Optimization based methods for unit commitment: Lagrangian relaxation versus general mixed integer programming

Lagrangian Relaxation (LR) and General Mixed Integer programming (MIP) are two main approaches for solving Unit Commitment (UC) problems. This paper compares the LR and the state of art general MIP method for solving UC problems based on performance analysis and numerical testing. In this paper we have rigorously proved that UC is indeed an NP complete problem, and therefore it is impossible to develop an algorithm with polynomial computation time to solve it. In comparison with the general MIP methods, the LR methodology is more scaleable and efficient to obtain near optimal schedules for large scale and hard UC problems at the cost of a small percentage of deviation from the optimal solution. In particular, solving hydro generation sub-problems within the LR framework can take advantages of both LR and general MIP methods and provide a synergetic combination of both approaches.