Time Frequency Aggregation Perormance Otimization o Power Quality Disturbances Based on Generalized S Transorm Mengda Li Shanghai Dianji University, Shanghai 01306, China limd @ sdju.edu.cn Abstract In order to study the roblem o ower quality disturbance signal detection and localization more accurately, this aer studies a method or analyzing the time-requency aggregation erormance o disturbance signal based on generalized S transorm. According to the theory o standard S transorm based derivation o the generalized discrete S transorm ormula, to extract eatures o various disturbance signals rom dierent angles, and determine the starting and ending time o the disturbance signal, the results were analyzed and comared with the standard S transorm. The results show that the generalized S transorm is more lexible than the standard S transorm. It can not only eectively detect the instantaneous change o signal amlitude, but also accurately determine the requency variation o higher order comonents. Keywords Power Quality Disturbances, Generalized S Transorm, Time - requency aggregation. 1. Introduction The solution and imrovement o the ower quality roblem is the hot sot o the current ower system research, and correctly identiy the ower quality disturbance such as harmonics, voltage sike, voltage interrution, voltage sags, Problem, there must be accurate and raid detection and analysis methods. Exerts at home and abroad have ut orward dierent methods, such as short time Fourier transorm, short time Fourier transorm, wavelet transorm WT (Wavelet Transorm) and so on. The S-transorm roosed by Stockwell et al is an extension o the idea o continuous wavelet transorm. The undamental wavelet consists o the roduct o the simle harmonic and the Gaussian window unction. The simle harmonic wave is scaled only in the time domain, and the Gaussian window unction is scaled and translated comared with short-time Fourier transorm, wavelet transorm has its unique advantages, such as the signal S-transorm resolution and requency-related, while maintaining a direct relationshi with its Fourier sectrum, the basic wavelet does not have to meet the ermissibility conditions [1]. However, due to the act that the undamental wavelet is ixed in the S transorm, it is restricted in the alication o the actual signal rocessing and analysis. For this reason, many scholars have develoed and generalized the S transorm, and roosed the generalized S transorm [1-]. They have their own advantages and disadvantages when dealing with dierent actual signals. In this aer, the time-requency clustering measure roosed by Jones and Parks is introduced into the generalized S-transorm, and the simulation results are roved by the synthesized ower quality disturbance signal. The eectiveness o the method is roved and the detection eect is good. 11
. S- transorm and Generalized S transorm In 1996, R.G. Stockwell et al roosed S-transorm [3-5]. The S-transorm is a generalization o the idea o continuous wavelet transorm. It has some roerties lacking continuous wavelet transorm. It is based on a Gaussian window which is localized by translation and extension. When it is used to detect non-stationary signals, it can not only maintain the requency relevant resolution, but also with the Fourier sectrum also has a direct link, which is any other transormation does not have the nature. The transormation ormula is: S(, ) h( t) ex ( t ) / jtdt Where: is the requency; is the center oint o the window unction, and controls the osition o the Gaussian window unction on the time axis. 1 And or generalized S transorm, let ( ), where is the otimal adjustment actor corresonding to the requency, then the generalized S transorm has the ollowing exression: S (, ) h( t) ( t) ex[ 1 ( ) ]ex( jt) dt The arameter controls the width o the window unction. For a given signal, the generalized S transorm can be realized as long as the otimal value o the arameter can be determined. 3. An Algorithm or Imroving Time - Frequency Aggregation by Generalized S-Transorm In this aer, Jones and Parks roosed the time-requency aggregation measure into the calculation, used to determine the otimal value o P, the entire calculation rocess is as ollows [6]. 1) Calculate each value in (0,1 ] according to the discrete orm o generalized S transorm and calculate the generalized S time-requency distribution o time domain signal resectively. ) For each and according to Jones and Parks time-requency aggregation metrics: M 3) Take M JP (, ) to the maximum requency : JP 4 S (, ) d /[ S (, ) d ] (3[ - ]) (, ) P value as the otimal adjustment actor corresonding to ( ) arg max[ M (, )] ot 4) to imrove the time-requency aggregation o the generalized S-transorm: S Pot( ) (, ) S JP (, ) 4. Algorithm Simulation and Result Comarison In this aer, the use o MATLAB rogramming to achieve harmonics, voltage sikes, voltage interrut, voltage sag tyical signal, samling requency 1.6KHz. 4.1 Signal Analysis and Comarison o Harmonics Figure1 (a) is to synthesize the third harmonic, 7th harmonic, 11th harmonic time domain signal, resulting in strong erturbation; Figure1 (b) or the generalized S transorm ater the energy (1) ()
aggregation measure ater the calculation o the three-dimensional network Figure1 (c) is the equivalent curve; Figure1 (d) is the amlitude enveloe. Figure is the equivalent curve ater S transormation. Comared with Fig 1 (c), although the harmonic requency can be roosed, it can be seen that the resolution ater calculating the energy aggregation measure is obviously imroved. (c)equivalent curve (d)amlitude enveloe diagram Fig.1 Generalized S transorm o harmonic signal Fig. S transorm o harmonic signal 4. Signal Analysis and Comarison o Voltage Sikes Fig.3 and Fig.4 show the simulation results o the voltage sike signals in the generalized S-transorm and the S-transorm. Comaring Fig.3 (c) and Fig.4, it can be seen that the ormer has a high resolution, and the singularity is detected and the energy aggregation erormance is revealed. (c)equivalent curve (d)amlitude enveloe diagram Fig.3 Generalized S transorm o voltage sike signal Fig.4 S transorm o voltage sike signal 13
4.3 Signal Analysis and Comarison o Voltage Interrution Figure5 (a) is a set o voltage interrut the time domain signal, resulting in a strong disturbance; Figure5 (b) or the generalized S-transorm ater the energy aggregation measure ater the calculation o the three-dimensional grid; Figure5 (c) Figure5 (d) is an amlitude enveloe grah. Figure6 is the equivalent curve o S transormation. Comared with Fig.5 (c), although the osition o the singular oint o the signal can be detected, it can be seen that the resolution ater calculating the energy aggregation measure is obviously imroved. (c)equivalent curve (d)amlitude enveloe diagram Fig.5 Generalized S transorm o voltage interrution signal Fig.6 S transorm o voltage interrution signal 4.4 Signal Analysis and Comarison o Voltage Sag Figure7 (a) shows the time domain signal o the set voltage dro; Figure7 (b) is a three-dimensional grid diagram o the generalized S-transorm ater the energy aggregation measure; Figure7 (c) is the equivalent grah; Figure7 (d) is the amlitude enveloe. Figure8 is the equivalent curve o S transormation. Comared with Fig.7 (c), it can be seen that the resolution ater energy accumulation measure is obviously imroved. (c)equivalent curve (d)amlitude enveloe diagram Fig.7 Generalized S transorm o voltage sag signal Fig.8 S transorm o voltage sag signal 14
Acknowledgements Heilongjiang Province Natural Science Fund Project, E01410. Reerences [1] Zhan Yong, Cheng Haozhong, Ding Yieng, et al. S-transorm- based classiication o ower quality disturbance signals by suort vector machines[j]. Proceedings o the CSEE, 005, 5(4):51-56. [] Gao Jinghuai, ChenWenchao, Li Youming, et al. Generalized S transorm and seismic resonse analysis o thin interbeds[j]. Chinese Journal o Geohysics, 003, 46(4): 56-53. [3] Mallat Stehane. Wavelet guidance or signal rocessing (English version )[M]. Beijing: Mechanical Industry Press, 00. [4] Liu Sho uliang, Xiao Xianyong, Yang Honggeng. Classiication o short duration ower quality disturbance based on module time-requency matrixes similarity by S transorm[j]. Power System Technology, 006, 30(5): 67-71. [5] Stockwell, R.G.Mansinha L, Lowe R P. Localization o the comlex sectrum: the S-transorm[J].IEEE Transaction on Signal Processing, 1996, 44(4):998-1001. [6] Pinnegar C R, Eeton D W. Alication o the Stransorm to restack noise attenuation iltering[j].journal o Geohysical Research, 003, 108(B9):4-431. 15