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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
DOE OSTI2023

A Mixed integer linear programming‐based distributed energy management for networked microgrids considering network operational objectives and constraints

Abstract Mixed integer linear programming (MILP)–based distributed energy management for networked microgrids embedded modern distribution systems is proposed. Considering the diverse ownership of microgrids, distributed energy resources (DERs) that interface directly with utilities and responsive loads, an alternating direction method of multipliers–based distributed framework was formulated for the scheduling of networked microgrids embedded modern distribution systems by adjusting nodal price signals iteratively. In addition, to make the formulated optimization problems resolvable through more accessible and popular MILP solvers, different linearisation techniques were employed to transform the nonlinear terms into linear or mixed integer linear formats. The proposed MILP‐based distributed method preserves all participants' autonomy (e.g., microgrids, DERs that interface directly with utilities and responsive loads), while incentivising them to actively participate in the distribution system operation with price signals. The proposed method is validated with results of numerical simulation using a modern distribution system consisting of multiple networked microgrids, DERs that interface directly with utilities, as well as responsive loads.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Optimal sizing of battery energy storage systems for peak shaving and demand response using a degradation-aware Bayesian Optimization-Mixed-Integer Linear Programming framework

The increasing integration of renewable energy and rising electricity demand highlight the importance of battery energy storage systems for peak shaving and demand response. Unlike prior approaches that overlook operational impacts on degradation, this study proposes a Bayesian Optimization–Mixed Integer Linear Programming framework for optimal battery energy storage system sizing. In this framework, Mixed Integer Linear Programming determines short-term scheduling while a calibrated electrochemical model iteratively evaluates degradation. The central hypothesis is that the framework can efficiently identify optimal sizes that yield realistic and economically robust outcomes. The method is tested across three scenarios: peak shaving, peak shaving with energy-reduction demand response, and peak shaving with power-reduction demand response. Results show that the framework converge to the optimum within 20 iterations out of 150 possible sizes. Under baseline conditions, the framework consistently selects the smallest feasible system, minimizing unnecessary degradation costs from oversized storage. Sensitivity analyses reveal that larger systems are favored as demand rates or incentives increase. Comparisons of demand response programs indicate that power-reduction demand response offers greater economic benefits than energy-reduction demand response, although demand savings from peak shaving remain the dominant contributor to overall performance. This study demonstrates that the proposed framework balances computational tractability with degradation fidelity, identifies critical economic thresholds for investment, and offers a practical, flexible tool to guide industrial stakeholders in cost-effective battery energy storage system deployment.

Batteries↗
DOE OSTI2024

A mixed integer linear programming approach for the design of chemical process families

Tackling climate change goals requires widespread deployment of process technology variants across many decentralized sites with different geographical, environmental, and operational requirements. Conventional engineering approaches focus on unique designs for each installation (process variant), while missing opportunities for manufacturing standardization. Here, instead we seek to optimize a process platform of common unit designs while simultaneously designing an entire family of process variants that make use of that platform. This reduces engineering effort, deployment timelines, and manufacturing costs. We propose a nonlinear generalized disjunctive programming formulation and convert this to an efficient mixed-integer linear programming (MILP) formulation through discretization of the design space. We formulate our optimization in Pyomo with costing from IDAES, and we demonstrate the computational performance and solution quality on a water treatment desalination system from the PARETO framework and a carbon capture system built in Aspen Plus as part of CCSI2.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Alternative mixed integer linear programming optimization for joint job scheduling and data allocation in grid computing

This paper presents a novel approach to the joint optimization of job scheduling and data allocation in grid computing environments. We formulate this joint optimization problem as a mixed integer quadratically constrained program. To tackle the nonlinearity in the constraint, we alternatively fix a subset of decision variables and optimize the remaining ones via Mixed Integer Linear Programming (MILP). We solve the MILP problem at each iteration via an off-the-shelf MILP solver. Our experimental results show that our method significantly outperforms existing heuristic methods, employing either independent optimization or joint optimization strategies. We have also verified the generalization ability of our method over grid environments with various sizes and its high robustness to the algorithm setting.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Multi-parametric analysis for mixed integer linear programming: An application to transmission upgrade and congestion management

Upgrading the capacity of existing transmission lines is essential for meeting the growing energy demands, facilitating the integration of renewable energy, and ensuring the security of the transmission system. This study focuses on the selection of lines whose capacities and by how much should be expanded from the perspective of the Independent System Operators (ISOs) to minimize the total system cost. We employ advanced multi-parametric programming and an enhanced branch-and-bound algorithm to address complex mixed-integer linear programming (MILP) problems, considering multi-period time constraints and physical limitations of generators and transmission lines. To characterize the various decisions in transmission expansion, we model the increased capacity of existing lines as parameters within a specified range. This study first relaxes the binary variables to continuous variables and applies the Lagrange method and Karush-Kuhn-Tucker (KKT) conditions to obtain optimal solutions and identify critical regions associated with active and inactive constraints. Moreover, we extend the traditional branch-and-bound (B&B) method by determining the problem’s upper and lower bounds at each node of the B&B decision tree, helping to manage computational challenges in large-scale MILP problems. Here, we compare the difference between the upper and lower bounds to obtain an approximate optimal solution within the decision-makers’ tolerable error range. In addition, the first derivative of the objective function on the parameters of each line is used to inform the selection of lines for easing congestion and maximizing social welfare. Finally, the capacity upgrades are selected by weighing the reductions in system costs against the expense of upgrading line capacities. The findings are supported by numerical simulations and provide transmission-line planners with decision-making guidance.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Optimizing district energy systems by integrating Borehole Thermal Energy Storage Using a Mixed-Integer Linear Programming g-function framework with a Multi-Timescale Rolling Horizon method

Shallow geothermal has gained increasing attention in recent years; however, a reliable framework for its accurate incorporation into large-scale energy system optimization remains lacking. This study proposes a Mixed-Integer Linear Programming (MILP) framework combined with the g-function approach to integrate Borehole Thermal Energy Storage (BTES) technology into energy system optimization. Validation against a Modelica-based reservoir network simulation demonstrates that the proposed framework effectively captures the ground thermal response under varying energy loads and accurately estimates the borefield energy supply. To enhance scalability, a Rolling Horizon with Multi-Timescale (RH-MTS) method is further introduced, reducing computational time by 73 % for the 1-year optimization model with only minor loss of optimality. The framework is demonstrated through the case study of the UC Berkeley campus. Results indicate that BTES is a cost-effective and low-carbon solution: two borefields comprising 382 boreholes can meet 8.0 % and 6.6 % of the total campus heating and cooling demand, respectively, at an average energy rate of 0.70–0.77 USD/kWh and carbon intensity of 0.54 kg-CO2/kWh. Short-term analysis reveals a 35%–65% decline in BTES energy flow after 3–6 months of continuous heating/cooling operation, while long-term simulation shows that annual energy production of BTES can vary by up to 12.0 % after four years before stabilizing. Overall, this study develops a novel optimization framework that couples physics-based g-function method with MILP optimization framework, thereby advancing methodological development for shallow-geothermal integration and providing actionable guidance for BTES deployment in district-energy systems.

Yang, Jiahui↗
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 OSTI2024

Optimal Electrification Using Renewable Energies: Microgrid Installation Model with Combined Mixture k-Means Clustering Algorithm, Mixed Integer Linear Programming, and Onsset Method

Optimal planning and design of microgrids are priorities in the electrification of off-grid areas. Indeed, in one of the Sustainable Development Goals (SDG 7), the UN recommends universal access to electricity for all at the lowest cost. Several optimization methods with different strategies have been proposed in the literature as ways to achieve this goal. This paper proposes a microgrid installation and planning model based on a combination of several techniques. The programming language Python 3.10 was used in conjunction with machine learning techniques such as unsupervised learning based on K-means clustering and deterministic optimization methods based on mixed linear programming. These methods were complemented by the open-source spatial method for optimal electrification planning: onsset. Four levels of study were carried out. The first level consisted of simulating the model obtained with a cluster, which is considered based on the elbow and k-means clustering method as a case study. The second level involved sizing the microgrid with a capacity of 40 kW and optimizing all the resources available on site. The example of the different resources in the Togo case was considered. At the third level, the work consisted of proposing an optimal connection model for the microgrid based on voltage stability constraints and considering, above all, the capacity limit of the source substation. Finally, the fourth level involved a planning study of electrification strategies based mainly on microgrids according to the study scenario. The results of the first level of study enabled us to obtain an optimal location for the centroid of the cluster under consideration, according to the different load positions of this cluster. Then, the results of the second level of study were used to highlight the optimal resources obtained and proposed by the optimization model formulated based on the various technology costs, such as investment, maintenance, and operating costs, which were based on the technical limits of the various technologies. In these results, solar systems account for 80% of the maximum load considered, compared to 7.5% for wind systems and 12.5% for battery systems. Next, an optimal microgrid connection model was proposed based on the constraints of a voltage stability limit estimated to be 10% of the maximum voltage drop. The results obtained for the third level of study enabled us to present selective results for load nodes in relation to the source station node. Finally, the last results made it possible to plan electrification using different network technologies and systems in the short and long term. The case study of Togo was taken into account. The various results obtained from the different techniques provide the necessary leads for a feasibility study for optimal electrification of off-grid areas using microgrid systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Mixed-Integer Linear Programming Formulation with Embedded Machine Learning Surrogates for the Design of Chemical Process Families

In previous work, we introduced process family design. The main idea is to design a platform of common elements, and, allowing us to capture additional cost savings, simultaneously design a family of processes, and reducing both engineering and deployment timelines. We formulate this as an optimization problem, specifically a nonlinear generalized disjunctive program (GDP). We have proposed two approaches for reformulating and solving this problem: one based on full-discretization of the design space and one that uses Machine Learning (ML) surrogates to replace the nonlinear process models. Using ML surrogates to predict required system costs and performance indicators allows us to reformulate the nonlinearities in the GDP generate an efficient MILP formulation. In this work, we apply the ML surrogate approach to two case studies. One case study involves designing a family of carbon capture systems to cover a set of different flue gas flow rates and inlet CO 2 concentrations, where we consider the absorber and stripper as common unit module types. The second case study focuses on a water-desalination process, where we design a family of these processes for a variety of salt concentrations and flow rates. In both of these case studies, we demonstrate a scalable optimization approach that enables the design of multiple processes simultaneously, reducing the time-to-market and overall costs by maximizing the cost savings due to both economies of scale and economies of numbers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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 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↗
DOE OSTI2024

Flexible dynamic boundary microgrid operation considering network and load unbalances

Flexible microgrids with dynamic boundaries have recently been introduced in the literature. With the ability to reconfigure the topology of the microgrids dynamically through remotely controlled switches, flexible microgrids with dynamic boundaries can further improve the resiliency and energy efficiency of microgrids with distributed energy resources (DERs). This paper focuses on the optimal operation considering one of the predominant characteristics of microgrids and distribution systems – unbalanced networks and loads. In existing literature, balanced modeling of microgrids is more common due to its attractive simplicity. The three-phase power unbalance has not been considered as a constraint on the generation units in a microgrid. Further, negative sequence constraints have also been neglected. In this article, we propose a set of constraints that is specifically related to the capabilities of inverter interfaced resources to supply unbalanced current/power when the microgrid is islanded from the main distribution grid. We incorporate the new set of constraints into two optimization formulations leveraging two convex relaxations of the three-phase power flow equations: mixed-integer linear programming (MILP) and mixed-integer semidefinite programming (MISDP) that optimize the dispatch of controllable switches and DERs in the microgrid. The algorithms are then extended to networked microgrids with grid-forming sources. We test the algorithms on a realistic community microgrid model in Puerto Rico as well as standardized IEEE distribution test feeders. The testing results demonstrate the performance of the proposed algorithms. The MILP is fast and scalable, and the MISDP enforces the negative sequence voltage constraints.

24 POWER TRANSMISSION AND DISTRIBUTION↗
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 OSTI2021

Disjunctive linear separation conditions and mixed-integer formulations for aircraft conflict resolution

In this paper, we address the aircraft conflict resolution problem in air traffic control. We introduce new mixed-integer programming formulations for aircraft conflict resolution with speed, heading and altitude control which are based on disjunctive linear separation conditions. We first examine the two-dimensional aircraft conflict resolution problem with speed and heading control represented as continuous decision variables. We show that the proposed disjunctive linear separation conditions are equivalent to the classical nonlinear conditions for aircraft separation. Further, we characterise conflict-free trajectories based on aircraft velocity bounds and propose a simple pre-processing algorithm to identify aircraft pairs which are either always conflict-free, or which cannot be separated using speed and heading control only. We then incorporate altitude control and propose a lexicographic optimisation formulation that aims to minimise the number of flight level changes before resolving outstanding conflicts via two-dimensional velocity control. The proposed mixed-integer programming formulations are nonconvex, and we propose convex relaxations, decomposition methods and constraint generation algorithms to solve the two-dimensional and lexicographic optimisation formulations to guaranteed optimality. Numerical experiments on four types of conflict resolution benchmarking instances are conducted to test the performance of the proposed mixed-integer formulations. Further, the proposed method is compared against two benchmarks based on state-of-the-art approaches for the aircraft conflict resolution problem. Our numerical results show that the proposed method largely outperforms both benchmarks in terms of runtime and is able to solve significantly more instances to global optimality.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment

Nonlinear power flow constraints render a variety of power system optimization problems computationally intractable. Emerging research shows, however, that the nonlinear AC power flow equations can be successfully modeled using neural networks. These neural networks can be exactly transformed into mixed integer linear programs and embedded inside challenging optimization problems, thus replacing nonlinearities that are intractable for many applications with tractable piecewise linear approximations. Such approaches, though, suffer from an explosion of the number of binary variables needed to represent the neural network. Accordingly, this paper develops a technique for training an "optimally compact'' neural network, i.e., one that can represent the power flow equations with a sufficiently high degree of accuracy while still maintaining a tractable number of binary variables. We demonstrate the use of this neural network as an approximator of the nonlinear power flow equations by embedding it in the AC unit commitment problem, transforming the problem from a mixed integer nonlinear program into a more manageable mixed integer linear program. We use the 14-, 57-, and 89-bus networks as test cases and compare the AC-feasibility of commitment decisions resulting from the neural network, DC, and linearized power flow approximations. Our results show that the neural network model outperforms both the DC and linearized power flow approximations when embedded in the unit commitment problem. The neural network formulation most often selects a feasible unit commitment schedule, and furthermore, it only s

AC power flow↗
DOE OSTI2023

Linear model decision trees as surrogates in optimization of engineering applications

Machine learning models are promising as surrogates in optimization when replacing difficult to solve equations or black-box type models. This work demonstrates the viability of linear model decision trees as piecewise-linear surrogates in decision-making problems. Linear model decision trees can be represented exactly in mixed-integer linear programming (MILP) and mixed-integer quadratic constrained programming (MIQCP) formulations. Furthermore, they can represent discontinuous functions, bringing advantages over neural networks in some cases. We present several formulations using transformations from Generalized Disjunctive Programming (GDP) formulations and modifications of MILP formulations for gradient boosted decision trees (GBDT). We then compare the computational performance of these different MILP and MIQCP representations in an optimization problem and illustrate their use on engineering applications. Importantly, we observe faster solution times for optimization problems with linear model decision tree surrogates when compared with GBDT surrogates using the Optimization and Machine Learning Toolkit (OMLT).

42 ENGINEERING↗