Polyphase stator winding can be used for increasing the unit capacity of high-power turbine generators. This includes six-phase winding consisting of two separate three-phase windings displaced by 30 electrical degrees. The modern high-power six-phase turbine generators are widely used in the construction of nuclear power plant units. Six-phase turbine generators have some specifics compared with three-phase generators due to mutual inductive coupling between three-phase stator winding systems. Some issues regarding six-phase generators have been described in literature; however, the operation conditions and related aspects have not been studied enough. This article has obtained differential equations defining the operation conditions of a six-phase turbine generator in phase coordinates using the common assumptions from the theory of three-phase machines. The relationship between self and mutual induction of rotor and stator circuits is defined. Leakage reactance of stator circuits is presented as a sum of leakage reactance for the self and mutual induction paths between three-phase stator winding systems. The equations were converted to rotating coordinates synchronous with rotor to provide higher clarity and reduce the amount of resources required for the calculations. We have explored the differences from the well-known equations for three-phase machines. The equation for the rotor movement of the six-phase generator has been determined. We have chosen the relative units allowing to simplify the obtained expressions and compare the parameters with those of ordinary three-phase generators. By this equations of six-phase generator operation are obtained. These relative units enables us to find the equations similar to the Park-Gorev-form equations for three-phase turbine generators. Solving these equations by traditional methods known for three-phase machines allow studying the operation modes and transient processes of six-phase turbine generators.