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A two-stage robust Newton-type numerical algorithm for power quality assessment in electric power systems is described. The robust Newton-type algorithm is applied to estimate current and voltage spectra and the fundamental frequency simultaneously, in the first algorithm stage. The algorithm robustness is achieved by developing an extra module called a 'bad data detector'. In the second algorithm stage power quality indicators are calculated, particularly the active, reactive, apparent and distortion powers. The main advantage is that the technique provides estimates which are insensitive to frequency deviations and to bad data appearing as a consequence of communication error, incomplete measurement, errors in mathematical models etc. The algorithm performance is tested under laboratory conditions using the distorted voltage and current signals digitised during an AC motor start. A simulation example of processing distorted currents and voltages of an arc furnace is also presented.