Tighter relaxation method for unit commitment based on second-order cone programming and valid inequalities

A tighter relaxation method (RM) for unit commitment (UC) is proposed based on second-order cone programming (SOCP) and valid inequalities (VIs). First, a tighter mixed integer SOCP (MI-SOCP) reformulation of UC is constructed using the traditional mixed integer quadratic programming (MI-QP) formulation and a convex hull description of a simple mixed integer set. The continuous relaxation of the MI-SOCP which is called a SOCP relaxation can give tighter lower bounds for UC than the continuous relaxation of the MI-QP. Then, the SOCP relaxation is strengthened by two categories of VIs, i.e., minimal cover inequalities (MCIs) for minimum on/off time constraints and generalized flow cover inequalities for ramp rate constraints. Moreover, it is proved that all the MCIs for minimum on/off time constraints can be obtained by explicit formulas. Finally, the strengthened SOCP relaxation is solved, and the minor relaxed integer variables between 0 and 1 are repaired by a simple heuristic method. The numerical results show that the proposed RM has good convergence properties in term of the total operation costs and the CPU time.