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We study the performance of a decentralized inte- gral control scheme for joint power grid frequency regulation and economic dispatch. We show that by properly designing the controller gains, after a power flow perturbation, the control achieves near-optimal economic dispatch while recovering the nominal frequency, without requiring any communication. We quantify the gap between the controllable power generation cost under the decentralized control scheme and the optimal cost, based on the DC power flow model. Moreover, we study the tradeoff between the cost and the convergence time, by adjusting parameters of the control scheme. Communication between generators reduces the convergence time. We identify key communication links whose failures have more significant impacts on the performance of a distributed power grid control scheme that requires information exchange between neighbors. 

Identifying the location of a disturbance and its magnitude is an important component for stable operation of power systems. We study the problem of localizing and estimating a disturbance in the interconnected power system. We take a model-free approach to this problem by using frequency data from generators. Specifically, we develop a logistic regression based method for localization and a linear regression based method for estimation of the magnitude of disturbance. Our model-free approach does not require the knowledge of system parameters such as inertia constants and topology, and is shown to achieve highly accurate localization and estimation performance even in the presence of measurement noise and missing data. 

We propose an interdependent random geometric graph (RGG) model for interdependent networks. Based on this model, we study the robustness of two interdependent spatially embedded networks where interdependence exists between geographically nearby nodes in the two networks. We study the emergence of the giant mutual component in two interdependent RGGs as node densities increase, and define the percolation threshold as a pair of node densities above which the giant mutual component first appears. In contrast to the case for a single RGG, where the percolation threshold is a unique scalar for a given connection distance, for two interdependent RGGs, multiple pairs of percolation thresholds may exist, given that a smaller node density in one RGG may increase the minimum node density in the other RGG in order for a giant mutual component to exist. We derive analytical upper bounds on the percolation thresholds of two interdependent RGGs by discretization, and obtain 99% confidence intervals for the percolation thresholds by simulation. Based on these results, we derive conditions for the interdependent RGGs to be robust under random failures and geographical attacks. 

Complex systems such as smart cities and smart power grids rely heavily on their interdependent components. The failure of a component in one network may lead to the failure of the supported component in another network. Components which support a large number of interdependent components may be more vulnerable to attacks and failures. In this paper, we study the robustness of two interdependent networks under node failures. By modeling each network using a random geometric graph (RGG), we study conditions for the percolation of two interdependent RGGs after in-homogeneous node failures. We derive analytical bounds on the interdependent degree thresholds (k 1 ,k 2 ), such that the interdependent RGGs percolate after removing nodes in G i that support more than k j nodes in G j (∀i, j ∈ {1, 2}, i ≠ j). We verify the bounds using numerical simulation, and show that there is a tradeoff between k 1 and k 2 for maintaining percolation after the failures.