A Pricing-based Game Theoretic Framework for Distributed-MPC in Voltage Stabilization

A pricing based game theoretic approach of distributed model predictive control (MPC), suitable for controlling voltage instability in power systems, is devloped and presented. MPC is a promising technique in power system control, but its centralized implementation is computationally expensive for real-time application. A non-cooperative distributed-MPC framework is a computationally viable alternative. However in such framework, distributed agents acting selfishly optimize own utility functions, attaining a Nash equilibrium, which in general is less efficient with respect to the global cost/utility function of a dynamically coupled system. A cooperative alternative to this scheme distributively optimizes the global cost, but with an increase in computational complexity by a factor equal to the number of buses. In this paper, we introduce a pricing scheme to incentivize agents' individual utility functions in an iterative manner, improving the efficiency of non-cooperative Nash-equilibrium and attaining results comparable to global optimal of the centralized case. Additionally, to design the distributed-MPC framework, a distributed time domain simulation as well as trajectory sensitivity estimation framework, considering bus level decomposition, is developed and provided. Trajectory sensitivity supports linearization around a trajectory, attaining an accurate approximation of nonlinear dynamics. Finally, the efficacy of the proposed scheme is validated using the WECC 9 bus test system.