arXiv subjects

Tom Brown

Publications and source records attributed to Tom Brown.

88 records · Page 5Linked to original sources

arXiv2018

Linear Optimal Power Flow Using Cycle Flows

Linear optimal power flow (LOPF) algorithms use a linearization of the alternating current (AC) load flow equations to optimize generator dispatch in a network subject to the loading constraints of the network branches. Common algorithms use the voltage angles at the buses as optimization variables, but alternatives can be computationally advantageous. In this article we provide a review of existing methods and describe a new formulation that expresses the loading constraints directly in terms of the flows themselves, using a decomposition of the network graph into a spanning tree and closed cycles. We provide a comprehensive study of the computational performance of the various formulations, in settings that include computationally challenging applications such as multi-period LOPF with storage dispatch and generation capacity expansion. We show that the new formulation of the LOPF solves up to 7 times faster than the angle formulation using a commercial linear programming solver, while another existing cycle-based formulation solves up to 20 times faster, with an average speed-up of factor 3 for the standard networks considered here. If generation capacities are also optimized, the average speed-up rises to a factor of 12, reaching up to factor 213 in a particular instance. The speed-up is largest for networks with many buses and decentral generators throughout the network, which is highly relevant given the rise of distributed renewable generation and the computational challenge of operation and planning in such networks.

nlin.AO↗

arXiv2018

PyPSA: Python for Power System Analysis

Python for Power System Analysis (PyPSA) is a free software toolbox for simulating and optimising modern electrical power systems over multiple periods. PyPSA includes models for conventional generators with unit commitment, variable renewable generation, storage units, coupling to other energy sectors, and mixed alternating and direct current networks. It is designed to be easily extensible and to scale well with large networks and long time series. In this paper the basic functionality of PyPSA is described, including the formulation of the full power flow equations and the multi-period optimisation of operation and investment with linear power flow equations. PyPSA is positioned in the existing free software landscape as a bridge between traditional power flow analysis tools for steady-state analysis and full multi-period energy system models. The functionality is demonstrated on two open datasets of the transmission system in Germany (based on SciGRID) and Europe (based on GridKit).

physics.soc-ph↗

arXiv2018

Opening the black box of energy modelling: Strategies and lessons learned

The global energy system is undergoing a major transition, and in energy planning and decision-making across governments, industry and academia, models play a crucial role. Because of their policy relevance and contested nature, the transparency and open availability of energy models and data are of particular importance. Here we provide a practical how-to guide based on the collective experience of members of the Open Energy Modelling Initiative (Openmod). We discuss key steps to consider when opening code and data, including determining intellectual property ownership, choosing a licence and appropriate modelling languages, distributing code and data, and providing support and building communities. After illustrating these decisions with examples and lessons learned from the community, we conclude that even though individual researchers' choices are important, institutional changes are still also necessary for more openness and transparency in energy research.

cs.CY↗

arXiv2017

The Benefits of Cooperation in a Highly Renewable European Electricity Network

To reach ambitious European CO$_2$ emission reduction targets, most scenarios of future European electricity systems rely on large shares of wind and solar photovoltaic power generation. We interpolate between two concepts for balancing the variability of these renewable sources: balancing at continental scales using the transmission grid and balancing locally with storage. This interpolation is done by systematically restricting transmission capacities from the optimum level to zero. We run techno-economic cost optimizations for the capacity investment and dispatch of wind, solar, hydroelectricity, natural gas power generation and transmission, as well as storage options such as pumped-hydro, battery, and hydrogen storage. The simulations assume a 95% CO$_2$ emission reduction compared to 1990, and are run over a full historical year of weather and electricity demand for 30 European countries. In the cost-optimal system with high levels of transmission expansion, energy generation is dominated by wind (65%) and hydro (15%), with average system costs comparable to today's system. Restricting transmission shifts the balance in favour of solar and storage, driving up costs by a third. As the restriction is relaxed, 85% of the cost benefits of the optimal grid expansion can be captured already with only 44% of the transmission volume.

physics.soc-ph↗

arXiv2017

Optimal heterogeneity in a simplified highly renewable European electricity system

The resource quality and the temporal generation pattern of variable renewable energy sources vary significantly across Europe. In this paper spatial distributions of renewable assets are explored which exploit this heterogeneity to lower the total system costs for a high level of renewable electricity in Europe. Several intuitive heuristic algorithms, optimal portfolio theory and a local search algorithm are used to find optimal distributions of renewable generation capacities that minimise the total costs of backup, transmission and renewable capacity simultaneously. Using current cost projections, an optimal heterogeneous distribution favours onshore wind, particularly in countries bordering the North Sea, which results in average electricity costs that are up to 11% lower than for a homogeneous reference distribution of renewables proportional to each country's mean load. The reduction becomes even larger, namely 18%, once the transmission capacities are put to zero in the homogeneous reference distribution. Heuristic algorithms to distribute renewable capacity based on each country's wind and solar capacity factors are shown to provide a satisfactory approximation to fully optimised renewable distributions, while maintaining the benefits of transparency and comprehensibility. The sensitivities of the results to changing costs of solar generation and gas supply as well as to the possible cross-sectoral usage of unavoidable curtailment energy are also examined.

physics.soc-ph↗

arXiv2017

The role of spatial scale in joint optimisations of generation and transmission for European highly renewable scenarios

The effects of the spatial scale on the results of the optimisation of transmission and generation capacity in Europe are quantified under a 95% CO2 reduction compared to 1990 levels, interpolating between one-node-per-country solutions and many-nodes-per-country. The trade-offs that come with higher spatial detail between better exposure of transmission bottlenecks, exploitation of sites with good renewable resources (particularly wind power) and computational limitations are discussed. It is shown that solutions with no grid expansion beyond today's capacities are only around 20% more expensive than with cost-optimal grid expansion.

physics.soc-ph↗

arXiv2017

Dual theory of transmission line outages

A new graph dual formalism is presented for the analysis of line outages in electricity networks. The dual formalism is based on a consideration of the flows around closed cycles in the network. After some exposition of the theory is presented, a new formula for the computation of Line Outage Distribution Factors (LODFs) is derived, which is not only computationally faster than existing methods, but also generalizes easily for multiple line outages and arbitrary changes to line series reactance. In addition, the dual formalism provides new physical insight for how the effects of line outages propagate through the network. For example, in a planar network a single line outage can be shown to induce monotonically decreasing flow changes, which are mathematically equivalent to an electrostatic dipole field.

nlin.AO↗

arXiv2015

A new method for deriving the stellar birth function of resolved stellar populations

We present a new method for deriving the stellar birth function (SBF) of resolved stellar populations. The SBF (stars born per unit mass, time, and metallicity) is the combination of the initial mass function (IMF), the star-formation history (SFH), and the metallicity distribution function (MDF). The framework of our analysis is that of Poisson Point Processes (PPPs), a class of statistical models suitable when dealing with points (stars) in a multidimensional space (the measurement space of multiple photometric bands). The theory of PPPs easily accommodates the modeling of measurement errors as well as that of incompleteness. Compared to most of the tools used to study resolved stellar populations, our method avoids binning stars in the color-magnitude diagram and uses the entirety of the information (i.e., the whole likelihood function) for each data point; the proper combination of the individual likelihoods allows the computation of the posterior probability for the global population parameters. This includes unknowns such as the IMF slope and combination of SFH and MDF, which are rarely solved for simultaneously in the literature, however entangled and correlated they might be. Our method also allows proper inclusion of nuisance parameters, such as distance and extinction distributions. The aim of this paper, is to assess the validity of this new approach under a range of assumptions, using only simulated data. Forthcoming work will show applications to real data. Although it has a broad scope of possible applications, we have developed this method to study multi-band HST observations of the Milky Way Bulge. Therefore we will focus on simulations with characteristics similar to those of the Galactic Bulge.

astro-ph.IM↗

arXiv2013

On Double 3-Term Arithmetic Progressions

In this note we are interested in the problem of whether or not every increasing sequence of positive integers $x_1x_2x_3...$ with bounded gaps must contain a double 3-term arithmetic progression, i.e., three terms $x_i$, $x_j$, and $x_k$ such that $i + k = 2j$ and $x_i + x_k = 2x_j$. We consider a few variations of the problem, discuss some related properties of double arithmetic progressions, and present several results obtained by using RamseyScript, a high-level scripting language.

math.CO↗

arXiv2012

The M31 Velocity Vector. II. Radial Orbit Towards the Milky Way and Implied Local Group Mass

We determine the velocity vector of M31 with respect to the Milky Way and use this to constrain the mass of the Local Group, based on HST proper-motion measurements presented in Paper I. We construct N-body models for M31 to correct the measurements for the contributions from stellar motions internal to M31. We also estimate the center-of-mass motion independently, using the kinematics of satellite galaxies of M31 and the Local Group. All estimates are mutually consistent, and imply a weighted average M31 heliocentric transverse velocity of (v_W,v_N) = (-125.2+/-30.8, -73.8+/-28.4) km/s. We correct for the reflex motion of the Sun using the most recent insights into the solar motion within the Milky Way. This implies a radial velocity of M31 with respect to the Milky Way of V_rad = -109.3+/-4.4 km/s, and a tangential velocity V_tan = 17.0 km/s (<34.3 km/s at 1-sigma confidence). Hence, the velocity vector of M31 is statistically consistent with a radial (head-on collision) orbit towards the Milky Way. We revise prior estimates for the Local Group timing mass, including corrections for cosmic bias and scatter. Bayesian combination with other mass estimates yields M_LG = M_MW(vir) + M_M31(vir) = (3.17 +/- 0.57) x 10^12 solar masses. The velocity and mass results imply at 95% confidence that M33 is bound to M31, consistent with expectation from observed tidal deformations. (Abridged)

astro-ph.GA↗

arXiv2011

Approximations of additive squares in infinite words

We show that every infinite word $ω$ on a finite subset of $\mathbb{Z}$ must contain arbitrarily large factors $B_1B_2$ which are "close" to being \textit{additive squares}. We also show that for all $k>1, \ ω$ must contain a factor $U_1U_2 ... U_k$ where $U_1,U_2,..., U_k$ all have the same \textit{average.}

math.CO↗

arXiv2011

On abelian and additive complexity in infinite words

The study of the structure of infinite words having bounded abelian complexity was initiated by G. Richomme, K. Saari, and L. Q. Zamboni. In this note we define bounded additive complexity for infinite words over a finite subset of Z^m. We provide an alternative proof of one of the results of Richomme, Saari, and Zamboni.

math.CO↗

arXiv2011

UV friendly T-parity in the SU(6)/Sp(6) little Higgs model

Electroweak precision tests put stringent constraints on the parameter space of little Higgs models. Tree-level exchange of TeV scale particles in a generic little Higgs model produce higher dimensional operators that make contributions to electroweak observables that are typically too large. To avoid this problem a discrete symmetry dubbed T-parity can be introduced to forbid the dangerous couplings. However, it was realized that in simple group models such as the littlest Higgs model, the implementation of T-parity in a UV completion could present some challenges. The situation is analogous to the one in QCD where the pion can easily be defined as being odd under a new $Z_2$ symmetry in the chiral Lagrangian, but this $Z_2$ is not a symmetry of the quark Lagrangian. In this paper we examine the possibility of implementing a T-parity in the low energy $SU(6)/Sp(6)$ model that might be easier to realize in the UV. In our model, the T-parity acts on the low energy non-linear sigma model field in way which is different to what was originally proposed for the Littlest Higgs, and lead to a different low energy theory. In particular, the Higgs sector of this model is a inert two Higgs doublets model with an approximate custodial symmetry. We examine the contributions of the various sectors of the model to electroweak precision data, and to the dark matter abundance.

hep-ph↗

arXiv2010

Science drivers and requirements for an Advanced Technology Large Aperture Space Telescope (ATLAST): Implications for technology development and synergies with other future facilities

The Advanced Technology Large-Aperture Space Telescope (ATLAST) is a concept for an 8-meter to 16-meter UVOIR space observatory for launch in the 2025-2030 era. ATLAST will allow astronomers to answer fundamental questions at the forefront of modern astronphysics, including "Is there life elsewhere in the Galaxy?" We present a range of science drivers that define the main performance requirements for ATLAST (8 to 16 milliarcsec angular resolution, diffraction limited imaging at 0.5 μm wavelength, minimum collecting area of 45 square meters, high sensitivity to light wavelengths from 0.1 μm to 2.4 μm, high stability in wavefront sensing and control). We will also discuss the synergy between ATLAST and other anticipated future facilities (e.g., TMT, EELT, ALMA) and the priorities for technology development that will enable the construction for a cost that is comparable to current generation observatory-class space missions.

astro-ph.IM↗

arXiv2009

Advanced Technology Large-Aperture Space Telescope (ATLAST): A Technology Roadmap for the Next Decade

The Advanced Technology Large-Aperture Space Telescope (ATLAST) is a set of mission concepts for the next generation of UVOIR space observatory with a primary aperture diameter in the 8-m to 16-m range that will allow us to perform some of the most challenging observations to answer some of our most compelling questions, including "Is there life elsewhere in the Galaxy?" We have identified two different telescope architectures, but with similar optical designs, that span the range in viable technologies. The architectures are a telescope with a monolithic primary mirror and two variations of a telescope with a large segmented primary mirror. This approach provides us with several pathways to realizing the mission, which will be narrowed to one as our technology development progresses. The concepts invoke heritage from HST and JWST design, but also take significant departures from these designs to minimize complexity, mass, or both. Our report provides details on the mission concepts, shows the extraordinary scientific progress they would enable, and describes the most important technology development items. These are the mirrors, the detectors, and the high-contrast imaging technologies, whether internal to the observatory, or using an external occulter. Experience with JWST has shown that determined competitors, motivated by the development contracts and flight opportunities of the new observatory, are capable of achieving huge advances in technical and operational performance while keeping construction costs on the same scale as prior great observatories.

astro-ph.IM↗

arXiv2007

Bounds on Van der Waerden Numbers and Some Related Functions

For positive integers $s$ and $k_1, k_2, ..., k_s$, let $w(k_1,k_2,...,k_s)$ be the minimum integer $n$ such that any $s$-coloring $\{1,2,...,n\} \to \{1,2,...,s\}$ admits a $k_i$-term arithmetic progression of color $i$ for some $i$, $1 \leq i \leq s$. In the case when $k_1=k_2=...=k_s=k$ we simply write $w(k;s)$. That such a minimum integer exists follows from van der Waerden's theorem on arithmetic progressions. In the present paper we give a lower bound for $w(k,m)$ for each fixed $m$. We include a table with values of $w(k,3)$ which match this lower bound closely for $5 \leq k \leq 16$. We also give an upper bound for $w(k,4)$, an upper bound for $w(4;s)$, and a lower bound for $w(k;s)$ for an arbitrary fixed $k$. We discuss a number of other functions that are closely related to the van der Waerden function.

math.CO↗