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With the continuous expansion of the dimensions of dynamic systems, particularly those governed by predominantly nonlinear equations such as power systems, computational costs and the time required for analyzing these systems have been increased to the extent that certain studies, which necessitate repeated executions, have been rendered very time-consuming and, in some cases, deemed impractical. Alongside the increasing processing power, various methods have been proposed in scientific literature to mitigate this issue, aiming to reduce the order of dynamic systems while preserving their dynamic behavior, thereby reducing the dimensions of the governing equations. Methods for reducing the order of dynamic systems are broadly categorized into two groups: those based on linear analyses and those based on nonlinear analyses, each having its own characteristics, advantages, and limitations. In this paper, an overview is provided of existing methods based on nonlinear analysis for reducing the order of nonlinear dynamic systems, particularly focusing on power systems, and the significance and efficacy of these methods are examined. Accordingly, proper orthogonal decomposition methods, trajectory piecewise-linear approaches, and empirical Gramians are thoroughly investigated, followed by a comparison of these methods. Furthermore, while elucidating the advantages and disadvantages of each method, a generalization for implementing trajectory piecewise-linear approaches on differential algebraic dynamic systems is presented.

Keywords: Dynamic order reduction, nonlinear system, empirical Gramian, proper orthogonal decomposition, trajectory piecewise-linear approach

     

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