Feasibility of fractal-based methods for visualization of power system disturbances

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Abstract

In this paper, an application of a fractal-based approach is proposed to detect power quality disturbances. In the proposed method, a fractal number computation is embedded within the detection procedure. These computed fractals are refined through the moving average technique, and then compared with the predetermined threshold in order to signal encountered events. In this way, the characteristics of non-stationary disturbances can be more closely monitored. The transient behavior, cavities and discontinuities in the signals can be all investigated. The proposed method has been tested on various disturbances, including voltage sag, voltage swell, momentary interruption, oscillatory transient and harmonic distortion scenarios. The results have demonstrated the feasibility of the approach for visualization of power system disturbances.

Introduction

A power quality problem is any occurrence manifested in voltage, current or frequency deviation that results in failure or misoperation of electronic equipment. Due to the broader applications of highly nonlinear devices in a modern power system, the waveform distortion has been found to be increasingly serious [1]. Because electric utilities cannot provide better services until they have determined existing levels of power quality [2], [3], [4], the detection of power quality disturbance issue has become an increasing concern to system operators.

Implementation of discrete Fourier transform by various algorithms has been constructed as the basis for modern spectral analysis. Such transforms have been successfully applied to stationary signals where properties do not evolve over time. However, for those non-stationary signals, any abrupt change may spread over the whole frequency axis. In this situation, the Fourier transform is less efficient in tracking the signal dynamics [5]. With the introduction of new network topologies and improved training algorithms, neural networks have demonstrated their effectiveness in several power system applications [6], [7]. In power quality applications, the feature extraction has been applied to select the key features from the acquired waveforms for the training. Once the networks are well trained, the disturbance can be identified that corresponds to the new scenario [8], [9]. This method was shown effective in their tests; however, its trained neural network can only apply to detect a particular type of disturbance. When encountering different disturbances, the neural network structure needs to be reorganized, plus the training process must be performed again. With the emergence of wavelets, such a technique has shown its success in power quality studies [10], [11], [12]. In contrast to those Fourier transform-based approaches where a window is used uniformly for spreaded frequencies, the wavelet uses short windows at high frequencies and long windows at low frequencies. In other words, by wavelets, both time and frequency information can be obtained. However, the effectiveness of this method is highly dependent on the selection of basis functions. A poor selection of the basis function may inversely degrade the performance.

In several applications, fractal geometry has been suggested as an alternative for analyzing time-varying signals where other techniques have not achieved the desired speed, accuracy or efficiency [13], [14], [15], [16]. For nonlinear systems, this concept has been employed for the quantization of chaotic behaviors [17], [18], [19]. A quantization of fractal dimension has served as an aid to distinct those physical processes presenting chaos characteristics [20], [21]. In power engineering fields, high impedance fault behavior has been well-analyzed through such an analysis [22]. The results obtained from that test were proved satisfactory, which further motivated our interests in investigation the feasibility of applying fractals to visualize power system disturbances.

In this paper, we apply a fractal-based technique to investigate various power quality disturbances. A fractal number computation is embedded within the overall detection algorithm. Note that although the fractals can not provide the frequency information, its flexible quantization capability of chaos is especially useful in detecting disturbance events. Following this computation, the obtained fractal numbers can hence be compared with a threshold to signal the outcome. In this way, characteristics of non-stationary disturbances can be better visualized. The transient behavior, cavities and discontinuities in the signals can be all investigated. Some useful features of the new method are listed below:

  • 1.

    It is effective in monitoring the signal dynamics as time varies. For those time intervals where the function changes rapidly, the method can locate the area of interest for a better visualization of signal characteristics.

  • 2.

    The approach has both fractals and time information presented simultaneously.

  • 3.

    The approach can be broadly applied to localize various disturbances. For those cases where the power quality is highly required, the method is a good candidate for visualizing disturbances besides the traditional approaches.

The paper is organized as follows. Section 2 presents paradigms of the proposed approach, Section 3 shows the detection results, and Section 4 draws the conclusions.

Section snippets

Fractal number calculation

In fractal geometry research, the concept of fractal dimension is most often used for the applications. This paradigm attempts to quantify how densely the fractals occupy the metric space where it lies [19]. For comparing fractals between two objects, fractal dimensions provide a systematic measure. All functions defined in the metric space can be quantified by fractal dimensions. For example, let (X,d) denotes a complete metric space. Now, for each ε>0, if N(A,ε) denotes the smallest number of

Simulation results

In this work, the software was developed and completed in our laboratory. The program was developed under matlab environment with a graphic user interface written in C++ language. The proposed approach has been applied to investigate various types of disturbances, including voltage sag, voltage swell, momentary interruption, oscillatory transient and harmonic distortion. The disturbance signals were simulated to generate by using Microsoft™ Visual C++ language that runs on an IBM compatible

Conclusions

A fractal-based technique has been proposed to visualize various power quality disturbances. This proposed method is integrated with the fractal computation and moving average technique in order to improve the visualization performance. From the testing results, we have demonstrated that the proposed approach was very effective in investigating various power quality disturbances. This reveals the feasibility and practicality of the method in the area of power quality problems. Currently, we are

Acknowledgements

The authors would like to express their thanks for the financial support given by the National Science Council of the Republic of China under contract number NSC86-2213-E-214-012 and the technical support from Taiwan Power Company.

Shyh-Jier Huang received his PhD degree in Electrical Engineering from the University of Washington, Seattle, in 1994. Currently, he is with Department of Electrical Engineering, and is the project manager in Computational Intelligence Applied to Power (CIAP) laboratory, National Cheng Kung University, Tainan, Taiwan. He worked on projects at the Department of Electrical Engineering and Computer Science, University of California, Berkeley, from 1989 to 1991. Dr Huang received Research Awards

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  • Cited by (0)

    Shyh-Jier Huang received his PhD degree in Electrical Engineering from the University of Washington, Seattle, in 1994. Currently, he is with Department of Electrical Engineering, and is the project manager in Computational Intelligence Applied to Power (CIAP) laboratory, National Cheng Kung University, Tainan, Taiwan. He worked on projects at the Department of Electrical Engineering and Computer Science, University of California, Berkeley, from 1989 to 1991. Dr Huang received Research Awards from the National Science Council, Taiwan, from 1996 to 2000. His main areas of interests are power system analysis, power quality and signal processing applications.

    Cheng-Tao Hsieh is working towards his PhD degree in Electrical Engineering at National Cheng Kung University. His main areas of interests are power quality and digital signal processing.

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