57 research outputs found
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
Continuum Swarm Tracking Control: A Geometric Perspective in Wasserstein Space
We consider a setting in which one swarm of agents is to service or track a
second swarm, and formulate an optimal control problem which trades off between
the competing objectives of servicing and motion costs. We consider the
continuum limit where large-scale swarms are modeled in terms of their
time-varying densities, and where the Wasserstein distance between two
densities captures the servicing cost. We show how this non-linear
infinite-dimensional optimal control problem is intimately related to the
geometry of Wasserstein space, and provide new results in the case of
absolutely continuous densities and constant-in-time references. Specifically,
we show that optimal swarm trajectories follow Wasserstein geodesics, while the
optimal control tradeoff determines the time-schedule of travel along these
geodesics. We briefly describe how this solution provides a basis for a
model-predictive control scheme for tracking time-varying and real-time
reference trajectories as well.Comment: 7 page
On sensor fusion for airborne wind energy systems
A study on filtering aspects of airborne wind energy generators is presented.
This class of renewable energy systems aims to convert the aerodynamic forces
generated by tethered wings, flying in closed paths transverse to the wind
flow, into electricity. The accurate reconstruction of the wing's position,
velocity and heading is of fundamental importance for the automatic control of
these kinds of systems. The difficulty of the estimation problem arises from
the nonlinear dynamics, wide speed range, large accelerations and fast changes
of direction that the wing experiences during operation. It is shown that the
overall nonlinear system has a specific structure allowing its partitioning
into sub-systems, hence leading to a series of simpler filtering problems.
Different sensor setups are then considered, and the related sensor fusion
algorithms are presented. The results of experimental tests carried out with a
small-scale prototype and wings of different sizes are discussed. The designed
filtering algorithms rely purely on kinematic laws, hence they are independent
from features like wing area, aerodynamic efficiency, mass, etc. Therefore, the
presented results are representative also of systems with larger size and
different wing design, different number of tethers and/or rigid wings.Comment: This manuscript is a preprint of a paper accepted for publication on
the IEEE Transactions on Control Systems Technology and is subject to IEEE
Copyright. The copy of record is available at IEEEXplore library:
http://ieeexplore.ieee.org
Coherence in Large-Scale Networks: Dimension-Dependent Limitations of Local Feedback
We consider distributed consensus and vehicular formation control problems.
Specifically we address the question of whether local feedback is sufficient to
maintain coherence in large-scale networks subject to stochastic disturbances.
We define macroscopic performance measures which are global quantities that
capture the notion of coherence; a notion of global order that quantifies how
closely the formation resembles a solid object. We consider how these measures
scale asymptotically with network size in the topologies of regular lattices in
1, 2 and higher dimensions, with vehicular platoons corresponding to the 1
dimensional case. A common phenomenon appears where a higher spatial dimension
implies a more favorable scaling of coherence measures, with a dimensions of 3
being necessary to achieve coherence in consensus and vehicular formations
under certain conditions. In particular, we show that it is impossible to have
large coherent one dimensional vehicular platoons with only local feedback. We
analyze these effects in terms of the underlying energetic modes of motion,
showing that they take the form of large temporal and spatial scales resulting
in an accordion-like motion of formations. A conclusion can be drawn that in
low spatial dimensions, local feedback is unable to regulate large-scale
disturbances, but it can in higher spatial dimensions. This phenomenon is
distinct from, and unrelated to string instability issues which are commonly
encountered in control problems for automated highways.Comment: To appear in IEEE Trans. Automat. Control; 15 pages, 2 figure
- …