54 research outputs found
Synchronization and Transient Stability in Power Networks and Non-Uniform Kuramoto Oscillators
Motivated by recent interest for multi-agent systems and smart power grid
architectures, we discuss the synchronization problem for the network-reduced
model of a power system with non-trivial transfer conductances. Our key insight
is to exploit the relationship between the power network model and a
first-order model of coupled oscillators. Assuming overdamped generators
(possibly due to local excitation controllers), a singular perturbation
analysis shows the equivalence between the classic swing equations and a
non-uniform Kuramoto model. Here, non-uniform Kuramoto oscillators are
characterized by multiple time constants, non-homogeneous coupling, and
non-uniform phase shifts. Extending methods from transient stability,
synchronization theory, and consensus protocols, we establish sufficient
conditions for synchronization of non-uniform Kuramoto oscillators. These
conditions reduce to and improve upon previously-available tests for the
standard Kuramoto model. Combining our singular perturbation and Kuramoto
analyses, we derive concise and purely algebraic conditions that relate
synchronization and transient stability of a power network to the underlying
system parameters and initial conditions
Distributed Generation and Resilience in Power Grids
We study the effects of the allocation of distributed generation on the
resilience of power grids. We find that an unconstrained allocation and growth
of the distributed generation can drive a power grid beyond its design
parameters. In order to overcome such a problem, we propose a topological
algorithm derived from the field of Complex Networks to allocate distributed
generation sources in an existing power grid.Comment: proceedings of Critis 2012 http://critis12.hig.no
Sharp Upper Bounds for the Laplacian Spectral Radius of Graphs
The spectrum of the Laplacian matrix of a network plays a key role in a wide range of dynamical problems associated with the network, from transient stability analysis of power network to distributed control of formations. Let G=(V,E) be a simple connected graph on n vertices and let μ(G) be the largest Laplacian eigenvalue (i.e., the spectral radius) of G. In this paper, by using the Cauchy-Schwarz inequality, we show that the upper bounds for the Laplacian spectral radius of G
Self-Organized Synchronization and Voltage Stability in Networks of Synchronous Machines
The integration of renewable energy sources in the course of the energy
transition is accompanied by grid decentralization and fluctuating power
feed-in characteristics. This raises new challenges for power system stability
and design. We intend to investigate power system stability from the viewpoint
of self-organized synchronization aspects. In this approach, the power grid is
represented by a network of synchronous machines. We supplement the classical
Kuramoto-like network model, which assumes constant voltages, with dynamical
voltage equations, and thus obtain an extended version, that incorporates the
coupled categories voltage stability and rotor angle synchronization. We
compare disturbance scenarios in small systems simulated on the basis of both
classical and extended model and we discuss resultant implications and possible
applications to complex modern power grids.Comment: 9 pages, 9 figure
The Price of Synchrony: Resistive Losses due to Phase Synchronization in Power Networks
We investigate the total resistive losses incurred in returning a power
network of identical generators to a synchronous state following a transient
stability event or in maintaining this state in the presence of persistent
stochastic disturbances. We formulate this cost as the input-output norm
of a linear dynamical system with distributed disturbances. We derive an
expression for the total resistive losses that scales with the size of the
network as well as properties of the generators and power lines, but is
independent of the network topology. This topologically invariant scaling of
what we term the price of synchrony is in contrast to typical power system
stability notions like rate of convergence or the region of attraction for
rotor-angle stability. Our result indicates that highly connected power
networks, whilst desirable for higher phase synchrony, do not offer an
advantage in terms of the total resistive power losses needed to achieve this
synchrony. Furthermore, if power flow is the mechanism used to achieve
synchrony in highly-distributed-generation networks, the cost increases
unboundedly with the number of generators.Comment: 7 pages; 2 figure
- …