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The processes of voltage distortion variations which are characterized by such electric power quality indices as harmonic voltages and voltage unbalance are random. The paper shows that in power networks with different types of loads these random processes are characterized by correlation functions of different types with different numerical values of their parameters. To obtain the necessary level of measurement accuracy, the sampling rate within the period of the power network voltage and the amount of the sample during measurement in each concrete case must be different. The research revealed that neglecting the random process features in the measurement of the levels of the above-mentioned electric power quality indices may sometimes reach tens of percent. In addition, errors of voltage harmonics measurement in high-voltage power networks appear due to the nonlinearity of the frequency response of the voltage transformers. These errors can be over ten percent also. The possible large values of the measurement errors, caused by the two factors mentioned above, show the expediency of smart meters which can automatically correct the measurement results.