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This paper treats a parallel 12-pulse rectifier as the study subject. The influence of unbalanced terminal voltage, the triggering angle, as well as the commutation angle of a thyristor-controlled rectifier circuit are considered in switching functions. Then, a frequency-domain harmonic coupled admittance matrix under the effect of positive sequence and negative sequence voltages are proposed, respectively. With the integration of the above matrices, a harmonic coupled admittance matrix model of a parallel 12-pulse rectifier under unbalanced voltage is proposed. On this basis, a simplified harmonic model of a 12-pulse rectifier is established, which only considers the effect of major elements through analyzing the elements' distribution and magnitude of the harmonic coupled admittance matrix, as well as the AC current harmonic producing mechanism. All the models proposed in this paper are verified with high accuracy through simulation in MATLAB/Simulink. The models proposed in this paper can be used to guide the selection of harmonic suppression measures and equipment. [ABSTRACT FROM AUTHOR]