Stability analysis for cooperative distributed generation dispatch in a Cyber-Physical environment

Distributed algorithms for economically managing the energy in smart grids are getting more attention because they can remove the need for central controllers and are computationally scalable, as well as robust to single point of failure. The Incremental Cost Consensus (ICC) algorithm has been developed as a cooperative distributed algorithm for solving the Economic Dispatch Problem (EDP). This paper models and analyzes the nominal stability of the ICC algorithm implemented in a smart grid environment. The grid has continuous time dynamics in the physical layer, while the ICC algorithm in the cyber layer has discrete time dynamics. To study the interconnected Cyber-Physical System (CPS), the grid dynamics are linearized and discretized at their operating points. Then, the equivalent discrete time dynamics of the grid are integrated with the ICC dynamics in a joint cyber-physical model. The stability of the interconnected system is then analyzed by studying the eigenvalues of the joint dynamics. The IEEE 9-bus system is used to demonstrate the proposed analysis approach.