Non recursive multi-harmonic least squares fitting for grid frequency estimation

• We derived a closed form frequency estimator based on least square fitting.
• Estimation error reaches the CRB for a range of frequencies around a central value.
• This range can be broaden increasing the Taylor’s approximation order.
• Second order approximation is sufficient for the typical grid frequency fluctuations.
• Execution time is strongly reduced allowing real-time measurements.

A new method to approximate the least squares multi-harmonic fitting is proposed. The basic idea is to expand in Taylor’s series the derivative on ω of the least squares cost function around a central value, so reducing the frequency estimation to a calculation of a root of a polynomial. In this way the method provides a frequency estimation in a closed form avoiding the recursion that is necessary in the classical approach. The results show that the proposed algorithm reaches the Cramer–Rao bound in a narrow range of frequency around a pre-estimation. Increasing the approximation orders of the Taylor’s expansion the range of maximum accuracy widens. This method is particularly suitable in grid frequency estimation due its low variability. The proposed algorithm, preserving the accuracy, requires an execution time up to 8 times lower compared to a single iteration of the classical recursive approach.