Application of semidefinite programming relaxation and selective pruning to the unit commitment problem

The objective of this paper is to introduce a semidefinite programming relaxation based technique combined with selective pruning (SDPSP) to achieve faster convergence to a (near)-optimal solution of the unit commitment problem. The compact form of the SDP variable matrix and the concise formulation of the start-up cost constraints contribute to a reduced constraint framework dimension which has profound implications on performance. The computation time is also significantly enhanced by the selective pruning algorithm that prunes all the feasible periods and effectively shrinks the scheduling horizon as the solution is approached. The selective pruning algorithm incorporates two complementary repair mechanisms that exploit the characteristics of the constraint formulation and the properties of SDP relaxation to correct the binary variable violations. The method efficiently handles inter-temporal constraints such as ramp rates that are deemed crucial in practical systems. The prowess of the method is demonstrated by comparing it with other recently proposed techniques.

► A combination of compact formulations contributed to a significant framework dimension reduction reflecting in an enhanced timing performance.
► The formulation generates very few violations of the integrality constraints (commitment variables U take non (0, l) values) which can be subsequently adjusted using the repair technique.
► The superiority of the method is most salient in larger systems.
► The method efficiently handles inter-temporal constraints such as ramp rates.