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Nonsinusoidal conditions in modern power systems require special definitions to quantify power. A clear physical interpretation of different conditions, leading to different phenomena, is essential to enable engineers to relate power measurements to meaningful physical manifestations in the power network with the objective of tariff implementation and the design of compensation strategies. L.S. Czarnecki originated a number of unique power definitions in the frequency domain that conform very well to these requirements. Unfortunately an important, but hitherto neglected deficiency appears to be present in the Czarnecki definitions: under practical conditions, the summation of power in three-phase networks with distorted waveforms yields erroneous results. This paper investigates this important inherent deficiency of the Czarnecki power theory.