A control strategy of Hamilton realization and mechanics Lagrangization in doubly-fed wind power generation system

• The controller of GSC and MSC of DFWPG system is designed based on Hamilton realization.
• Realizing a rapid response of the dc bus voltage control by output feedback control strategy.
• Realizing grid-side unit power factor control of doubly-fed wind power generation system.
• Comparing with transient response effects of PI control in Matlab/Simulink environment.

With the nonlinear characteristic of doubly-fed wind power generation (DFWPG) system, Hamilton realization based on analytical mechanics plays a significant role in the system problems of stability analysis and controller design. Hamilton system expression of grid-side converter (GSC) and machine-side converter (MSC) is obtained and the stability control is designed with Lagrange theory of analytical mechanics in this paper. Firstly, to obtain the differential equations which satisfy satisfies self-adjoint conditions, coordinate transformations of dynamic equations of GSC and MSC are conducted. The system Hamilton function and Hamilton realization expression are determined based on Euler–Lagrange process and generalized force method. On the basis of feedback control theory the controller is designed, which can make the system tend to be asymptotically stable in the neighborhood of the equilibrium point. With Hessian matrix positive-definite the Hamilton system is determined to be stable. Additionally, within Matlab/Simulink environment, the transient simulation of DFWPG system is carried out and the effectiveness of controller derived in this paper is verified, by comparisons of response effects with PI control and regulation performances under different wind speeds. The rapid response of the dc bus voltage control, grid-side unit power factor control, a maximum capture of wind energy can be realized, using control design process of Hamilton realization. The system analysis and control design process of Hamilton realization have broad prospects of applications and developments.