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In order to reduce the fuel cost of thermal units, a semidefinite programming (SDP) method is used to solve a hydrothermal coordination (HTC) optimization problem. By manipulating the structure of decision variable matrix, the original nonconvex problem is reformulated into a convex SDP relaxation model without sacrificing the nonlinear relation among hydropower generation, reservoir storage volume, and discharge water. A global minimum is therefore guaranteed and well-developed convex optimization theories can thus be employed to solve the problem. Both sparse matrix techniques and a simplified SDP model are discussed to reduce computational cost. One mostly used HTC case is employed to test the performance of the proposed method. Detailed comparisons between the proposed and other methods show that the final result of SDP model is by far the best result ever. In addition, a large-sized HTC case shows the potential of SDP in practical use. Finally, we prove that as a relaxation technique, the SDP solution, which satisfies all the constraints, is indeed the optimal solution of the original nonconvex problem. [ABSTRACT FROM PUBLISHER]

This paper presents a novel method to solve the unit commitment (UC) problem by solving a sequence of increasingly tight continuous relaxations based on the techniques of reformulation and lift-and-project (L&P). After projecting the power output of unit onto [0, 1], the continuous relaxation of the UC problem can be tightened with the reformulation techniques. Then, a tighter model which is called L&P-TMIP is established by strengthening the continuous relaxation of the feasible region of the tight UC problem iteratively using L&P. High-quality suboptimal solutions can be obtained from the solutions of the relaxation for this tight model. The simulation results for realistic instances that range in size from 10 to 200 units over a scheduling period of 24 h show that the proposed tight relaxation method is competitive with general-purpose mixed integer programming solvers based methods for large-scale UC problems due to the excellent performance and the good quality of the solutions it generates. [ABSTRACT FROM PUBLISHER]