A novel projected two-binary-variable formulation for unit commitment in power systems

The thermal unit commitment (UC) problem in power systems can usually be formulated as a mixed-integer quadratic programming (MIQP) problem, which is an NP-hard problem for practical-scale systems and thus is difficult to solve efficiently. In this paper, by projecting the unit generation level onto the interval [0,1] and using reformulation techniques, a novel two-binary-variable (2-bin) MIQP formulation for the UC problem is proposed. The proposed 2-bin formulation is more compact than the state-of-the-art one-binary-variable (1-bin) and three-binary-variable (3-bin) formulations. Moreover, the 2-bin formulation is tighter than the 1-bin and 3-bin formulations in terms of the quadratic cost function, and it is tighter than the 1-bin formulation in terms of linear constraints. The proposed model was tested on 73 instances, including 43 realistic instances and 30 8-unit-based instances, over a scheduling period of 24 h for systems ranging from 10 to 1040 generating units. The simulation results show that our proposed MIQP UC formulation is the tightest and most compact model and can be solved most efficiently. After introducing a sequence of piecewise perspective cuts to approximate the quadratic operational cost function, the three UC MIQP formulations can be approximated by three corresponding mixed-integer linear programming (MILP) formulations. Our experiments show that the proposed 2-bin MILP formulation also performs the best in terms of solution times.