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To transmit high power very-low-frequency signals with low harmonic content, the high-frequency cascaded H-bridge multilevel inverter (HF-MLI) usually has large number of levels and uses the selective harmonic elimination (SHE) technique for modulation. However, when the number of levels exceeds 25, the conventional SHE switching angle computation methods have a problem since the computed switching angles tend to be located at 0 and π/2, which makes the harmonic suppression effect worse. To realize a good harmonic suppression effect for HF-MLIs with a large number of levels, an interior-point-method-based switching angle computation method is proposed in this paper. With the aid of the interior point method (IPM), the constraints of switching angles are combined with the harmonic function in the objective function through a penalty function. The iteration is divided into the inner loop and the outer loop. The switching angles are computed in the inner loop and the weight of the penalty function is updated in the outer loop. The penalty function can keep the switching angles away from constraints. When compared with conventional methods, the proposed method has a higher accuracy, a shorter execution time and better harmonic suppression effect when computing the switching angles of MLIs with more than 25 levels. The harmonics from 9 to 19th-order of the proposed method are suppressed to less than 0.1%, which is experimentally verified on a single-phase 49-level HF-MLI. [ABSTRACT FROM AUTHOR]