基于Takenaka-Malmquist系统的电力系统暂态电气量测量

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

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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

Received: 08 February 2025

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TM76

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	Zhao Boyu
	Liu Hao
	Bi Tianshu
	Liu Xinyu
	Bao Zhipeng

Cite this article:

Zhao Boyu,Liu Hao,Bi Tianshu等. Power System Transient Electrical Quantity Measurement Based on the Takenaka-Malmquist System[J]. Transactions of China Electrotechnical Society, 2026, 41(5): 1482-1494.

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https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.250192 OR https://dgjsxb.ces-transaction.com/EN/Y2026/V41/I5/1482

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