A Revised Subgradient Method for Solving the Dual Problem of Hydrothermal Scheduling

Lagrangian relaxation based methods (LR) are among the most successful approaches for solving hydrothermal scheduling problems (HTS). Standard subgradient method (SSM) has long been the widely accepted choice for solving the dual problem when LR is used to solve HTS. However, solution oscillations and slow convergence are often observed in implementation of SSM. In this paper, a revised subgradient method is presented to improve the performance of SSM. The basic idea is to update the multipliers along a direction determined by a convex combination of the subgradients obtained in previous steps. The method is different from the bundle method (BM) since no quadratic program and line search are required. Meanwhile, the dual subproblems are solved simultaneously on different processors to further accelerate the convergence. Numerical testing is performed for a 31-bus system and 118-bus system. The results suggest that both the convergence and solution quality are greatly improved.