Global Optimization of Non-Convex Hydro-Thermal Coordination Based on Semidefinite Programming

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.