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In order to meet the power flow regulation requirements of distribution network and improve the power flow regulation ability as well as response speed, a novel multi-line hybrid unified power flow controller for distribution network (D-MHUPFC) is proposed. Based on Sen transformer, unified power flow controller (UPFC), and hybrid on-load tap changer, D-MHUPFC can quickly adjust the multi-line power flow of distribution network. Compared with the traditional regulation mode, D-MHUPFC has the advantages of compact structure, fast response, good economy, and high reliability. Then, the multi-line power flow equation considering D-MHUPFC is derived with the ZIP load model, and its cooperative control strategy is optimized. Finally, the effectiveness of proposed D-MHUPFC is proved by a 10 kV distribution network simulation platform. The results show that D-MHUPFC and its control strategy can quickly adjust the multi-line power flow within 0.15 s, and transfer the overload power as well as improve the section transmission limit. Moreover, D-MHUPFC can realize decoupling control, and the compensation errors are less than 1%. It is verified that D-MHUPFC has the same power flow regulation ability as UPFC.