Chance-Constrained Transient Stability Optimal Power Flow Considering Wind Power Uncertainty Based on DDPCE-MEM

To address the dependence of uncertainty analysis methods on assumed probability density functions of wind power output and the computational burden of time-domain simulations in transient stability-constrained optimal power flow (TSCOPF) problems, this paper proposes a chance-constrained transient stability-constrained optimal power flow (CCTSCOPF) solution method based on data-driven polynomial chaos expansion (DDPCE) and the maximum entropy method (MEM). The method eliminates the need for predefined distribution assumptions for wind power variables. Specifically, using N = 5000 historical wind power forecast error samples, raw statistical moments up to order 2p = 8 are extracted, and orthogonal polynomial basis functions up to order p = 4 are derived by solving a 5 × 5 linear algebraic equation system constructed from these moments. Based on the constructed polynomials, Gaussian quadrature collocation points of wind power output are obtained, and time-domain simulations are performed at these points to solve the expansion coefficients, establishing a surrogate model that maps wind power fluctuations to transient responses. The surrogate model then computes the statistical moments of transient stability indices. MEM is subsequently used to reconstruct the probability density function of the transient stability index, and the transient stability chance constraint is converted into an algebraic boundary condition. Finally, an optimization model incorporating power system operating constraints is formulated and solved. Case studies conducted on the modified IEEE 39-bus test system with two 100 MW wind farms demonstrate that the proposed surrogate model achieves high accuracy with R2 = 0.987, significantly improving uncertainty quantification accuracy over the standard Wiener–Askey polynomial chaos expansion (PCE) method. Furthermore, the total computational runtime is reduced from 66,280.00 s under full-scale Monte Carlo simulations to 47.92 s, achieving a 1383× computational speedup while strictly satisfying transient stability chance constraints.