Modelling of Sequential Optimal Power Flow by Piecewise Linear Convexificated Quadratic Approximations

Formulating Optimal Power Flow Problems is well- known since the 1960s, but solving those problems to global optimality is challenging until today, due to the nonconvex characteristic of the embedded functions and the huge number of variables and constraints.To handle nonconvexities they have to be eliminated or convexificated. Nonlinear equality constraints are always nonconvex and can be eliminated by inserting them or their inverse function into the objective functions and into all constraints. In this paper the power equation is expanded by a distributed slack, inverted end eliminated as described.The optimization in this paper is done by sequentially solving quadratically constrained quadratic programs (SQCQP). The remaining nonconvex parts of the objective function and the constraints of each QCQP are identified by principal axis transformation and analysis of eigenvalues and then convexificated by piecewise linearization.Thus, a mixed-integer convex quadratically constrained quadratic problem results, which can be solved fast and reliably with e.g., CPLEX or Gurobi. The high accuracy of the convexficated quadratic approximations and fast convergence of the sequential approach is shown in case studies.