17,504 research outputs found
Demonstrating demand response from water distribution system through pump scheduling
Significant changes in the power generation mix are posing new challenges for the balancing systems of the grid. Many of these challenges are in the secondary electricity grid regulation services and could be met through demand response (DR) services. We explore the opportunities for a water distribution system (WDS) to provide balancing services with demand response through pump scheduling and evaluate the associated benefits. Using a benchmark network and demand response mechanisms available in the UK, these benefits are assessed in terms of reduced green house gas (GHG) emissions from the grid due to the displacement of more polluting power sources and additional revenues for water utilities. The optimal pump scheduling problem is formulated as a mixed-integer optimisation problem and solved using a branch and bound algorithm. This new formulation finds the optimal level of power capacity to commit to the provision of demand response for a range of reserve energy provision and frequency response schemes offered in the UK. For the first time we show that DR from WDS can offer financial benefits to WDS operators while providing response energy to the grid with less greenhouse gas emissions than competing reserve energy technologies. Using a Monte Carlo simulation based on data from 2014, we demonstrate that the cost of providing the storage energy is less than the financial compensation available for the equivalent energy supply. The GHG emissions from the demand response provision from a WDS are also shown to be smaller than those of contemporary competing technologies such as open cycle gas turbines. The demand response services considered vary in their response time and duration as well as commitment requirements. The financial viability of a demand response service committed continuously is shown to be strongly dependent on the utilisation of the pumps and the electricity tariffs used by water utilities. Through the analysis of range of water demand scenarios and financial incentives using real market data, we demonstrate how a WDS can participate in a demand response scheme and generate financial gains and environmental benefits
Approximation of System Components for Pump Scheduling Optimisation
© 2015 The Authors. Published by Elsevier Ltd.The operation of pump systems in water distribution systems (WDS) is commonly the most expensive task for utilities with up to 70% of the operating cost of a pump system attributed to electricity consumption. Optimisation of pump scheduling could save 10-20% by improving efficiency or shifting consumption to periods with low tariffs. Due to the complexity of the optimal control problem, heuristic methods which cannot guarantee optimality are often applied. To facilitate the use of mathematical optimisation this paper investigates formulations of WDS components. We show that linear approximations outperform non-linear approximations, while maintaining comparable levels of accuracy
Lower Bounds in the Preprocessing and Query Phases of Routing Algorithms
In the last decade, there has been a substantial amount of research in
finding routing algorithms designed specifically to run on real-world graphs.
In 2010, Abraham et al. showed upper bounds on the query time in terms of a
graph's highway dimension and diameter for the current fastest routing
algorithms, including contraction hierarchies, transit node routing, and hub
labeling. In this paper, we show corresponding lower bounds for the same three
algorithms. We also show how to improve a result by Milosavljevic which lower
bounds the number of shortcuts added in the preprocessing stage for contraction
hierarchies. We relax the assumption of an optimal contraction order (which is
NP-hard to compute), allowing the result to be applicable to real-world
instances. Finally, we give a proof that optimal preprocessing for hub labeling
is NP-hard. Hardness of optimal preprocessing is known for most routing
algorithms, and was suspected to be true for hub labeling
Matching Conditions in Atomistic-Continuum Modeling of Materials
A new class of matching condition between the atomistic and continuum regions
is presented for the multi-scale modeling of crystals. They ensure the accurate
passage of large scale information between the atomistic and continuum regions
and at the same time minimize the reflection of phonons at the interface. These
matching conditions can be made adaptive if we choose appropriate weight
functions. Applications to dislocation dynamics and friction between
two-dimensional atomically flat crystal surfaces are described.Comment: 6 pages, 4 figure
A Rigorous Derivation of Electromagnetic Self-force
During the past century, there has been considerable discussion and analysis
of the motion of a point charge, taking into account "self-force" effects due
to the particle's own electromagnetic field. We analyze the issue of "particle
motion" in classical electromagnetism in a rigorous and systematic way by
considering a one-parameter family of solutions to the coupled Maxwell and
matter equations corresponding to having a body whose charge-current density
and stress-energy tensor scale to zero size
in an asymptotically self-similar manner about a worldline as . In this limit, the charge, , and total mass, , of the body go to
zero, and goes to a well defined limit. The Maxwell field
is assumed to be the retarded solution associated with
plus a homogeneous solution (the "external field") that varies
smoothly with . We prove that the worldline must be a
solution to the Lorentz force equations of motion in the external field
. We then obtain self-force, dipole forces, and spin force
as first order perturbative corrections to the center of mass motion of the
body. We believe that this is the first rigorous derivation of the complete
first order correction to Lorentz force motion. We also address the issue of
obtaining a self-consistent perturbative equation of motion associated with our
perturbative result, and argue that the self-force equations of motion that
have previously been written down in conjunction with the "reduction of order"
procedure should provide accurate equations of motion for a sufficiently small
charged body with negligible dipole moments and spin. There is no corresponding
justification for the non-reduced-order equations.Comment: 52 pages, minor correction
Time and Geometric Quantization
In this paper we briefly review the functional version of the Koopman-von
Neumann operatorial approach to classical mechanics. We then show that its
quantization can be achieved by freezing to zero two Grassmannian partners of
time. This method of quantization presents many similarities with the one known
as Geometric Quantization.Comment: Talk given by EG at "Spacetime and Fundamental Interactions: Quantum
Aspects. A conference to honour A.P.Balachandran's 65th birthday
Polarizations and differential calculus in affine spaces
Within the framework of mappings between affine spaces, the notion of -th
polarization of a function will lead to an intrinsic characterization of
polynomial functions. We prove that the characteristic features of derivations,
such as linearity, iterability, Leibniz and chain rules, are shared -- at the
finite level -- by the polarization operators. We give these results by means
of explicit general formulae, which are valid at any order , and are based
on combinatorial identities. The infinitesimal limits of the -th
polarizations of a function will yield its -th derivatives (without
resorting to the usual recursive definition), and the above mentioned
properties will be recovered directly in the limit. Polynomial functions will
allow us to produce a coordinate free version of Taylor's formula
Equivalence between two-dimensional alternating/random Ising model and the ground state of one-dimensional alternating/random XY chain
It is derived that the two-dimensional Ising model with alternating/random
interactions and with periodic/free boundary conditions is equivalent to the
ground state of the one-dimensional alternating/random XY model with the
corresponding periodic/free boundary conditions. This provides an exact
equivalence between a random rectangular Ising model, in which the
Griffiths-McCoy phase appears, and a random XY chain.Comment: 10 page
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