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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Assessing the Optimality of LinDist3Flow for Optimal Tap Selection of Step Voltage Regulators in Unbalanced Distribution Networks: Preprint

The adoption of distributed energy resources such as photovoltaics (PVs) has increased dramatically during the previous decade. The increased penetration of PVs into distribution networks (DNs) can cause voltage fluctuations that have to be mitigated. One of the key utility assets employed to this end are step-voltage regulators (SVRs). It is desirable to include tap selection of SVRs in optimal power flow (OPF) routines, a task that turns out to be challenging because the resultant OPF problem is nonconvex with added complexities stemming from accurate SVR modeling. While several convex relaxations based on semi-definite programming (SDP) have been presented in the literature for optimal tap selection, SDP based schemes do not scale well and are challenging to implement in large-scale planning or operational frameworks. This paper deals with the optimal tap selection (OPTS) problem for wye-connected SVRs using linear approximations of power flow equations. Specifically, the LinDist3Flow model is adopted and the effective SVR ratio is assumed to be continuous–enabling the formulation of a problem called LinDist3Flow-OPTS, which amounts to a linear program. The scalability and optimality gap of LinDist3Flow-OPTS are evaluated with respect to existing SDP-based and nonlinear programming techniques for optimal tap selection in three standard feeders, namely, the IEEE 13-bus, 123-bus, and 8500-node DNs. For all DNs considered, LinDist3Flow-OPTS achieves an optimality gap of approximately 1% or less while significantly lowering the computational burden.

linear approximations↗
DOE OSTI2024

Optimal Membrane Cascade Design for Critical Mineral Recovery Through Logic-based Superstructure Optimization

Critical minerals and rare earth elements play an important role in our climate change initiatives, particularly in applications related with energy storage. Here, we use discrete optimization approaches to design a process for the recovery of Lithium and Cobalt from battery recycling, through membrane separation. Our contribution involves proposing a Generalized Disjunctive Programming (GDP) model for the optimal design of a multistage diafiltration cascade for Li-Co separation. By solving the resulting nonconvex mixed-integer nonlinear program model to global optimality, we investigated scalability and solution quality variations with changes in the number of stages and elements per stage. Results demonstrate the computational tractability of the nonlinear GDP formulation for design of membrane separation processes while opening the door for decom-position strategies for multicomponent separation cascades. Future work aims to extend the GDP formulation to account for stage installation and explore various decomposition techniques to enhance solution efficiency.

Ovalle, Daniel↗
DOE OSTI2025

McCormick envelopes in mixed-integer PDE-constrained optimization

McCormick envelopes are a standard tool for deriving convex relaxations of optimization problems that involve polynomial terms. Such McCormick relaxations provide lower bounds, for example, in branch-and-bound procedures for mixed-integer nonlinear programs but have not gained much attention in PDE-constrained optimization so far. This lack of attention may be due to the distributed nature of such problems, which on the one hand leads to infinitely many linear constraints (generally state constraints that may be difficult to handle) in addition to the state equation for a pointwise formulation of the McCormick envelopes and renders bound-tightening procedures that successively improve the resulting convex relaxations computationally intractable. We analyze McCormick envelopes for a model problem class that is governed by a semilinear PDE involving a bilinearity and integrality constraints. We approximate the nonlinearity and in turn the McCormick envelopes by averaging the involved terms over the cells of a partition of the computational domain on which the PDE is defined. This yields convex relaxations that underestimate the original problem up to an a priori error estimate that depends on the mesh size of the discretization. These approximate McCormick relaxations can be improved by means of an optimization-based bound-tightening procedure. We show that their minimizers converge to minimizers to a limit problem with a pointwise formulation of the McCormick envelopes when driving the mesh size to zero. We provide a computational example, for which we certify all of our imposed assumptions. The results point to both the potential of the methodology and the gaps in the research that need to be closed. Our methodology provides a framework first for obtaining pointwise underestimators for nonconvexities and second for approximating them with finitely many linear inequalities in an infinite-dimensional setting.

Approximations and Expansions↗
DOE OSTI2019

A mathematical programming approach for the optimal placement of flame detectors in petrochemical facilities

Flame detectors provide an important layer of protection for personnel in petrochemical plants, but effective placement can be challenging. A mixed-integer nonlinear programming formulation is proposed for optimal placement of flame detectors while considering non-uniform probabilities of detection failure. We show that this approach allows for the placement of fire detectors using a fixed sensor budget and outperforms models that do not account for imperfect detection. In this study, we develop a linear relaxation to the formulation and an efficient solution algorithm that achieves global optimality with reasonable computational effort. We integrate this problem formulation into the Python package, Chama, and demonstrate the effectiveness of this formulation on a small test case and on two real-world case studies using the fire and gas mapping software, Kenexis Effigy.

47 OTHER INSTRUMENTATION↗
NASA NTRS2016

Hybrid Differential Dynamic Programming with Stochastic Search

Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASAs Dawn mission. The Dawn trajectory was designed with the DDP-based Static Dynamic Optimal Control algorithm used in the Mystic software. Another recently developed method, Hybrid Differential Dynamic Programming (HDDP) is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.

Aziz, Jonathan↗
NASA NTRS1990

Multilevel decomposition approach to the preliminary sizing of a transport aircraft wing

A multilevel/multidisciplinary optimization scheme for sizing an aircraft wing structure is described. A methodology using nonlinear programming in application to a very large engineering problem is presented. This capability is due to the decomposition approach. Over 1300 design variables are considered for this nonlinear optimization task. In addition, a mathematical link is established coupling the detail of structural sizing to the overall system performance objective, such as fuel consumption. The scheme is implemented as a three level system analyzing aircraft mission performance at the top level, the total aircraft structure as the middle level, and individual stiffened wing skin cover panels at the bottom level. Numerical show effectiveness of the method and its good convergence characteristics.

Wrenn, Gregory A.↗
DOE OSTI2018

Global Solution Strategies for the Network-Constrained Unit Commitment Problem with AC Transmission Constraints

Here, we propose a novel global solution algorithm for the network-constrained unit commitment problem that incorporates a nonlinear alternating current (AC) model of the transmission network, which is a nonconvex mixed-integer nonlinear programming (MINLP) problem. Our algorithm is based on the multi-tree global optimization methodology, which iterates between a mixed-integer lower-bounding problem and a nonlinear upper-bounding problem. We exploit the mathematical structure of the unit commitment problem with AC power flow constraints (UC-AC) and leverage second-order cone relaxations, piecewise outer approximations, and optimization-based bounds tightening to guarantee a globally optimal solution at convergence. Numerical results on four benchmark problems illustrate the effectiveness of our algorithm, both in terms of convergence rate and solution quality.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS2016

Hybrid Differential Dynamic Programming with Stochastic Search

Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASA's Dawn mission. The Dawn trajectory was designed with the DDP-based Static/Dynamic Optimal Control algorithm used in the Mystic software.1 Another recently developed method, Hybrid Differential Dynamic Programming (HDDP),2, 3 is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.

Aziz, Jonathan↗
NASA NTRS1991

Trajectory optimization and guidance for a hypersonic vehicle

The optimal ascent problem for a hypersonic vehicle is formulated as an inverse dynamic problem. This formulation is essential in solving the trajectory optimization problem via the nonlinear programming approach. Both minimum-fuel and minimax type of performance indices are considered. The results reveal important features of the optimal trajectory and controls, and they are subsequently used to construct a nonlinear feedback midcourse control law. This control law not only greatly simplifies the difficult constrained optimization problem and yields improved solutions, but is also suitable for onboard implementation. Finally, off-nominal trajectory guidance is addressed using combination of feedback compensation and onboard generation of control through the inverse dynamics approach.

Lu, Ping↗
NASA NTRS1990

TROJID: A portable software package for upper-stage trajectory optimization

Performance optimization for upper-stage exoatmospheric vehicles often is performed within the framework of a full capability trajectory simulation package requiring either a large mainframe computer or powerful work-station. Since these software packages tend to include capabilities providing for high-fidelity boost and reentry simulations, the programs usually are quite large and not very portable. The program TROJID is an attempt to provide an environment for the optimization of upper-stage trajectories within a small package capable of being run on a standard desktop microcomputer. Utilizing a state-of-the-art nonlinear programming algorithm and a trajectory simulator implementing impulsive burns and an analytic coast phase propagator, TROJID is capable of producing trajectories for optimal multi-burn upper-stage orbit transfers. The package has been designed to allow full generality in definition of both the trajectory simulator and the parameter optimization problem.

Hammes, Steven M.↗
NASA NTRS1984

Manual of phosphoric acid fuel cell power plant optimization model and computer program

An optimized cost and performance model for a phosphoric acid fuel cell power plant system was derived and developed into a modular FORTRAN computer code. Cost, energy, mass, and electrochemical analyses were combined to develop a mathematical model for optimizing the steam to methane ratio in the reformer, hydrogen utilization in the PAFC plates per stack. The nonlinear programming code, COMPUTE, was used to solve this model, in which the method of mixed penalty function combined with Hooke and Jeeves pattern search was chosen to evaluate this specific optimization problem.

Lu, C. Y.↗
NASA NTRS1977

Modeling and Analysis of Power Processing Systems (MAPPS), initial phase 2

The overall objective of the program is to provide the engineering tools to reduce the analysis, design, and development effort, and thus the cost, in achieving the required performances for switching regulators and dc-dc converter systems. The program was both tutorial and application oriented. Various analytical methods were described in detail and supplemented with examples, and those with standardization appeals were reduced into computer-based subprograms. Major program efforts included those concerning small and large signal control-dependent performance analysis and simulation, control circuit design, power circuit design and optimization, system configuration study, and system performance simulation. Techniques including discrete time domain, conventional frequency domain, Lagrange multiplier, nonlinear programming, and control design synthesis were employed in these efforts. To enhance interactive conversation between the modeling and analysis subprograms and the user, a working prototype of the Data Management Program was also developed to facilitate expansion as future subprogram capabilities increase.

Yu, Y.↗
DOE OSTI2021

Convergence of sum-up rounding schemes for cloaking problems governed by the Helmholtz equation

In this work, we consider the problem of designing a cloak for waves described by the Helmholtz equation from an integer programming point of view. The problem can be modeled as a PDE-constrained optimization problem with integer-valued control inputs that are distributed in the computational domain. A first-discretize-then-optimize approach results in a large-scale mixed-integer nonlinear program that is in general intractable because of the large number of integer variables that arise from the discretization of the domain. Instead, we propose an efficient algorithm that is able to approximate the local infima of the underlying nonconvex infinite-dimensional problem arbitrarily close without the need to solve the discretized finite-dimensional integer programs to optimality. We optimize only the continuous relaxations of the approximations for local minima and then apply the sum-up rounding methodology to obtain integer-valued controls. If the solutions of the discretized continuous relaxations converge to a local minimizer of the continuous relaxation, then the resulting discrete-valued control sequence converges weakly \(^*\) in \(L^\infty\) to the same local minimizer. These approximation properties follow under suitable refinements of the involved discretization grids. Our results use familiar concepts arising from the analytical properties of the underlying PDE and complement previous results, derived from a topology optimization point of view.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1987

Structural optimization of an alternate design for the Space Shuttle solid rocket booster field joint

A structural optimization procedure is used to determine the shape of an alternate design for the Shuttle's solid rocket booster field joint. In contrast to the tang and clevis design of the existing joint, this alternate design consists of two flanges bolted together. Configurations with 150 studs of 1 1/8 in diameter and 135 studs of 1 3/16 in diameter are considered. Using a nonlinear programming procedure, the joint weight is minimized under constraints on either von Mises or maximum normal stresses, joint opening and geometry. The procedure solves the design problem by replacing it by a sequence of approximate (convex) subproblems; the pattern of contact between the joint halves is determined every few cycles by a nonlinear displacement analysis. The minimum weight design has 135 studs of 1 3/16 in diameter and is designed under constraints on normal stresses. It weighs 1144 lb per joint more than the current tang and clevis design.

Barthelemy, Jean-Francois M.↗
DOE OSTI2020

Piecewise polyhedral formulations for a multilinear term

Herein, we present a mixed-integer linear programming (MILP) formulation of a piecewise, polyhedral relaxation (PPR) of a multilinear term using its convex-hull representation. Based on the PPR’s solution, we also present a MILP formulation whose solutions are feasible for nonconvex, multilinear equations. We then present computational results showing the effectiveness of proposed formulations on standard benchmark nonlinear programs (NLPs) with multilinear terms and compare with a traditional formulation that is built using recursive bilinear groupings of multilinear terms.

42 ENGINEERING↗
DOE OSTI2017

Optimal design and dispatch of a system of diesel generators, photovoltaics and batteries for remote locations

Renewable energy technologies, specifically, solar photovoltaic cells, combined with battery storage and diesel generators, form a hybrid system capable of independently powering remote locations, i.e., those isolated from larger grids. If sized correctly, hybrid systems reduce fuel consumption compared to diesel generator-only alternatives. We present an optimization model for establishing a hybrid power design and dispatch strategy for remote locations, such as a military forward operating base, that models the acquisition of different power technologies as integer variables and their operation using nonlinear expressions. Our cost-minimizing, nonconvex, mixed-integer, nonlinear program contains a detailed battery model. Due to its complexities, we present linearizations, which include exact and convex under-estimation techniques, and a heuristic, which determines an initial feasible solution to serve as a “warm start” for the solver. We determine, in a few hours at most, solutions within 5% of optimality for a candidate set of technologies; these solutions closely resemble those from the nonlinear model. Lastly, our instances contain real data spanning a yearly horizon at hour fidelity and demonstrate that a hybrid system could reduce fuel consumption by as much as 50% compared to a generator-only solution.

14 SOLAR ENERGY↗
DOE OSTI2026

Adaptive nonlinear wavefront shaping in layered TMDs

Two-dimensional transition metal dichalcogenides are promising candidates for nonlinear photonics applications, offering strong nonlinear susceptibility and compatibility with integrated platforms. Although considerable effort has been devoted to manipulating second harmonic generation in these materials, the dynamic control of nonlinear wavefronts remains largely unexplored. Metasurfaces have enabled significant progress in nonlinear beam engineering, yet their practical implementation is limited by low conversion efficiencies and restricted design flexibility. In this work, we employ feedback-based wavefront shaping using spatial light modulators to enhance SHG from pyramid-like WS 2 multilayer structures by over three orders of magnitude in selected spatial regions. This approach allows us to program nonlinear holograms and dynamically shape the SHG signal through phase-only modulation, opening new possibilities for nonlinear imaging, optical information processing, and data communication.

Mavian, Alex [Rensselaer Polytechnic Inst., Troy, ↗