Abstract：The nonlinear loads and power electronic equipment have introduced a large number of harmonics and inter-harmonics into the power system, posing a threat to the safe and stable operation of the power system. The existing DFT technology has a low frequency resolution. When the frequency interval between the interharmonic and the fundamental or harmonic is small, the adjacent frequency components cannot be accurately distinguished. Algorithms with higher frequency resolution, such as Matrix Pencil Method, usually require a lot of calculations and can only perform offline analysis of harmonics and inter-harmonics. Combining ApFFT and Taylor Fourier multi-frequency model, this paper proposes a harmonic and interharmonic analysis model with high frequency resolution and small calculation amount, and its frequency resolution is much greater than that of traditional DFT technology, and its operation speed is about 39 times that of the Matrix Pencil Method. The noise robustness, frequency resolution, calculation speed of it have been simulated and verified by experiments in this paper. The simulation and experimental results show that the proposed model has good noise robustness and needs small amount of calculation, the frequency resolution can reach 12Hz. The frequency error and amplitude error during harmonic and inter-harmonic analysis is less than 0.01Hz and 5% respectively, and it can realize rapid detection of harmonics and inter-harmonics.
[1] Manikandan M S, Samantaray S R, Kamwa I.Detection and classification of power quality disturbances using sparse signal decomposition on hybrid dictionaries[J]. IEEE Transactions on Instrumentation and Measurement, 2015, 64(1): 27-38. [2] 孟令辉, 舒泽亮, 闫晗, 等. 基于特征次谐波补偿的单相统一电能质量调节器并联变换器控制策略[J]. 电工技术学报, 2020, 35(24): 5125-5133. Meng Linghui, Shu Zeliang, Yan Han, et al.Control strategy for single-phase unified power quality conditioner of parallel converter based on specific order harmonics compensation[J]. Transactions of China Electrotechnical Society, 2020, 35(24): 5125-5133. [3] 严静, 邵振国. 电能质量谐波监测与评估综述[J]. 电气技术, 2020, 21(7): 1-7. Yan Jing, Shao Zhenguo.Summary of harmonic monitoring and evaluation[J]. Electrical Engineering, 2020, 21(7): 1-7. [4] Arenas L D, Melo G D E, Canesin C A. A methodology for power quantities calculation applied to an FPGA-based smart-energy meter[J]. IEEE Transactions on Instrumentation and Measurement, 2021, 70. [5] Nie Xiaohua.Detection of grid voltage fundamental and harmonic components using kalman filter based on dynamic tracking model[J]. IEEE Transactions on Industrial Electronics, 2020, 67(2): 1191-1200. [6] Platas-Garza M A, De La O Serna J A. Dynamic harmonic analysis through Taylor-Fourier transform[J]. IEEE Transactions on Instrumentation and Measurement, 2011, 60(3): 804-813. [7] 辛国庆, 董唯光, 高锋阳, 等. 感应电能供电技术下含间谐波的谐波信号重构[J]. 电工技术学报, 2020, 35(21): 4544-4552. Xin Guoqing, Dong Weiguang, Gao Fengyang, et al.Reconstruction of harmonic signal with inter-harmonics under inductive power supply technology[J]. Transactions of China Electrotechnical Society, 2020, 35(21): 4544-4552. [8] 王鹤, 李石强, 于华楠, 等. 基于分布式压缩感知和边缘计算的配电网电能质量数据压缩存储方法[J]. 电工技术学报, 2020, 35(21): 4553-4564. Wang He, Li Shiqiang, Yu Huanan.Compression acquisition method for power quality data of distribution network based on distributed compressed sensing and edge computing[J]. Transactions of China Electrotechnical Society, 2020, 35(21): 4553-4564. [9] Chen C I, Chen Y C.Comparative study of harmonic and interharmonic estimation methods for stationary and time-varying signals[J]. IEEE Transactions on Industrial Electronics, 2014, 61(1): 397-404. [10] 曾博, 唐求, 卿柏元, 等. 基于Nuttall自卷积窗的改进FFT谱分析方法[J]. 电工技术学报, 2014, 29(7): 59-65. Zeng Bo, Tang Qiu, Qing Baiyuan, et al.Spectral analysis method based on improved FFT by Nuttall self-convolution window[J]. Transactions of China Electrotechnical Society, 2014, 29(7): 59-65. [11] Wen He, Li Chengcheng, Yao Wenxuan.Power system frequency estimation of Sine-wave corrupted with noise by windowed three-point interpolated DFT[J]. IEEE Transactions on Smart Grid, 2018, 9(5): 5163-5172. [12] Wang Kai, Wen He, Tai Wensi, et al.Estimation of damping factor and signal frequency for damped sinusoidal signal by three points interpolated DFT[J]. IEEE Signal Processing Letters, 2019, 26(12): 1927-1930. [13] 杨超, 张淮清, 王耀, 等. 计及全泄漏影响的多点插值离散傅里叶变换校正方法[J]. 电工技术学报, 2020, 35(16): 3385-3395. Yang Chao, Zhang Huaiqing, Wang Yao, et al.Multipoint interpolated discrete Fourier transform correction method considering total leakage effect[J]. Transactions of China Electrotechnical Society, 2020, 35(16): 3385-3395. [14] 黄翔东, 王兆华. 基于全相位频谱分析的相位差频谱校正法[J]. 电子与信息学报, 2008(2): 293-297. Huang Xiangdong, Wang Zhaohua.Phase difference correcting spectrum method based on all-phase spectrum analysis[J]. Journal of Electronics and Information Technology, 2008(2): 293-297. [15] Costa F F, Cardoso A J M. Harmonic and interharmonic identification based on improved prony's method[C]//IECON 2006-32nd Annual Conference on IEEE Industrial Electronics, Paris, France, 2006: 4963. [16] Sheshyekani K, Fallahi G, Hamzeh M, et al.A general noise-resilient technique based on the matrix pencil method for the assessment of harmonics and interharmonics in power systems[J]. IEEE Transactions on Power Delivery, 2017, 32(5): 2179-2188. [17] Bernard L, Goondram S, Bahrani B, et al.Harmonic and interharmonic phasor estimation using matrix pencil method for phasor measurement units[J]. IEEE Sensors Journal, 2021, 21(2): 945-954. [18] Bracale A, Caramia P, Carpinelli G.Optimal evaluation of waveform distortion indices with prony and root music methods[J]. International Journal of Power and Energy Systems, 2007, 27(4): 371-379. [19] Jain S K, Singh S N.Exact model order ESPRIT technique for harmonics and interharmonics estimation[J]. IEEE Transactions on Instrumentation and Measurement, 2012, 61(7): 1915-1923. [20] De Almeida Prado T, Macario Barros A, Guarneri G A. An algorithm based on sparse decomposition for estimating harmonic and interharmonic components of stationary signals in power systems[J]. IEEE Access, 2019, 7: 163958-163968. [21] Chen Lei, Zhao Wei, Wang Fuping, et al.An interharmonic phasor and frequency estimator for subsynchronous oscillation identification and monitoring[J]. IEEE Transactions on Instrumentation and Measurement, 2019, 68(6): 1714-1723. [22] Bertocco M, Frigo G, Narduzzi C, et al.Compressive sensing of a Taylor-Fourier multifrequency model for synchrophasor estimation[J]. IEEE Transactions on Instrumentation and Measurement, 2015, 64(12): 3274-3283. [23] Narduzzi C, Bertocco M, Frigo G, et al.Fast-TFM—multifrequency phasor measurement for distribution networks[J]. IEEE Transactions on Instrumentation and Measurement, 2018, 67(8): 1825-1835.
2022, Vol. 37 
