327 research outputs found
Engineering Stable Discrete-Time Quantum Dynamics via a Canonical QR Decomposition
We analyze the asymptotic behavior of discrete-time, Markovian quantum
systems with respect to a subspace of interest. Global asymptotic stability of
subspaces is relevant to quantum information processing, in particular for
initializing the system in pure states or subspace codes. We provide a
linear-algebraic characterization of the dynamical properties leading to
invariance and attractivity of a given quantum subspace. We then construct a
design algorithm for discrete-time feedback control that allows to stabilize a
target subspace, proving that if the control problem is feasible, then the
algorithm returns an effective control choice. In order to prove this result, a
canonical QR matrix decomposition is derived, and also used to establish the
control scheme potential for the simulation of open-system dynamics.Comment: 12 pages, 1 figur
Distributed reactive power feedback control for voltage regulation and loss minimization
We consider the problem of exploiting the microgenerators dispersed in the
power distribution network in order to provide distributed reactive power
compensation for power losses minimization and voltage regulation. In the
proposed strategy, microgenerators are smart agents that can measure their
phasorial voltage, share these data with the other agents on a cyber layer, and
adjust the amount of reactive power injected into the grid, according to a
feedback control law that descends from duality-based methods applied to the
optimal reactive power flow problem. Convergence to the configuration of
minimum losses and feasible voltages is proved analytically for both a
synchronous and an asynchronous version of the algorithm, where agents update
their state independently one from the other. Simulations are provided in order
to illustrate the performance and the robustness of the algorithm, and the
innovative feedback nature of such strategy is discussed
A distributed control strategy for reactive power compensation in smart microgrids
We consider the problem of optimal reactive power compensation for the
minimization of power distribution losses in a smart microgrid. We first
propose an approximate model for the power distribution network, which allows
us to cast the problem into the class of convex quadratic, linearly
constrained, optimization problems. We then consider the specific problem of
commanding the microgenerators connected to the microgrid, in order to achieve
the optimal injection of reactive power. For this task, we design a randomized,
gossip-like optimization algorithm. We show how a distributed approach is
possible, where microgenerators need to have only a partial knowledge of the
problem parameters and of the state, and can perform only local measurements.
For the proposed algorithm, we provide conditions for convergence together with
an analytic characterization of the convergence speed. The analysis shows that,
in radial networks, the best performance can be achieved when we command
cooperation among units that are neighbors in the electric topology. Numerical
simulations are included to validate the proposed model and to confirm the
analytic results about the performance of the proposed algorithm
Time-varying Projected Dynamical Systems with Applications to Feedback Optimization of Power Systems
This paper is concerned with the study of continuous-time, non-smooth
dynamical systems which arise in the context of time-varying non-convex
optimization problems, as for example the feedback-based optimization of power
systems. We generalize the notion of projected dynamical systems to
time-varying, possibly non-regular, domains and derive conditions for the
existence of so-called Krasovskii solutions. The key insight is that for
trajectories to exist, informally, the time-varying domain can only contract at
a bounded rate whereas it may expand discontinuously. This condition is met, in
particular, by feasible sets delimited via piecewise differentiable functions
under appropriate constraint qualifications. To illustrate the necessity and
usefulness of such a general framework, we consider a simple yet insightful
power system example, and we discuss the implications of the proposed
conditions for the design of feedback optimization schemes
Real-time Curative Actions for Power Systems via Online Feedback Optimization
Curative or remedial actions are the set of immediate actions intended to
bring the power grid to a safe operating point after a contingency. The
effectiveness of these actions is essential to guarantee curative N-1 security.
Nowadays, curative actions are derived ahead of time, based on the anticipated
future grid state. Due to the shift from steady to volatile energy resources,
the grid state will frequently change and the curative actions would need to be
pre-planned increasingly often. Furthermore, with the shift from large bulk
production to many small decentralized energy sources more devices need to be
actuated simultaneously to achieve the same outcome. Instead of pre-planning,
we propose to calculate these complex curative actions in real-time after the
occurrence of a contingency. We show how the method of Online Feedback
Optimization (OFO) is well suited for this task. As a preliminary demonstration
of these capabilities, we use an (OFO) controller, that after a fault, reduces
the voltage difference over a breaker to enable the operators to reclose it.
This test case is inspired by the 2003 Swiss-Italian blackout, which was caused
by a relatively minor incident followed by ineffective curative actions.
Finally, we identify and discuss some open questions, including closed-loop
stability and robustness to model mismatch
Fully Distributed Peer-to-Peer Optimal Voltage Control with Minimal Model Requirements
This paper addresses the problem of voltage regulation in a power
distribution grid using the reactive power injections of grid-connected power
inverters. We first discuss how purely local voltage control schemes cannot
regulate the voltages within a desired range under all circumstances and may
even yield detrimental control decisions. Communication and, through that,
coordination are therefore needed. On the other hand, short-range peer-to-peer
communication and knowledge of electric distances between neighbouring
controllers are sufficient for this task. We implement such a peer-to-peer
controller and test it on a 400~V distribution feeder with asynchronous
communication channels, confirming its viability on real-life systems. Finally,
we analyze the scalability of this approach with respect to the number of
agents on the feeder that participate in the voltage regulation task
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