基于Takenaka-Malmquist系统的电力系统暂态电气量测量方法

doi:10.19595/j.cnki.1000-6753.tces.250192

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摘要

电力系统故障后电磁暂态期间电气量波形畸变严重、动态变化快速,传统基于傅里叶基底和动态相量的测量方法难以捕捉电气量在时间窗内的局部动态行为,导致暂态期间的同步相量和频率测量结果无意义,且容易发生较大偏差,难以支撑稳定性分析等暂态应用。针对该问题,提出了一种基于Takenaka-Malmquist (TM)系统的电力系统暂态电气量测量方法。分析了基于传统傅里叶基底和同步相量的表征方法在暂态电气量测量中的局限性,揭示并证明了暂态期间基于傅里叶基底的动态相量表征存在冗余;定义了形式类似传统相量和频率的TM相量和TM频率,提出了兼容现有同步测量体系的TM表征方法;在表征的基础上,提出了基于自适应傅里叶变换的TM表征量快速计算方法。仿真和现场故障数据测试表明,相比动态基频相量测量方法和宽频相量测量方法,所提方法可以捕捉暂态电气量在时间窗内的局部特征,且支持高精度、无冗余的暂态电气量波形重构,可还原更完整的暂态信息。

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关键词 ：同步相量测量, 电力系统暂态测量, Takenaka-Malmquist系统, 同步相量测量单元

Abstract：

Electromagnetic transients that occur following faults in power systems are often characterized by severe waveform distortions and rapid dynamic changes in electrical quantities. However, conventional measurement methods based on the Fourier basis operate under the assumption that the amplitude and frequency remain static within a predefined time window. Additionally, only a single phasor estimate is generated per window, rendering these methods incapable of capturing localized dynamic behaviors that unfold within the window. Consequently, synchrophasor and frequency measurements derived from such methods during transient conditions often become unreliable or even meaningless, with significant estimation errors that limit their applicability in critical transient scenarios such as stability analysis and low-voltage ride-through (LVRT) control.
To address this limitation, this paper introduces a novel method for transient electrical quantity measurement in power systems, based on the Takenaka-Malmquist (TM) system. The TM system is a rational orthogonal function system constructed using the Blaschke basis. When all free parameters in the system are set to zero, the TM system degenerates into a complex trigonometric system that includes only non-negative power terms, equivalent to the classical Fourier system. In this sense, the TM system can be viewed as a generalized extension of the Fourier system, offering the capability to decompose highly dynamic and non-stationary signals. Although the TM system has been widely applied in fields such as biomedical signal processing, this work pioneers its application in the domain of synchrophasor-based measurement for power systems.
This study first analyzes the inherent limitations of conventional Fourier-based phasor representations for transient measurements, revealing and theoretically demonstrating the redundancy present in dynamic phasor representations during transients. To overcome this issue, the concept of TM phasors and TM frequencies is introduced. These newly defined quantities structurally resemble traditional phasors and frequencies and are designed to maintain compatibility with existing synchrophasor measurement frameworks. Building upon this representation framework, a fast computational approach for TM quantities is proposed based on adaptive fourier decomposition (AFD).
Theoretical analysis shows that the proposed TM-based quantities exhibit similar features to both synchrophasors and wideband phasors. According to the proposed computational procedure, the first layer of TM quantities is obtained by averaging the analytic signal, corresponding to the DC component of the signal. When the frequency parameter in the AFD process is set to the power system's nominal frequency, the second layer of TM quantities represents the fundamental-frequency component of a steady-state signal or the dominant fundamental-frequency component in a transient signal. Higher-order TM quantities capture the residual energy of the signal and, when combined with the first two layers, enable accurate reconstruction of the waveform and effective restoration of transient signal information.
The effectiveness of the proposed method has been validated using both simulated fault signals and real-world fault data. Experimental results demonstrate that, in comparison with advanced dynamic fundamental-frequency phasor measurement techniques, the proposed approach is capable of capturing localized characteristics of transient electrical quantities within the observation window and tracking instantaneous variations induced by LVRT controls and other dynamic processes. Moreover, when compared with wideband phasor measurement methods, the TM-based approach offers higher accuracy and redundancy-free waveform reconstruction, enabling more complete recovery of transient signal information. These results indicate that the TM system provides a promising new foundation for transient measurement in power systems, offering enhanced resolution, adaptability, and physical interpretability.

Key words： Synchrophasor measurement power system transient measurement takenaka-malmquist system phasor measurement units

收稿日期: 2025-02-08

PACS:

TM76

基金资助:

国家自然科学基金（52377098）和国家留学基金资助项目

通讯作者: 刘灏男,1985年生,教授,博士生导师,研究方向为广域同步相量测量技术及应用。E-mail：hliu@ncepu.edu.cn

作者简介: 赵博宇男,1999年生,博士研究生,研究方向为电力系统暂态电气量表征与测量技术。E-mail：byzhao@ncepu.edu.cn

引用本文:

赵博宇, 刘灏, 毕天姝, 刘昕宇, 鲍志鹏. 基于Takenaka-Malmquist系统的电力系统暂态电气量测量方法[J]. 电工技术学报, 0, (): 20250192-20250192. Zhao Boyu, Liu Hao, Bi Tianshu, Liu Xinyu, Bao Zhipeng. Power System Transient Electrical Quantity Measurement Method Based on the Takenaka-Malmquist System. Transactions of China Electrotechnical Society, 0, (): 20250192-20250192.

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