Modal Parameter Identification of Low Frequency Oscillation in Power System Based on Ambient Data

doi:10.12096/j.2096-4528.pgt.21083

Abstract

Abstract:

Low frequency oscillation is one of the key problem affecting the safe and stable operation of interconnected power system, variational modal decomposition (VMD) was used to extract low-frequency oscillation signals from ambient data, and a method of low-frequency oscillation modal identification for power systems discrete Fourier transform (DFT)-based curve fitting was proposed in this paper. Firstly, the DC component of ambient data signals was filtered by VMD decomposition to extract low-frequency oscillation signals. The number of VMD decomposition was determined by modal correlation coefficient, which improved the timeliness of signal decomposition. Secondly, the auto regressive moving average (ARMA) model of ambient data was established to simulate the generation of data signals. The DFT curve fitting of low-frequency oscillation signal autocorrelation function was used to estimate the Laplace transform coefficient and extract characteristic parameters of electromechanical oscillation. Finally, Simulation data and some measured phasor measurement unit (PMU) data are used to verify the feasibility and effectiveness of the method. The experiment shows that the sampling VMD algorithm and the curve fitting method based on DFT can extract the characteristic parameters of low-frequency oscillation, which effectively improves the real-time performance of electromechanical small interference stability.

Key words: low frequency oscillation, ambient data, auto regressive moving average (ARMA) model, variational modal decomposition (VMD), discrete Fourier transform (DFT) curve-fitting

CLC Number:

TM 76

Hongyan YAN, Jin Kwon HWANG, Yanfeng GAO. Modal Parameter Identification of Low Frequency Oscillation in Power System Based on Ambient Data[J]. Power Generation Technology, 2022, 43(1): 19-31.

Figures/Tables 16

Tab. 1 Parameters of the analog DC component

DC 趋势项	数值
1/K_s(幅值)	0.3
K_sf₀/(2J)	0.2

Tab. 2 Parameters of low-frequency oscillation components

k	f_k /Hz	ζ_k	γ_k
1	0.3	0.07	0.4
2	0.5	0.05	0.5

Tab. 3 Maximum correlation coefficients of K different values

模态个数	2	3	4	5
最大相关系数	0.003 0	0.061 2	0.124 1	0.147 6

Fig. 1 The spectrum and VMD modal component

Fig. 2 The spectrum and EMD modal component

Fig. 3 Frequency deviation waveform and autocorrelation function of IMF1

Fig. 4 DFT amplitude and angle of IMF1

Fig. 5 Frequencies and damping rates identification results of IMF1

Tab. 4 Identification results of simulated data

算法	模态	$f ̂ k$ /Hz	ζ_k	$A ̂ k / 10 - 2$	$φ ̂ k$ /(°)	S_NRe
本文算法 SNR=30 dB	1	0.296 8	0.072 7	0.487 1	78.910 0	12.358 0
本文算法 SNR=30 dB	2	0.500 6	0.051 3	0.261 3	95.591 0	13.455 7
MEYW方法 SNR=30 dB	1	0.304 6	0.061 3	0.430 3	73.776 0	10.548 1
MEYW方法 SNR=30 dB	2	0.504 8	0.058 5	0.181 9	102.673 3	12.909 1
本文算法 SNR=10 dB	1	0.295 4	0.070 8	0.611 7	86.660 2	11.351 7
本文算法 SNR=10 dB	2	0.503 4	0.046 7	0.312 5	99.217 9	12.765 3
MEYW方法 SNR=10 dB	1	0.305 2	0.054 0	0.489 6	82.909 7	10.840 1
MEYW方法 SNR=10 dB	2	0.505 5	0.037 4	0.220 3	97.576 4	11.890 3

Tab. 4 Identification results of simulated data

算法	模态	$f ̂ k$ /Hz	ζ_k	$A ̂ k / 10 - 2$	$φ ̂ k$ /(°)	S_NRe
本文算法 SNR=30 dB	1	0.296 8	0.072 7	0.487 1	78.910 0	12.358 0
本文算法 SNR=30 dB	2	0.500 6	0.051 3	0.261 3	95.591 0	13.455 7
MEYW方法 SNR=30 dB	1	0.304 6	0.061 3	0.430 3	73.776 0	10.548 1
MEYW方法 SNR=30 dB	2	0.504 8	0.058 5	0.181 9	102.673 3	12.909 1
本文算法 SNR=10 dB	1	0.295 4	0.070 8	0.611 7	86.660 2	11.351 7
本文算法 SNR=10 dB	2	0.503 4	0.046 7	0.312 5	99.217 9	12.765 3
MEYW方法 SNR=10 dB	1	0.305 2	0.054 0	0.489 6	82.909 7	10.840 1
MEYW方法 SNR=10 dB	2	0.505 5	0.037 4	0.220 3	97.576 4	11.890 3

Fig. 6 Fitting precision diagram

Fig. 7 The measured frequency fluctuation of a power grid

Fig. 8 Modal components and spectrum of a power network measured frequency data

Tab. 5 Identification results of measured data

算法	模态	$f ̂ k$ /Hz	ζ_k	$A ̂ k / 10 - 6$	$φ ̂ k$ /(°)	S_NRe
本文算法	1	0.319 5	0.049 40	0.885 2	89.987 9	15.626 3
本文算法	2	0.675 3	0.135 1	0.323 8	112.821 0	12.260 1
MEYW法	1	0.319 3	0.063 7	0.982 4	93.850 4	14.963 0
MEYW法	2	0.667 4	0.098 7	0.266 7	113.287 0	11.762 7

Tab. 5 Identification results of measured data

算法	模态	$f ̂ k$ /Hz	ζ_k	$A ̂ k / 10 - 6$	$φ ̂ k$ /(°)	S_NRe
本文算法	1	0.319 5	0.049 40	0.885 2	89.987 9	15.626 3
本文算法	2	0.675 3	0.135 1	0.323 8	112.821 0	12.260 1
MEYW法	1	0.319 3	0.063 7	0.982 4	93.850 4	14.963 0
MEYW法	2	0.667 4	0.098 7	0.266 7	113.287 0	11.762 7

Fig. 9 IMF1 DFT amplitude and angle of measured data

Fig. 10 Two modes identification results of measured data

Fig. 11 Fitting accuracy of measured data

References 34

1	李青兰，吴琛，陈磊，等．抑制频率振荡的电力系统稳定器参数优化[J]. 电力系统自动化，2020，44(7)：93-98． doi:10.7500/AEPS20190803005
	LI Q L， WU C， CHEN L，et al ．Parameter optimization of power system stabilizer for suppressing frequency oscillation[J]．Automation of Electric Power Systems，2020，44(7)：93-98． doi:10.7500/AEPS20190803005
2	张虹，王迎丽，勇天泽，等. 基于IEWT和噪能转移SR-MLS反演识别技术的低频振荡信号分析[J]．电网技术，2019，38(1)：1-10．
	ZHANG H， WANG Y L, YONG T Z，et al ．Analysis of low frequency oscillatory signals by IEWT and energy transfer SR-MLS inversion recognition techniques[J]．Power System Technology，2019，38(1)：1-10．
3	丁仁杰，沈钟婷．基于 EMO-EDSNN 的电力系统低频振荡模态辨识[J]．电力系统自动化，2020，44(3)：122-130．
	DING R J， SHEN Z T ．Power system low frequency oscillation mode identification based on exact mode order-exponentially damped sinusoids neural network[J]．Automation of Electric Power Systems，2020，44(3)：122-130．
4	肖怀硕，贾梧桐，肖冰莹，等．基于改进变分模态分解的低频振荡模式辨别[J]．电力工程技术，2020，39(2)：95-102．
	XIAO H S， JIA W T， XIAO B Y，et al ．An identification method for power system low-frequency oscillation based on parameter optimized variational mode decomposition[J]．Electric Power Engineering Technology，2020，39(2)：95-102．
5	习工伟，胡涛，朱艺颖，等．基于新型交直流协调控制抑制电力系统低频振荡的仿真试验[J]．电网与清洁能源，2019，35(4)：8-15． doi:10.3969/j.issn.1674-3814.2019.04.002
	XI G W， HU T， ZHU Y Y，et al ．Simulation test of low frequency oscillation suppression in power system based on new AC-DC coordinated control[J]．Power System and Clean Energy，2019，35(4)：8-15． doi:10.3969/j.issn.1674-3814.2019.04.002
6	HWANG J K， LIU Y L. Discrete Fourier transform-based parametric modal identification from ambient data of the power system frequency[J]．IET Generation Transmission Distribution，2016，10(1)：213-220． doi:10.1049/iet-gtd.2015.0699
7	HWANG J K， LIU Y ．Noise analysis of power system frequency estimated from angle difference of discrete Fourier transform coefficient[J]．IEEE Transactions Power Delivery，2014，29(4)：1533-1541． doi:10.1109/tpwrd.2014.2315618
8	于笑，陈武晖．风力发电并网系统次同步振荡研究[J]．发电技术，2018，39(4)：304-312． doi:10.12096/j.2096-4528.pgt.2018.047
	YU X， CHEN W H ．Review of subsynchronous oscillation induced by wind power generation integrated system [J]．Power Generation Technology，2018，39(4)：304-312． doi:10.12096/j.2096-4528.pgt.2018.047
9	吴涛，梁浩，谢欢，等．励磁系统控制关键技术与未来展望[J]．发电技术，2021，42(2)：160-170． doi:10.12096/j.2096-4528.pgt.21007
	WU T， LIANG H， XIE H，et al ．Key technologies and future prospects of excitation system control[J]．Power Generation Technology，2021，42(2)：160-170． doi:10.12096/j.2096-4528.pgt.21007
10	和萍，申润杰，祁盼，等．四种FACTS装置对改善风光互补系统稳定性的研究[J]．智慧电力，2020，48(7)：65-72． doi:10.3969/j.issn.1673-7598.2020.07.010
	HE P， SHEN R J， QI P，et al ．Four kinds of FACTS devices to improve the stability of wind-solar complementary system[J]．Smart Power，2020，48(7)：65-72． doi:10.3969/j.issn.1673-7598.2020.07.010
11	潘学萍．电力系统低频振荡[M]．北京：中国水利水电出版社，2013：123-125．
	PAN X P ．Low frequency oscillation of power system[M]．Beijing：China Water Power Press，2013：123-125．
12	孙英云，游亚雄，侯建兰，等．基于差分正交匹配追踪和 Prony算法的低频振荡模态辨识[J]．电力系统自动化，2015，39(10)：69-74．
	SUN Y Y， YOU Y X， HOU J L，et al ．Identification of lowfrequency oscillation mode based on difference orthogonal matchingpursuit and Prony algorithm[J]．Electric Power Automation Equipment，2015，39(10)：69-74．
13	张程，金涛．基于ISPM和SDM-Prony算法的电力系统低频振荡模式识别[J]．电网技术，2016，40(4)：1209-1216．
	ZHANG C， JIN T ．Identification of low frequency oscillations in power systems using an improved smoothness priors method and second-derivative method-Prony[J]．Power System Technology，2016，40(4)： 1209-1216．
14	YANG J Z， LIU C W， WU W G ．A hybrid method for the estimation of power system low-frequency oscillation parameters[J]．IEEE Transactions of Power System，2007，22(4)：2115-2123． doi:10.1109/tpwrs.2007.907405
15	RUEDA J L， JUÁREZ C A， ERLICH I ．Wavelet-based analysis of power system low-frequency electromechanical oscillations[J]．IEEE Transactons of. Power System，2011，26(3)：1733-1743． doi:10.1109/tpwrs.2010.2104164
16	Zadrozny P A ．Extended Yule-Walker identification of VARMA models with singleor mixed-frequency data[J]． Journal of Econometrics，2016，193：438-446． doi:10.1016/j.jeconom.2016.04.017
17	WIES R W， PIERRE J W， TRUNDNOWSKI D J ．Use of least-mean squares (LMS) adaptive filtering technique for estimating low-frequency electromechanical modes in power systems[C]//IEEE Power Engineering Society General Meeting，2002：4867-4873. doi:10.1109/acc.2002.1025429
18	ZHOU N， PIERRE J W， TRUNDNOWSKI D J，et al ．Robust RLS methods for online estimation of power system electromechanical modes[J]．IEEE Transactions of Power System，2007，22(3)：1240-1249． doi:10.1109/tpwrs.2007.901104
19	董飞飞，刘涤尘，涂炼，等．基于MM-ARMA算法的次同步振荡模态参数辨识[J]．高电压技术，2013，39(5)：1252-1257． doi:10.3969/j.issn.1003-6520.2013.05.034
	DONG F F， LIU D C， TU L，et al ．Subsynchronous oscillation modal parameter identification based on MM-ARMA algorithm[J]．High Voltage Engineering， 2013，39(5)：1252-1257． doi:10.3969/j.issn.1003-6520.2013.05.034
20	耿海璇，张济民．基于Yule-Walker AR方法的振动信号除噪研究[J]．机电一体化，2016(1)：34-37． doi:10.1115/imece2016-65487
	GENG H X， ZHANG J M ．A Study on vibration signal based on Yule-Walker AR method[J]．Mechatronics，2016(1)：34-37． doi:10.1115/imece2016-65487
21	ANDERSON M G， ZHOU N， PIERRE J W，et al ．Bootstrap-based confidence interval estimates for electromechanical modes from multiple output analysis of measured ambient data[J]．IEEE Transactions of Power System，2005，20(2)：943-950． doi:10.1109/tpwrs.2005.846125
22	吴超，陆超，韩英铎，等．基于类噪声信号和 ARMA-P 方法的振荡模态辨识[J]．电力系统自动化，2020，34(6)：1-6．
	WU C， LU C， HAN Y D，et al ．Identification of mode shape based on ambient signals and ARMA-P method[J]．Automation of Electric Power Systems，2020，34(6)：1-6．
23	杨德友，王文嘉，高际惟，等. 随机数据驱动下的机电振荡参数在线提取与阻尼调制(一)：基于 ORSSI 的模态参数在线辨识[J]．中国电机工程学报，2018, 38(8)：2253-2261．
	YANG D Y， WANG W J， GAO J W，et al ．On-line electromechanical oscillation analysis and damping modulation for power system using ambient data (part I): modal parameters identification based on ORSSI[J]．Proceedings of the CSEE，2018，38(8)：2253-2261．
24	杨德昌， REHTANZ C，李勇，等．基于改进希尔伯特-黄变换算法的电力系统低频振荡分析[J]．中国电机工程学报，2011，31(10)：102-108．
	YANG D C， REHTANZ C， LI Y，et al ．Researching on low frequency oscillation in power system based on improved HHT algorithm[J]．Proceedings of the CSEE，2011，31(10)：102-108．
25	朱永利，王刘旺．并行 EEMD 算法及其在局部放电信号特征提取中的应用[J]．电工技术学报，2018，33(11)：2508-2518．
	ZHU Y L， WANG L W ．Parallel ensemble empirical mode decomposition and its application in feature extraction of partial discharge signals[J]．Transactions of China Electrotechnical Society，2018，33(11)：2508-2518．
26	DRAGOMIRETSKIY K， ZOSSO D ．Variational mode decomposition[J]．IEEE Transactions on Signal Processing， 2014，62(3)：531-544． doi:10.1109/tsp.2013.2288675
27	郑小霞，陈广宁，任浩翰，等．基于改进VMD和深度置信网络的风机易损部件故障预警[J]．振动与冲击，2019，38(8)：153-160．
	ZHENG X X， CHEN G N， REN H H，et al ．Fault detection of vulnerable units of wind turbine based on improved VMD and DBN[J]．Journal of Vibration and Shock，2019，38(8)：153-160．
28	PIERRE J W， TRUDNOWSKI D J， DONNELLY M K ．Initial results in lectromechanical mode identification from ambient data[J]．IEEE Transactions of Power System，1997，12(3)：1245-1251． doi:10.1109/59.630467
29	INOUE T， TANIGUCHI N， IKEGUCHI Y，et al ．Estimation of power system inertia constant and capacity of spinning-reserve support generators using measured frequency transients[J]．IEEE Transactions of Power System，1997， 12(1)：136-143． doi:10.1109/59.574933
30	李东辉，臧晓明，鞠平，等. 电力系统频率响应的改进模型与参数估计[J]．电力工程技术，2019，38(5)：85-90．
	LI D H， ZANG X M， JU P，et al ．The improved model and parameter estimation for frequency response of power system[J]．Electric Power Engineering Technology，2019，38(5)：85-90．
31	KAKIMOTO N， SUGUMI M， MAKINO T，et al ．Monitoring of interarea oscillation mode by synchronized phasor measurement[J]．IEEE Transactions of Power System，2006，21(1)： 260-268． doi:10.1109/tpwrs.2005.861960
32	奥本海默．信号与系统[M]．西安：西安交通大学出版社，1999：156-157．
	OPPENHEIM A V.Signals and systems[M]．Xi’an：Xi’an Jiaotong University Press，1999：156-157．
33	张俊甲，马增强，王梦奇，等．基于VMD与自相关分析的滚动轴承故障特征提取[J]．电子测量与仪器学报，2017，31(9)：1372-1378．
	ZHANG J J， MA Z Q， WANG M Q，et al ．Fault feature extraction of rolling bearing based on VMD and autocorrelation analysis[J]．Journal of Electronic Measurement and Instrumentation，2017，31(9)： 1372-1378．
34	胡楠，李兴源，李宽，等．基于CCF-TLS-ESPRIT算法的低频振荡在线辨识[J]．物理学报，2014，63(6)：316-324． doi:10.7498/aps.63.068401
	HU N， LI X Y， LI K，et al ．Online identification of low frequency oscillation based on CCF-TLS-ESPRIT algorithm[J]．Acta Physica Sinica，2014，63(6)：316-324． doi:10.7498/aps.63.068401