Solving the unit commitment problem using semidefinite programming combined with Lagrangian relaxation / by Sleiman Nassif Mhanna.

Abstract

In a power system, the unit commitment problem involves determining an optimal start-up and shut down schedule of the generating units to meet the forecasted load, over a future short term period (24-168 hours), while ensuring reliability by allocating adequate spinning reserve. The objective of this research is to introduce two distinct Semidefinite Programming (SDP) relaxation based techniques to achieve faster convergence to a (near)-optimal solution of the unit commitment problem. In both techniques, 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 that has profound implications on performance. In the first technique, SDP aims at replacing conventional dynamic programming used to solve the subproblems in the unit commitment Lagrangian relaxation method. In the second technique, SDP solves a relaxation of the complete problem and employs a selective pruning to efficiently correct any binary variable violations emanating from the relaxation this technique is referred to as SDPSP - SDP with selective pruning. The computation time is significantly enhanced in the SDPSP algorithm by pruning all the feasible periods this 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 SDP based methods efficiently handle inter-temporal constraints such as ramp rates that are deemed crucial in practical systems. Both techniques were tested on a set of benchmark systems and compared with recently published methods. The SDPSP method demonstrated its superiority over other proposed techniques through a set of compelling results and time efficient computations. However, for large systems, the Lagrangian relaxation based method fails to generate satisfactory results within rea