Network Reconfiguration of Distributed Controlled Homogenous Power Inverter Network using Composite Lyapunov Function Based Reachability Bound
Sudip Mazumder
Summer Computer Simulation Conference 2007 (SCSC 2007)
San Diego, California (USA), July 15-18, 2007
Abstract
We outline a methodology to analyze the reaching condition of a homogeneous network of power inverters with wireless distributed control using Lyapunov’s direct method and a piecewise linear model of the system. By formulating a convex optimization problem based on a composite Lyapunov function and solving this problem using linear-matrix-inequality solvers, we predict the reaching criteria for the orbital existence of a switching power converter. We investigate the impacts of time delays due to the wireless network and communication channel disruptions on the stability, convergence and performance of the IPN. Because of the infeasibility of modeling such network control systems (NCS) in a deterministic framework, we adopt a probabilistic approach based on Markov chains to modeling the wireless network and incorporate these models into the piecewise linear state-space models of the IPNs. Using these models, we analyze the dynamics of the system in a probabilistic domain and comment on the mean-square stability of the system. Further, we demonstrate how communication fault-tolerant protocols can be implemented to ensure that the IPNs operate within their stability and performance bounds, despite one or more disruptions in the communication channels.