Some features of Hilbert transform and their use in energy informatics

Abstract

Information-measuring technologies (IMT) are an important instrument for solving problems of energy informatics. They allow to form primary information based on the interaction of energy facilities with IMT sensors that form information signals. In many practical applications, the constructive model of information signals is the model of narrowband signals. The article summarizes the features of the discrete Hilbert transform and its application to obtain the primary characteristics of information signals – bypass and phase as functions of time. The main advantages of using the discrete Hilbert transform in signal processing for energy informatics are considered, including the consistency of obtaining frequency and time characteristics, high information content, the ability to analyze the dynamics of changes in signal characteristics, the possibility of obtaining samples of characteristics of information signals of significant volumes, etc. It is proposed to use a phase characteristic to select the time interval that limits the signal sample and sets it to a multiple of the signal period, and the sampling rate of information signals to reduce the errors in estimating their spectrum. The possibility of obtaining on their basis secondary deterministic (voltage level, voltage deviations from the nominal level, attenuation coefficient, signal period, signal phase shift, oscillation frequency, etc.) and statistical (sample characteristic, sample variance, sample median, sample circular variance, sample circular median, sample circular kurtosis, etc.) of signal information characteristics, which allows more complete to use their information resource. These characteristics can be used both for assessing power quality characteristics and for monitoring and diagnosing of energy facilities. Keywords: energy informatics, information signals, signal processing, discrete Hilbert transform, amplitude signal characteristics, phase signal characteristics

Properties of Discrete-Time Conditional Linear Cyclostationary Random Processes in the Problems of Energy Informatics

“…The characteristics of representation (2), that is probability properties of the kernel and generating white noise, as well as moment (3), (4) and characteristic (7) functions can be used in the different areas in energy informatics, such as electricity consumption monitoring and forecasting, computer simulation, identification of the electricity consumption profile features etc.…”

“…This can be done within the energy informatics framework, a highly interdisciplinary and dynamic field of research and development. Energy informatics combines computer science, control systems, and energy management systems in a single methodology [1][2][3]. Important directions of energy informatics are associated with the collection, analysis, deployment, and exploitation of energy status data, modeling, simulation, and prediction of the behavior of energy systems and processes [1], including energy loads and consumption mathematical modeling and computer simulation.…”

“…is a real-valued random function (kernel), which can be considered a random matrix as well as a two-dimensional random field on2 Let us denote the mathematical expectation and variance of the above white noise ( )…”