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This paper proposes a new modeling method for Buck three-level (TL) converter. Based on the equivalent translation principle, the operating conditions of the Buck TL converter in different modes can be transformed into linear inequalities. Then, a new model of Buck TL converter containing matrix inequality is obtained. Compared with other Buck TL converter models, the proposed model of Buck TL converter is more concise. Finally, the proposed model is simulated in MATLAB and its effectiveness is verified by simulation and experimental results. Moreover, the experimental results are consistent with the simulation results.