| The technology used the SCR is universally applied to the large DC power supply and the stepless reactive power compensator. The distortion of the voltage wave, that is the wave form rises as straight line at trigger point because of the avalanche phenomenon when the controlled silicon is triggered off ,it is equal to the standard sine wave is cut off a angle. It is the source which produced the higherharmonic. when the SCR is triggered at the time which the instantaneous value of the voltage or current isn't equal to zero. In this paper, the kind of the higherharmonic source is studied theoretically and the mathematics description of the wave is given. So the project problem is abstracted as a pure mathematics problem and is studied and the process forming the fast Fournier transformation the mathematics reasoning,the characteristic analysis,the present situation and the development are discussed.A new harmonic analysis algorithm is presented directly on the basis of the discrete Fourier transform thorough the research and the strict mathematics reasoning .so the more succinct expression than old one is obtained and the computation of the new algorithm are much less than FFT. At the same time the relations between the higher harmonic and the triggered angles are studied. Four important characters are obtained and are proved strictly used mathematics induction. According to the second character, the higher harmonics are not calculated on the four discrete point; According to the third character, the count of higher harmonics is reduced fifty percent;According to the fourth character, the area of rises of sine wave is calculated only; According to the first character , the calculation of the last discrete point base on the calculation of next discrete point; so the calculation become more simple.In the paper there are the examples and it indicated the algorithm is correct and quicker more than FFT. This algorithm is applied to stepless reactive power compensation.
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