An algorithm for solving the dual problem of hydrothermal scheduling

Lagrangian relaxation has been widely used for the hydrothermal scheduling of power systems. The idea is to use Lagrangian multipliers to relax system-wide demand and reserve requirements, and decompose the problem into unit-wise subproblems that are much easier to solve. The multipliers are then updated at the high level, most commonly by using a subgradient method (SGM). Since the high level dual function is nondifferentiable with many “ridges”, the SGM may zigzag across ridges resulting in slow convergence. This paper presents an algorithm that utilizes a recently developed “reduced complexity bundle method” (RCBM) to update the multipliers at the high level. The RCBM is a kind of “bundle method” that enjoy faster convergence compared to SGM, but has much reduced complexity as compared to a conventional bundle method. Testing results show that RCBM can find better directions, avoid zigzagging behavior and obtain better dual and feasible solutions as compared to the SGM