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Computational fluid dynamics (CFD) with the Lagrangian method has been widely used in predicting transient particle transport in indoor environments. The Lagrangian method calculates the trajectories of individual particles on the basis of Newton's law. Statistically speaking, a large number of particles are needed in the calculations in order to ensure accuracy. Traditionally, modelers have conducted an independence test in order to find a reasonable value for this particle number. However, the unguided process of an independence test can be highly time-consuming when no simple method is available for estimating the necessary particle number. Therefore, this investigation developed a method for estimating the necessary particle number in the Lagrangian method. Furthermore, the computing cost of the Lagrangian method is positively associated with the particle number. If this number is too large, the computing cost may not be affordable. Thus, this study proposed the superimposition and time-averaging methods to reduce the necessary particle number. This investigation designed multiple cases to verify the proposed methods. The verification results show that the estimation method can provide the necessary particle number with a reasonable magnitude. Moreover, the superimposition method can reduce the necessary particle number when the particle source duration is relatively long. On the other hand, the time-averaging method can reduce the necessary particle number by up to 30 times. When compared with experimental data, predictions of transient particle transport in indoor environments by the combined Lagrangian, superimposition, and time-averaging method with the estimated particle number are reasonably accurate.

The integration of distributed generations (DGs) is transforming the traditional radial single-source distribution system into a complex multi-source one which requires its related protection is able to maintain proper coordination under bidirectional power flow conditions. Although the conventional backup protection methods are effective up to a certain level of DG penetration, they are incompetent for higher service demands such as high DG penetration and protective rapidity. To deal with such a problem, a fast and reliable backup protection strategy is presented on the basis of a proposed device detection method. In the proposed backup strategy, the device failure-related backup protection is started in advance to accelerate the fault isolation by locking the failed primary protection which can be predicted by the proposed device detection method. The presented strategy possesses an excellent performance on rapidity and stability. Particularly, the fault isolation area is only expanded to the upper level circuit breaker via our protection strategy. The performance of the proposed backup strategy has been validated by the realistic system and the real-time digital simulator (RTDS) system. INDEX TERMS Backup protection, differential protection, device detection, distribution networks.

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The threat of a malicious attack is one of the major security problems in complex networks. Resilience is the system-level self-adjusting ability of a complex network to retain its basic functionality and recover rapidly from major disruptions. Despite numerous heuristic enhancement methods, there is a research gap in maximizing network resilience: current heuristic methods are designed to immunize vital nodes or modify a network to a specific onion-like structure and cannot maximize resilience theoretically via network structure. Here we map complex networks onto a physical elastic system to introduce indices of network resilience, and propose a unified theoretical framework and general approach, which can address the optimal problem of network resilience by slightly modifying network structures (i.e., by adding a set of structural edges). We demonstrate the high efficiency of this approach on three realistic networks as well as two artificial random networks. Case studies show that the proposed approach can maximize the resilience of complex networks while maintaining their topological functionality. This approach helps to unveil hitherto hidden functions of some inconspicuous components, which in turn, can be used to guide the design of resilient systems, offer an effective and efficient approach for mitigating malicious attacks, and furnish self-healing to reconstruct failed infrastructure systems.