This paper describes a new formulation of the security-constrained optimal power flow (SCOPF) problem and proposes a sequential linear programming algorithm for its solution. The new formulation introduces mismatch variables to ensure that the algorithm remains in the feasible region. Thus the algorithm starts from an arbitrary state: mismatch currents are computed and introduced at each bus to make the present iterate appear in a feasible region. The algorithm moves the solution towards the optimal while minimizes the mismatch variables. When the mismatch variables are zeroed, the optimal has been found. At each iteration, the problem is formulated as a nonlinear optimization problem with linear or quadratic equations via a quadratization procedure presented in earlier papers. The formulation and algorithm is demonstrated on a three-bus system.