Abstract: In order to improve the accuracy of multiharmonic detection,this paper improves the multi-component spectral superposition algorithm, and proposes a unified calculation formula for arbitrary inter-harmonics near the harmonic wave based on the higher order equation of one variable Vieta theorem. Firstly,the spectral leakage values near the fundamental and harmonic waves after multiple interharmonic DFTs are vectorially superimposed to obtain the interharmonic correlative equations. Secondly, according to the unified calculation formula,the complex equations are solved and the estimated frequency of inter-harmonics is obtained.Finally,the amplitude and phase of each frequency is obtained by combining the estimated frequency with the initial hypothesis signal. The experimental examples show that the proposed method can accurately identify multiple inter-harmonics near the base wave and harmonic wave,and effectively solve the limitation of the number and type of inter-harmonics in the traditional detection and identification of inter-harmonics.