A performance comparison of a primal-dual interior point method vs. Lagrangian relaxation to solve the medium term hydro-thermal coordination problem

In deregulated electric energy systems, the solution time of hydro-thermal scheduling problems has become critical. This large scale, nonlinear, nonconvex problem has been solved using various methods. In this paper, the computational performances of direct and decomposition methods are compared using stand alone applications of these techniques running in the same platform. The direct method is based on a primal-dual interior-point method. The binary variables of the thermal generator's status are relaxed; the relaxed solution is subsequently treated by a rounding strategy based on thermal operational constraints so that an integer solution is achieved. The decomposition approach is based on Lagrangian relaxation. The thermal subproblems are solved using dynamic programming and the hydro supbroblems are solved using linear programming techniques. The maximization of the dual function is accomplished using cutting-plane methods. A validation heuristic technique is implemented to reschedule the necessary plants in order to satisfy the relaxed constraints. Both solution methods are coded in C programming language, and they are run under Linux operating system. Several test systems are used to make a performance comparison of both solution techniques.