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.
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[J]. 电工技术学报, 2026, 41(5): 1482-1494.
Zhao Boyu, Liu Hao, Bi Tianshu, Liu Xinyu, Bao Zhipeng. Power System Transient Electrical Quantity Measurement Based on the Takenaka-Malmquist System. Transactions of China Electrotechnical Society, 2026, 41(5): 1482-1494.
[1] Xin Huanhai, Liu Xinyu, Zheng Di, et al.Risk assessment of post-fault temporary overvoltage using generalized short-circuit ratio[J]. IEEE Transactions on Power Systems, 2024, 39(1): 1837-1849. [2] 单永鹏, 刘昕宇, 汪莹, 等. 基于等效同步机的新能源基地同步调相机暂态功角失稳机理和稳定裕度分析[J]. 电工技术学报, 2025, 40(17): 5448-5463. Shan Yongpeng, Liu Xinyu, Wang Ying, et al.Transient power angle instability mechanism and stability margin analysis of renewable energy base co-located with synchronous condenser based on equivalent synchronous generator[J]. Transactions of China Electrotechnical Society, 2025, 40(17): 5448-5463. [3] 宫泽旭, 艾力西尔·亚尔买买提, 辛焕海, 等. 新能源电力系统并网设备小扰动稳定分析(二): 导出机理与稳定性分类探讨[J]. 中国电机工程学报, 2022, 42(14): 5126-5140. Gong Zexu, Yaermaimaiti Ailixier, Xin Huanhai, et al.Small signal stability analysis of grid-connected equipment in power system(part Ⅱ): discussion on mechanism derivation and classification of stability[J]. Proceedings of the CSEE, 2022, 42(14): 5126-5140. [4] North American Electric Reliability Council. Recommended disturbance monitoring for inverter-based resources[R]. NERC Synchronized Measurements Subcommittee (SMS), White Paper, Feb. 2020. [5] 国家市场监督管理总局, 国家标准化管理委员会. 量度继电器和保护装置第118部分:电力系统同步相量测量: GB/T 14598.118—2021[S]. 北京: 中国标准出版社, 2021. [6] IEC. Measuring relays and protection equipment-part 118-1: Synchrophasor for power systems-measurements: IEC/IEEE 60255-118-1-2018[S]. Geneva: IEC, 2018. [7] Wang Kai, Liu Shan, Wang Lanlan, et al.Novel interpolation method of multi-DFT-bins for frequency estimation of signal with parameter step change[J]. IEEE Transactions on Instrumentation and Measurement, 2021, 71: 6500914. [8] Derviškadić A, Frigo G, Paolone M.Beyond phasors: modeling of power system signals using the Hilbert transform[J]. IEEE Transactions on Power Systems, 2020, 35(4): 2971-2980. [9] Karpilow A, Derviškadić A, Frigo G, et al.Step detection in power system waveforms for improved RoCoF and frequency estimation[J]. Electric Power Systems Research, 2022, 212: 108527. [10] Karpilow A, Derviškadić A, Paolone M.Functional basis analysis for the characterization of power system signal dynamics: formulation, implementation, and validation[J]. IEEE Transactions on Instrumentation and Measurement, 2025, 74: 9001014. [11] Zhan Lingwei, Xiao Bailu, Li Fuhua, et al.Fault-tolerant grid frequency measurement algorithm during transients[J]. IET Energy Systems Integration, 2020, 2(3): 173-178. [12] 赵博宇, 刘灏, 毕天姝, 等. 增强型三复带通滤波器频率测量方法[J]. 中国电机工程学报, 2024, 44(21): 8568-8580. Zhao Boyu, Liu Hao, Bi Tianshu, et al.Enhanced triple complex bandpass filters method for frequency measurement[J]. Proceedings of the CSEE, 2024, 44(21): 8568-8580. [13] Milano F, Ortega Á.Frequency divider[J]. IEEE Transactions on Power Systems, 2017, 32(2): 1493-1501. [14] Milano F.Complex frequency[J]. IEEE Transactions on Power Systems, 2022, 37(2): 1230-1240. [15] Liu Hao, Liu Shuo, Zhao Junbo, et al.Dual-channel convolutional network-based fault cause identification for active distribution system using realistic waveform measurements[J]. IEEE Transactions on Smart Grid, 2022, 13(6): 4899-4908. [16] 余晨. 一种改进的小波变换电力系统谐波检测抗混叠方法[D]. 长沙: 长沙理工大学, 2020. Yu Chen.An improved wavelet transform power system harmonic detection anti-aliasing method[D]. Changsha: Changsha University of Science & Technology, 2020. [17] 姜涛, 张鹏, 李雪, 等. 基于多元同步压缩广义S变换的电力系统次同步振荡源定位[J]. 电力系统自动化, 2025, 49(9): 135-145. Jiang Tao, Zhang Peng, Li Xue, et al.Location of subsynchronous oscillation source in power systems using multivariate synchrosqueezing generalized S-transform[J]. Automation of Electric Power Systems, 2025, 49(9): 135-145. [18] 孙勇, 张鹏, 姜涛, 等. 基于同步压缩广义S变换的电力系统次/超同步振荡检测[J]. 电网技术, 2024, 48(10): 4002-4014. Sun Yong, Zhang Peng, Jiang Tao, et al.Detection of sub/supersynchronous oscillation in power system using synchrosqueezing generalized S-transform[J]. Power System Technology, 2024, 48(10): 4002-4014. [19] 金涛, 陈毅阳, 段小华, 等. 基于改进DFT的电力系统同步相量测量算法研究[J]. 电工技术学报, 2017, 32(17): 1-10. Jin Tao, Chen Yiyang, Duan Xiaohua, et al.Research on synchronous phasor measurement algorithm of power system based on improved DFT[J]. Transactions of China Electrotechnical Society, 2017, 32(17): 1-10. [20] 靳宗帅, 张恒旭, 曾一鸣, 等. 适应频率偏移及动态变化场景的动态谐波相量在线测量方法[J]. 中国电机工程学报, 2024, 44(22): 8759-8771. Jin Zongshuai, Zhang Hengxu, Zeng Yiming, et al.Online measurement method of dynamic harmonic phasor for frequency deviation and frequency dynamic changing conditions[J]. Proceedings of the CSEE, 2024, 44(22): 8759-8771. [21] 许苏迪, 刘灏, 毕天姝, 等. 一种适用于同步相量测量装置校准器的高精度相量测量方法[J]. 电工技术学报, 2020, 35(2): 372-382. Xu Sudi, Liu Hao, Bi Tianshu, et al.A high accuracy phasor estimation algorithm for phasor measurement units calibrator[J]. Transactions of China Electrotechnical Society, 2020, 35(2): 372-382. [22] Liu Xin, Lewandowski M, Nair N K C. A morlet wavelet-based two-point FIR filter method for phasor estimation[J]. IEEE Transactions on Instrumentation and Measurement, 2021, 70: 6503310. [23] Qian Tao, Zhang Liming, Li Zhixiong.Algorithm of adaptive Fourier decomposition[J]. IEEE Transactions on Signal Processing, 2011, 59(12): 5899-5906. [24] Qian Tao, Wang Yanbo.Adaptive Fourier series: a variation of greedy algorithm[J]. Advances in Computational Mathematics, 2011, 34(3): 279-293. [25] Wang Ze, Wong C M, Rosa A, et al.Adaptive Fourier decomposition for multi-channel signal analysis[J]. IEEE Transactions on Signal Processing, 2022, 70: 903-918. [26] Ma Jiali, Zhang Tantan, Dong Mingchui.A novel ECG data compression method using adaptive Fourier decomposition with security guarantee in e-health applications[J]. IEEE Journal of Biomedical and Health Informatics, 2015, 19(3): 986-994. [27] Wang Ze, Wong C M, Rosa A, et al.Stimulus-stimulus transfer based on time-frequency-joint representation in SSVEP-based BCIs[J]. IEEE Transactions on Bio-Medical Engineering, 2023, 70(2): 603-615. [28] 陈维国, 钱涛, 李建平, 等. 基于Takenaka-Malmquist自适应时频分布的特征指标: 来自上证和深证的数据[J]. 系统工程理论与实践, 2020, 40(12): 3112-3123. Chen Weiguo, Qian Tao, Li Jianping, et al.Characteristic index based on Takenaka-Malmquist adaptive time-frequency distribution: data from Shanghai Composite Index and Shenzhen Component Index[J]. Systems Engineering-Theory & Practice, 2020, 40(12): 3112-3123. [29] Xu Sudi, Liu Hao, Bi Tianshu.A general design method for phasor estimation in different applications[J]. IEEE Transactions on Smart Grid, 2020, 12(3): 2307-2319. [30] 邵冲, 汪芙平, 韩自奋, 等. 宽频振荡下同步相量测量算法研究[J/OL]. 中国电机工程学报, 2024: 1-11[2024-11-14]. https://kns.cnki.net/kcms/detail/11.2107.TM.20241114.1031.005.html. Shao Chong, Wang Fuping, Han Zifen, et al. Research on synchronous phasor measurement algorithm under broadband oscillation[J/OL]. Proceedings of the CSEE, 2024: 1-11[2024-11-14]. https://kns.cnki.net/kcms/detail/11.2107.TM.20241114.1031.005.html. [31] 张旸, 贾科, 毕天姝, 等. 规模化新能源场站接入弱电网场景的故障暂态电压支撑控制[J]. 中国电机工程学报, 2025, 45(13): 4956-4967. Zhang Yang, Jia Ke, Bi Tianshu, et al.Fault transient voltage support control for large-scale renewable power plant connecting to weak grid[J]. Proceedings of the CSEE, 2025, 45(13): 4956-4967. [32] Zhang Yang, Jia Ke, Jiang Xinying, et al.Multistage parameter identification for fault control parameters of the IIRES[J]. IEEE Transactions on Power Electronics, 2023, 38(11): 14590-14600. [33] 田书新, 陈武晖, 王盼盼, 等. 变无功电流比例系数的直驱风电并网系统电压连续穿越控制策略[J]. 中国电机工程学报, 2024, 44(19): 7671-7684. Tian Shuxin, Chen Wuhui, Wang Panpan, et al.Continuous voltage ride through segmentation control strategy for PMSG-based wind power integrated systems with dynamic reactive current scale factor[J]. Proceedings of the CSEE, 2024, 44(19): 7671-7684. [34] Shabestary M M, Mohamed Y A I. Maximum asymmetrical support in parallel-operated grid-interactive smart inverters[J]. IEEE Transactions on Sustainable Energy, 2022, 13(1): 14-30. [35] Liu Hao, Bi Tianshu, Xu Sudi, et al.A full-view synchronized measurement system for the renewables, controls, loads, and waveforms of power-electronics-enabled power distribution grids[J]. IEEE Transactions on Smart Grid, 2022, 13(5): 3879-3890.
2026, Vol. 41 
