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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 OSTI2018

Convex Relaxations in Power System Optimization, A Brief Introduction

Convex relaxations of the AC power ow equations have attracted signi cant interest in the power systems research community in recent years. The following collection of video lectures provides a brief introduction to the mathematics of AC power systems, continuous nonlinear optimization, and relaxations of the power ow equations. The aim of the videos is to provide the high level ideas of convex relaxations and their applications in power system optimization, and could be used as a starting point for researchers who want to study, use or develop new convex relaxations for use in their own research. The videos do not aim to provide an in-depth tutorial about speci c convex relaxations, but rather focus on ideas that are common to all convex relaxations of the AC optimal power ow problem. The videos assume minimal prerequisite knowledge and are designed to be accessible to a variety of disciplines (e.g. power system engineers, industrial engineers and computer scientists). They are designed to be modular, such that interested listeners can either watch the series as a whole, or choose only the subset that matches their interest. The following sections provide a brief overview of the topics and references covered in each video.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

First and second order convex approximation strategies in structural optimization

In this paper, various methods based on convex approximation schemes are discussed that have demonstrated strong potential for efficient solution of structural optimization problems. First, the convex linearization method (Conlin) is briefly described, as well as one of its recent generalizations, the method of moving asymptotes (MMA). Both Conlin and MMA can be interpreted as first-order convex approximation methods that attempt to estimate the curvature of the problem functions on the basis of semiempirical rules. Attention is next directed toward methods that use diagonal second derivatives in order to provide a sound basis for building up high-quality explicit approximations of the behavior constraints. In particular, it is shown how second-order information can be effectively used without demanding a prohibitive computational cost. Various first-order and second-order approaches are compared by applying them to simple problems that have a closed form solution.

Fleury, C.↗
NASA NTRS1987

Computable optimal value bounds for generalized convex programs

It has been shown by Fiacco that convexity or concavity of the optimal value of a parametric nonlinear programming problem can readily be exploited to calculate global parametric upper and lower bounds on the optimal value function. The approach is attractive because it involves manipulation of information normally required to characterize solution optimality. A procedure is briefly described for calculating and improving the bounds as well as its extensions to generalized convex and concave functions. Several areas of applications are also indicated.

Fiacco, Anthony V.↗
DOE OSTI2025

Global stellarator coil optimization with quadratic constraints and objectives

Most present stellarator designs are produced by costly two-stage optimization: the first for an optimized equilibrium, and the second for a coil design reproducing its magnetic configuration. Few proxies for coil complexity and forces exist at the equilibrium stage. Rapid initial state finding for both stages is a topic of active research. Most present convex coil optimization codes use the least square winding surface method by Merkel (NESCOIL), with recent improvements in conditioning, regularization, sparsity, and physics objectives. While elegant, the method is limited to modeling the norms of linear functions in coil current. We present QUADCOIL, a global coil optimization method that targets combinations of linear and quadratic functions of the current. It can directly constrain and/or minimize a wide range of physics objectives unavailable in NESCOIL and REGCOIL, including the Lorentz force, magnetic energy, curvature, field-current alignment, and the maximum density of a dipole array. QUADCOIL requires no initial guess and runs nearly $10$ 2 x faster than filament optimization. Integrating it in the equilibrium optimization stage can potentially exclude equilibria with difficult-to-design coils, without significantly increasing the computation time per iteration. QUADCOIL finds the exact, global minimum in a large parameter space when possible, and otherwise finds a well-performing approximate global minimum. It supports most regularization techniques developed for NESCOIL and REGCOIL. We demonstrate QUADCOIL’s effectiveness in coil topology control, minimizing non-convex penalties, and predicting filament coil complexity with three numerical examples.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Finding MIDDLE Ground: Scalable and Secure Distributed Learning

Edge computing methods allow devices to efficiently train a high-performing, robust, and personalized model for predictive tasks. However, these methods succumb to privacy and scalability concerns such as adversarial data recovery and expensive model communication. Furthermore, edge computing methods unrealistically assume that all devices train an identical model. In practice, edge devices have varying computational and memory constraints which may not allow certain devices to have the space or speed to train a specific model. To overcome these issues, we propose MIDDLE: a model independent distributed learning algorithm which allows heterogeneous edge devices to assist each other’s training while communicating only non-sensitive information. MIDDLE unlocks the ability for edge devices, regardless of computational or memory constraints, to assist each other even with completely different model architectures. Furthermore, MIDDLE does not require model or gradient communication which greatly reduces communication size and time. We prove that MIDDLE attains the optimal convergence rate O(1/sqrt(TM)) of stochastic gradient descent for convex and non-convex smooth optimization (for total iterations T and batch size M). Finally, our experimental results demonstrate that MIDDLE (even in non-IID data settings) attains robust and high-performing models without model or gradient communication.

Bornstein, Marc I.↗
DOE OSTI2021

Extended convex hull-based distributed optimal energy flow of integrated electricity-gas systems

Integrated electricity and gas systems are constructed to facilitate the gas-fired generation, and the distributed operation of these integrated systems have received much attention due to the increased emphasis on data security and privacy between different agencies. This paper proposes an extended convex hull based method to address optimal energy flow problems for the integrated electricity and gas systems in a distributed manner. First, a multi-block electricity-gas system model is constructed by dividing the whole system into N blocks considering both physical and regional differences. This multi-block model is then convexified by replacing the nonconvex gas transmission equation with the extended convex hull-based constraints. The Jacobi-Proximal alternating direction method of multipliers algorithm is adopted to solve the convexified model and minimize its operation cost. Finally, the feasibility of the optimal solution for the convexified model is checked, and a sufficient condition is developed. If the sufficient condition is satisfied, the optimal solution for the original nonconvex problem can be recovered from that for the convexified problem. Simulation results demonstrate that the proposed method is tractable and effective in obtaining feasible optimal solutions for multi-block optimal energy flow problems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Enhancing the cooling performance of thermocouples: a power-constrained topology optimization procedure

Abstract Heat pumping through thermoelectric devices has many advantages over traditional cooling. However, their current efficiency is a limiting factor in their implementation. In this paper, we approach the non-convex topology optimization of thermoelectrical elements for cooling applications through the method of moving asymptotes (MMA) to improve their cooling capabilities per watt usage. The optimization problem is defined for a given power budget, aiming for the minimum temperature with a known heat pumping need. The introduction of power as a constraint justifies the introduction of the voltage gradient across the thermocouple as a design variable to maintain the thermoelectrical device in its optimum power-to-heat extraction ratio. To better understand the convergence of this non-convex problem, we present a two-variable analytical thermoelectric optimization model. This example provides information on how to select the penalty parameters used to scale the three material coefficients involved in the problem to obtain lower objective values and better convergence using MMA. The analytical model shows the non-convexity of the problem and provides the recommendation to use penalization coefficients of the form $$p_k=p_{\sigma }>p_{\alpha }=1$$ p k = p σ > p α = 1 for the thermal conductivity, electrical conductivity, and Seebeck coefficients. We tested these penalization coefficients through optimizations of a model based on the 1MC10-031 commercial thermoelectric-cooler (TEC) using the finite element method (FEM). These penalization coefficients provided local minima without the need for volume constraints. With this procedure, we found designs that provided temperatures close to 10 degrees lower using 60% less semiconductor material volume compared to the initial design.

Gutiérrez, G. Reales↗
DOE OSTI2021

A method for convex black-box integer global optimization

Here we study the problem of minimizing a convex function on a nonempty, finite subset of the integer lattice when the function cannot be evaluated at noninteger points. We propose a new underestimator that does not require access to (sub)gradients of the objective; such information is unavailable when the objective is a blackbox function. Rather, our underestimator uses secant linear functions that interpolate the objective function at previously evaluated points. These linear mappings are shown to underestimate the objective in disconnected portions of the domain. Therefore, the union of these conditional cuts provides a nonconvex underestimator of the objective. We propose an algorithm that alternates between updating the underestimator and evaluating the objective function. We prove that the algorithm converges to a global minimum of the objective function on the feasible set. We present two approaches for representing the underestimator and compare their computational effectiveness. We also compare implementations of our algorithm with existing methods for minimizing functions on a subset of the integer lattice. We discuss the difficulty of this problem class and provide insights into why a computational proof of optimality is challenging even for moderate problem sizes.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

Numerical optimization in Hilbert space using inexact function and gradient evaluations

Trust region algorithms provide a robust iterative technique for solving non-convex unstrained optimization problems, but in many instances it is prohibitively expensive to compute high accuracy function and gradient values for the method. Of particular interest are inverse and parameter estimation problems, since function and gradient evaluations involve numerically solving large systems of differential equations. A global convergence theory is presented for trust region algorithms in which neither function nor gradient values are known exactly. The theory is formulated in a Hilbert space setting so that it can be applied to variational problems as well as the finite dimensional problems normally seen in trust region literature. The conditions concerning allowable error are remarkably relaxed: relative errors in the gradient error condition is automatically satisfied if the error is orthogonal to the gradient approximation. A technique for estimating gradient error and improving the approximation is also presented.

Carter, Richard G.↗
DOE OSTI2018

Probabilistic N - k failure-identification for power systems

This work considers a probabilistic generalization of the N - k failure-identification problem in power transmission networks, where the probability of failure of each component in the network is known a priori and the goal of the problem is to find a set of k components that maximizes disruption to the system loads weighted by the probability of simultaneous failure of the k components. The resulting problem is formulated as a bilevel mixed-integer nonlinear program. Convex relaxations, linear approximations, and heuristics are developed to obtain feasible solutions that are close to the optimum. A general cutting-plane algorithm is proposed to solve the convex relaxation and linear approximations of the N - k problem. Extensive numerical results corroborate the effectiveness of the proposed algorithms on small-, medium-, and large-scale test instances; the test instances include the IEEE 14-bus system, the IEEE single-area and three-area RTS96 systems, the IEEE 118-bus system, the WECC 240-bus test system, the 1354-bus PEGASE system, and the 2383-bus Polish winter-peak test system.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRSDate not supplied

Improving Kinetic Consistency Across Elastic Model Transitions With Quadratic Inequality Constrained Weighted Least Squares (WLSQI)

Flexible body modeling presents a large challenge in the development of simulations to aid in design of flight control systems for launch and landing vehicles. Typically, the flexible body model is not a single continuous model but are rather discrete sets of Linear Time Invariant (LTI) Finite Element Models (FEM) incremented by propellant levels. This introduces the problem of smoothly transitioning modal and physical states of the vehicle when switching from one FEM to the next. This paper introduces a new approach to optimally transition flexible body states with weighted least squares, building off previous methods.

Convex Optimization↗
DOE OSTI2021

On Anomaly Detection for Transactive Energy Systems with Competitive Market

Two anomaly-detection criteria are proposed for transactive energy systems with competitive markets. Participants of transactive energy systems seek an optimal power allocation through hybrid economic-control methods to facilitate the integration of various types of distributed energy resources to power distribution systems. In transactive energy systems, every participant is assumed to be a rational entity, and consumers have diminishing marginal utility and suppliers have increasing marginal cost. With the first proposed anomaly-detection criterion, the monotonicity of marginal cost and marginal utility are examined. The impact of line flow constraints is also taken into consideration. Then, the second anomaly-detection criterion is proposed for TESs with marginal cost and marginal utility which change faster than a certain rate. The second criterion is more accurate than the first one for TES with marginal cost and marginal utility which change faster than a certain rate, but it requires the knowledge of that rate. Neither criteria requires more data than those necessary to find the optimal power allocation and the market-clear price in a transactive energy system. Therefore, the proposed criteria do not disclose any more data than necessary. As the monotonicity of marginal cost and marginal utility in a TES with competitive markets results in convex objective functions in an optimization problem and strongly convex ones when marginal cost and marginal utility changes faster than a certain rate, the two detection criteria are also applicable to anomaly detection of general convex optimization problems. Simulations are carried out to show the efficacy of the proposed criteria to detect anomalies caused by cyberattacks.

Wang, Peng↗
DOE OSTI2021

The impacts of convex piecewise linear cost formulations on AC optimal power flow

Despite strong connections through shared application areas, research efforts on power market optimization (e.g., unit commitment) and power network optimization (e.g., optimal power flow) remain largely independent. A notable illustration of this is the treatment of power generation cost functions, where nonlinear network optimization has largely used polynomial representations and market optimization has adopted piecewise linear encodings. This work combines state-of-the-art results from both lines of research to understand the best mathematical formulations of the nonlinear AC optimal power flow problem with piecewise linear generation cost functions. An extensive numerical analysis of non-convex models, linear approximations, and convex relaxations across fifty-four realistic test cases illustrates that nonlinear optimization methods are surprisingly sensitive to the mathematical formulation of piecewise linear functions. The results indicate that a poor formulation choice can slow down algorithm performance by a factor of ten, increasing the runtime from seconds to minutes. Furthermore, these results provide valuable insights into the best formulations of nonlinear optimal power flow problems with piecewise linear cost functions, an important step towards building a new generation of energy markets that incorporate the nonlinear AC power flow model.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
NASA NTRSDate not supplied

Improving Kinetic Consistency Across Elastic Model Transitions With Quadratic Inequality Constrained Weighted Least Squares (WLSQI)

Flexible body modeling presents a large challenge in the development of simulations to aid in design of flight control systems for launch and landing vehicles. Typically, the flexible body model is not a single continuous model but are rather discrete sets of Linear Time Invariant (LTI) Finite Element Models (FEM) incremented by propellant levels. This introduces the problem of smoothly transitioning modal and physical states of the vehicle when switching from one FEM to the next. This paper introduces a new approach to optimally transition flexible body states with weighted least squares, building off previous methods.

GN&C↗