In power system studies the unit commitment problem (UC) is solved to support market decisions and assess system adequacy. Simplifications are made to solve the UC faster, but they are made without considering the consequences on solution quality. In this study we thoroughly investigated the impacts of simplifications on solution quality and computation time on a benchmark set consisting of almost all the available instances in the literature. We found that omitting the minimum up- and downtime and simplifying the startup cost resulted in a significant quality loss without reducing the computation time. Omitting reserve requirements, ramping limits and transmission limits reduced the computation time, but degraded the solution significantly. However, the linear relaxation resulted in less quality loss with a significant speed-up and resulted in no difference when unserved energy was minimized. Finally, we found that the average and maximum capacity factor difference is large for all model variants.

The unit commitment problem (UC) is an optimization problem concerning the operation of electrical generators. Many algorithms have been proposed for the UC and in recent years a more decentralized approach, by solving the UC with alternating direction method of multipliers (ADMM), has been investigated. For convex problems ADMM is guaranteed to find an optimal solution. However, because UC is non-convex additional steps need to be taken in order to ensure convergence to a feasible solution of high quality. Therefore, solving UC by a MIL(Q)P formulation and running an off-the-shelf solver like Gurobi until now seems to be the most efficient approach to obtain high quality solutions. In this paper, we introduce a new and efficient way to solve the UC with ADMM to near optimality. We relax the supply-demand balance constraint and deal with the non-convexity by iteratively increasing a penalty coefficient until we eventually force convergence and feasibility. At each iteration the subproblems are solved by our efficient algorithm for the single UC subproblem developed in earlier work and our new ADMM algorithm for the transmission subproblems. Computational experiments on benchmark instances demonstrated that our algorithm produces high-quality solutions. The computation time seems to grow practically linear with the length of the time horizon. For the case with quadratic generation cost our algorithm is significantly faster than solving the problem by a state-of-the-art MIL(Q)P formulation. For the case of linear generation cost, it outperforms the MILP approach for longer time horizons.