Affine algorithm for power system transient stability considering wind power uncertainty

To investigate the impact of conventional generator mechanical output uncertainty, caused by wind power fluctuations, on the transient stability of power systems. An affine algorithm (AA) is introduced to account for uncertainty in power system simulations. Firstly, affine numbers are used to represent the mechanical output range of conventional generators affected by wind power fluctuations. A dynamic characteristic model is then constructed based on wind turbine low voltage ride through (LVRT) parameters during voltage sags. Then, the problem of transient stability assessment under power system uncertainty is formulated as affine differential-algebraic equations (DAEs) that reflects the system's dynamic behavior. Finally, the trapezoidal integration method is employed to solve the affine differential equations, alternating between the differential and algebraic equations. The proposed method allows a rigorous analysis of the impact of uncertainty on system transient stability with only one simulation. A modified IEEE 39-bus system is used to compare the affine calculation results with the Monte Carlo (MC), demonstrating that the proposed algorithm has lower conservativeness and higher computational efficiency.