富立叶算法的圆图分析法

在数字式继电保护中应用最多的是富氏算法。在应用代数方法分析富氏算法的频率响应、计算基波或谐波的相量或考虑非周期分量的影响时,计算量大且物理概念不清。特别是分析变窗口的小矢量算法时其物理过程更不清楚。本语提出的圆图分析法可作为离散型富氏变换（ＤＦＴ）与快速富氏变换（ＦＦＴ）之间的一个实用分析工具,且分析简明扼要。它能形象地描述富氏算法的整个过程,使得富立叶变换的物理概念比较清晰。与代数方法相比较,

CIRCLE DIAGRAM ANALYSIS FOR FOURIER ALGORITHM

Fourier algorithms are widely used in digital protective relaying. When the algebraic Fourier Transformation is used in following aspects, i.e., analyzing the frequency response of Fourier algorithm, calculating the phasors of fundamental and harmonics components and considering the influence of non-periodical components, the amount of calculation is often enormous and the physical concepts are not clear, especially, in the analysis of small phasor with variable window the physical concept will be more vague. In this paper a new method named Circle Diagram Analysis is presented which could be used as a practical analytical tool between DFT and FFT, and makes the above mentioned analyses more concise. It can describe the whole process of Fourier algorithm vividly and makes the physical concept of Fourier Transformation more clear. Comparing with the conventional algebraic method, with Circle Diagram Analysis it is easier to obtain and understand some conclusions of Fourier algorithm, for example, the phase and the amplitude of a certain order harmonic. Using Circle Diagram Analysis, the following conclusion can be obtained: To filtrate an integral order harmonic the sampling frequency must be the integral multiples of 4.