75 research outputs found
Real-Time Feedback-Based Optimization of Distribution Grids: A Unified Approach
This paper develops an algorithmic framework for real-time optimization of
distribution-level distributed energy resources (DERs). The proposed framework
optimizes the operation of both DERs that are individually controllable and
groups of DERs (i.e., aggregations) at an electrical point of connection that
are jointly controlled. From an electrical standpoint, wye and delta single-
and multi-phase connections are accounted for. The algorithm enables (groups
of) DERs to pursue given performance objectives, while adjusting their
(aggregate) powers to respond to services requested by grid operators and to
maintain electrical quantities within engineering limits. The design of the
algorithm leverages a time-varying bi-level problem formulation capturing
various performance objectives and engineering constraints, and an online
implementation of primal-dual projected-gradient methods. The gradient steps
are suitably modified to accommodate appropriate measurements from the
distribution network and the DERs. By virtue of this approach, the resultant
algorithm can cope with inaccuracies in the distribution-system modeling, it
avoids pervasive metering to gather the state of non-controllable resources,
and it naturally lends itself to a distributed implementation. Analytical
stability and convergence claims are established in terms of tracking of the
solution of the formulated time-varying optimization problem. The proposed
method is tested in a realistic distribution system with real data
Statistical Routing for Multihop Wireless Cognitive Networks
To account for the randomness of propagation channels and interference levels
in hierarchical spectrum sharing, a novel approach to multihop routing is
introduced for cognitive random access networks, whereby packets are randomly
routed according to outage probabilities. Leveraging channel and interference
level statistics, the resultant cross-layer optimization framework provides
optimal routes, transmission probabilities, and transmit-powers, thus enabling
cognizant adaptation of routing, medium access, and physical layer parameters
to the propagation environment. The associated optimization problem is
non-convex, and hence hard to solve in general. Nevertheless, a successive
convex approximation approach is adopted to efficiently find a
Karush-Kuhn-Tucker solution. Augmented Lagrangian and primal decomposition
methods are employed to develop a distributed algorithm, which also lends
itself to online implementation. Enticingly, the fresh look advocated here
permeates benefits also to conventional multihop wireless networks in the
presence of channel uncertainty.Comment: Accepted for publication on the IEEE Journal on Selected Areas in
Communications - Cognitive Radio Series (Nov 2012 Issue
Risk-Constrained Microgrid Reconfiguration Using Group Sparsity
The system reconfiguration task is considered for existing power distribution
systems and microgrids, in the presence of renewable-based generation and load
foresting errors. The system topology is obtained by solving a
chance-constrained optimization problem, where loss-of-load (LOL) constraints
and Ampacity limits of the distribution lines are enforced. Similar to various
distribution system reconfiguration renditions, solving the resultant problem
is computationally prohibitive due to the presence of binary line selection
variables. Further, lack of closed form expressions for the joint probability
distribution of forecasting errors hinders tractability of LOL constraints.
Nevertheless, a convex problem re-formulation is developed here by resorting to
a scenario approximation technique, and by leveraging the underlying
group-sparsity attribute of currents flowing on distribution lines equipped
with tie and sectionalizing switches. The novel convex LOL-constrained
reconfiguration scheme can also afford a distributed solution using the
alternating direction method of multipliers, to address the case where
multi-facilities are managed autonomously from the rest of the system.Comment: The paper will appear in IEEE Transactions on Sustainable Energy
(accepted May 2014
Online Stochastic Optimization of Networked Distributed Energy Resources
This paper investigates distributed control and incentive mechanisms to
coordinate distributed energy resources (DERs) with both continuous and
discrete decision variables as well as device dynamics in distribution grids.
We formulate a multi-period social welfare maximization problem, and based on
its convex relaxation propose a distributed stochastic dual gradient algorithm
for managing DERs. We further extend it to an online realtime setting with
time-varying operating conditions, asynchronous updates by devices, and
feedback being leveraged to account for nonlinear power flows as well as reduce
communication overhead. The resulting algorithm provides a general online
stochastic optimization algorithm for coordinating networked DERs with discrete
power setpoints and dynamics to meet operational and economic objectives and
constraints. We characterize the convergence of the algorithm analytically and
evaluate its performance numerically
Online Optimization as a Feedback Controller: Stability and Tracking
This paper develops and analyzes feedback-based online optimization methods
to regulate the output of a linear time-invariant (LTI) dynamical system to the
optimal solution of a time-varying convex optimization problem. The design of
the algorithm is based on continuous-time primal-dual dynamics, properly
modified to incorporate feedback from the LTI dynamical system, applied to a
proximal augmented Lagrangian function. The resultant closed-loop algorithm
tracks the solution of the time-varying optimization problem without requiring
knowledge of (time-varying) disturbances in the dynamical system. The analysis
leverages integral quadratic constraints to provide linear matrix inequality
(LMI) conditions that guarantee global exponential stability and bounded
tracking error. Analytical results show that, under a sufficient time-scale
separation between the dynamics of the LTI dynamical system and the algorithm,
the LMI conditions can be always satisfied. The paper further proposes a
modified algorithm that can track an approximate solution trajectory of the
constrained optimization problem under less restrictive assumptions. As an
illustrative example, the proposed algorithms are showcased for power
transmission systems, to compress the time scales between secondary and
tertiary control, and allow to simultaneously power re-balancing and tracking
of DC optimal power flow points
Online Proximal-ADMM For Time-varying Constrained Optimization
This paper considers a convex optimization problem with cost and constraints
that evolve over time. The function to be minimized is strongly convex and
possibly non-differentiable, and variables are coupled through linear
constraints. In this setting, the paper proposes an online algorithm based on
the alternating direction method of multipliers(ADMM), to track the optimal
solution trajectory of the time-varying problem; in particular, the proposed
algorithm consists of a primal proximal gradient descent step and an
appropriately perturbed dual ascent step. The paper derives tracking results,
asymptotic bounds, and linear convergence results. The proposed algorithm is
then specialized to a multi-area power grid optimization problem, and our
numerical results verify the desired properties
Dynamic Network Delay Cartography
Path delays in IP networks are important metrics, required by network
operators for assessment, planning, and fault diagnosis. Monitoring delays of
all source-destination pairs in a large network is however challenging and
wasteful of resources. The present paper advocates a spatio-temporal Kalman
filtering approach to construct network-wide delay maps using measurements on
only a few paths. The proposed network cartography framework allows efficient
tracking and prediction of delays by relying on both topological as well as
historical data. Optimal paths for delay measurement are selected in an online
fashion by leveraging the notion of submodularity. The resulting predictor is
optimal in the class of linear predictors, and outperforms competing
alternatives on real-world datasets.Comment: Part of this paper has been published in the \emph{IEEE Statistical
Signal Processing Workshop}, Ann Arbor, MI, Aug. 201
Regulation of Dynamical Systems to Optimal Solutions of Semidefinite Programs: Algorithms and Applications to AC Optimal Power Flow
This paper considers a collection of networked nonlinear dynamical systems,
and addresses the synthesis of feedback controllers that seek optimal operating
points corresponding to the solution of network-wide constrained optimization
problems. Particular emphasis is placed on the solution of semidefinite
programs (SDPs). The design of the feedback controller is grounded on a dual
epsilon-subgradient approach, with the dual iterates utilized to dynamically
update the dynamical-system reference signals. Global convergence is guaranteed
for diminishing stepsize rules, even when the reference inputs are updated at a
faster rate than the dynamical-system settling time. The application of the
proposed framework to the control of power-electronic inverters in AC
distribution systems is discussed. The objective is to bridge the time-scale
separation between real-time inverter control and network-wide optimization.
Optimization objectives assume the form of SDP relaxations of prototypical AC
optimal power flow problems.Comment: This is a longer version of a paper submitted to the 2015 American
Control Conference. This version contains proofs and additional numerical
result
Optimal Dispatch of Photovoltaic Inverters in Residential Distribution Systems
Low-voltage distribution feeders were designed to sustain unidirectional
power flows to residential neighborhoods. The increased penetration of roof-top
photovoltaic (PV) systems has highlighted pressing needs to address power
quality and reliability concerns, especially when PV generation exceeds the
household demand. A systematic method for determining the active- and
reactive-power set points for PV inverters in residential systems is proposed
in this paper, with the objective of optimizing the operation of the
distribution feeder and ensuring voltage regulation. Binary PV-inverter
selection variables and nonlinear power-flow relations render the novel optimal
inverter dispatch problem nonconvex and NP-hard. Nevertheless,
sparsity-promoting regularization approaches and semidefinite relaxation
techniques are leveraged to obtain a computationally feasible convex
reformulation. The merits of the proposed approach are demonstrated using
real-world PV-generation and load-profile data for an illustrative low-voltage
residential distribution system
Photovoltaic Inverter Controllers Seeking AC Optimal Power Flow Solutions
This paper considers future distribution networks featuring
inverter-interfaced photovoltaic (PV) systems, and addresses the synthesis of
feedback controllers that seek real- and reactive-power inverter setpoints
corresponding to AC optimal power flow (OPF) solutions. The objective is to
bridge the temporal gap between long-term system optimization and real-time
inverter control, and enable seamless PV-owner participation without
compromising system efficiency and stability. The design of the controllers is
grounded on a dual epsilon-subgradient method, and semidefinite programming
relaxations are advocated to bypass the non-convexity of AC OPF formulations.
Global convergence of inverter output powers is analytically established for
diminishing stepsize rules and strictly convex OPF costs for cases where: i)
computational limits dictate asynchronous updates of the controller signals,
and ii) inverter reference inputs may be updated at a faster rate than the
power-output settling time. Although the focus is on PV systems, the framework
naturally accommodates different types of inverter-interfaced energy resources.Comment: Accepted for publication on IEEE Transactions on Power System
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