Surrogate Lagrangian relaxation and branch-and-cut for unit commitment with combined cycle units

Combined cycle (CC) units are efficient because heat from combustion turbines is not wasted but is used for steam turbines. However, when state transitions are followed, CC units complicate the unit commitment and economic dispatch (UCED) problem. While branch-and-cut has been successful in solving UCED problems without considering CC units, transitions in one such unit affect the entire problem. Therefore, the convex hull is difficult to obtain and the UCED problem with CC units is difficult to solve. To efficiently solve the problem, we exploit linearity as well as separability. To decompose the problem into subproblems associated with conventional and CC units, our recently developed surrogate Lagrangian relaxation will be used to relax coupling system-wide constraints, and each subproblem will then be solved by using branch-and-cut. Constraints as well as transitions within a CC unit are handled locally and no longer affect the entire problem. Moreover, we will demonstrate that branch-and-cut can handle individual subproblems much more efficiently as compared to the original problem. The linear structure of coupling constraints is then exploited to obtain feasible costs. Numerical results demonstrate that the new approach is computationally efficient and generates good feasible solutions.