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At least 703 records · Page 39

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DOE OSTI2025

Recurrent features of amplitudes in planar $\mathcal{N}$ = 4 super Yang-Mills theory

The planar three-gluon form factor for the chiral stress tensor operator in planar maximally supersymmetric Yang-Mills theory is an analog of the Higgs-to-three-gluon scattering amplitude in QCD. The amplitude (symbol) bootstrap program has provided a wealth of high-loop perturbative data about this form factor, with results up to eight loops available. The symbol of the form factor at L loops is given by words of length 2L in six letters with associated integer coefficients. In this paper, we analyze this data, describing patterns of zero coefficients and relations between coefficients. We find many sequences of words whose coefficients are given by closed-form expressions which we expect to be valid at any loop order. Moreover, motivated by our previous machine-learning analysis, we identify simple recursion relations that relate the coefficient of a word to the coefficients of particular lower-loop words. These results open an exciting door for understanding scattering amplitudes at all loop orders.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2017

Polyhedral approximation in mixed-integer convex optimization

Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. Here, we intend to provide a broadly accessible introduction to our recent work in developing algorithms and software for this problem class. Our approach is based on constructing polyhedral outer approximations of the convex constraints, resulting in a global solution by solving a finite number of mixed-integer linear and continuous convex subproblems. The key advance we present is to strengthen the polyhedral approximations by constructing them in a higher-dimensional space. In order to automate this extended formulation we rely on the algebraic modeling technique of disciplined convex programming (DCP), and for generality and ease of implementation we use conic representations of the convex constraints. Although our framework requires a manual translation of existing models into DCP form, after performing this transformation on the MINLPLIB2 benchmark library we were able to solve a number of unsolved instances and on many other instances achieve superior performance compared with state-of-the-art solvers like Bonmin, SCIP, and Artelys Knitro.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

TAS: 89 0227: TAS Recovery Act - Optimization and Control of Electric Power Systems: ARRA

The name SuperOPF is used to refer several projects, problem formulations and soft-ware tools intended to extend, improve and re-define some of the standard methods of optimizing electric power systems. Our work included applying primal-dual interior point methods to standard AC optimal power flow problems of large size, as well as extensions of this problem to include co-optimization of multiple scenarios. The original SuperOPF problem formulation was based on co-optimizing a base scenario along with multiple post-contingency scenarios, where all AC power flow models and constraints are enforced for each, to find optimal energy contracts, endogenously determined locational reserves and appropriate nodal energy prices for a single period optimal power flow problem with uncertainty. This led to example non-linear programming problems on the order of 1 million constraints and half a million variables. The second generation SuperOPF formulation extends this by adding multiple periods and multiple base scenarios per period. It also incorporates additional variables and constraints to model load following reserves, ramping costs, and storage resources. A third generation of the multi-period SuperOPF, adds both integer variables and a receding horizon framework in which the problem type is more challenging (mixed integer), the size is even larger, and it must be solved more frequently, pushing the limits of currently available algorithms and solvers. The consideration of transient stability constraints in optimal power flow (OPF) problems has become increasingly important in modern power systems. Transient stability constrained OPF (TSCOPF) is a nonlinear optimization problem subject to a set of algebraic and differential equations. Solving a TSCOPF problem can be challenging due to (i) the differential-equation constraints in an optimization problem, (ii) the lack of a true analytical expression for transient stability in OPF. To handle the dynamics in TSCOPF, the set of differential equations can be approximated or converted into equivalent algebraic equations before they are included in an OPF formulation. In Chapter 4, a rigorous evaluation of using a predefined and fixed threshold for rotor angles as a mean to determine transient stability of the system is developed. TSCOPF can be modeled as a large-scale nonlinear programming problem including the constraints of differential-algebraic equations (DAE). Solving a TSCOPF problem can be challenging due to (i) the differential-equation constraints in an optimization problem, (ii) the lack of a true analytical expression for transient stability constraint in OPF. Unfortunately, even the current best TSCOPF solvers still suffer from the curse of dimensionality and unacceptable computational time, especially for large-scale power systems with multiple contingencies. In chapter 5, thse issues will be addressed and a new method to incorporate the transient stability constraints will be presented.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2016

Graphical models for optimal power flow

Optimal power flow (OPF) is the central optimization problem in electric power grids. Although solved routinely in the course of power grid operations, it is known to be strongly NP-hard in general, and weakly NP-hard over tree networks. In this paper, we formulate the optimal power flow problem over tree networks as an inference problem over a tree-structured graphical model where the nodal variables are low-dimensional vectors. We adapt the standard dynamic programming algorithm for inference over a tree-structured graphical model to the OPF problem. Combining this with an interval discretization of the nodal variables, we develop an approximation algorithm for the OPF problem. Further, we use techniques from constraint programming (CP) to perform interval computations and adaptive bound propagation to obtain practically efficient algorithms. Compared to previous algorithms that solve OPF with optimality guarantees using convex relaxations, our approach is able to work for arbitrary tree-structured distribution networks and handle mixed-integer optimization problems. Further, it can be implemented in a distributed message-passing fashion that is scalable and is suitable for “smart grid” applications like control of distributed energy resources. In conclusion, numerical evaluations on several benchmark networks show that practical OPF problems can be solved effectively using this approach.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2018

Sub-Libraries in ORIGEN

Libraries produced for the ORIGEN depletion code have the ability to label nuclides with a sublibrary integer tag. While this is useful for tracking different sources of the nuclides, it adds some complexity, increasing memory usage and computational effort. This report documents the effort of making the sublibraries optional in an ORIGEN calculation, with a focus on the creation of libraries using the LibraryBuilder application programming interface (API). ORIGEN will gain the ability to either use the normal sublibrary set, a reduced, unique, sublibrary set, or no sublibrary at all.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2017

MESH2D Grid generator design and use

Mesh2d is a Fortran90 program originally designed to generate two-dimensional structured grids of the form [x(i),y(i,j)] where [x,y] are grid coordinates identified by indices (i,j). x-coordinates depending only on index i implies strictly vertical x-grid lines, whereas the y-grid lines can undulate. Mesh2d also assigns an integer material type to each grid cell, mtyp(i,j), in a user-specified manner. The complete grid is specified through three separate input files defining the x(i), y(i,j), and mtyp(i,j) variations. Since the original development effort, Mesh2d has been extended to more general two-dimensional structured grids of the form [x(i,j),(i,j)].

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2016

New bounding and decomposition approaches for MILP investment problems: Multi-area transmission and generation planning under policy constraints

A novel two-phase bounding and decomposition approach to compute optimal and near-optimal solutions to large-scale mixed-integer investment planning problems is proposed and it considers a large number of operating subproblems, each of which is a convex optimization. Our motivating application is the planning of power transmission and generation in which policy constraints are designed to incentivize high amounts of intermittent generation in electric power systems. The bounding phase exploits Jensen’s inequality to define a lower bound, which we extend to stochastic programs that use expected-value constraints to enforce policy objectives. The decomposition phase, in which the bounds are tightened, improves upon the standard Benders’ algorithm by accelerating the convergence of the bounds. The lower bound is tightened by using a Jensen’s inequality-based approach to introduce an auxiliary lower bound into the Benders master problem. Upper bounds for both phases are computed using a sub-sampling approach executed on a parallel computer system. Numerical results show that only the bounding phase is necessary if loose optimality gaps are acceptable. But, the decomposition phase is required to attain optimality gaps. Moreover, use of both phases performs better, in terms of convergence speed, than attempting to solve the problem using just the bounding phase or regular Benders decomposition separately.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Seismic Retrofit for Electric Power Systems

Our paper develops a two-stage stochastic program and solution procedure to optimize the selection of seismic retrofit strategies to increase the resilience of electric power systems against earthquake hazards. The model explicitly considers the range of earthquake events that are possible and, for each, an approximation of the distribution of damage experienced. Furthermore, this is important because electric power systems are spatially distributed and so their performance is driven by the distribution of component damage. We also test this solution procedure against the nonlinear integer solver in LINGO 13 and apply the formulation and solution strategy to the Eastern Interconnection, where seismic hazard stems from the New Madrid seismic zone.

58 GEOSCIENCES↗

DOE OSTI2016

ZONAL TOROIDAL HARMONIC EXPANSIONS OF EXTERNAL GRAVITATIONAL FIELDS FOR RING-LIKE OBJECTS

We present an expression of the external gravitational field of a general ring-like object with axial and plane symmetries such as oval toroids or annular disks with an arbitrary density distribution. The main term is the gravitational field of a uniform, infinitely thin ring representing the limit of zero radial width and zero vertical height of the object. The additional term is derived from a zonal toroidal harmonic expansion of a general solution of Laplace’s equation outside the Brillouin toroid of the object. The special functions required are the point value and the first-order derivative of the zonal toroidal harmonics of the first kind, namely, the Legendre function of the first kind of half integer degree and an argument that is not less than unity. We developed a recursive method to compute them from two pairs of seed values explicitly expressed by some complete elliptic integrals. Numerical experiments show that appropriately truncated expansions converge rapidly outside the Brillouin toroid. The truncated expansion can be evaluated so efficiently that, for an oval toroid with an exponentially damping density profile, it is 3000–10,000 times faster than the two-dimensional numerical quadrature. A group of the Fortran 90 programs required in the new method and their sample outputs are available electronically.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2011

Mesh2d

Smith, Frank↗

DOE OSTI2012

Mesh2d Grid Generator Design and Use

Mesh2d is a Fortran90 program designed to generate two-dimensional structured grids of the form [x(i),y(i,j)] where [x,y] are grid coordinates identified by indices (i,j). The x(i) coordinates alone can be used to specify a one-dimensional grid. Because the x-coordinates vary only with the i index, a two-dimensional grid is composed in part of straight vertical lines. However, the nominally horizontal y(i,j 0 ) coordinates along index i are permitted to undulate or otherwise vary. Mesh2d also assigns an integer material type to each grid cell, mtyp(i,j), in a user-specified manner. The complete grid is specified through three separate input files defining the x(i), y(i,j), and mtyp(i,j) variations. The overall mesh is constructed from grid zones that are typically then subdivided into a collection of smaller grid cells. The grid zones usually correspond to distinct materials or larger-scale geometric shapes. The structured grid zones are identified through uppercase indices (I,J). Subdivision of zonal regions into grid cells can be done uniformly, or nonuniformly using either a polynomial or geometric skewing algorithm. Grid cells may be concentrated backward, forward, or toward both ends. Figure 1 illustrates the above concepts in the context of a simple four zone grid.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

WORM (Write One, Read Many)

WORM (Write One, Run Many) is an easy to use, cross platform, embedded and extensible, functional programming language designed to facilitate the creation of input-decks for computer codes that use standard ASCII text files for input. WORM makes it easy to create generic (yet, complex and powerful) reusable models. Additionally its nature allows for complex calculations and routines to be coded once and easily reused, further simplifying the creation of input decks. WORM (Write One, Run Many) is a powerful and versatile tool designed to improve the efficiency of today’s criticality safety analyst by allowing: + input decks for parametric studies to be created quickly and easily, + calculations and variables to be imbedded into any input deck, thus allowing for meaningful parameter specifications, + problems to be specified using any combination of units, and + complex mathematically defined models to be created. A very simple syntax is employed, and therefore the WORM is easy to learn. A WORM model is essentially a standard input deck with some of its numerical values replaced by WORM code. WORM code may include and evaluate the following mathematical operators and functions: addition, subtraction, multiplication, division, exponentiation, modulus, sine, cosine, tangent, arcsine, arccosine, arctangent, the natural logarithm, logarithm base 10, integer truncation, absolute value, and random number. Several common constants, e.g., pi, e, and Avogadros’s Number (both as 6.022e23 and 0.6022), are predefined in WORM. Additionally, many unit conversion factors are also predefined: millimeters, meters, inches, feet, yards, and mils to centimeters; kilograms, pounds, and ounces to grams; liters, milliliters, gallons, and fluid ounces to cubic centimeters; and angular degrees to radians. For parametric studies, WORM supports various shorthand list specifications: the explicit step size, linear interpolation, and logarithmic interpolation. The list notation sequentially assigns multiple values to a name. WORM creates an input deck for each value of the name. If multiple lists are used, WORM steps through each list individually, i.e., WORM creates input decks corresponding to each and every permutation of the list values. Additionally, a library of standard material definitions and Perl subroutines are included. Any one of these files can be incorporated into the subject model with a simple WORM read command. WORM is completely written in Perl, the Practical Extraction and Reporting Language. Perl is one of the most portable programming languages available today. As such, the WORM works on practically any computer platform.

Sartor, Raymond↗

DOE OSTI2018

Toplogical optimization of structures using Fourier representations

The minimization of compliance subject to a mass constraint is the topology optimization design problem of interest. The goal is to determine the optimal configuration of material within an allowed volume. Our approach builds upon the well-known density method in which the decision variable is the material density in every cell in a mesh. In it’s most basic form the density method consists of three steps: 1) the problem is convexified by replacing the integer material indicator function with a volume fraction, 2) the problem is regularized by filtering the volume fraction field to impose a minimum length scale; 3) the filtered volume fraction is penalized to steer the material distribution toward binary designs. The filtering step is used to yield a mesh-independent solution and to eliminate checkerboard instabilities. In image processing terms this is a low-pass filter, and a consequence is that the decision variables are not independent and a change of basis could significantly reduce the dimension of the nonlinear programming problem. Based on this observation, we represent the volume fraction field with a truncated Fourier representation. Furthermore, this imposes a minimal length scale on the problem, eliminates checkerboard instabilities, and also reduces the number of decision variables by over 100 × (two dimensions) or 1000 × (three dimensions).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2010

Implementation of a New DTSTEP Algorithm for use in RELAP5-3D and PVMEXEC Completion Report

The PVM Coupling methodology for decomposing a complex model into domains onto which individual programs may be applied has proven effective for solving many multi-physics problems. There have been, from the outset, some detailed and/or long-running models that cause the process to fail. This project addressed the PVM coupling issues surrounding the DTSTEP subroutines on RELAP5-3D and PVMEXEC. Some 25 errors are listed in Tables 1 and 18 and in Section 11. These arise from deficiencies in the floating point calculation and testing of time steps, cumulative time, and time targets. The algorithmic replacement of floating point control of these items with integer based timestepping was developed and implemented. The result of the first phase, undertaken by the INL was that all but three of these issues were resolved. Moreover, two conceptual errors in DTSTEP that were not PVM coupling related were discovered and solved. The final, and most difficult three PVM Bettis User Problems, were solved during the Bettis phase of development and debugging. In 8 months since the conclusion of the project, no further DTSTEP related PVM Coupling errors have been reported.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

The impact of short-term stochastic variability in solar irradiance on optimal microgrid design

This paper proposes a new methodology to capture the impact of fast moving clouds on utility power demand charges observed in microgrids with photovoltaic (PV) arrays, generators, and electrochemical energy storage. It consists of a statistical approach to introduce sub-hourly events in the hourly economic accounting process. The methodology is implemented in the Distributed Energy Resources Customer Adoption Model (DER-CAM), a state of the art mixed integer linear model used to optimally size DER in decentralized energy systems. Results suggest that previous iterations of DER-CAM could undersize battery capacities. The improved model depicts more accurately the economic value of PV as well as the synergistic benefits of pairing PV with storage.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Preliminary results of the 2023 International Fermilab Booster Studies

Here, an overview is given of the methods and preliminary results from dedicated beam studies on three topics conducted over five days in July 2023. In the first study, the Fermilab Booster magnets were held constant at magnetic fields corresponding to the injection energy. The beam loss and emittance growth were observed under varying intensity, tunes, and sextupole resonances. The corresponding beam conditions were also simulated with the MADX-SC code [1]. In the second study, measurements of the vertical half-integer resonance and correction methods are conducted for high-intensity beams ramping in the Booster. Finally, syncho-betatron instabilities are observed during transition-crossing in the Booster under strong space-charge conditions.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

A New Hybrid Quantum-Classical Algorithm for Solving the Unit Commitment Problem

Solving problems related to planning and operations of large-scale power systems is challenging on classical computers due to their inherent nature as mixed-integer and nonlinear problems. Quantum computing provides new avenues to approach these problems. We develop a hybrid quantum-classical algorithm for the Unit Commitment (UC) problem in power systems which aims at minimizing the total cost while optimally allocating generating units to meet the hourly demand of the power loads. The hybrid algorithm combines a variational quantum algorithm (VQA) with a classical Benders-type heuristic. The resulting algorithm computes approximate solutions to UC in three stages: i) a collection of UC vectors capable meeting the power demand with lowest possible operating costs is generated based on VQA; ii) a classical sequential least squares programming (SLSQP) routine is leveraged to find the optimal power level corresponding to a predetermined number of candidate vectors; iii) in the last stage, the approximate solution of UC along with generating units power level combination is given. To demonstrate the effectiveness of the presented method, three different systems with 3 generating units, 10 generating units, and 26 generating units were tested for different time periods. In addition, convergence of the hybrid quantum-classical algorithm for select time periods is proven out on IonQ's Forte system.

Aboumrad, Willie [IonQ, Inc]↗

DOE OSTI2025

Stability evaluation and mitigation strategies in advanced tokamaks using 3D MHD spectroscopy

Multi-modal, active 3D MHD spectroscopy is applied in high-performance advanced tokamak scenarios to study their stability time evolution, revealing an intriguing dependence on both and . A tailored applied 3D field provides a 3D plasma response to extract the growth rate of the least stable mode. The estimated growth rate finds a decrease in stability when the minimum in the safety factor (q) passes through 2.0 and reveals inherent risks of crossing an additional rational surface at integer q min , even above the usual q = 1 sawtooth condition. Based on this result, the potential scenario in which q min ~ 2 can be safely crossed during a more stable lower β N phase was investigated, and the improved stability of this scenario is confirmed by the estimated growth rate. This shows that 3D MHD spectroscopy can offer insights into strategies for improving stability by identifying the vulnerable aspects of such scenarios. In addition, the method highlights its potential for instability avoidance by enabling early detection of multiple modes, even before magnetic coils can measure them. The measured growth rate by the 3D MHD spectroscopy shows its reliability by exhibiting a correlation with the programmed rises in plasma beta across various high β N and high q min discharges. In addition, this method is successfully applied during rapidly evolving I p ramp-up phases, a key part of the scenario development. By achieving reasonable growth rate measurements at high-performance scenario developments, this technique contributes to the development of advanced diagnostic tools for tokamak scenario stability, which will help identify an effective pathway to stable, high-performance scenarios.

Yang, S. M. [Princeton Plasma Physics Laboratory (↗