Unit commitment with ramp multipliers

This paper presents a new decomposition method, based on the Lagrangian Rel axation technique, for solving the unit commitment problem with ramp rate c onstraints. By introducing an additional vector of multipliers to represent the cost of "system ramping demand," this method can handle the coupling c onstraints between time periods while still keeping the simplicity of the o riginal decomposition method. A new algorithm for updating multipliers is also proposed. Similar to the b undle algorithm [6], this algorithm maintains the previous iteration histor y to approximate the dual envelope. Unlike the bundle algorithm, this new a lgorithm generates an update step along the subgradient direction without a ny quadratic programming (QP) code. The new algorithm combines the bundle a lgorithm's smooth approach to the dual optimum with the sub-gradient method 's fast update.