In this paper, a new two-stage Newton-type algorithm for the measurement of power components according to the IEEE Standard 1459-2000 is presented. To estimate their spectra and fundamental frequency, in the first stage, the current and voltage signals are processed, whereas in the second stage, the power components are calculated based on the results obtained in the first stage. The algorithm considers the frequency as an unknown parameter and simultaneously estimates it with the input signal spectrum. Through this, the algorithm becomes insensitive to frequency changes and the problem becomes non-linear. The algorithm performance is tested using computer-simulated and laboratory tests.