In HVDC transmission systems, DC magnetic bias in converter transformers can cause the transformer core to saturate, resulting in a substantial amplification of AC/DC harmonic components. This phenomenon prolongs the commutation duration and reduces the commutation margin, thereby significantly increasing the commutation failure risk. While the area-minimum (AMIN) control employed in engineering can calculate the fundamental-frequency commutation margin area in real time and promptly adjust firing angles, this approach neglects the influence of DC magnetic bias on the AMIN control strategy. This oversight limits the effectiveness of AMIN control in mitigating commutation failures. To address this limitation, this study first investigates the impact of DC magnetic bias on AMIN control performance. Subsequently, a critical threshold for single-harmonic distortion rate is defined, and harmonic content boundaries for commutation failure avoidance are analytically derived. Then, a novel commutation failure detection method based on harmonic content boundaries is proposed, along with a modified AMIN control that incorporates harmonic compensation and phase-shift adjustments. Finally, the proposed methodology is validated through simulations using the Three-Gorges-Shanghai DC project model. Comparative analysis against conventional schemes demonstrates that the modified control exhibits superior performance in suppressing commutation failures and mitigating DC current discontinuity during system recovery period.