Comparison of Lagrangian relaxation and truncated dynamic programming methods for solving hydrothermal coordination problems

A comparative study of Lagrangian relaxation and dynamic programming methods for solving large scale hydrothermal coordination problems is presented in this paper. In the Lagrangian relaxation approach, commitment states of thermal units are obtained by solving only thermal subproblems. In the dynamic programming approach, truncated dynamic programming is used to get the commitment states of thermal units. An efficient hydro-thermal scheduling algorithm is used to solve for the output levels of hydro units in both methods. The demand and spinning reserve constraints, the capacity limits, the minimum up and down time constraints, the ramp rate and the hydro constraints are considered in the problem formulation of both methods. Non-linear cost function and dispatches are used. Accurate transmission losses are incorporated. The two methods are compared with speed of execution and operating cost by testing them on a practical utility system.