With the continuous increase of penetration level of wind power

and the step-by-step promotion and application of virtual inertia and primary frequency control technology

the accurate calculation of wind power penetration limit has important significance to ensure the safe and stable operation of power grid and to guide the planning and construction of wind power integration system. For this purpose

the inertial response of wind farm is expressed quantitatively

and the primary frequency regulation response of wind farm is described by employing transfer function model. Furthermore

swing equations of an equivalent rotor

including the frequency regulation control of synchronous generator and wind turbine

are established to describe the frequency response characteristics of power system. On this basis

taking the grid steady-state frequency deviation and frequency change rate constraints as boundary conditions

an analytic solution method for calculating the wind power penetration limit is proposed. Finally

the accuracy and effectiveness of the proposed method are verified by case studies of IEEE 14-bus power system.