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 $J^a(\lambda)$ and stress-energy tensor $T_{ab} (\lambda)$ scale to zero size in an asymptotically self-similar manner about a worldline $\gamma$ as $\lambda \to 0$. In this limit, the charge, $q$, and total mass, $m$, of the body go to zero, and $q/m$ goes to a well defined limit. The Maxwell field $F_{ab}(\lambda)$ is assumed to be the retarded solution associated with $J^a(\lambda)$ plus a homogeneous solution (the "external field") that varies smoothly with $\lambda$. We prove that the worldline $\gamma$ must be a solution to the Lorentz force equations of motion in the external field $F_{ab}(\lambda=0)$. 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 $n$-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 $n$, and are based on combinatorial identities. The infinitesimal limits of the $n$-th polarizations of a function will yield its $n$-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