The Fractal Application Analysis Of Several Problems In Power System Engineering

Fractal theory is a nonlinear subject developed in the past few decades, which mainly research the largely existence non-normal geometry object and nonlinear systems of irregular form in nature. As depict fractal characteristic quantifying parameter, fractal dimension describes the fractal inner complexity. The more fractal set complex, the higher the fractal dimension is. The application of fractal dimension has its uique advantage in power system. Fractal dimension which can describe the complexity has a strong tolerated interim resistance ability. Multifractal spectrum has some advantage for describing waveform in details. It describes the nonuniform extent characteristics of the waveform. In this paper it is used difference as the quality parameters of probability density in multifractal spectrum. And it is applied to power system who also has strong tolerance of interim resistance ability.It takes Yunguang HVDC transmission lines as an example, which tells the application of fractal dimension and multifractal spectrum in DC transmission line protection. The existing physical entity boundary consisted by smoothing reactor and DC filters makes high frequency component attenuated strongly. It makes the aerial mode voltage of two terminals of the line smooth in short time window when external fault occurs, while for internal fault, the transient voltage contains more high frequency components whose waveform showed irregular. It is described the internal and external fault by fractal dimension. The fractal dimension is low because of the wave smoothness when external fault occurs, while for internal fault, the fractal dimension is higher because of the irregular waveform. It is depicted the internal and external fault by multifractal spectrum which can describe the homogeneous degree characteristics of the waveform. When external fault occurs, the fault component of the aerial mode voltage in short time window is relatively uniform, and the nonuniform extent is lower. When internal fault occurs, the fault component of the aerial mode voltage in short time window distributes uneven, and the homogeneous degree is higher.For the AC transmission line, the existing trap installed in both ends of the line makes the high frequency component attenuated. The fractal dimension is low when external fault occurs because of the waveform of voltage fault component change slowly. The high frequency component is higher and the fractal is bigger without the barrier of trap when internal fault occurs. Simulating the fault distance, transition resistance and the fault initial Angle found that the fractal dimension is sensitive to fault distance and initial Angle, particularly to the latter. And it is further checked that the fractal dimension is unaffected by interim resistance.It can be made a distinction between normal ground fault and fundamental frequency ferro resonance by multifractal spectrum algorithm used the difference as the quality parameters. It takes the larger transition resistance and smaller fault Angle as an example, which analyzes the nonuniform extent difference of the zero sequence voltage of the common ground fault and fundamental frequency ferroresonance. And the concept of singularity index growth is proposed. Distinguished by nonuniform extent and singularity index growth can see that the latter method will be better.