Optimization-based scheduling of hydrothermal power-systems with pumped-storage units

This paper presents an optimization-based method for scheduling hydrothermal systems based on the Langrangian relaxation technique. After system-wide constraints are relaxed by Lagrange multipliers, the problem is converted into the scheduling of individual units. This paper concentrates on the solution methodology for pumped-storage units. A pumped-storage unit can be operated in generation, pumping or idle states. It can smooth peak loads and provide reserve, and therefore plays an important role in reducing total generation costs. There are, however, many constraints limiting the operation of a pumped-storage unit, such as pond level dynamics and constraints, and discontinuous generation and pumping regions. Moreover, according to the current practice, the dynamic transitions among operating states (generation, pumping and idle) are not arbitrary. The most challenging issue in solving pumped-storage subproblems within the Lagrangian relaxation framework is the integrated consideration of these constraints. The basic idea of our method is to relax the pond level dynamics and constraints by using another set of multipliers. The subproblem is then converted into the optimization of generation or pumping levels for each operating state at individual hours, and the optimization of operating states across hours. The optimal generation or pumping level for a particular operating state at each hour can be obtained by optimizing a single variable function without discretizing pond levels. Dynamic programming is then used to optimize operating states across hours with only a small number of states and transitions. A subgradient algorithm is used to update the pond level Lagrangian multipliers. This method provides an efficient way to solve a class of subproblems involving continuous dynamics and constraints, discontinuous operating regions, and discrete operating states. Testing results based on Northeast Utilities power system show that this algorithm is efficient, and near optimal solutions are obtained.