A Convexification Approach for Small-Signal Stability Constrained Optimal Power Flow

In this article, a novel convexification approach for small-signal stability constraint optimal power flow has been presented that does not rely on eigenvalue analysis. The proposed methodology is based on the sufficient condition for the small-signal stability, developed as a bilinear matrix inequality (BMI), and uses network structure-preserving differential algebraic equation modeling of the power system. The proposed formulation is based on semidefinite programming and objective penalization that has been proposed for feasible solution recovery, making the method computationally efficient for large-scale systems. A vector-norm based objective penalty function has also been proposed for feasible solution recovery while working over large and dense BMIs with matrix variables. An effectiveness study carried out on WECC 9-bus, New England 39-bus, and IEEE 118-bus test systems shows that the proposed method is capable of achieving a stable equilibrium point without inflicting a high stability-induced additional cost.