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The complication of the structure, topology and composition of the future electrical networks is characterized by difficult-to-recognize circuit-mode situations and requires modern methods for analyzing information parameters. The growing trend of digitizing signals in substations and the use of the IEC 61850 standard results in a huge amount of new data available at the nodes of the electrical network. The development and analysis of new methods for detecting and recognizing the modes of electrical networks (normal and emergency) are topical research issues. The article explores a new approach to recognizing a faulted section of an electrical network with branches by concurrently analyzing several information features and applying machine learning methods: decision tree, random forest, and gradient boosting. The application of this approach for decision-making by relay protection has not been previously implemented. Simulation modeling and the Monte Carlo method are at the heart of obtaining training samples. The results of testing the studied methods under review showed the required flexibility, the ability to use a large number of information parameters, as well as the best results of fault recognition in comparison with the distance protection relay.

The analysis of global epidemics, such as SARS, MERS, and COVID-19, suggests a hierarchical structure of the epidemic process. The pandemic wave starts locally and accelerates through human-to-human interactions, eventually spreading globally after achieving an efficient and sustained transmission. In this paper, we propose a hierarchical model for the virus spread that divides the spreading process into three levels: a city, a region, and a country. We define the virus spread at each level using a modified susceptible–exposed–infected–recovery–dead (SEIRD) model, which assumes migration between levels. Our proposed controlled hierarchical epidemic model incorporates quarantine and vaccination as complementary optimal control strategies. We analyze the balance between the cost of the active virus spread and the implementation of appropriate quarantine measures. Furthermore, we differentiate the levels of the hierarchy by their contribution to the cost of controlling the epidemic. Finally, we present a series of numerical experiments to support the theoretical results obtained.

In the current study, we define a hierarchical epidemic model that helps to describe the propagation of a pathogen in a clustered human population. The estimation of a novel coronavirus spreading worldwide leads to the idea of the hierarchical structure of the epidemic process. Thus, the propagation process is divided into three possible levels: a city, a country, and a worldwide. On each level, the pathogen propagation process is based on the susceptible-exposed-infected-recovered (SEIR) model. We thus formulate a modified transmission model of infected individuals between levels. The control of the pathogen’s spread can be seen as an optimal control problem. A trade-off exists between the cost of active virus propagation and the design of appropriate quarantine measures. Each level of the hierarchy is defined by its network. A series of numerical experiments was conducted to corroborate the obtained results.