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Modern power grids, functioning as a cyber-physical system (CPS), accommodate high penetration level of distributed generations (DGs) to ensure sustainability. Achieving sustainability through grid-scale DGs, however, increases the likelihood of islanding occurrences, which jeopardizes a major parameter of CPS implementation: security. This paper proposes an artificial intelligence-based approach for detecting islanding in modern power grids. The method utilizes measured voltage and frequency to develop a fuzzy center of gravity (COG)-based equivalent model of the system. The model is derived by combining data collected from phasor measurement units (PMUs) with fundamental dynamical equations that govern power system dynamics. In this model, the system is represented using a set of fictitious reactances calculated using goal programming, which are then utilized to connect the COG to the local centers of inertia (COIs). By having a set of fictitious reactances for various operating points fed into a fuzzy model, one could develop an online model to calculate the fictitious reactances with high accuracy and speed at specific snapshots. By incorporating the maximum allowable phase differences between areas into the COG model to ensure transient stability, one could enhance the developed model to be robust against cyber-physical contingencies and cyber-attacks, albeit at the expense of a slight reduction in accuracy. The calculated fictitious reactances, represented in terms of local frequencies throughout the system, serve as valuable indicators for detecting islanding. By classifying the calculated fictitious reactances using support vector clustering over a period of time, islanding could be detected with high accuracy. Furthermore, incorporating the COG concept with the clustering based on fictitious reactances makes it possible to detect false data injection in an area of the system. The efficacy of the proposed method is assessed using simulated data from the renewable integrated 73-bus IEEE test system. • This paper deals with the application of computational intelligence for stability assessment of large-scale power systems. • Data-driven based approach is proposed to detect islanding occurrence. • A combination of Fuzzy-modeling and support vector clustering is used to propose a fast and accurate farmwork. • The highly non-linear model of power system is represented using a combination of COIs and center of gravity. [ABSTRACT FROM AUTHOR]

Singular minimal surfaces are models in architecture of domes where compression forces are the only ones acting on the dome. This paper investigates if catenary rotation surfaces and paraboloids are good candidates to substitute the singular minimal surfaces as designs for the construction of domes. Assuming that these surfaces have the same surface area and the same boundary curve, a numerical comparison of the heights of their centers of gravity and the curvatures is presented. This method is performed with Mathematica together with an analysis based on the slope linear regression line. The numerical results demonstrate that the centers of gravity of the two candidates are considerably close to that of the mathematical model. It is also proved that the paraboloids adjust better than catenary rotation surfaces. • Ideal models of domes are not computable by quadratures. • Catenary rotation surfaces and paraboloids are good approximations of domes. • Centers of gravity of paraboloids and rotational tectums are almost identical. • Paraboloids adjust better catenary rotation surfaces to the ideal model. [ABSTRACT FROM AUTHOR]