Benefits of empirical orthogonal functions in pattern recognition applied to vulnerability assessment

Abstract

One of the main challenges of power system vulnerability assessment is to handle adequate tools capable of analyzing huge volumes of data in real time. For instance, phasor measurement units (PMUs) offer lots of dynamic time series data regarding phasor electric signals. This dynamic data can be analyzed via signal processing tools, such as Fourier Transform, in order to obtain patterns that alert about possible system stress. However, due to the specific dynamic behavior of postcontingency electric signals, they do not exactly correspond to pure periodic signals. Thus, applying classical Fourier-related transforms might not allow obtaining relevant patterns from these types of signals. In this connection, the present paper proposes to use a well-proven time series data mining technique, called empirical orthogonal functions (EOFs), instead of Fourierrelated transforms. EOFs better adapt to the peculiar shape of the post-contingency system variables, which allows getting a better pattern recognition, and so a better vulnerability assessment. With the aim of showing the benefits of EOF, a fair comparison of this data mining tool with Discrete Fourier Transform (DFT) is presented in this paper via three different signal examples. IndexTerms-Electric power systems, vulnerability assessment, data mining, empirical orthogonal functions (EOF), Discrete Fourier Transform (DFT).

Evaluation of tropospheric ozone and ozone precursors in simulations from the HTAPII and CCMI model intercomparisons – a focus on the Indian Subcontinent

“…EOF analysis is analogous to Fourier transform (FT) analysis, but performs better than FT when the signal differs from the pure sinusoidal waveform (Cepeda and Colome, 2014). EOF analysis was applied to both the OMI/MLS and modelled TOC across a domain of The spatial patterns depicted by EOF1 (Fig12a) for models are similar to the spatial pattern for the 5 OMI/MLS observations: they show higher values in the north-western part of domain and lower in the southern part and over the ocean.…”

Power System Dynamic Data Generation Based on Monte Carlo Simulations for Machine Learning Applications

“…It is possible to observe how the proposed MC simulation can determine possible cases with different stability statuses, which is important for training machine learning tools for system security assessments. Finally, with the aim of appreciating how the MC-based dynamic data are capable of being used as the inputs of machine learning tools, the results of applying empirical orthogonal functions (EOFs) [14] to the largest Lyapunov exponent (LLE) [15], as proposed in [6], is presented in Figure 8. This figure presents the parallel coordinates plot of the 15 EOF scores of the LLE, corresponding to the MC-based simulations of G2.…”

Evaluation of tropospheric ozone and ozone precursors in simulations from the HTAPII and CCMI model intercomparisons – a focus on the Indian subcontinent

“…CO was measured using an Ecotech model EC 9830 analyzer based on the infrared (IR) photometry. Information on the maintenance and calibration of these instruments has been reported before Z. Q. Hakim et al: Evaluation of ozone across the Indian subcontinent (Chakraborty et al, 2015;Yadav et al, 2014). Monthly mean values for O 3 , NO x and CO were calculated from the 24 h averages of the hourly data.…”