Lagrangian Relaxation of Large-scale Congestion Management using Extended Subgradient Methods

Modeling a high amount of decentralized flexibility options within the congestion management simulation of transmission grids leads to a significant increase in the complexity of the resulting optimization problem. For this purpose, this paper presents a decomposition approach of a congestion management model using the Lagrangian relaxation method in combination with the volume algorithm to find a reliable primal solution. The decomposed model is applied to a benchmark case, and the results are validated by comparison to the closed solution. Therefore, a comparison of the primal objective function value and locational marginal prices for redispatch derived from shadow prices of system coupling constraints occurs. It can be observed that the shadow prices are matched with very high precision, thus validating the approach.