Semidefinite Programming: A Practical Application to Hydro -Thermal Coordination

A non-decomposition solution method for the Hydro-Thermal Coordination (HTC) problem based on Semidefinite Programming (SDP) is presented in this paper. SDP is a convex programming method. The variables of the problem are sorted in a vector, which is used to con- struct a positive-definite matrix; the optimal solution is then found in the cone defined by the set of positive-definite ma- trices. An HTC problem can be formulated as a quadratic optimization problem without explicitly stating the integer value requirements for the thermal-plants (commitment) dis- crete variables. Therefore, the non-convex integer-value con- straints can by replaced by convex quadratic constraints so that SDP can be used. SDP has polynomial solution time be- cause it can be solved using Interior Point Methods (IPM). The technique can be used to solve a problem without relax- ations typically used in large scale combinatorial problems like (HTC), such as relaxations of coupling constraints (de- mand and spinning reserve) or integer variables relaxations. A SDP relaxation (solution) shows only minor mismatches in the integer variables, which are easily corrected by a heuris- tic method. For different size test cases, the solution provided by SDP is compared to other classic solution techniques, such as Lagrangian Relaxation (LR) and Interior Point Method (IPM).