Lagrangian Relaxation has been proposed in the literature as an attractive UC solving methodology because the problem is decomposable if the “coupling” constraints Energy Balance and Reserve Requirements are relaxed. The convergence criterion is usually based on the duality gap which is the difference between the best feasible integer solution and the dual solution (lower bound). The dual comes from evaluation of the Lagrangian functional.
If these constraints are relaxed, the problem becomes an individual generator’s commitment problem. Therefore, there are 2 observable advantages: 1) Classical: linear reduction of computational burden and 2) Modern: parallel computing. Theoretically, LR can be used to solve large UC problems. The recognized disadvantages are: Lagragian multipliers fine tuning, erratic convergence and difficulty to obtain feasible solutions. More modern approaches also suggest that LR solutions also suffer from over commitment.