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Due to an increase of power-electronic equipment installation and other harmonic sources, the identification and estimation of harmonic loads are of concern in electric power transmission and distribution systems. Conventional harmonic state estimation requires a redundant number of expensive harmonic measurements. In this paper, we explore the use of a statistical signal-processing technique, known as independent component analysis (ICA) for harmonic source identification and estimation. If the harmonic currents are statistically independent, ICA is able to estimate the currents using a limited number of harmonic voltage measurements and without any knowledge of the system admittances or topology. The results are presented with computer simulations for the modified IEEE 30-bus test system.