339 research outputs found
Distributed Learning of Neural Lyapunov Functions for Large-Scale Networked Dissipative Systems
This paper considers the problem of characterizing the stability region of a
large-scale networked system comprised of dissipative nonlinear subsystems, in
a distributed and computationally tractable way. One standard approach to
estimate the stability region of a general nonlinear system is to first find a
Lyapunov function for the system and characterize its region of attraction as
the stability region. However, classical approaches, such as sum-of-squares
methods and quadratic approximation, for finding a Lyapunov function either do
not scale to large systems or give very conservative estimates for the
stability region. In this context, we propose a new distributed learning based
approach by exploiting the dissipativity structure of the subsystems. Our
approach has two parts: the first part is a distributed approach to learn the
storage functions (similar to the Lyapunov functions) for all the subsystems,
and the second part is a distributed optimization approach to find the Lyapunov
function for the networked system using the learned storage functions of the
subsystems. We demonstrate the superior performance of our proposed approach
through extensive case studies in microgrid networks
Distributed reactive power feedback control for voltage regulation and loss minimization
We consider the problem of exploiting the microgenerators dispersed in the
power distribution network in order to provide distributed reactive power
compensation for power losses minimization and voltage regulation. In the
proposed strategy, microgenerators are smart agents that can measure their
phasorial voltage, share these data with the other agents on a cyber layer, and
adjust the amount of reactive power injected into the grid, according to a
feedback control law that descends from duality-based methods applied to the
optimal reactive power flow problem. Convergence to the configuration of
minimum losses and feasible voltages is proved analytically for both a
synchronous and an asynchronous version of the algorithm, where agents update
their state independently one from the other. Simulations are provided in order
to illustrate the performance and the robustness of the algorithm, and the
innovative feedback nature of such strategy is discussed
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