Active front-end is often used in power supply systems, such as regulated electric drive, electric generators of various types, including those based on renewable energy sources, used to power their own needs or as systems for maintaining the electrical network in parallel operation. In such systems, if necessary, the neutral wire can be connected to the midpoint of the capacitors on the DC side of the Converter or create an additional channel for the flow of zero-sequence currents through an additional branch of transistors. It should be noted that the scheme for connecting the neutral wire to the midpoint of the capacitors has a number of disadvantages, such as the voltage imbalance between the capacitors in the DC link, as well as the flow of currents of higher harmonics and zero-sequence currents through the capacitors when they are compensated. These problems can be resolved by using a scheme with an additional branch. This arrangement of an electric semiconductor Converter makes it possible to use the full voltage in the DC link and control the zero-sequence currents. The article discusses the construction of a mathematical model of an active front-end with four transistor branches as a control object based on the analysis of key state combinations when working on a load. A mathematical description of an active front-end with an additional branch in matrix form is given. The proposed mathematical model can be used for the synthesis of regulators of the automatic control system of the Converter and the allocation of zero-sequence currents in order to compensate for them, which is a significant factor for future research of the entire system of an active front-end with an additional branch.