A Distributed Optimization Algorithm Considering Inequality Constraints and its Application in Economic Dispatch Problem

The economic dispatch problem (EDP) is crucial in optimizing and controlling power systems. As modern power system become more complex, traditional centralized communication methods are becoming less reliable. Therefore, distributed optimization method that relie on communication between neighboring nodes without the need for a central node are proposed. Existing distributed optimization methods for economic dispatch problems mainly focus on equality constraints like supply-demand balance, while problems with global inequality constraints are rarely studied. To address this gap, we propose a distributed optimization algorithm based on the primal-dual method and gradient tracking technique that can handle both global equality and inequality constraints. We thoroughly analyze its convergence and successfully apply it to the EDP with emission constraints to demonstrate its effectiveness.