Digital modeling and control of multiple time-delayed distributed power grid

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• 作者：V.V. Joshi^a ; L.B. Xie^b ; J.J. Park^c ; L.S. Shieh^a ; Y.H. Chen^a ; K. Grigoriadis^d ; J.S.H. Tsai^e ; ^{shtsai@mail.ncku.edu.tw}
• 关键词：Multiple time-delayed systems ; Distributed power grid ; Hankel matrix ; Singular value decomposition ; Balanced model reduction
• 刊名：Applied Mathematical Modelling
• 出版年：2012
• 期刊代码：6_0307904x
• 类别：cp
• 出版时间：September, 2012
• 卷：36
• 期：9
• 页码：4118-4134
• 文件大小：740 K

摘要

Distributed power grid (DPG) control systems are so highly interconnected that the effects of local disturbances as well as transmission time delays can be amplified as they propagate through a complex network of transmission lines. These effects deteriorate control performance and could possibly destabilize the overall system. In this paper, a new approximated discretization method and digital design for DPG control systems with multiple state, input and output delays as well as a generalized bilinear transformation method are presented. Based on a procedure for the generation of impulse response data, the multiple fractional/integer time-delayed continuous-time system is transformed to a discrete-time model with multiple integer time delays. To implement the digital modeling, the singular value decomposition (SVD) of a Hankel matrix together with an energy loss level is employed to obtain an extended discrete-time state space model. Then, the extended discrete-time state space model of the DPG control system is reformulated as an integer time-delayed discrete-time system by computing its observable canonical form. The proposed method can closely approximate the step response of the original continuous time-delayed DPG control system by choosing various energy loss levels. For completeness, an optimal digital controller design for the DPG control system and a generalized bilinear transformation method with a tunable parameter are also provided, which can re-transform the integer time-delayed discrete-time model to its continuous-time model. Illustrative examples are given to demonstrate the effectiveness of the developed method.