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In this paper, the coreless medium-frequency induction melting furnace (IMF) system is represented by alternative field-data-based models, developed specifically for power quality studies. The IMF operation has been represented by a variable series RL circuit, to model the fundamental components of electrical quantities, and a shunt-connected current source, to model the generated harmonics and interharmonics over a typical melting cycle. Both the sinusoidal coding method applied to the major harmonics and interharmonics in the supply line currents obtained from field measurements and the raw data have been used in the developed models. It has been shown that the sinusoidal coding method can be used to satisfactorily represent the operation of the IMF system as seen from the supply terminals, with a minimum data storage requirement, and can be used to construct efficient IMF databases for power quality studies. The power quality problems of the IMF system, particularly the problematic time-varying interharmonic voltage distortion, and the interaction of those time-varying interharmonic currents with the passive shunt filter installations connected to the same bus have been investigated in detail, using the developed models.