Multi-jagged: A Scalable Multi-section based Spatial Partitioning Algorithm.
Abstract Not Provided
Rajamanickam, Sivasankaran↗
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Multi-jagged: A Scalable Multi-section based Spatial Partitioning Algorithm.
Abstract not provided.
Rajamanickam, Sivasankaran↗
Accelerated Voltage Regulation in Multi-Phase Distribution Networks Based on Hierarchical Distributed Algorithm
Here, we introduce a hierarchical distributed algorithm to solve optimal power flow (OPF) problems that aim at dispatching controllable distributed energy resources (DERs) for voltage regulation at minimum cost. The proposed algorithm highlights unprecedented scalability to large multi-phase distribution networks by jointly exploring the tree/subtrees structure of a large radial distribution network and the structure of the linearized distribution power flow (LinDistFlow) model to derive a hierarchical, distributed implementation of the primal-dual gradient algorithm that solves OPF. The proposed implementation significantly reduces the computation loads compared to the centrally coordinated implementation of the same primal-dual algorithm without compromising optimality. Numerical findings on a 4,521-node test feeder show that the designed algorithm achieves more than 10-fold acceleration in the speed of convergence compared to the centrally coordinated primal-dual algorithm through reducing and distributing computational loads.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Network-Level Optimization for Unbalanced Power Distribution System: Approximation and Relaxation
The nonlinear programming (NLP) problem to solve distribution-level optimal power flow (D-OPF) poses convergence issues and does not scale well for unbalanced distribution systems. The existing scalable D-OPF algorithms either use approximations that are not valid for an unbalanced power distribution system, or apply relaxation techniques to the nonlinear power flow equations that do not guarantee a feasible power flow solution. In this paper, we propose scalable D-OPF algorithms that simultaneously achieve optimal and feasible solutions by solving multiple iterations of approximate, or relaxed, D-OPF subproblems of low complexity. The first algorithm is based on a successive linear approximation of the nonlinear power flow equations around the current operating point, where the D-OPF solution is obtained by solving multiple iterations of a linear programming (LP) problem. The second algorithm is based on the relaxation of the nonlinear power flow equations as conic constraints together with directional constraints, which achieves optimal and feasible solutions over multiple iterations of a second-order cone programming (SOCP) problem. Finally, it is demonstrated that the proposed algorithms are able to reach an optimal and feasible solution while significantly reducing the computation time as compared to an equivalent NLPD-OPF model for the same distribution system.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Variable Time-Step Implementation for Rapid Quasi-Static Time-Series (QSTS) Simulations of Distributed PV
Distribution system analysis with high penetrations of distributed PV require quasi-static time-series (QSTS) analysis to model the variability introduced on the distribution system, but current QSTS algorithms are prohibitively burdensome and computationally intensive. This paper proposes a variable timestep algorithm to calculate the critical time periods when QSTS simulations should be solved at higher or lower time-resolution and to backtrack for any critical periods that were missed. This variable time-step solver is a new method of performing timeseries simulations with high accuracy while performing the simulation more than 50 times faster. The scalability of the algorithm is demonstrated using a real utility distribution system model with thousands of buses.
14 SOLAR ENERGY↗
Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model
In this paper we present a time-parallel algorithm for the 3D neutrons calculation of a transient model in a nuclear reactor core. The neutrons calculation consists in numerically solving the time dependent diffusion approximation equation, which is a simplified transport equation. The numerical resolution is done with finite elements method based on a tetrahedral meshing of the computational domain, representing the reactor core, and time discretization is achieved using a θ-scheme. The transient model presents moving control rods during the time of the reaction. Therefore, cross-sections (piecewise constants) are taken into account by interpolations with respect to the velocity of the control rods. The parallelism across the time is achieved by an adequate use of the parareal in time algorithm to the handled problem. This parallel method is a predictor corrector scheme that iteratively combines the use of two kinds of numerical propagators, one coarse and one fine. Our method is made efficient by means of a coarse solver defined with large time step and fixed position control rods model, while the fine propagator is assumed to be a high order numerical approximation of the full model. The parallel implementation of our method provides a good scalability of the algorithm. Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the Langenbuch–Maurer–Werner benchmark.
97 MATHEMATICS AND COMPUTING↗
Space–time reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems
A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing much accuracy, which results in a considerably more speed-up than the spatial reduction only. Recently, a novel space–time reduced order model for dynamical problems has been developed [17], where the space–time reduced order model shows an order of a hundred speed-up with a relative error of 10 –4 for small academic problems. However, in order for the method to be applicable to a large-scale problem, an efficient space–time reduced basis construction algorithm needs to be developed. Here we present the incremental space–time reduced basis construction algorithm. The incremental algorithm is fully parallel and scalable. Additionally, the block structure in the space–time reduced basis is exploited, which enables the avoidance of constructing the reduced space–time basis. These novel techniques are applied to a large-scale particle transport simulation with million and billion degrees of freedom. The numerical example shows that the algorithm is scalable and practical. Also, it achieves a tremendous speed-up, maintaining a good accuracy. Finally, error bounds for space-only and space–time reduced order models are derived.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
An Empirical Validation of a Constrained Bin Packing Algorithm for a Home Energy Management System
The increasing number of intelligent electrical appliances and home energy management systems provide a big opportunity for demand response services from residential and small commercial buildings to the grid. Simultaneously, direct control of individual devices by utilities can cause communication bottlenecks, as well as coordination and privacy concerns. These challenges can be addressed by combining the constituent devices into a single house battery equivalent for the purposes of demand response, using Minkowski sum and a 2d bin packing problem. However, the well-studied traditional problems have not been tested in a real house, as implementation carries significant challenges of its own. We deploy the packing problem on residential devices in a controllable house. We report the barriers we found, such as charge forecast and scalability of the algorithm, and discuss our solutions. The study serves as an intermediate step between existing theoretical research and possible future steps, such as prototype deployments of systems that provide residential demand response.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
Reduced Hardware NOrec: A Safe and Scalable Hybrid Transactional Memory
Because of hardware TM limitations, software fallbacks are the only way to make TM algorithms guarantee progress. Nevertheless, all known software fallbacks to date, from simple locks to sophisticated versions of the NOrec Hybrid TM algorithm, have either limited scalability or weakened semantics. We propose a novel reduced-hardware (RH) version of the NOrec HyTM algorithm. Instead of an all-software slow path, in our RH NOrec the slow-path is a "mix" of hardware and software: one short hardware transaction executes a maximal amount of initial reads in the hardware, and the second executes all of the writes. Furthermore, this novel combination of the RH approach and the NOrec algorithm delivers the first Hybrid TM that scales while fully preserving the hardware's original semantics of opacity and privatization. Our GCC implementation of RH NOrec is promising in that it shows improved performance relative to all prior methods, at the concurrency levels we could test today.
97 MATHEMATICS AND COMPUTING↗
Hierarchical Distributed Voltage Regulation in Networked Autonomous Grids
We propose a novel algorithm to solve optimal power flow (OPF) that aims at dispatching controllable distributed energy resources (DERs) for voltage regulation at minimum cost. The proposed algorithm features unprecedented scalability to large distribution networks by utilizing an information structure based on networked autonomous grids (AGs). Specifically, each AG is a subtree of a large distribution network that has a tree topology. The topology and line parameters of each AG are known only to a regional coordinator (RC) that is responsible for communicating with and dispatching the DERs within this AG. The reduced network, where each AG is treated as a node, is managed by a central coordinator (CC), which knows the topology and line parameters of the reduced network only and communicates with all the RCs. We jointly explore this information structure and the structure of the linearized distribution power flow (LinDistFlow) model to derive a hierarchical, distributed implementation of the primal-dual gradient algorithm that solves the OPF. The proposed implementation significantly reduces the computation burden compared to the centrally coordinated implementation of the primal-dual algorithm. Numerical results on a 4,521-node test feeder show that the proposed hierarchical distributed algorithm can achieve an improvement of more than tenfold in the speed of convergence compared to the centrally coordinated primal-dual algorithm.
Zhou, Xinyang↗
Hierarchical Distributed Voltage Regulation in Networked Autonomous Grids: Preprint
We propose a novel algorithm to solve optimal power flow (OPF) that aims at dispatching controllable distributed energy resources (DERs) for voltage regulation at minimum cost. The proposed algorithm features unprecedented scalability to large distribution networks by utilizing an information structure based on networked autonomous grids (AGs). Specifically, each AG is a subtree of a large distribution network that has a tree topology. The topology and line parameters of each AG are known only to a regional coordinator (RC) that is responsible for communicating with and dispatching the DERs within this AG. The reduced network, where each AG is treated as a node, is managed by a central coordinator (CC), which knows the topology and line parameters of the reduced network only and communicates with all the RCs. We jointly explore this information structure and the structure of the linearized distribution power flow (LinDistFlow) model to derive a hierarchical, distributed implementation of the primal-dual gradient algorithm that solves OPF. The proposed implementation significantly reduces the computation burden compared to the centrally coordinated implementation of the primal-dual algorithm. Numerical results on a 4,521-node test feeder show that the proposed hierarchical distributed algorithm can achieve more than 10-fold improvement in the speed of convergence compared to the centrally coordinated primal-dual algorithm.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Hierarchical Distributed Voltage Regulation in Networked Autonomous Grids
We propose a novel algorithm to solve optimal power flow (OPF) that aims at dispatching controllable distributed energy resources (DERs) for voltage regulation at minimum cost. The proposed algorithm features unprecedented scalability to large distribution networks by utilizing an information structure based on networked autonomous grids (AGs). Specifically, each AG is a subtree of a large distribution network that has a tree topology. The topology and line parameters of each AG are known only to a regional coordinator (RC) that is responsible for communicating with and dispatching the DERs within this AG. The reduced network, where each AG is treated as a node, is managed by a central coordinator (CC), which knows the topology and line parameters of the reduced network only and communicates with all the RCs. We jointly explore this information structure and the structure of the linearized distribution power flow (LinDistFlow) model to derive a hierarchical, distributed implementation of the primal-dual gradient algorithm that solves the OPF. The proposed implementation significantly reduces the computation burden compared to the centrally coordinated implementation of the primal-dual algorithm. Numerical results on a 4,521-node test feeder show that the proposed hierarchical distributed algorithm can achieve an improvement of more than tenfold in the speed of convergence compared to the centrally coordinated primal-dual algorithm.
24 POWER TRANSMISSION AND DISTRIBUTION↗
How to estimate the 3D power spectrum of the Lyman-α forest
Here, we derive and numerically implement an algorithm for estimating the 3D power spectrum of the Lyman-α (Lyα) forest flux fluctuations. The algorithm exploits the unique geometry of Lyα forest data to efficiently measure the cross-spectrum between lines of sight as a function of parallel wavenumber, transverse separation and redshift. We start by approximating the global covariance matrix as block-diagonal, where only pixels from the same spectrum are correlated. We then compute the eigenvectors of the derivative of the signal covariance with respect to cross-spectrum parameters, and project the inverse-covariance-weighted spectra onto them. This acts much like a radial Fourier transform over redshift windows. The resulting cross-spectrum inference is then converted into our final product, an approximation of the likelihood for the 3D power spectrum expressed as second order Taylor expansion around a fiducial model. We demonstrate the accuracy and scalability of the algorithm and comment on possible extensions. Our algorithm will allow efficient analysis of the upcoming Dark Energy Spectroscopic Instrument dataset.
79 ASTRONOMY AND ASTROPHYSICS↗
Trigger Detection for Adaptive Scientific Workflows Using Percentile Sampling
The increasing complexity of both scientific simulations and high-performance computing system architectures are driving the need for adaptive workflows, in which the composition and execution of computational and data manipulation steps dynamically depend on the evolutionary state of the simulation itself. Consider, for example, the frequency of data storage. Critical phases of the simulation should be captured with high frequency and with high fidelity for postanalysis; however, we cannot afford to retain the same frequency for the full simulation due to the high cost of data movement. We can instead look for triggers, indicators that the simulation will be entering a critical phase, and adapt the workflow accordingly. In this paper, we present a methodology for detecting triggers and demonstrate its use in the context of direct numerical simulations of turbulent combustion using S3D. We show that chemical explosive mode analysis (CEMA) can be used to devise a noise-tolerant indicator for rapid increase in heat release. However, exhaustive computation of CEMA values dominates the total simulation, and thus is prohibitively expensive. To overcome this computational bottleneck, we propose a quantile sampling approach. Our sampling-based algorithm comes with provable error/confidence bounds, as a function of the number of samples. Most importantly, the number of samples is independent of the problem size, and thus our proposed sampling algorithm offers perfect scalability. Our experiments on homogeneous charge compression ignition and reactivity controlled compression ignition simulations show that the proposed method can detect rapid increases in heat release, and its computational overhead is negligible. Our results will be used to make dynamic workflow decisions regarding data storage and mesh resolution in future combustion simulations.
97 MATHEMATICS AND COMPUTING↗
Evaluating a quantum-classical quantum Monte Carlo algorithm with Matchgate shadows
Solving the electronic structure problem of molecules and solids to high accuracy is a major challenge in quantum chemistry and condensed matter physics. The rapid emergence and development of quantum computers offer a promising route to systematically tackle this problem. Recent work by [Huggins et al ., Nature (London) 603 , 416 (2022)] proposed a hybrid quantum-classical quantum Monte Carlo (QC-QMC) algorithm using Clifford shadows to determine the ground state of a Fermionic Hamiltonian. This approach displayed inherent noise resilience and the potential for improved accuracy compared to its purely classical counterpart. Nevertheless, the use of Clifford shadows introduces an exponentially scaling postprocessing cost. In this work, we investigate an improved QC-QMC scheme utilizing the recently developed Matchgate shadows technique [Commun. Math. Phys. 404 , 629 (2023)], which removes the aforementioned exponential bottleneck. We observe from experiments on quantum hardware that the use of Matchgate shadows in QC-QMC is inherently noise robust. We show that this noise resilience has a more subtle origin than in the case of Clifford shadows. Nevertheless, we find that classical postprocessing, while asymptotically efficient, requires hours of runtime on thousands of classical CPUs for even the smallest chemical systems, presenting a major challenge to the scalability of the algorithm.
Monte Carlo methods↗
Mesh-free data transfer algorithms for partitioned multiphysics problems: Conservation, accuracy, and parallelism
In this study we analyze and extend mesh-free algorithms for three-dimensional data transfer problems in partitioned multiphysics simulations. We first provide a direct comparison between a mesh-based weighted residual method using the common-refinement scheme and two mesh-free algorithms leveraging compactly supported radial basis functions: one using a spline interpolation and one using a moving least square reconstruction. Through the comparison we assess both the conservation and accuracy of the data transfer obtained from each of the methods. We do so for a varying set of geometries with and without curvature and sharp features and for functions with and without smoothness and with varying gradients. Our results show that the mesh-based and mesh-free algorithms are complementary with cases where each was demonstrated to perform better than the other. We then focus on the mesh-free methods by developing a set of algorithms to parallelize them based on sparse linear algebra techniques. This includes a discussion of fast parallel radius searching in point clouds and restructuring the interpolation algorithms to leverage data structures and linear algebra services designed for large distributed computing environments. The scalability of our new algorithms is demonstrated on a leadership class computing facility using a set of basic scaling studies. Finally, these scaling studies show that for problems with reasonable load balance, our new algorithms for both spline interpolation and moving least square reconstruction demonstrate both strong and weak scalability using more than 100,000 MPI processes with billions of degrees of freedom in the data transfer operation.
97 MATHEMATICS AND COMPUTING↗