Stochastic stability analysis method for doubly fed generator sets considering random blade stress

Abstract

Abstract With the increasing capacity of doubly fed induction generators (DFIGs), the diameter of the wind turbine is increasing, the blades are getting longer and longer, and in the process of power generation, the tower shadow effect as well as the role of wind shear are more obvious, and the random blade stresses caused by this is also getting bigger. Random blade stresses cause random and cyclic fluctuations in the power generated by the wind turbine, and power fluctuations often cause voltage flicker, which affects the control system and power quality. To address the impact of random blade stresses on the grid‐connected stability of DFIG, the results of the traditional stability analysis methods may be too conservative or lead to too high a dimensionality to be analyzed. To solve the above problems, this paper proposes a grid‐connected stochastic stability analysis method for DFIG sets considering random blade stresses based on the stochastic averaging method under the Hamiltonian system. a stochastic dynamics model of the doubly fed wind farm was established by considering random blade stress. Subsequently, using the proposed generalized Hamiltonian principle, the model and energy functions in the proposed Hamiltonian form H, based on the stochastic averaging method (SAM), were established to obtain the system energy diffusion equation. Probability density function and regional stability probability were obtained from explicit expressions of the mean and regression square root processes. The drift and diffusion coefficients were obtained using the SAM, and the backward Kolmogorov equation was derived from the Ito equation to obtain the conditional reliability function and the probability density of the first crossing time. Finally, the effects of torque fluctuations with different stochastic intensities on the grid‐connected stability of doubly fed wind farms were investigated, and the effectiveness of the proposed generalized Hamiltonian SAM applied to the stochastic stability analysis of DFIG was verified by numerical analysis and Monte Carlo simulation. This provides a theoretical foundation for analyzing the grid‐connected stability of DFIG affected by random blade stresses.

Keywords

• Hamiltonian theory
• probability density of first‐passage time
• random blade stress
• regional stability probability
• stochastic stability