An Accurate Second-Order Cone Approximation of Frequency Nadir Security Constraints Under Large Disturbances

Frequency nadir is one of the key indicators for power system frequency security under power disturbances. However, its inherent nonlinearity presents significant challenges in optimization. This letter proposes a new approximation of frequency nadir security constraints, which is accurate, adaptative and easily solvable for frequency-constrained optimization problems. By investigating the analytical frequency nadir expression, we find that, within the range of actual system parameters, the highly nonlinear expression can be accurately approximated by a linear expression through variable substitutions. This approximation can be used to formulate second-order cone (SOC) constraints that commercial solvers can efficiently handle. Compared to existing methods, the proposed method provides a global and accurate approximation without increasing the complexity of optimization model.