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A new definition that can be used to evaluate the unbalance in electrical power systems in the presence of harmonic and interharmonic distortion is presented. A new unique transformation matrix that is capable of suitably extracting the balanced, first unbalanced, and second unbalanced components suitable for all of the harmonic and interharmonic orders is introduced. This new decomposition method overcomes the limitation of a similar method previously presented in the literature, a method that is not in agreement with Fortescue transformation and does not to take into account the presence of interharmonic components. The decomposition presented makes it possible to evaluate the quantities defined in the IEEE Standard 1459-2010, taking into account the unbalances produced by harmonics and interharmonics and extending some important definitions to signals characterized by interharmonic distortion. Numerous numerical case studies and experimental results show the applicability of the proposed method and its usefulness.