The invention discloses an electromagnetic transient mathematical model of a distributed power-flow controller based on an MMC, control system and a modeling method. The distributed power-flow controller comprises a parallel connection side converter composed of a three-phase converter based on the MMC at the parallel connection side and a parallel connection side single-phase converter and a series connection side converter composed of multiple sets of series connection side single-phase converter; the electromagnetic transient mathematical model mainly comprises a parallel connection side converter model and a series connection side converter model; the control system comprises a parallel connection side control model and a series connection side control model, the parallel connection side control model comprises a three-phase converter control module based on the MMC at the parallel connection side and a parallel connection side single-phase converter module, and the series connection side control model comprises a series connection side third harmonic control module and a series connection converter active power reactive power control module. The electromagnetic transient mathematical model is designed by adopting modularization, the sub module switch-on and switch-off frequency is lowered, and the loss is lowered; the control system adapts to different voltage grades, and is applicable to flexible alternating current transmission occasions.