In this paper we present a method for reconstructing the true harmonic composition of power quality indices, such as voltages and currents in cases when the actual fundamental frequency in a power grid differs from its nominal value. We have shown that even if an instrument incorrectly assumes the fundamental frequency to be equal to the nominal value, it is still possible to use the measurement results to obtain the exact signal spectrum under a certain set of conditions. The proposed procedure has proved to be in full compliance both with standards and practical observations concerning frequency drifts in power grids. The method has been applied in an improved version of the power quality instrument based on stochastic ADC which measures up to 50 harmonics of 3 voltages and 4 currents within 20 ms.