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Using Cluster Analysis and Dynamic programming for Demand Response applied to Electricity Load in Residential Homes

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Journal of Engineering for Sustainable Buildings and Cities 2020年第1期1卷 011006页

作者： Chanpiwat, Pattanun Gabriel, Steven A. Moglen, Rachel L. Siemann, Michael J. Department of Mechanical Engineering University of Maryland College Park 20742 MD United States Department of Mechanical Engineering and the Applied Mathematics Statistics and Scientific Computation Program University of Maryland College Park 20742 MD United States Department of Industrial Economics and Technology Management Norwegian University of Science and Technology Trondheim NO-7491 Norway Operations Research and Industrial Engineering The University of Texas at Austin Austin 78712 TX United States Resideo Technologies Austin 78702 TX United States

This paper develops means to analyze and cluster residential households into homogeneous groups based on the electricity load. Classifying customers by electricity load profiles is a top priority for retail electric providers (REPs), so they can plan and conduct demand response (DR) effectively. We present a practical method to identify the most DR-profitable customer groups as opposed to tailoring DR programs for each separate household, which may be computationally prohibitive. Electricity load data of 10,000 residential households from 2017 located in Texas was used. The study proposed the clustered load-profile method (CLPM) to classify residential customers based on their electricity load profiles in combination with a dynamic program for DR scheduling to optimize DR profits. The main conclusions are that the proposed approach has an average 2.3% profitability improvement over a business-as-usual heuristic. In addition, the proposed method on average is approximately 70 times faster than running the DR dynamic programming separately for each household. Thus, our method not only is an important application to provide computational business insights for REPs and other power market participants but also enhances resilience for power grid with an advanced DR scheduling tool. Copyright © 2020 by ASME.

关键词： cluster analysis customer classification demand response dynamic programming energy efficiency integrated systems occupant behavior optimization residential household

Low-rank solution methods for stochastic eigenvalue problems

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arXiv 2018年

作者： Elman, Howard C. Su, Tengfei Department of Computer Science Institute for Advanced Computer Studies University of Maryland College ParkMD20742 United States Applied Mathematics & Statistics Scientific Computation Program University of Maryland College ParkMD20742 United States

We study efficient solution methods for stochastic eigenvalue problems arising from discretization of self-adjoint partial differential equations with random data. With the stochastic Galerkin approach, the solutions are represented as generalized polynomial chaos expansions. A low-rank variant of the inverse subspace iteration algorithm is presented for computing one or several minimal eigenvalues and corresponding eigenvectors of parameter-dependent matrices. In the algorithm, the iterates are approximated by low-rank matrices, which leads to significant cost savings. The algorithm is tested on two benchmark problems, a stochastic diffusion problem with some poorly separated eigenvalues, and an operator derived from a discrete stochastic Stokes problem whose minimal eigenvalue is related to the inf-sup stability constant. Numerical experiments show that the low-rank algorithm produces accurate solutions compared to the Monte Carlo method, and it uses much less computational time than the original algorithm without low-rank approximation. Copyright © 2018, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

An Assessment of the Supremizer and Aggregation Methods of Stabilization for Reduced-Order Models

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arXiv 2023年

作者： Davie, Kayla D. Elman, Howard C. Applied Mathematics & Statistics Scientific Computation Program University of Maryland College ParkMD20742 United States Department of Computer Science Institute for Advanced Computer Studies University of Maryland College ParkMD20742 United States

MSC Codes 65N22, 65K10, 65F45We explore the features of two methods of stabilization, aggregation and supremizer methods, for reduced-order modeling of parametrized optimal control problems. In both methods, the reduced basis spaces are augmented to guarantee stability. For the aggregation method, the reduced basis approximation spaces for the state and adjoint variables are augmented in such a way that the spaces are identical. For the supremizer method, the reduced basis approximation space for the state-control product space is augmented with the solutions of a supremizer equation. We implement both of these methods for solving several parametrized control problems and assess their performance. Results indicate that the number of reduced basis vectors needed to approximate the solution space to some tolerance with the supremizer method is much larger, possibly double, that for aggregation. There are also some cases where the supremizer method fails to produce a converged solution. We present results to compare the accuracy, efficiency, and computational costs associated with both methods of stabilization which suggest that stabilization by aggregation is a superior stabilization method for control problems. © 2023, CC BY.

关键词： Stabilization

A Low-rank solver for the stochastic unsteady navier-stokes problem

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arXiv 2019年

作者： Elman, Howard Su, Tengfei Department of Computer Science Institute for Advanced Computer Studies University of Maryland College ParkMD20742 United States Applied Mathematics & Statistics and Scientific Computation Program University of Maryland College ParkMD20742 United States

We study a low-rank iterative solver for the unsteady Navier–Stokes equations for incompressible flows with a stochastic viscosity. The equations are discretized using the stochastic Galerkin method, and we consider an all-at-once formulation where the algebraic systems at all the time steps are collected and solved simultaneously. The problem is linearized with Picard’s method. To efficiently solve the linear systems at each step, we use low-rank tensor representations within the Krylov subspace method, which leads to significant reductions in storage requirements and computational costs. Combined with effective mean-based preconditioners and the idea of inexact solve, we show that only a small number of linear iterations are needed at each Picard step. The proposed algorithm is tested with a model of flow in a two-dimensional symmetric step domain with different settings to demonstrate the computational efficiency. Copyright © 2019, The Authors. All rights reserved.

关键词： Navier Stokes equations

Parsimonious reconstruction of network evolution

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Parsimonious reconstruction of network evolution

Lecture Notes in Computer Science

作者： Patro, Rob Sefer, Emre Malin, Justin Marçais, Guillaume Navlakha, Saket Kingsford, Carl Center for Bioinformatics and Computational Biology University of Maryland College Park MD 20742 United States Department of Computer Science University of Maryland College Park MD 20742 United States Computational Biology Bioinformatics and Genomics Concentration Biological Sciences Graduate Program University of Maryland College Park MD 20742 United States Program in Applied Mathematics Statistics and Scientific Computation University of Maryland College Park MD 20742 United States School of Computer Science Carnegie Mellon University Pittsburgh PA 15213 United States

ISBN: (纸本)9783642230370

We consider the problem of reconstructing a maximally parsimonious history of network evolution under models that support gene duplication and loss and independent interaction gain and loss. We introduce a combinatorial framework for encoding network histories, and we give a fast procedure that, given a set of duplication histories, in practice finds network histories with close to the minimum number of interaction gain or loss events. In contrast to previous studies, our method does not require knowing the relative ordering of unrelated duplication events. Results on simulated histories suggest that common ancestral networks can be accurately reconstructed using this parsimony approach. © 2011 Springer-Verlag.

关键词： Genes

Estimation of Parameter Distributions for Reaction-Diffusion Equations with Competition using Aggregate Spatiotemporal Data

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arXiv 2023年

作者： Nguyen, Kyle Rutter, Erica M. Flores, Kevin Biomathematics Graduate Program North Carolina State University RaleighNC United States Center for Research in Scientific Computation North Carolina State University RaleighNC United States Department of Applied Mathematics University of California Merced MercedCA United States Department of Mathematics North Carolina State University RaleighNC United States

Reaction diffusion equations have been used to model a wide range of biological phenomenon related to population spread and proliferation from ecology to cancer. It is commonly assumed that individuals in a population have homogeneous diffusion and growth rates, however, this assumption can be inaccurate when the population is intrinsically divided into many distinct subpopulations that compete with each other. In previous work, the task of inferring the degree of phenotypic heterogeneity between subpopulations from total population density has been performed within a framework that combines parameter distribution estimation with reaction-diffusion models. Here, we extend this approach so that it is compatible with reaction-diffusion models that include competition between subpopulations. We use a reaction-diffusion model of Glioblastoma multiforme, an aggressive type of brain cancer, to test our approach on simulated data that are similar to measurements that could be collected in practice. We use Prokhorov metric framework and convert the reaction-diffusion model to a random differential equation model to estimate joint distributions of diffusion and growth rates among heterogeneous subpopulations. We then compare the new random differential equation model performance against other partial differential equation models’ performance. We find that the random differential equation is more capable at predicting the cell density compared to other models while being more time efficient. Finally, we use k-means clustering to predict the number of subpopulations based on the recovered distributions. © 2023, CC BY.

关键词： Parameter estimation

Characterizing the nonlinear structure of shared variability in cortical neuron populations using latent variable models

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arXiv 2019年

作者： Whiteway, Matthew R. Socha, Karolina Bonin, Vincent Butts, Daniel A. Program in Applied Mathematics and Statistics and Scientific Computation University of Maryland College ParkMD United States Neuro-Electronics Research Flanders Leuven Belgium Department of Biology Leuven Brain Institute KU Leuven Leuven Belgium VIB Leuven Belgium Department of Biology and Program in Neuroscience and Cognitive Sciences University of Maryland College ParkMD United States

Sensory neurons often have variable responses to repeated presentations of the same stimulus, which can significantly degrade the stimulus information contained in those responses. This information can in principle be preserved if variability is shared across many neurons, but depends on the structure of the shared variability and its relationship to sensory encoding at the population level. The structure of this shared variability in neural activity can be characterized by latent variable models, although they have thus far typically been used under restrictive mathematical assumptions, such as assuming linear transformations between the latent variables and neural activity. Here we introduce two nonlinear latent variable models for analyzing large-scale neural *** first present a general nonlinear latent variable model that is agnostic to the stimulus tuning properties of the individual neurons, and is hence well suited for exploring neural populations whose tuning properties are not well characterized. This motivates a second class of model, the Generalized Affine Model, which simultaneously determines each neuron's stimulus selectivity and a set of latent variables that modulate these stimulus-driven responses both additively and multiplicatively. While these approaches can detect very general nonlinear relationships in shared neural variability, we find that neural activity recorded in anesthetized primary visual cortex (V1) is best described by a single additive and single multiplicative latent variable, i.e., an "affine model". In contrast, application of the same models to recordings in awake macaque prefrontal cortex discover more general nonlinearities to compactly describe the population response variability. These results thus demonstrate how nonlinear latent variable models can be used to describe population variability, and suggest that a range of methods is necessary to study different brain regions under different experimental conditions. C

关键词： Neurons

A bicriteria perspective on l-penalty approaches a corrigendum to siddiqui and gabriel's L-Penalty Approach for Solving MPECs

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arXiv 2018年

作者： Dächert, D. Siddiqui, Kerstin Saez-Gallego, Sauleh Gabriel, Javier Morales, Steven A. Miguel, Juan University of Duisburg-Essen Faculty of Economics and Business Administration Department for Management Science and Energy Economics Berliner Platz 6-8 Essen45127 Germany Departments of Civil Engineering and Applied Mathematics Statisitics Johns Hopkins University 3400 N Charles Street BaltimoreMD21218 United States Siemens Wind Power A/S Borupvang 9 Ballerup2750 Denmark Department of Mechanical Engineering Applied Mathematics Statistics and Scientific Computation Program University of Maryland College ParkMD20742-3021 United States University of Málaga Department of Applied Mathematics School of Industrial Engineers Málagaroom 2.556L-B

This paper presents a corrigendumto Theorems 2 and 3 in Siddiqui and Gabriel (2013). In brief, we revise the claim that their L-penalty approach yields a so-lution satisfying complementarity for any positive value of L, in general. This becomes evident when interpreting the L-penalty method as a weighted-sum scalarization of a bicriteria optimization problem. We also elaborate further assumptions under which the L-penalty approach yields a solution satisfying complementarity. Copyright © 2018, The Authors. All rights reserved.

关键词： Constrained optimization

Resonant responses to variance modulation in stochastic integrate-and-fire neurons

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BMC Neuroscience 2007年第2期8卷 1-1页

作者： Joanna Pressley Todd W Troyer Applied Mathematics and Scientific Computation Program University of Maryland College Park MD 20742 USA Neuroscience and Cognitive Science Program University of Maryland College Park MD 20742 USA Department of Psychology University of Maryland College Park MD 20742 USA