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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Optimal inventories for overhaul of repairable redundant systems - A Markov decision model

A Markovian decision model was developed to calculate the optimal inventory of repairable spare parts for an avionics control system for commercial aircraft. Total expected shortage costs, repair costs, and holding costs are minimized for a machine containing a single system of redundant parts. Transition probabilities are calculated for each repair state and repair rate, and optimal spare parts inventory and repair strategies are determined through linear programming. The linear programming solutions are given in a table.

Schaefer, M. K.↗
DOE OSTI2023

IM3 GO WEST Parameter Search Dataset

GO WEST is an open-source power grid modeling framework for U.S. Western Interconnection, which allows users to tailor the model depending on their research study and science questions. It is developed to address weather and water dynamics, and associated vulnerabilities in this bulk power system. It covers 28 balancing authorities (BA) and 12 states in U.S. Western Interconnection. GO WEST allows users to select different number of nodes and come up with a simplified network by utilizing 10,000 nodal topology of U.S. Western Interconnection created by Texas A&M University. Users can try and select different number of nodes, mathematical formulations (linear programming vs. mixed-integer linear programming), transmission line limit scaling factors, and hurdle rate scaling factors. GO WEST offers a unit commitment and economic dispatch (UC/ED) module to simulate grid operations on an hourly scale. In this sense, users can calibrate and validate their model versions by comparing model outputs to historical datasets. Therefore, GO WEST can help researchers to strike a balance between model fidelity (i.e. accuracy) and computational complexity (i.e. runtime). This dataset includes model inputs and outputs from 600 model versions for each 2019, 2020, and 2021. The folder naming convention is as follows: Exp{Number of Nodes}_{Mathematical Formulation}_{Transmission Line Limit Scaling Factor in MW}_{Hurdle Rate Scaling Factor in %}_{Year}. Linear programming is designated with "simple" label whereas mixed-integer linear programming is designated with "coal" label. For example, "Exp100_simple_1000_50_2019" folder contains inputs and outputs from 2019 model version with 100 nodes, linear programming, +1000 MW transmission line limit scaling factor, and +50% hurdle rate scaling factor. GO WEST GitHub repository hosts all raw datasets, processing scripts, and model scripts. Please refer to the README file for a detailed description of the included files.

Economics↗
DOE OSTI2023

Mathematical Programming Models for Shale Oil & Gas Development: A Review and Perspective

Here, in this paper, we provide a comprehensive review of mathematical programming models for shale oil & gas development, and we offer a perspective on outstanding research opportunities. We distinguish contributions in five major topic areas, namely: (1) development planning, (2) water management, (3) production optimization, (4) supplies, gathering & processing, and (5) life cycle analysis & sustainability. We highlight how various types of mathematical programming models (i.e., linear programs, nonlinear programs, mixed-integer linear programs, mixed-integer nonlinear programs) have been proposed primarily by the Process Systems Engineering community to address the respective decision-making problems, and we highlight instances of successful deployment in industry. Finally, based on a critical assessment of the existing body of work, we identify opportunities for future research across the major topic areas.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Battery and backup generator sizing for a resilient microgrid under stochastic extreme events

Owing to the recent power outages caused by extreme events, installing battery energy storage and backup generators is important to improve resiliency for a grid-tied microgrid. In the design stage, the event occurrence time and duration, which are highly uncertain and cannot be effectively predicted, may affect the needed battery and backup generator capacity but are usually assumed to be pre-determined in utility planning tools. This study investigates the optimal battery and backup generator sizing problem considering the stochastic event occurrence time and duration for the grid-tied microgrid under islanded operation. The reliability requirement is quantified by the mean value of the critical customer interruption time in each stochastic islanding time window (ITW), whose length is the duration and the centre is the occurrence time. The stochastic ITW constraint is then transformed to a probability-weighted expression to derive an equivalent Mixed Integer Linear Programming model. Numerical simulations on a realistic grid-tied PV-based microgrid demonstrate that the total cost is reduced by 11.5% considering the stochastic ITW, compared with the deterministic ITW under the same reliability requirement.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2018

Optimal distribution system restoration using PHEVs

Power outages cost billions of dollars every year and jeopardise the lives of hospital patients. Traditionally, power distribution system takes a long time to recover after a major blackout, due to its top-down operation strategy. New technologies in modern distribution systems bring opportunities and challenges to distribution system restoration. As fast response energy resources, plug-in hybrid electric vehicles (PHEVs) can accelerate the load pickup by compensating the imbalance between available generation and distribution system load. This study provides a bottom-up restoration strategy to use PHEVs for reliable load pickup and faster restoration process. The optimisation problem of finding load pickup sequence to maximise restored energy is formulated as a mixed integer linear programming (MILP) problem. Moreover, the coordination between transmission and distribution restoration is developed to efficiently restore the entire system back to normal operating conditions. Simulation results on one 100-feeder test system demonstrate the efficiency of MILP-based restoration strategy and the benefit from PHEVs to restore more energy in given restoration time. The proposed restoration strategy has great potential to facilitate system operators to achieve efficient system restoration plans. It also provides incentives to deploy a large amount of PHEVs to improve system resiliency.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Optimal PMU Restoration for Power System Observability Recovery After Massive Attacks

Cyber-physically resilient power system operation requires rapid recovery of situational awareness after disastrous scenarios such as massive cyber attacks. In this article, the concept of optimal sequential restoration of Phasor Measurement Units is introduced, aiming at rapid recovery of power system observability in post-attack scenarios. Additionally, the observability recovery problem is formulated as a Mixed Integer Linear Programming problem to maximize the cumulative observability level gained over time during the restoration process. Three alternative objective functions-maximizing the number of observable buses, the number of observable branches, and the total amount of observable power flow-are considered. The effectiveness of the proposed optimal strategy is verified by comparing it with heuristic approaches on the IEEE 57-bus system.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1971

ELAS8 - Computer program for linear structure equilibrium problems

Program generates and solves governing equations for unknown deflection of mesh points as if problem were to locate stationary point of total potential function associated with given loading and unknown deflections. Solution is obtained by means of displacement method and finite element technique.

Utku, S.↗
DOE OSTI2024

A Mixed Integer Linear Programming-basedDistributed Energy Management for Three-phaseUnbalanced Active Distribution Network

A mixed integer linear programming (MILP)–baseddistributed energy management for three-phase unbalancedactive distribution network is proposed. Modern distributionnetworks have becoming more and more active with increasingdeployment of microgrids, distributed energy resources (DERs)as well as controllable loads. Considering various ownership andcontrol models of microgrids, DERs and controllable loads, adistributed energy management was formulated using the alternatingdirection method of multipliers (ADMM) algorithm. ByADMM, the distribution management system (DMS) and theseactive components are coordinated through price signals, whichare adjusted according to the generation-load mismatch per nodeper phase. To enable resolution of the ADMM-based distributedoptimization using more accessible and popular MILP solver,different linearization techniques were proposed to linearize theaugmented Lagrangian terms and other nonlinear terms. Resultsof case studies on a three-phase active distribution network withthree microgrids and several DERs and controllable loads validatedthe effectiveness of proposed MILP-based distributed energymanagement. In addition, the capability of proposed method inmitigating phase power unbalance has been demonstrated.

Liu, Guodong↗
NASA NTRS1986

Alternative mathematical programming formulations for FSS synthesis

A variety of mathematical programming models and two solution strategies are suggested for the problem of allocating orbital positions to (synthesizing) satellites in the Fixed Satellite Service. Mixed integer programming and almost linear programming formulations are presented in detail for each of two objectives: (1) positioning satellites as closely as possible to specified desired locations, and (2) minimizing the total length of the geostationary arc allocated to the satellites whose positions are to be determined. Computational results for mixed integer and almost linear programming models, with the objective of positioning satellites as closely as possible to their desired locations, are reported for three six-administration test problems and a thirteen-administration test problem.

Reilly, C. H.↗
DOE OSTI2021

Sequence of polyhedral relaxations for nonlinear univariate functions

Here, given a nonlinear, univariate, bounded, and differentiable function f(x), this article develops a sequence of Mixed Integer Linear Programming (MILP) and Linear Programming (LP) relaxations that converge to the graph of f(x) and its convex hull, respectively. Theoretical convergence of the sequence of relaxations to the graph of the function and its convex hull is established. For nonlinear non-convex optimization problems, the relaxations presented in this article can be used to construct tight MILP and LP relaxations. These MILP and the LP relaxations can also be used with MILP-based and spatial branch-and-bound based global optimization algorithms, respectively.

42 ENGINEERING↗
DOE OSTI2024

Cooperative Transmission Expansion Planning Experiment Data and Results

GO WEST is an open-source power grid modeling framework for U.S. Western Interconnection, which allows users to tailor the model depending on their research study and science questions. It covers 28 balancing authorities (BA) and 12 states in U.S. Western Interconnection. GO WEST allows users to select different number of nodes and come up with a simplified network by utilizing 10,000 nodal topology of U.S. Western Interconnection created by Texas A&M University. Users can try and select different number of nodes, mathematical formulations (linear programming vs. mixed-integer linear programming), transmission line limit scaling factors, and hurdle rate scaling factors. GO WEST offers a unit commitment and economic dispatch (UC/ED) module to simulate grid operations on an hourly scale. In this sense, users can calibrate and validate their model versions by comparing model outputs to historical datasets. TEP is an open-source transmission capacity expansion model, built on GO WEST framework. It utilizes linear programming to optimize transmission capacity addition investment on existing lines within GO WEST framework. In this sense, TEP model only increases the thermal capacity of existing transmission lines and does not add new lines to the system, which leaves the topology preserved. TEP minimizes the total cost of the system which comprises the operational cost of satisfying electricity demand (i.e., generation cost), cost of loss of load (i.e., unserved energy), cost of power flow, and cost of new transmission capacity additions (i.e., investment cost). In order to use TEP model, users need to create scenarios with GO WEST framework. In this analysis, outputs from several models are used to create future inputs to GO WEST and TEP models, including GCAM-USA, TELL, CERF and reV. This dataset includes experiment inputs and outputs from three different transmission expansion scenarios (cooperative, intermediate, and individual) for 2019 and 2059. For 2019, a base scenario to illustrate the default (i.e., historical) power grid operations is also included. This study utilizes rcp45hotter_ssp3 scenario from a previous version of GCAM-USA simulations. Sources of the shapefiles in supplementary data are HIFLD Open and U.S. Energy Atlas. Please see the README file for a detailed description of the main and supplementary data.

Capacity Expansion Model↗
DOE OSTI2025

IM3 Projected U.S. Western Interconnection Grid Stress Dataset

This dataset provides projected grid stress and reliability results (including all model inputs and outputs from GO WEST and TEP) for Integrated Multisector, Multiscale Modeling (IM3) Phase 2 simulations across eight different scenarios for the U.S. Western Interconnection through 2055. The scenarios include combinations of two Shared Socioeconomic Pathways (SSP3 and SSP5) with four high-resolution climate projections specific to the United States from a set of Thermodynamic Global Warming (TGW) simulations. These climate projections include "hotter" and "cooler" variants for two Representative Concentration Pathways (RCP4.5 and RCP8.5). The resulting eight simulations are: rcp45cooler_ssp3 rcp45cooler_ssp5 rcp45hotter_ssp3 rcp45hotter_ssp5 rcp85cooler_ssp3 rcp85cooler_ssp5 rcp85hotter_ssp3 rcp85hotter_ssp5 GO WEST is an open-source power grid modeling framework for the U.S. Western Interconnection, which allows users to tailor the model depending on their research study and science questions. It covers 28 balancing authorities (BAs) and 12 states in U.S. Western Interconnection. GO WEST allows users to select different number of nodes and come up with a simplified network by utilizing 10,000 nodal topology of the U.S. Western Interconnection (ACTIVSg10k). Users can select different number of nodes, mathematical formulations (linear programming vs. mixed-integer linear programming), transmission line limit scaling factors, and hurdle rate scaling factors. GO WEST offers a unit commitment and economic dispatch (UC/ED) module to simulate grid operations on an hourly scale. In this sense, users can calibrate and validate their model versions by comparing model outputs to historical datasets. TEP is an open-source transmission capacity expansion model, built on the GO WEST framework. It utilizes linear programming to optimize transmission capacity addition investment on existing lines within the GO WEST framework. The TEP model only increases the thermal capacity of existing transmission lines and does not add new lines to the system, which leaves the topology preserved. In order to use TEP model, users need to create scenarios with the GO WEST framework. Please refer to README file for a detailed description of the dataset including individual files and references.

Capacity Expansion Model↗
DOE OSTI2019

Utilising demand response for distribution service restoration to achieve grid resiliency against natural disasters

The increased frequency of power outages due to natural disasters in recent years has highlighted the urgency of enhancing distribution grid resilience. The effective distribution service restoration (DSR) is an important measure for a resilient distribution grid. In this work, the authors demonstrate that DSR can be significantly improved by leveraging the flexibility provided by the inclusion of demand response (DR). The authors propose a framework for this by considering integrated control of household-level flexible appliances to vary the load demand at the distribution-grid level to improve DSR. The overall framework of the proposed system is modelled as a three-step method considering three optimization problems to (i) calculate feasible controllable aggregated load range for each bus, (ii) determine candidate buses to perform DR and their target load demand, and (iii) maintain the load level in each house through home energy management during the DSR, considering uncertainties in load and solar generation sequentially. The optimization problems are formulated as linear programming, mixed-integer linear programming, and multistage stochastic programming (solved using the stochastic dual dynamic programming) models. Finally, case studies performed in the IEEE 123-node test feeder show improvements in resilience in terms of energy restored compared to the restoration process without DR.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Piecewise linear approximation with minimum number of linear segments and minimum error: A fast approach to tighten and warm start the hierarchical mixed integer formulation

In several areas of economics and engineering, it is often necessary to fit discrete data points or approximate nonlinear functions with continuous functions. Piecewise linear (PWL) functions are a convenient way to achieve this. PWL functions can be modeled in mathematical problems using only linear and integer variables. Moreover, there is a computational benefit in using PWL functions that have the least possible number of segments. This work proposes a novel hierarchical mixed integer linear programming (MILP) formulation that identifies a continuous PWL approximation with minimum number of linear segments for a given target maximum error. The proposed MILP formulation also identifies the solution with the least maximum error among the solutions with minimum number of segments. Then, this work proposes a fast iterative algorithm that identifies non necessarily continuous PWL approximations by solving O(S log N) linear programming (LP) problems, where N is the number of data points and S is the minimum number of segments in the non necessarily continuous case. This work demonstrates that tight bounds for the MILP problem can be derived from these approximations. Next, a fast algorithm is introduced to transform a non necessarily continuous PWL approximation into a continuous one. Finally, the tight bounds and the continuous PWL approximations are used to tighten and warm start the MILP problem. The tightened formulation is shown in experimental results to be more efficient, especially for large data sets, with a solution time that is up to two orders of magnitude less than the existing literature.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

or-topas: Operations Research Toolkit for Pyomo Alternative Solutions

SAND2026-16702O OR-TOPAS: Operations Research Toolkit for Pyomo Alternative Solutions is a tool that enhances optimization applications defined by the Pyomo modeling library. It offers functions to generate optimal or near-optimal solutions, operating independently of Pyomo’s solver interface. Users can configure these functions with specific solver names and options, resulting in a custom solution object that returns a list of solutions. The OR-TOPAS library includes methods tailored to the properties of the model, such as binary integer programs versus linear programs, and specific solver interfaces like Gurobi. It does not provide models for specific applications, but it is applicable to a wide range of Pyomo optimization models. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Siirola, John [Sandia National Lab. (SNL-CA), Live↗
DOE OSTI2017

Security and Cloud Outsourcing Framework for Economic Dispatch

The computational complexity and problem sizes of power grid applications have increased significantly with the advent of renewable resources and smart grid technologies. The current paradigm of solving these issues consist of inhouse high performance computing infrastructures, which have drawbacks of high capital expenditures, maintenance, and limited scalability. Cloud computing is an ideal alternative due to its powerful computational capacity, rapid scalability, and high cost-effectiveness. A major challenge, however, remains in that the highly confidential grid data is susceptible for potential cyberattacks when outsourced to the cloud. In this work, a security and cloud outsourcing framework is developed for the Economic Dispatch (ED) linear programming application. As a result, the security framework transforms the ED linear program into a confidentiality-preserving linear program, that masks both the data and problem structure, thus enabling secure outsourcing to the cloud. Results show that for large grid test cases the performance gain and costs outperforms the in-house infrastructure.

97 MATHEMATICS AND COMPUTING↗