DC-based security constraints formulation: A perspective of primal-dual interior point method

The DC network security constraints have been extensively studied in numerous power system problems, such as optimal power flow (OPF), security-constrained economic dispatch (SCED), and security-constrained unit commitment (SCUC). Power transfer distribution factors (PTDFs) are widely applied in DC network constraints. However, the PTDF matrix is extremely dense, making it difficult to solve security-constraint optimization problems. This paper investigates the computational inefficiency of PTDF-based security constraints from the perspective of matrix sparsity of primal-dual interior point method (IPM), and proposes a matrix transformation to restore sparsity during IPM iterations. It turns out that the transformation method is equivalent to solving the original optimization problem expressed in pure voltage angle. The regular B-theta formulation is also a variant of the proposed transformation. Numerical studies show that sparsity rather than the size of variables and constraints is the key factor impacting the speed of solving convex quadratic problems, i.e., OPF and SCED problems. The proposed transformation significantly outperforms the PTDF-based approach, achieving a 100x reduction in non-zero elements of the coefficient matrix and a 40x speed increase in barrier processes in a 25,000-bus network.