Unit commitment with ramp multipliers

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