Optimal frequency control method for large-scale offshore wind farm integrated power system under stochastic continuous disturbances

With the growing integration of large-scale wind power into power systems, the low inertia of wind turbines weakens the disturbance rejection capability of power systems, posing significant challenges to frequency security control. In this paper, an optimal frequency control (OFC) method for a large-scale offshore wind farm (OWF)-integrated power system under stochastic continuous disturbances (SCDs) of node powers is proposed. First, a feedback control strategy is developed to enable wind power participation in frequency support. By taking the probability density function (PDF) of steady-state frequency deviation as the control objective and incorporating the chance constraint to ensure that the maximum transient frequency deviation satisfies safety requirements, an OFC model under SCDs is formulated. A corresponding solution method for the stochastic OFC model is then proposed. The system frequency dynamics are represented using the Itô stochastic differential equations. Based on the Fokker–Planck–Kolmogorov equation, mixed-moment differential equations (MMDEs) of the state variables are derived, and the PDF of steady-state frequency deviation in the objective function is approximated using statistical moments. The approximate solutions of the MMDEs are obtained through the parameterized approximation method, and the analytical expression of the transient frequency deviation PDF is derived using cumulants and Gram-Charlier series expansion. Consequently, the stochastic OFC model is transformed into a nonlinear algebraic optimization model that can be solved directly. Finally, a case study on a modified IEEE-39 bus system integrated with an OWF demonstrates the effectiveness of the proposed method.