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A method for the evaluation of the uncertainties in the measurement of power in distorted signals is described. A sampling method is utilized for the acquisition of the signals and the power is computed from the harmonic components obtained by the best fit. An equivalent algorithm is applied to derive a simplified relation between the correlation matrix of the harmonics and that of the samples. The uncertainties are then evaluated by a model of the uncertainty in a single sample given by the manufacturer of the sampling voltmeters.