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This work presents a data-driven analysis of minimal length necessary for coherency detection considering a recursive form of the typicality-based Data analysis (TDA). It proposes a methodology that encloses the observation of the variance of the typicality ({\tau} ) to asses the minimal window length necessary to determine the coherent buses, where the properties of the TDA approach and the groups of buses are iteratively calculated at every new data point sampled. Once the variance of each group reaches a certain value, the minimal window length is determined. Besides, this method preserves the TDA characteristics of using exclusively measurements, not requiring pre-determination of number of groups, group centers or cut-off constants. The method is applied to the well know 2-area Kundur test system, allowing to corroborate its effectiveness and draw conclusions regarding minimal window length dependence on the slowest inter-area mode., Comment: 6 pages, 7 figures

This paper proposes a new comprehensive and fully data-driven methodology to estimate the center of inertia (COI) and the regional inertia, considering the displacement of the COI due to disturbances and load inertial contributions. The strategy uses the typicality-based data analysis (TDA) technique to detect the right pilot-bus that represents the COI. In the TDA, a compound of correlation and cosine similarities is implemented to approximate the actual distribution of the data and find the point (bus) closest to the mean which is elected as the pilot-bus. Then, the frequency response at the pilot-bus and the active power deviations are embedded into an autoregressive moving average exogenous input (ARMAX)-based approach to determine the regional inertia represented by an equivalent machine, whose inertia constant corresponds to the inertial contribution in the Region. % the This is done in order to perform the inertial estimation of the region using the frequency response of the pilot-bus and the active power of the region interconnections to model the region as and equivalent machine whose inertial constant is estimated using ARMAX identification technique. The methodology is tested using the IEEE 68-bus benchmark test system and an adapted version with aggregated dynamical loads, corroborating the method effectiveness.

The increasing uptake of inverter based resources (IBRs) has resulted in many new challenges for power system operators around the world. The high level of complexity of IBR generators makes accurate classical model-based stability analysis a difficult task. This paper proposes a novel methodology for solving the problem of estimating the Region of Attraction (ROA) of a nonlinear system by combining classical model based methods with modern data driven methods. Our method yields certifiable inner approximations of the ROA, typical to that of model based methods, but also harnesses trajectory data to yield an improved accurate ROA estimation. The method is carried out by using analytical Lyapunov functions, such as energy functions, in combination with data that is used to fit a converse Lyapunov function. Our methodology is independent of the function fitting method used. In this work, for implementation purposes, we use Bernstein polynomials to function fit. Several numerical examples of ROA estimation are provided, including the Single Machine Infinite Bus (SMIB) system, a three machine system and the Van-der-Pol system., 6 pages, 4 figures