Hydrothermal scheduling based Lagrangian relaxation approach to hydrothermal coordination

This paper presents an improved Lagrangian relaxation based hydrothermal coordination algorithm. By using Lagrangian multipliers to relax system-wide demand and reserve requirements, the problem is decomposed into thermal and hydro subproblems. The thermal subproblem is solved by using dynamic programming without discretizing generation levels. Instead of solving the hydro subproblems independently as done in the standard Lagrangian relaxation formulation, the hydrothermal scheduling is used to solve for the output levels of hydro units. The hydrothermal scheduling uses the commitment status of thermal units obtained from the thermal subproblem. Extensive constraints are considered such as power balance, spinning reserve, minimum up/down time, capacity limits, ramp rate and hydro constraints. Accurate transmission losses are incorporated and nonlinear cost functions are used. Numerical results based on a practical utility data show that this new approach consistently provides better schedules than the standard Lagrangian relaxation approach.