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The DC power supply system on the main railways of the Russian Federation has now almost exhausted its potential for maximum carrying capacity. At the same time, there is a tendency to increase the mass of the train and the train as a whole, which leads to failures of the DC traction network caused by low voltage at the current collector of the electric locomotive and high currents exceeding the current setting of high-speed switches. The DC power supply system needs to be strengthened. One of the amplification methods is the use of thyristor booster devices. The article discusses ways to enhance the DC power supply system and the theory of operation of a thyristor booster device for traction substations with a description and construction of a mathematical model. The description of processes in adjustable rectifiers occurs in the absence of active and reactive resistances, and semiconductor devices have an ideal current-voltage characteristic. The theory of operation and the shape of the rectified voltage of the converter are considered at various angles of regulation using the example of rectifier bridges with a twelve-pulse series-type rectification circuit. The key points in the description of the mathematical model are the angles equal to 0, 60, 90, 120 and 180 electrical degrees. The construction of the forms of the rectified voltage and their definition is carried out on the temporary sections between the key points. [ABSTRACT FROM AUTHOR]