电力系统Koopman动态等值方法

doi:10.19595/j.cnki.1000-6753.tces.242346

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摘要

目前尚缺乏能够同时适用于大扰动和小扰动工况的电力系统动态等值建模方法。为提升等值建模方法对电力系统不确定性和时变运行工况的适应能力,基于数据驱动方式提出了一种电力系统Koopman动态等值方法。首先建立外部系统状态方程和输出方程,通过Koopman算子对其进行高维线性化映射,在高维空间实现外部系统状态空间模型的全局线性化;然后分别通过动态模式分解和最小二乘辨识等值模型状态系数矩阵和输出系数矩阵,并在噪声影响下对模型参数进行了修正;对状态系数矩阵进行谱分解提取Koopman模态,通过压缩模态数目实现系统降阶;最后设置算例,验证所提方法合理性。结果表明,在算例系统处于不同程度的扰动下,所提等值模型与原系统具有基本一致的功角摇摆曲线和功率输出曲线,等值模型精度为97.74%,并与常用的同调方法和模态方法进行对比,说明了所提方法的鲁棒性和普适性。

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关键词 ：动态等值, Koopman, 模态方法, 同调方法, 不同扰动

Abstract：

There is a lack of dynamic equivalent modeling methods for power systems that can be applied to both large and small disturbances. To enhance the adaptability of the equivalence method to uncertainties and time-varying operating conditions in power systems, a Koopman dynamic equivalence method for power systems under different levels of disturbance is proposed, which unifies the dynamic equivalence methods for power systems under different operating conditions.
First, establish the state space equation of the external system, perform high-dimensional linearization mapping based on the Koopman operator, and establish its global linearized equivalent model in high-dimensional space. Through this mathematical mapping, the model is linearized without losing key information, so the model is applicable to all operating conditions of the power system.
Then, based on the data-driven approach, the parameters of the equivalent model are identified by collecting equivalent boundary data. The dynamic mode decomposition (DMD) and least squares are used to identify the state coefficient matrix and output coefficient matrix of the equivalent model, respectively. When the measurement data contains noise, the model parameters are adjusted using Least Squares Dynamic Mode Decomposition (LS-DMD) and Total Least Squares (TLS) to enhance the model's noise resistance. This process does not require explicit system detailed structure and operating parameters, thus reducing the workload of detailed modeling. The low-dimensional identification DMD matrix of the external system's state coefficient matrix K₁ shares the same state-space characteristics with the original matrix. Therefore, the numerical solution for the state of the original model can be obtained through the spectral decomposition of the DMD matrix.
Then, the Koopman modes are extracted by spectral decomposition of the system state coefficient matrix. The mode with eigenvalues closer to the imaginary axis has a greater impact on the system and will dominate the dynamic characteristics of the system. The rapidly decaying modes have a relatively small impact on the dynamic characteristics of the system. By retaining the analysis of modes that have a greater impact on the system and filtering out rapidly decaying modes, it is possible to achieve reduced order of the equivalent model and significantly reduce the computational load.
Finally, the proposed method is tested on examples of external systems experiencing transient (large disturbances) and steady-state (small disturbances), respectively. The results show that the proposed equivalent model has basically consistent power angle swing curves and equivalent boundary tie line power output curves with the original system, regardless of whether the system is under large or small disturbances. Quantitative analysis was conducted under large disturbance cases, and the fitting accuracy of the equivalent model and the original model for the transmission of active and reactive power on the five tie lines was 99.35%, 95.47%, 98.21%, 99.49%, 95.51%, 99.34%, 99.32%, 95.73%, 98.30%, and 96.72%, respectively, with an average model accuracy of 97.74%.
The following conclusions are obtained through the verification of the examples: (1) The proposed model, based on the high-dimensional linear Koopman operator, fully preserves the nonlinear dynamic characteristics of the original system. So the model has no restrictions on operating points and is suitable for dynamic equivalence of power systems under varying degrees of disturbance, enhancing the robustness and universality of power system equivalence models. (2 )The parameters of the equivalent model are identified based on the measured data of the system boundary, so the proposed method does not require explicit detailed structural and operational parameters of the system, reducing the workload associated with detailed modeling of the internal structure of the system. (3) The effectiveness of the proposed equivalent model was verified through examples. The results show that the proposed model has basically the same power angle swing curve and power output curve as the original system under large and small disturbances, with a model accuracy of 97.74%. The model can replace the original system for dynamic stability analysis under different levels of disturbance.

Key words： Dynamic equivalence Koopman modal method homology method different disturbance

收稿日期: 2024-12-26

PACS:

TM74

基金资助:

国家电网有限公司总部管理科技项目：5100-202355409A-3-2-ZN

通讯作者: 刘君女,1970年生,副教授,研究方向为电力系统分析与控制、先进输变电技术、新能源电力系统特性与多源互补等。

作者简介: 张子傲男,2000年生,硕士研究生,研究方向为新能源电力系统分析与控制。E-mail：zhangdabei1717@163.com

引用本文:

张子傲, 李岩松, 任必兴, 刘君, 李强. 电力系统Koopman动态等值方法[J]. 电工技术学报, 0, (): 250439-. Zhang Ziao, Li Yansong, Ren Bixing, Liu Jun, Li Qiang. Dynamic Equivalencing Method for Power Systems Based on Koopman Theory. Transactions of China Electrotechnical Society, 0, (): 250439-.

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