Closed dynamical model of a double propeller HAWT

The mathematical model of a counter-rotating horizontal axis wind turbine is constructed. It is supposed that an electrical generator is connected into a local circuit with variable external resistance. External resistance in a local electrical circuit of the generator is a varied parameter of the model. Dynamic equations of the model contain nonlinear functions that describe aerodynamic torque acting on each propeller. This nonlinearity leads to existence of several fixed points of the dynamic system corresponding to operation modes of the HAWT with different characteristics. Existence and stability of steady solutions of the model equations is studied. Parametric analysis of operation modes corresponding to stable fixed points is performed. Domains of attraction of stable steady points are described. Strategies of control via changing of the parameter which is responsible for the external resistance are discussed.