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We propose a new distributed learning-based framework for stability assessment of a class of networked nonlinear systems, where each subsystem is dissipative. The aim is to learn, in a distributed manner, a Lyapunov function and associated region of attraction for the networked system. We begin by using a neural network function approximation to learn a storage function for each subsystem such that the subsystem satisfies a local dissipativity property. We next use a satisfiability modulo theories (SMT) solver based falsifier that verifies the local dissipativity of each subsystem by deter- mining an absence of counterexamples that violate the local dissipativity property, as established by the neural network approximation. Finally, we verify network-level stability by using an alternating direction method of multipliers (ADMM) approach to update the storage function of each subsystem in a distributed manner until a global stability condition for the network of dissipative subsystems is satisfied. This step also leads to a network-level Lyapunov function that we then use to estimate a region of attraction. We illustrate the proposed algorithm and its advantages on a microgrid interconnection with power electronics interfaces. 

This paper proposes a data-driven method to pinpoint the source of a new emerging dynamical phenomenon in the power grid, referred to “forced oscillations” in the difficult but highly risky case where there is a resonance phenomenon. By exploiting the low-rank and sparse properties of synchrophasor measurements, the localization problem is formulated as a matrix decomposition problem, which can be efficiently solved by the exact augmented Lagrange multiplier algorithm. An online detection scheme is developed based on the problem formulation. The data-driven nature of the proposed method allows for a very efficient implementation. The efficacy of the proposed method is illustrated in a 68-bus power system. The proposed method may possibly be more broadly useful in other situations for identifying the source of forced oscillations in resonant systems. Index Terms—Forced oscillations, resonant systems, phasor measurement unit (PMU), robust principal component analysis (RPCA), Big Data.