107 research outputs found
An internal model approach to (optimal) frequency regulation in power grids with time-varying voltages
This paper studies the problem of frequency regulation in power grids under
unknown and possible time-varying load changes, while minimizing the generation
costs. We formulate this problem as an output agreement problem for
distribution networks and address it using incremental passivity and
distributed internal-model-based controllers. Incremental passivity enables a
systematic approach to study convergence to the steady state with zero
frequency deviation and to design the controller in the presence of
time-varying voltages, whereas the internal-model principle is applied to
tackle the uncertain nature of the loads.Comment: 16 pages. Abridged version appeared in the Proceedings of the 21st
International Symposium on Mathematical Theory of Networks and Systems, MTNS
2014, Groningen, the Netherlands. Submitted in December 201
Optimal pricing control in distribution networks with time-varying supply and demand
This paper studies the problem of optimal flow control in dynamic inventory
systems. A dynamic optimal distribution problem, including time-varying supply
and demand, capacity constraints on the transportation lines, and convex flow
cost functions of Legendre-type, is formalized and solved. The time-varying
optimal flow is characterized in terms of the time-varying dual variables of a
corresponding network optimization problem. A dynamic feedback controller is
proposed that regulates the flows asymptotically to the optimal flows and
achieves in addition a balancing of all storage levels.Comment: Submitted to 21st International Symposium on Mathematical Theory of
Networks and Systems (MTNS) in December 201
Topological and Graph-coloring Conditions on the Parameter-independent Stability of Second-order Networked Systems
In this paper, we study parameter-independent stability in qualitatively
heterogeneous passive networked systems containing damped and undamped nodes.
Given the graph topology and a set of damped nodes, we ask if output consensus
is achieved for all system parameter values. For given parameter values, an
eigenspace analysis is used to determine output consensus. The extension to
parameter-independent stability is characterized by a coloring problem, named
the richly balanced coloring (RBC) problem. The RBC problem asks if all nodes
of the graph can be colored red, blue and black in such a way that (i) every
damped node is black, (ii) every black node has blue neighbors if and only if
it has red neighbors, and (iii) not all nodes in the graph are black. Such a
colored graph is referred to as a richly balanced colored graph.
Parameter-independent stability is guaranteed if there does not exist a richly
balanced coloring. The RBC problem is shown to cover another well-known graph
coloring scheme known as zero forcing sets. That is, if the damped nodes form a
zero forcing set in the graph, then a richly balanced coloring does not exist
and thus, parameter-independent stability is guaranteed. However, the full
equivalence of zero forcing sets and parameter-independent stability holds only
true for tree graphs. For more general graphs with few fundamental cycles an
algorithm, named chord node coloring, is proposed that significantly
outperforms a brute-force search for solving the NP-complete RBC problem.Comment: 30 pages, accepted for publication in SICO
A Polyhedral Approximation Framework for Convex and Robust Distributed Optimization
In this paper we consider a general problem set-up for a wide class of convex
and robust distributed optimization problems in peer-to-peer networks. In this
set-up convex constraint sets are distributed to the network processors who
have to compute the optimizer of a linear cost function subject to the
constraints. We propose a novel fully distributed algorithm, named
cutting-plane consensus, to solve the problem, based on an outer polyhedral
approximation of the constraint sets. Processors running the algorithm compute
and exchange linear approximations of their locally feasible sets.
Independently of the number of processors in the network, each processor stores
only a small number of linear constraints, making the algorithm scalable to
large networks. The cutting-plane consensus algorithm is presented and analyzed
for the general framework. Specifically, we prove that all processors running
the algorithm agree on an optimizer of the global problem, and that the
algorithm is tolerant to node and link failures as long as network connectivity
is preserved. Then, the cutting plane consensus algorithm is specified to three
different classes of distributed optimization problems, namely (i) inequality
constrained problems, (ii) robust optimization problems, and (iii) almost
separable optimization problems with separable objective functions and coupling
constraints. For each one of these problem classes we solve a concrete problem
that can be expressed in that framework and present computational results. That
is, we show how to solve: position estimation in wireless sensor networks, a
distributed robust linear program and, a distributed microgrid control problem.Comment: submitted to IEEE Transactions on Automatic Contro
Topological and Graph-Coloring Conditions on the Parameter-Independent Stability of Second-Order Networked Systems
In this paper, we study parameter-independent stability in qualitatively heterogeneous passive networked systems containing damped and undamped nodes. Given the graph topology and a set of damped nodes, we ask if output consensus is achieved for all system parameter values. For given parameter values, an eigenspace analysis is used to determine output consensus. The extension to parameter-independent stability is characterized by a coloring problem, named the richly balanced coloring (RBC) problem. The RBC problem asks if all nodes of the graph can be colored red, blue, and black in such a way that (i) every damped node is black, (ii) every black node has blue neighbors if and only if it has red neighbors, and (iii) not all nodes in the graph are black. Such a colored graph is referred to as a richly balanced colored graph. Parameter-independent stability is guaranteed if there does not exist a richly balanced coloring. The RBC problem is shown to cover another well-known graph coloring scheme known as zero forcing sets. That is, if the damped nodes form a zero forcing set in the graph, then a richly balanced coloring does not exist, and thus parameter-independent stability is guaranteed. However, the full equivalence of zero forcing sets and parameter-independent stability holds true only for tree graphs. For more general graphs with few fundamental cycles, an algorithm, named chord node coloring, is proposed that significantly outperforms a brute-force search for solving the NP-complete RBC problem
A distributed solution to the adjustable robust economic dispatch problem
The problem of maintaining balance between consumption and production of electric energy in the presence of a high share of intermittent power sources in a transmission grid is addressed. A distributed, asynchronous optimization algorithm, based on the ideas of cutting-plane approximations and adjustable robust counterparts, is presented to compute economically optimal adjustable dispatch strategies. These strategies guarantee satisfaction of the power balancing constraint as well as of the operational constraints for all possible realizations of the uncertain power generation or demand. The communication and computational effort of the proposed distributed algorithm increases for each computational unit only slowly with the number of participants, making it well suited for large scale networks. A distributed implementation of the algorithm and a numerical study are presented, which show the performance in asynchronous networks and its robustness against packet loss
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