Analysis of Coupling Dynamics for Power Systems with Iterative Discrete Decision Making Architectures

Iterative “learning” by distributed control agents has been proposed for power system decision making. Such decision making can achieve agreement among control agents while preserving privacy. The iterative decision making process may interact with power system dynamics. In such cases, coupled dynamics are expected. The objective of this paper is to propose a modeling approach that can conduct stability analysis for these hybrid systems. In the proposed approach, the discrete decision making process is approximated by continuous dynamics. As a result, the entire hybrid system can be represented by a continuous dynamic system. Conventional stability analysis tools are then used to check system stability and identify key impacting factors. An example power system with multiple control agents is used to demonstrate the proposed modeling and analysis. The analysis results are then validated by nonlinear time-domain simulation. The continuous dynamics models developed in this paper sheds insights into the control nature of each distributed optimization algorithm. An important finding is documented in this paper: A consensus algorithm based decision making may act as an integrator of frequency deviation. It can bring the frequency back to nominal while the primal-dual based decision making cannot.