks. In this paper, a sufficient criterion based on the maximal current differences between adjacent transmission lines is proposed to promote selective configuration of protection scheme. The principle of the criterion and its advantages on current protection application are analyzed. The suppress influence of DG on the current of downstream transmission line current can be processed without high demand for communication in distribution network with DGs. Through the simulation in Matlab/Simulink, the effectiveness of the proposed criterion is validated.

The stable convergence and efficiency of reliability-based design optimization (RBDO) using performance measure approach (PMA) are the major issue to develop the reliability methods based on modified chaos control (MCC), hybrid chaos control (HCC) and finite-step length adjustment (FSL). However, these methods may be inefficient for RBDO problems with convex and concave probabilistic constraints. In this paper, an adaptive modified chaos control (AMC) is proposed to provide the robust and efficient results in RBDO. The proposed AMC is adjusted using dynamical chaos control factor, which is extracted using sufficient descent condition for PMA. Using sufficient criterion, the proposed AMC is adaptively combined with advanced mean value (AMV) to improve the performance of PMA, named as hybrid adaptive modified chaos control (HAMC). Considering the robustness and efficiency, the proposed HAMC is compared with several existing reliability methods by three nonlinear structural/mathematical performance functions and two RBDO problems. The results indicate that the proposed HAMC with sufficient descent condition provides superior convergences in terms of both robustness and efficiency, compared to existing PMA methods using AMV, MCC, HCC and FSL. [ABSTRACT FROM AUTHOR]

This study considers asymptotic stability in the mean square sense for stochastic delay Markovian reaction‐diffusion systems (SDMRDSs) via boundary control. Firstly, the authors present a boundary controller for the system. By constructing of a Lyapunov–Krasovskii functional and utilising of Poincaré inequality, a sufficient criterion of mean square asymptotic stability for SDMRDSs is established. Next, boundary control for stochastic Markovian reaction‐diffusion systems (SMRDSs) with time‐varying delays is also investigated, and a delay‐dependent sufficient condition for SMRDSs under the boundary control law is obtained. In addition, the robust boundary stabilisation of SMRDSs with parametric uncertainty is considered. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This study addresses the problem of exponential stability for a class of impulsive positive systems with mixed time‐varying delays. A delayed impulsive positive system model is introduced for the first time and a necessary and sufficient condition guaranteeing the positivity of this kind of system is proposed. By using a copositive Lyapunov–Krasovskii functional and the average impulsive interval method, a sufficient criterion of global exponential stability for delayed impulsive positive systems is established in terms of linear programming problems. A numerical example is given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]