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This paper presents a model to represent the harmonic generating characteristics of the thyristor controlled reactor (TCR). The model transforms the time domain nonlinear characteristics of the TCR into a frequency domain linear admittance matrix. The matrix couples the TCR harmonic voltages and currents and it does not vary with the harmonic conditions of the system. This paper presents the theoretical basis and analytical derivation of the model. Comparison of the matrix model results with the time domain simulation results is used to verify the validity and accuracy of the proposed model.