Second-Order Continuous-Time Algorithm for Optimal Resource Allocation in Power Systems

In this paper, based on differential inclusions and the saddle point dynamics, a novel second-order continuous-time algorithm is proposed to solve the optimal resource allocation problem in power systems. The considered cost function is the sum of all local cost functions with a set of affine equality demand constraints and an inequality constraint on generating capacity of the generator. In virtue of nonsmooth analysis, geometric graph theory, and Lyapunov stability theory, all generators achieve consensus on the Lagrange multipliers associated with a set of affine equality constraints while the proposed algorithm converges exponentially to the optimal solution of the resource allocation problem starting from any initial states over an undirected and connected graph. Moreover, the obtained results can be further extended to the optimal resource allocation problem in case of switching communication topologies. Finally, two numerical examples involving a smart grid system composed of five generators and the IEEE 30-bus system demonstrate the effectiveness and the performance of the theoretical results.