An optimization-based method for unit commitment

An optimization-based method for unit commitment using the Lagrangian relaxation technique is presented. The salient features of this method includes nondiscretization of generation levels, a systematic method to handle ramp rate constraints, and a good initialization procedure. By using Lagrange multipliers to relax system-wide demand and reserve requirements and ramp rate constraints, the problem is decomposed into the scheduling of individual units. The optimal generation level of a unit at each hour can be easily calculated since there are no system dynamics, and the cost function is stage-wise additive and piecewise linear with only a few corner points. A relaxed subproblem can therefore be efficiently solved by using the dynamic programming technique without discretizing generation levels. A subgradient algorithm with adoptive step sizing is used to update Lagrange multipliers. An effective method based on priority-list commitment and dispatch is adopted to initialize these multipliers, and a heuristic approach is developed to generate a good feasible schedule based on the dual solution. Numerical results based on data sets from Northwestern Utilities show that this algorithm is efficient, and near-optimal solutions are obtained.