一种基于Hamming自乘法窗函数和四插值的谐波分析方法

张俊敏，刘宗方，陈　勉

(中南民族大学 计算机科学学院，武汉 430074)



一种基于Hamming自乘法窗函数和四插值的谐波分析方法

张俊敏，刘宗方，陈勉

(中南民族大学 计算机科学学院，武汉 430074)

摘要针对谐波分析过程中常规窗函数存在精度不足的问题，提出了一种自乘法窗函数的构造方法，并以Hamming窗函数为例构造出1-9阶乘法窗函数，将这些窗函数应用于四谱线插值谐波分析方法中，仿真实验表明：构造出的自乘法窗函数相对于常规窗函数，在进行插值谐波分析中具有更高的准确度.工程实践中可根据精度需要选择所构造的窗函数阶次.

关键词谐波分析；自乘法窗函数；汉明窗；四插值

A Harmonic Analysis Method Based on Hamming Self-Multiplication Window Functions and Four-Spectrum-Line-Interpolation

ZhangJunmin,LiuZongfang,ChenMian

(College of Computer Science, South-Central University for Nationalities, Wuhan 430074, China)

AbstractIn view of precision insufficient of the conventional window functions used in harmonic analysis, this paper introduced a construction method of self-multiplication window functions, and gave self-multiplication window functions of 1-9 orders based on Hamming window, and meanwhile verified a harmonic analysis method of four-spectrum-line-interpolation based on these multiplication window functions. The simulation experiments show that the constructed window function has a higher accuracy comparing to the conventional window function interpolation algorithm. In practical engineering, we can choose the constructed window function orders according to the needs of precision.

Keywordsharmonic analysis; self-multiplication window function; Hamming window; four-spectrum-line-interpolation

电网中非线性器件的使用带来了谐波问题，不仅恶化了电能质量，对电网的安全稳定和经济运行也造成较大影响[1,2].因此，对电网中谐波参数进行测量，一方面可以明确当前系统的运行状态；另一方面对于减少谐波危害，维护电网安全稳定、高效运行是十分必要的.

谐波检测的关键问题为非同步采样下如何解决频谱泄漏和栅栏效应，常见检测方法主要有傅里叶变换插值算法、机器学习法、小波变换、功率谱估计、希尔伯特-黄变换.傅里叶插值算法是运用各种特殊窗函数对信号进行截断，然后结合谱线插值 FFT进行谐波分析[3].常用窗函数，例如汉宁(Hanning)窗函数[4]、布莱克曼汉斯(Blackman-Harris)窗函数[5]、纳托尔(Nuttall)窗函数[6]、莱夫文森特(Rife-Vincent)窗函数[7]在插值运算中得到应用；一系列自卷积窗函数，如三角自……