25,814 research outputs found
Dynamic Energy Management
We present a unified method, based on convex optimization, for managing the
power produced and consumed by a network of devices over time. We start with
the simple setting of optimizing power flows in a static network, and then
proceed to the case of optimizing dynamic power flows, i.e., power flows that
change with time over a horizon. We leverage this to develop a real-time
control strategy, model predictive control, which at each time step solves a
dynamic power flow optimization problem, using forecasts of future quantities
such as demands, capacities, or prices, to choose the current power flow
values. Finally, we consider a useful extension of model predictive control
that explicitly accounts for uncertainty in the forecasts. We mirror our
framework with an object-oriented software implementation, an open-source
Python library for planning and controlling power flows at any scale. We
demonstrate our method with various examples. Appendices give more detail about
the package, and describe some basic but very effective methods for
constructing forecasts from historical data.Comment: 63 pages, 15 figures, accompanying open source librar
Minimum-cost multicast over coded packet networks
We consider the problem of establishing minimum-cost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as both static multicast (where membership of the multicast group remains constant for the duration of the connection) and dynamic multicast (where membership of the multicast group changes in time, with nodes joining and leaving the group). For static multicast, we reduce the problem to a polynomial-time solvable optimization problem, and we present decentralized algorithms for solving it. These algorithms, when coupled with existing decentralized schemes for constructing network codes, yield a fully decentralized approach for achieving minimum-cost multicast. By contrast, establishing minimum-cost static multicast connections over routed packet networks is a very difficult problem even using centralized computation, except in the special cases of unicast and broadcast connections. For dynamic multicast, we reduce the problem to a dynamic programming problem and apply the theory of dynamic programming to suggest how it may be solved
Power packet transferability via symbol propagation matrix
Power packet is a unit of electric power transferred by a power pulse with an
information tag. In Shannon's information theory, messages are represented by
symbol sequences in a digitized manner. Referring to this formulation, we
define symbols in power packetization as a minimum unit of power transferred by
a tagged pulse. Here, power is digitized and quantized. In this paper, we
consider packetized power in networks for a finite duration, giving symbols and
their energies to the networks. A network structure is defined using a graph
whose nodes represent routers, sources, and destinations. First, we introduce
symbol propagation matrix (SPM) in which symbols are transferred at links
during unit times. Packetized power is described as a network flow in a
spatio-temporal structure. Then, we study the problem of selecting an SPM in
terms of transferability, that is, the possibility to represent given energies
at sources and destinations during the finite duration. To select an SPM, we
consider a network flow problem of packetized power. The problem is formulated
as an M-convex submodular flow problem which is known as generalization of the
minimum cost flow problem and solvable. Finally, through examples, we verify
that this formulation provides reasonable packetized power.Comment: Submitted to Proceedings of the Royal Society A: Mathematical,
Physical and Engineering Science
Graphical Models for Optimal Power Flow
Optimal power flow (OPF) is the central optimization problem in electric
power grids. Although solved routinely in the course of power grid operations,
it is known to be strongly NP-hard in general, and weakly NP-hard over tree
networks. In this paper, we formulate the optimal power flow problem over tree
networks as an inference problem over a tree-structured graphical model where
the nodal variables are low-dimensional vectors. We adapt the standard dynamic
programming algorithm for inference over a tree-structured graphical model to
the OPF problem. Combining this with an interval discretization of the nodal
variables, we develop an approximation algorithm for the OPF problem. Further,
we use techniques from constraint programming (CP) to perform interval
computations and adaptive bound propagation to obtain practically efficient
algorithms. Compared to previous algorithms that solve OPF with optimality
guarantees using convex relaxations, our approach is able to work for arbitrary
distribution networks and handle mixed-integer optimization problems. Further,
it can be implemented in a distributed message-passing fashion that is scalable
and is suitable for "smart grid" applications like control of distributed
energy resources. We evaluate our technique numerically on several benchmark
networks and show that practical OPF problems can be solved effectively using
this approach.Comment: To appear in Proceedings of the 22nd International Conference on
Principles and Practice of Constraint Programming (CP 2016
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