Related papers: Graph Laplacian Spectrum and Primary Frequency Reg…
To describe the flow of a miscible quantity on a network, we introduce the graph wave equation where the standard continuous Laplacian is replaced by the graph Laplacian. This is a natural description of an array of inductances and…
In this paper we investigate the controllability and observability properties of a family of linear dynamical systems, whose structure is induced by the Laplacian of a grid graph. This analysis is motivated by several applications in…
Many recent works in control of electric power systems have investigated their synchronization through global performance metrics under external disturbances. The approach is motivated by fundamental changes in the operation of power grids,…
Through an eigenanalysis of small perturbations, as typically done in small-signal stability studies, we intend to discover the underlying reasons that make those perturbations propagate in some way or another in the grid. To this end, we…
The transient response of power grids to external disturbances influences their stable operation. This paper studies the effect of topology in linear time-invariant dynamics of different power grids. For a variety of objective functions, a…
Determining the effect of structural perturbations on the eigenvalue spectra of networks is an important problem because the spectra characterize not only their topological structures, but also their dynamical behavior, such as…
Recent studies have been using graph theoretical approaches to model complex networks (such as social, infrastructural or biological networks), and how their hardwired circuitry relates to their dynamic evolution in time. Understanding how…
We present a method to design distributed generation and demand control schemes for primary frequency regulation in power networks that guarantee asymptotic stability and ensure fairness of allocation. We impose a passivity condition on net…
Complex real-world phenomena across a wide range of scales, from aviation and internet traffic to signal propagation in electronic and gene regulatory circuits, can be efficiently described through dynamic network models. In many such…
Pinning control of a complex network aims at forcing the states of all nodes to track an external signal by controlling a small number of nodes in the network. In this paper, an algebraic graph-theoretic condition is introduced to optimize…
Introduction of renewable generation leads to significant reduction of inertia in power system, which deteriorates the quality of frequency control. This paper suggests a new control scheme utilizing controllable load to deal with low…
The dynamic response of power grids to small disturbances influences their overall stability. This paper examines the effect of network topology on the linearized time-invariant dynamics of electric power systems. The proposed framework…
The dynamic response of power grids to small events or persistent stochastic disturbances influences their stable operation. Low-frequency inter-area oscillations are of particular concern due to insufficient damping. This paper studies the…
This paper investigates how a disturbance in the power network affects the nodal frequencies of certain network buses. To begin with, we show that the inertia of a single generator is in inverse proportion to the initial rate of change of…
In order to maintain stable grid operations, system monitoring and control processes require the computation of grid states (e.g. voltage magnitude and angles) at high granularity. It is necessary to infer these grid states from…
As bulk synchronous generators in the power grid are replaced by distributed generation interfaced through power electronics, inertia is removed from the system, prompting concerns over grid stability. Different metrics are available for…
The Laplacian eigenvalues of a network play an important role in the analysis of many structural and dynamical network problems. In this paper, we study the relationship between the eigenvalue spectrum of the normalized Laplacian matrix and…
Large-scale integration of distributed energy resources has led to a rapid increase in the number of controllable devices and a significant change in system dynamics. This has necessitating the shift towards more distributed and scalable…
There is a wealth of applied problems that can be posed as a dynamical system defined on a network with both attractive and repulsive interactions. Some examples include: understanding synchronization properties of nonlinear oscillator;,…
The increasing penetration of inertialess new renewable energy sources reduces the overall mechanical inertia available in power grids and accordingly raises a number of issues of grid stability over short to medium time scales. It has been…