The spectral leakage is the main cause of measurement error in windowed interpolation Fourier transform algorithm and the high-order window could be used to restrain it. However

it is still hard for improving the estimation accuracy of the second harmonic and other weak harmonics significantly. Moreover

it not only causes the loss of frequency resolution but also complicates the spectral expressions. An improved interpolation estimation algorithm is proposed to solve these problems. Using a low-order sine window

the traditional discrete Fourier transform(DFT)is shifted by 1/2 line spacing to the Odd-DFT domain for revision by the interpolated algorithm. The relative frequency offset of harmonics is used to subtract the sum of the long-range spectral leakage interference of other components

and then the interpolated algorithm is performed to obtain the more accurate relative frequency offset. Several iterations of loop are performed to restrain the impact of spectral leakage on estimation accuracy. The correction formula is deduced and the algorithm flow is given. The simulation analysis is carried out under different environments to obtain a reasonable number of iterations. The analysis results show that the measurement accuracy of this algorithm is higher than traditional windowing algorithm

the accuracy of weak harmonics is even more significantly improved and the number of required sampling time window is decreasing as well

which improve the measurement accuracy and meet the requirement of power grid.