By Yong Li, Dechang Yang, Fang Liu, Yijia Cao, Christian Rehtanz
This publication studies at the most modern findings within the program of the large zone dimension platforms (WAMS) within the research and keep watch over of strength structures. The booklet collects new examine principles and achievements together with a delay-dependent strong layout process, a large zone strong coordination method, a hybrid evaluation and selection procedure for extensive sector indications, a free-weighting matrices procedure and its software, in addition to the web identity tools for low-frequency oscillations. the most unique learn result of this e-book are a finished precis of the authors’ most modern six-year research. The ebook can be of curiosity to educational researchers, R&D engineers and graduate scholars in energy platforms who desire to examine the middle ideas, tools, algorithms, and functions of the WAMS.
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Extra resources for Interconnected Power Systems: Wide-Area Dynamic Monitoring and Control Applications
Example text
Thus, under the condition that xðtÞ is a multi-component signal, the obtained results are meaningless. A set of synthetic signals is used to illustrate this problem: 8 < x1 ¼ sinð1:2ptÞ ð2:49Þ x ¼ 1:5eÀ0:1t sinð1:5ptÞ : 2 x3 ¼ x1 þ x2 It is clear that x1 is a pure sine signal, x2 is an exponential decay signal, and x3 is a composite signal. At the given time t, x1 and x2 have the unique frequency. The value has no any relations with the values at other times. However, the instantaneous frequency of x3 is meaningless because it is a superposition value.
Then, the estimate of the exponential amplitude and sinusoidal initial phase can be received. Prony algorithm and multi-Prony estimate parameters of modes associated with a signal, or certain set of signals [13], such as mode frequency, amplitude, phase, and damping ratio. 30) by approximating in the least square sense to a certain set of equally sampled discrete data. ^yðtÞ ¼ m X i¼1 Ai eri t cosð2pfi t þ ui Þ for t ! 30) may be written in a complex exponential form as ^yðtÞ ¼ m X i¼1 Ã Bi eki t þ BÃi eki t for t !
In other words, it indicates on which system variables the mode is more observable [11]. The magnitudes of the elements of ui give the extent of the behaviors of the n state variables in the ith mode, and the angles of elements give the phase displacements of the state variables with regard to the mode. Thus, the right eigenvector is called mode shape. Similarly, if a n-row vector ui satisfies wi A ¼ ki wi i ¼ 1; 2; . ; n ð2:11Þ it is called the left eigenvector of the A matrix associated with the eigenvalue ki .