Detailed reasoning and derivation of a convexificated quadratic approximation approach for the Security Constrained Optimal Power Flow

In comparison to state of the art relaxation and approximation approaches an enhanced convexificated quadratic approximation for the Security Constrained Optimal Power Flow (SCOPF) is reasoned and derived. The detailed graphic interpretations have a focus on convexity and accuracy. First, variables are divided into different types and nonlinear equality constraints of the SCOPF are eliminated by implementing a distributed slack. Second, the nonconvex parts of the resulting quadratically approximated functions are identified by eigenvalue analysis and convexificated with piecewise linearizations. Additionally new algorithms for fast calculation of the required Hessians are derived.