Harmonic Vector Error Analysis Based on Lagrange Interpolation

With the development of smart substations and the promotion of 61850 standards, sampling values based on IEC61850-9-2 have become an important part of smart substation construction. With the popularization and application of the sample value (SV), the interpolation algorithm has been increasingly used in protection, measurement, control, wave recorder and power quality applications. However, the error in the interpolation algorithm poses a challenge to its use. This paper describes the basic methods of linear Lagrange and parabolic Lagrange interpolation and presents maximum theoretical values for the interpolation error when Lagrange linear and second-order approximations of sinusoidal signals are performed. The single-point error of each sampling point is analyzed using the remainder equation, and the harmonic error of the Fourier transform after interpolation is strictly mathematically derived. Finally, the accuracy of the theory is verified by real measurement data, and suggestions for the application of the interpolation method are introduced.