A Lagrangian Decomposition Model for Unit Commitment Problem

Abstract

This paper designs an optimization model for Unit Commitment Problem (UCP) which is formulated as a Non Linear Programming Problem (NLPP) with respect to various constraints. The model can be solved by Lagrangian Decomposition (LD) problem and it is obtained by relaxing the constraints from NLPP using Lagrangian Relaxation Method. Generation scheduling is used to find the maximum demand utilized in the planning horizon by the minimum generation cost. It reveals the fact that Maximum profit can be achieved for power generating utility in order to supply the load in a reliable manner. Based on the numerical calculations and graphical representations, the optimum value is obtained by the proposed model for electrical power system cycles.

Large-scale decentralized unit commitment

“…To the extent that DUC is deployed in a single computational environment in a centralized framework, it can be compared to other problem decompositions that leverage parallelizable subproblems. Some of the most important decomposition techniques for UC are Benders [20,21], dual [22], Lagrangian [23], and Dantzig-Wolfe [24]. Decomposition methods such as Benders and Dantzig-Wolfe use a master-slave architecture where subproblems may be solved on separate computational nodes but are coordinated by a master problem, which then requires the results of those subproblems to solve an iteration of its own algorithm.…”

A New Multi-Objective Unit Commitment Model Solved by Decomposition-Coordination

“…These subproblems are usually independent to each other and could be solved in parallel; besides, subproblems could be solved locally, which protects the data privacy of generating companies. Some decomposition techniques have been applied to solve UC problem, such as Benders [24], Lagrangian [25] and Dantzig-Wolfe [26]. In [27], a two level decomposition framework is presented, the lower level solve the local problem to optimize the local cost, while the upper level use the coordinators obtained in lower level to update the prices by subgradient method [28].…”