The theoretical and practical aspects and results of simulations based on a specialized tool that is used in the energy industry were adressed. The previously discussed cases in the literature by taking into account the worst case and critical states of networks in terms of complex networks were extended. Using the Monte-Carlo method, the vulnerability of the power grid to node failures was investigated, both in terms of the use of specialized software, which is used in the power industry, and a tool for the analysis of complex networks graphs. We present the results obtained and the observed analogy between the results of the analysis performed in specialized software and the complex network graph analysis tool. It has been shown that the results obtained coincide for both software packages, even though their application focuses on slightly different aspects of system operation. Moreover, further possibilities of extending the research in this direction are proposed, taking into account not only the improvement of the method used, but also a significant increase in the size of the tested structure model.

In this paper, a case study is conducted based on the real data obtained from the local Distribution System Operator (DSO) of electrical energy. The analyzed network represents connections and high-voltage switchgears of 110 kV. Selected graph parameters—vertex degree distribution, the average vertex degree, the graph density, network efficiency, the clustering coefficient, the average path length, and the graph diameter were examined, taking into account that in the analysis, some nodes were removed due to the different failures. For each failure, the possible effects on network parameters were tested. As a final result, it was shown that in the analyzed case, the removal of only five nodes could cause a significant (almost four times) fall of graph efficiency. In turn, this means that the whole analyzed network cannot be considered as a fault-tolerant.

The article deals with the subject of the failure of overhead power lines in south-eastern Poland. Based on data collected over the years, a technical and statistical analysis was done on the power outages that occurred in the selected area. The main purpose of this analysis was to gather information and show primarily the causes of failures, recognize tendencies, demonstrate trends over the years and perform a statistical analysis in order to assess the magnitude of the differences between the compared values in terms of the statistical indicators. The results of the technical and statistical analysis make it possible to assess the quality of the power supplied to customers located in the area covered by the analysis. This quality is closely related to the issue of the continuity of the power supply.

This study presents a comparative analysis of PLANS (v. /2019/12/10) and EA-PSM (v. 19.11.15.0) software for power system simulations, focusing on their applications in enhancing energy security and grid reliability. Utilizing the Newton–Raphson algorithm for power flow calculations, both tools offer robust solutions for network balance, addressing various issues, such as voltage distortions and reactive power injection. The research highlights the critical role of these simulations in integrating renewable energy sources and ensuring efficient, sustainable, and resilient power systems. Additionally, the study underscores the multidimensional aspect of energy security as a cornerstone of national stability and economic prosperity.

A case study based on the real data obtained from the Polish PSE System Operator of the highest voltages electrical energy network is shown. The data about the interconnection exchange and some complex networks (graphs) parameters were examined, after the removal of selected nodes. This allowed to test selected network parameters and to show that the breakdown of only three nodes in this network can cause significant drop of its average efficiency.