Abstract：Wideband oscillations in the power electronic power system seriously endangers the safe and stable operation of the power grid. Timely determination of the propagation path and source location of wideband oscillations is crucial for suppressing oscillations. Model based analysis methods have limitations such as unknown parameters and high complexity, restaining their wide application in practical power systems. With the development of information theory, the method based on mathematical statistics becomes a promising method for the analysis of wideband oscillations. These methods focus on the correlation between data items and discover the inherent laws of wideband oscillations. Considering that the data of wideband oscillations in the new-generation power system is a multivariable strongly nonlinear and causal time series, it is worth conducting in-depth research on how to analyze the propagation characteristics of wideband oscillations and achieve oscillations source localization from the perspective of causal relationships based on mathematical statistics. Therefore, this article proposes a device and network level wideband oscillations propagation path analysis and oscillations source localization method based on Copula transfer entropy from the perspective of causality. Firstly, the zero-mean normalization method is used to preprocess the analyzed oscillations data. Secondly, the original signal can be decomposed into a series of intrinsic mode components and a residual component using empirical mode decomposition (EMD). The residual component can be removed as it is independent of oscillations. Thirdly, for each mode, calculate the Copula transfer entropy between each variable to determine the direction of causal transfer. Then define the numerical value of Copula transfer entropy as the causal strength coefficient. Fourthly, a wideband oscillations causal network is constructed using directed weighted graphs, where each node in the network is a state variable or bus power signal, and the edge weights between each node are the causal strength coefficients between the corresponding variables. Fifthly, calculate the out-degree of each node in the network, and the node with the highest out-degree is determined as the position of the oscillations source. Finally, starting from the state variable or bus where the oscillations source is located, retain the branch with the highest causal strength coefficient, which is the main propagation path of the oscillation mode. At device level, the causal relationship between state variables within the controller can be revealed, thereby determining the key state variable and oscillations propagation path. At network level, the causal relationship between the power of each bus in the power grid can be revealed, and then the bus where the oscillations source is located and the oscillations propagation path can be determined. On one hand, a simulation example of PMSG connected to grid is used to analyze the causal relationship of oscillations in various links within the controller. The propagation path diagram of the internal oscillations of the PMSG is obtained using the method proposed in this article. The sub synchronous oscillation mode of the system is mainly related to the DC capacitor link, outer voltage loop, and inner current loop of the PMSG. These links form the internal propagation path of this oscillation mode. On the other hand, a simulation example of a four-machine two-area system containing a wind farm is used to analyze the causal relationship of oscillations between the busbars of a complex system. Simulation examples in forced oscillations, interaction between wind turbines and weak grid, and generator shaft system oscillations demonstrate that the proposed method is suitable for various mechanisms of wideband oscillations, and can achieve wideband oscillations propagation path analysis and oscillations source localization from the network level. The following conclusions can be drawn from the simulation analysis: (1) The method based on Copula transfer entropy avoids establishing a detailed model, and its simulation results are consistent with the oscillations propagation path obtained from theoretical derivation. (2) The method is suitable for various mechanisms of wideband oscillations such as forced oscillations, interaction between wind turbines and weak grid, and generator shaft system oscillations. (3) The method can simultaneously achieve wideband oscillations propagation path analysis and oscillations source localization at device and network level.
冯双, 杨浩, 崔昊, 汤奕, 雷家兴. 基于Copula传递熵的设备级和网络频振荡传播路径分析及振荡源定位方法[J]. 电工技术学报, 2024, 39(16): 4996-5010.
Feng Shuang, Yang Hao, Cui Hao, Tang Yi, Lei Jiaxing. Device and Network Level Wideband Oscillations Propagation Path Analysis and Source Localization Method Based on Copula Transfer Entropy. Transactions of China Electrotechnical Society, 2024, 39(16): 4996-5010.
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