On the equal substitution of MILP unit commitment subproblems with dynamic programming

By splitting unit commitment into a coupling problem and individual unit commitment subproblems, Lagrangian relaxation is very effective in decreasing the solving time of large scale problems. Consequently, unit commitment subproblems should be solved equally fast. If they have been originally formulated in mixed-integer linear programming, performance advantages can be expected by replacing it with dynamic programming. However, it has not been reported whether a one-to-one reformulation is feasible. We suggest approaches to choose states for dynamic programming that replicate equal solutions as well as measures to reduce memory requirements. Results of the two subproblem models differ only fractionally and for explicable reasons. Subproblem computation time has been reduced by up to 100 times at modest memory requirements.