Distributed Economic Dispatch Control via Saddle Point Dynamics and Consensus Algorithms

In this brief, a distributed control algorithm is proposed to solve the economic dispatch problem. Without a central control unit, the generators work collaboratively to minimize the generation cost while balancing the supply and demand. The proposed method is based on consensus protocols and the saddle point dynamics. The consensus protocols are employed to estimate the global information in a distributed fashion, and the saddle point dynamics are leveraged to search for the optimal solution of the economic dispatch problem. By utilizing Lyapunov stability analysis, exponential stability of the optimal solution is derived if the capacity limits of the generators are not considered; with the capacity limits, practical stability of the optimal solution is obtained. No global information is needed in the proposed method, and the requirement on initial conditions of the state variables is mild. Several case studies on the IEEE 9-bus and IEEE 118-bus systems are presented to demonstrate the effectiveness of the proposed algorithms.