This paper describes the general theory of the main circuit constructions and control methods of legs based on output neutral point voltage control under multi-leg power conversion circuits. A controllable fluctuation range of the output neutral point voltage is obtained by the linear programming method under the condition of the desired symmetrical sinusoidal line output voltage. From the analysis, the following points are obtained: (1) the main circuits and control methods of the multi-leg power conversion circuits are constructed by simple theory based on output neutral point voltage control; (2) the controllable maximum line voltage of the each ideal main power circuits is obtained by calculating of the minimum controllable fluctuation range of the output neutral point voltage; and (3) the removed and the common leg conversion circuits can also be realized by simple neutral point voltage control, and high efficiency, low cost and small size converters are achieved. It is clear that this theory expands conventional schemes and it is simple and standard theory on the all multi-leg conversion circuits in the case of symmetrical sinusoidal line output voltage.