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Determination of Parameters of Time-delayed Embedding Algorithm Using Koopman Operator-based Model Predictive Frequency Control

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CSEE Journal of Power and Energy Systems 2021年第6期7卷 1140-1151页

作者： Xiawen Li Chetan Mishra Shichao Chen Yajun Wang Jaime De La Ree Dominion Energy RichmondVAUSA Thorlabs Quantum Electronics. JessupMDUSA Department of Electrical and Computer Engineering Virginia Polytechnic Institute and State UniversityBlacksburgVAUSA

Power systems around the world have been registering a degenerating inertial response in view of the growth of inverter-based resources along with the withdrawal of conventional coal ***,there is a need for swift frequency support and its control,preferably by means of power electronic-interfaced storage devices,owing to their beneficial *** being particularly efficient,pragmatically,the traditional model-based non-linear control techniques are not highly popular in power system control design,primarily due to the complications faced in obtaining accurately suitable models for certain power system ***,the modelfree Koopman operator-based model predictive control(KMPC)has proven to be highly conducive for data-driven non-linear control *** principle behind KMPC is to change the coordinates in a manner to get an approximately linear model,which can then be controlled using a linear model predictive *** this study,we employed time-delayed embedding of measurements to reconstruct a new set of preferable coordinates,thereby suggesting an approach for finding the optimal number of time lags and the embedding dimensions which are the key parameters of this *** efficacy of this KMPC framework is established by adopting a decentralized frequency control problem through a decoupled synchronous machine system,which we proposed for both the Kundur two-area system as well as the IEEE 39-bus test system.

关键词： false nearest neighbors koopman operator model predictive control non-linear control time-delayed embedding

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Chaos in Time Series of Sakarya River Daily Flow Rate

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Journal of Applied Mathematics and Physics 2016年第10期4卷 1849-1858页

作者： Haci Ahmet Yildirim Avadis Simon Hacinliyan Ergun Eray Akkaya Cercis Ikiel Department of Physics Sakarya University Adapazari Turkey Department of Physics Yeditepe University Istanbul Turkey Department of Information Systems and Technologies Yeditepe University Istanbul Turkey Department of Geography Sakarya University Adapazari Turkey

In this study, possible low dimensional chaotic behavior of Sakarya river flow rates is investigated via nonlinear time series techniques. To reveal the chaotic dynamics, the maximal positive Lyapunov exponent is calculated from the reconstructed phase space, which is obtained using the phase space reconstruction method. The method reconstructs a phase space from the scalar time series, which depicts the real system’s invariants Positive values, because the Lyapunov exponent values calculated using the appropriate software program indicate possibility of chaotic behavior. Analyzed data involve the monthly average flow rates of eleven main branches of Sakarya River through the years 1960-2000.

关键词： Chaos Theory Time Series Analysis Lyapunov Exponent Mutual Information false nearest neighbors

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