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The paper proposes a novel approach to the measurement of the power grid voltage and/or current fundamental harmonic, using stochastic digital measurement method (SDMM) and 2-bit flash A/D converters. The power grid frequency variation in the European interconnection has been found as Gaussian. The influence of the frequency disturbance on the results of fundamental harmonic measurements is examined in detail. As theoretical analyses are extremely complex due to a high nonlinearity and stochastic nature of the problem, simulation analysis is employed as the primary method for fast testing and confirmation of the paper hypothesis. The results of realistic simulations give the measurement uncertainties below 0,01 % and 0,013 %, for the measured grid voltage and current, respectively. Experimental validation has been carried out by comparison of the commercial instrument measurements and the measurements of SDMM based prototype instrument. It has been found that results are in accordance.