宽带PLC信号单分形和多重分形特性研究

Research on mono-fractal and multi-fractal characteristics of broadband power line communication signal

宽带电力线通信(PLC)作为智能电网数据传输的有效途径,传统的线性模型和统计学参数难以描述电力线通信信号的非平稳、非线性特性缺点。为了更好地研究电力线通信信号特性,引入单分形和多重分形理论来分析宽带电力线通信信号的自相似特性。通过重标极差分析、变量时间图及周期图分析和小波改进理论等四种方法进行非线性特性分析,同时对不同频率和次数的分形分析方法进一步验证,结果表明宽带电力线通信信号存在自相似特性。此外,通过多重分形消除趋势波动分析法对宽带电力线通信信号进行单分形和多重分析特性测试,从实测的宽带电力线通信信号中估计了功率低指数的多重分形谱,同时提出了一种基于改进小波理论的多重分形消除趋势波动分析算法。

Broadband power line communications（ PLC） is considered to be one of the most promising technologies to fulfill data transmission in smart grids,and the traditional linear models and statistical properties cannot understand well describe the non-stationary and nonlinear characteristics of PLC signal. In order to further study the characteristics of PLC signal,the mono-fractal and multi-fractal theories are introduced to study the self-similarity characteristics of the PLC signals. Four common methods,namely,rescaled range analysis,variance time plot method,periodic diagram analysis and the improved wavelet-based method are used to study the nonlinear properties. Fractal analysis at different frequencies and times are also performed to verify further. The results reveal self-similarity of the PLC signals. Besides,the mono-fractal properties and the multi-fractal properties of PLC signals are verified by the means of multi-fractal detrended fluctuation analysis（ MFDFA）. We estimated the multi-fractal spectrum of power low exponents from the measured PLC signals. A new algorithm is proposed to improve the traditional MFDFA based on improved wavelet theory.