MILP Formulation for Thermal Unit Commitment Problem: Analysis Report

This report presents a new mixed-integer linear (MILP) formulation for the unit commitment problem in thermal units. The formulation aims to reduce computational complexity by using fewer constraints and binary variables, enabling efficient solutions for large-scale problems. It provides a detailed model for time-dependent start-up costs, minimum up and down times, and ramping limits. The report includes a comprehensive overview of the MILP algorithm, including pre-processing, cut generation, branch-and-bound methods, and heuristics. It also covers the objective function, including production cost, start-up cost, and shutdown cost, along with thermal constraints such as generating limits and ramping constraints. The report reviews the literature, discussing the use of GAMS and CPLEX for solving linear and non-linear programming problems. Finally, it provides a detailed design of the model, including equations for production cost, start-up cost, and shutdown cost, as well as constraints for generating limits, ramping, and minimum up/down times. The report demonstrates how the MILP-UC model helps in solving realistic applications through numerical experience demanding less binary variables and constraints to help in decreasing the computational problem of current MILP approaches.