The invention relates to a thermodynamic system of an extraction back pressure turbine and a control method of the thermodynamic system. According to the system, an ultrahigh pressure cylinder and an intermediate pressure cylinder are separately connected to a regenerative system; a high pressure cylinder is connected to a condensing turbine; and the turbine is connected to an auxiliary power grid through a generator motor and a converter. The control method comprises the steps that: a boiler is started, and the generator motor serves as a motor to drive the turbine and a feed pump shaft system to operate; after the turbine enters an impulse rotating mode, a turbine control valve is controlled to be enlarged, the turbine drags a feed pump to operate, and the generator motor operates as a generator; after the turbine rotates, the turbine and the feed pump enter a normal operation mode, the converter is adjusted to control and balance output of the turbine and the feed pump, and then the rotation speed of the feed pump is controlled; and when the converter and the motor generator break down, the turbine control valve is controlled to be turned down to prevent the turbine from overspeed. Compared with the prior art, the thermodynamic system has the advantages that the problem of a large heat transfer temperature difference can be solved, meanwhile, reliable operation of the system can be guaranteed, and the heat efficiency of the system is improved.