Linearised Optimal Power Flow Problem Solution using Dantzig - Wolfe decomposition

The optimal power flow problem can be used to determine the generation dispatch in electrical grids taking into account circuit physics and technical constraints. This paper uses an old-fashioned mathematical decomposition technique, the Dantzig-Wolfe decomposition, to solve such problems and compares the results to state-of-the-art commercial solvers.The linearised ’DC’ OPF model is reformulated to create a block angular structure of the problem and is optimized through a column generation algorithm based on the simplex method. Columns of variables are generated for each iteration of the optimization process, providing a solution where selected vertices from the feasible sets are assigned a weight and combined to get the optimal value.The results of three test cases consist of an useful starting point for further works with larger test systems and MILP problems such as the transmission network expansion planning problems.