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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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

A comparative evaluation plan for the Maintenance, Inventory, and Logistics Planning (MILP) System Human-Computer Interface (HCI)

The primary goal of this project was to develop a tailored and effective approach to the design and evaluation of the human-computer interface (HCI) to the Maintenance, Inventory and Logistics Planning (MILP) System in support of the Mission Operations Directorate (MOD). An additional task that was undertaken was to assist in the review of Ground Displays for Space Station Freedom (SSF) by attending the Ground Displays Interface Group (GDIG), and commenting on the preliminary design for these displays. Based upon data gathered over the 10 week period, this project has hypothesized that the proper HCI concept for navigating through maintenance databases for large space vehicles is one based upon a spatial, direct manipulation approach. This dialogue style can be then coupled with a traditional text-based DBMS, after the user has determined the general nature and location of the information needed. This conclusion is in contrast with the currently planned HCI for MILP which uses a traditional form-fill-in dialogue style for all data access and retrieval. In order to resolve this difference in HCI and dialogue styles, it is recommended that comparative evaluation be performed which combines the use of both subjective and objective metrics to determine the optimal (performance-wise) and preferred approach for end users. The proposed plan has been outlined in the previous paragraphs and is available in its entirety in the Technical Report associated with this project. Further, it is suggested that several of the more useful features of the Maintenance Operations Management System (MOMS), especially those developed by the end-users, be incorporated into MILP to save development time and money.

Overmyer, Scott P.↗
NASA NTRSDate not supplied

Planning Satellite Swarm Measurements for Climate Models: Comparing Dynamic Constraint Processing and MILP Methods

We present D-SHIELD, a challenging climate science application to plan coordinated measurements (observations) for a constellation of satellites, each containing two different sensors, each with 61 pointing angle options. The L-band and P-band radar sensors collect data fed into a soil moisture model which tracks and predicts soil moisture across 1.67 million Ground Positions (GP). Soil moisture is an important predictor of wildfires, and then a predictor of floods, landslides and debris flow after a fire. Each measurement covers multiple GP due to the sensor footprint. Each GP has a "model error" which represents the uncertainty of the the soil moisture state prediction. Model error changes at different rates for each GP as the time since last observation increases and after significant events like rain. The planner's goal is to select measurements which maximize soil moisture model improvement (reduce model uncertainty). This problem is combinatorically explosive, involving many degrees of freedom for planner choices. Good domain heuristics can find solutions within a reasonable time for our application needs but cannot be proven optimal. In this paper we compare two different planning approaches to this problem: Dynamic Constraint Processing (DCP) and Mixed Integer Linear Programming (MILP). We match inputs and metrics for both DCP and MILP algorithms to enable a direct apples-to-apples comparison. We demonstrate and discuss the trades between DCP flexibility and performance vs. MILP's promise of provable optimality.

Rich Levinson↗
DOE OSTI2025

PDPTW-DB: MILP-Based Offline Route Planning for PDPTW with Driver Breaks

The Pickup and Delivery Problem with Time Windows (PDPTW) involves optimizing routes for vehicles to meet pickup and delivery requests within specific time constraints, a challenge commonly faced in logistics and transportation. Microtransit, a flexible and demand-responsive service using smaller vehicles within defined zones, can be effectively modeled as a PDPTW. Yet, the need for driver breaks—a key human constraint—is frequently overlooked in PDPTW solutions, despite being necessary for regulatory compliance. This study presents a novel mixed-integer linear programming formulation for the Pickup and Delivery Problem with Time Windows and Driver Breaks (PDPTW-DB). To the best of our knowledge this formulation is the first to consider mandatory periodic driver breaks within optimized Microtransit routes. The proposed model incorporates regulatory compliant break scheduling directly within the vehicle routing optimization framework. By considering driver break requirements as an integral component of the optimization process, rather than as a post-processing step, the model enables the generation of routes that respect hours of service regulations while minimizing operational costs. This integrated approach facilitates the generation of schedules that are operationally efficient and prioritize driver welfare through driver breaks. We work with a public transit agency from the southern USA, and highlight the specific nuances of driver break optimization, and present a Pickup and Delivery Problem with Time Windows formulation for optimizing Microtransit operations and scheduling driver breaks. We validate our approach using real-world data from the transit agency. Our results validate our formulation in producing cost-effective, and regulation-compliant solutions.

Applied Computing, Transportation↗
NASA NTRS2009

A Mixed Integer Linear Program for Airport Departure Scheduling

Aircraft departing from an airport are subject to numerous constraints while scheduling departure times. These constraints include wake-separation constraints for successive departures, miles-in-trail separation for aircraft bound for the same departure fixes, and time-window or prioritization constraints for individual flights. Besides these, emissions as well as increased fuel consumption due to inefficient scheduling need to be included. Addressing all the above constraints in a single framework while allowing for resequencing of the aircraft using runway queues is critical to the implementation of the Next Generation Air Transport System (NextGen) concepts. Prior work on airport departure scheduling has addressed some of the above. However, existing methods use pre-determined runway queues, and schedule aircraft from these departure queues. The source of such pre-determined queues is not explicit, and could potentially be a subjective controller input. Determining runway queues and scheduling within the same framework would potentially result in better scheduling. This paper presents a mixed integer linear program (MILP) for the departure-scheduling problem. The program takes as input the incoming sequence of aircraft for departure from a runway, along with their earliest departure times and an optional prioritization scheme based on time-window of departure for each aircraft. The program then assigns these aircraft to the available departure queues and schedules departure times, explicitly considering wake separation and departure fix restrictions to minimize total delay for all aircraft. The approach is generalized and can be used in a variety of situations, and allows for aircraft prioritization based on operational as well as environmental considerations. We present the MILP in the paper, along with benefits over the first-come-first-serve (FCFS) scheme for numerous randomized problems based on real-world settings. The MILP results in substantially reduced delays as compared to FCFS, and the magnitude of the savings depends on the queue and departure fix structure. The MILP assumes deterministic aircraft arrival times at the runway queues. However, due to taxi time uncertainty, aircraft might arrive either earlier or later than these deterministic times. Thus, to incorporate this uncertainty, we present a method for using the MILP with "overlap discounted rolling planning horizon". The approach is based on valuing near-term decision results more than future ones. We develop a model of taxitime uncertainty based on real-world data, and then compare the baseline FCFS delays with delays using the above MILP in a simple rolling-horizon method and in the overlap discounted scheme.

Gupta, Gautam↗
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↗
NASA NTRS2018

Comparison of First-Come First-Served and Optimization Based Scheduling Algorithms for Integrated Departure and Arrival Management

Korea Aerospace Research Institute (KARI) and National Aeronautics and Space Administration (NASA) are investigating scheduling algorithms that will be a part of an integrated arrival and departure management system. Inha University, one of the Korean collaborators of KARI, developed an Extended First-Come First-Served (EFCFS) algorithm that is robust and efficient. However, since the EFCFS algorithm sequentially computes the schedule based on priority, the end results may not be optimal for system efficiency. The approach based on Mixed Integer Linear Programming (MILP) originally developed by NASA and modified by KARI is known to produce better schedules at the expense of computational cost. In this paper, the two different scheduling approaches are compared using common traffic scenarios and constraints at Incheon International Airport. Capabilities to apply weight class based wake turbulence runway separation minima and Miles-in-Trail (MIT) restrictions at selected meter fixes are added to the previously developed EFCFS scheduler. Based on historic data, 40 departures and 20 arrivals are chosen in a one-hour period and 100 scenarios were created by randomly assigning gate numbers, gate departure times, and runway landing times. With the current runway separation requirements, MILP resulted in about ten to twenty percent smaller average delays depending on the constraints. With artificially increased separation minima, the difference between MILP and EFCFS became more noticeable. However, the EFCFS was about ten times faster with smaller variations among different scenarios and constraints. The comparison suggests that the MILP-based algorithm has a small advantage at the current traffic level; however, has potential to be more effective in higher demand or severe weather situations. The EFCFS algorithm may be better suited for real-time applications or investigating larger scale scheduling problems.

air traffic optimization↗
NASA NTRSDate not supplied

Scheduling Position, Navigation and Time Service Requests from Non-dedicated Lunar Constellations

This paper presents a centralized scheduler that satisfies user requests for Position, Navigation, and Time (PNT) services from an ad-hoc, non-dedicated orbital constellation around the Moon. Traditional, dedicated GNSS networks provide service 24/7, which allows users to acquire localization services at-will. For ad-hoc networks, a coordinated schedule is needed to ensure Quality of Service (QoS) guarantees for user localization, while satisfying non-dedicated assets’ usage constraints. This scheduler bridges this coordination gap by leveraging Mixed Integer-Linear Programming (MILP) to schedule this “as-needed” localization service while respecting the constraints on each asset. In upcoming decades there is expected to be a substantial increase in Lunar missions. Many of these missions will feature low-cost surface assets near the moon’s polar regions and small-sat science missions in orbit. Most missions need PNT capabilities to ensure safe operations and meet their science objectives, but low-cost missions may not be able to support the large power, mass, and weight that a weak GNSS or DSN based navigation solution would entail. Asset localization has been demonstrated using a decentralized extended Kalman Filter (DEKF) in the previously presented Lunar Autonomous PNT System (LAPS). Within the LAPS simulation environment, a module has been developed to generate the coordinated user-asset schedules described above; this Service Scheduler Module (SSM) allows for complete end-to-end testing of the entire system. Within SSM, a user service request consists of a location on the Lunar surface, a cumulative service duration, and a window in which service must occur. SSM takes as input these requests and the LAPS-predicted positional degree of precision as the QoS for each available set of orbital assets. A simple, baseline MILP model is formulated to provide the highest-precision service balanced across all requests. To reflect the non-dedicated nature of the constellation, this baseline model is augmented with additional asset-specific load capacity constraints or availability constraints. The load capacity constraints limit total time spent providing service, and the availability constraints reflect blockout times or availability windows when the assets are not otherwise occupied. SSM outputs two schedules: the user schedule to indicate their service times and expected QoS, and a satellite schedule to be transmitted to the orbiting constellation, describing when each non-dedicated asset provides PNT service. SSM is predominantly implemented in MATLAB and allows the use of any MILP solver to generate the resulting schedules. This paper describes the SSM - LAPS interface, how the output of LAPS is used to construct the MILP, and how SSM provides user localization service while satisfying constraints. It will also demonstrate the tool’s flexibility for formulating schedules for the end user and the constellation, focusing on scenarios that match real-world proposed missions. It will detail how SSM can be used to compare the addition of load capacity constraints, satellite availability constraints, and QoS guarantees for the users. Finally, we describe how SSM can be used to support the design of the ad-hoc constellation itself. The resulting integrated capability will support the design of future ad-hoc Lunar PNT networks, enabling high-quality, low-cost Lunar exploration

Swarm↗
DOE OSTI2023

Holistic fleet optimization incorporating system design considerations

The methodology described in this article enables a type of holistic fleet optimization that simultaneously considers the composition and activity of a fleet through time as well as the design of individual systems within the fleet. Often, real-world system design optimization and fleet-level acquisition optimization are treated separately due to the prohibitive scale and complexity of each problem. Importantly, this means that fleet-level schedules are typically limited to the inclusion of predefined system configurations and are blind to a rich spectrum of system design alternatives. Similarly, system design optimization often considers a system in isolation from the fleet and is blind to numerous, complex portfolio-level considerations. In reality, these two problems are highly interconnected. To properly address this system-fleet design interdependence, we present a general method for efficiently incorporating multi-objective system design trade-off information into a mixed-integer linear programming (MILP) fleet-level optimization. This work is motivated by the authors' experience with large-scale DOD acquisition portfolios. However, the methodology is general to any application where the fleet-level problem is a MILP and there exists at least one system having a design trade space in which two or more design objectives are parameters in the fleet-level MILP.

97 MATHEMATICS AND COMPUTING↗
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↗
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 OSTI2025

An analysis of physics limited dispatch of nuclear renewable integrated energy systems using deep reinforcement learning and dynamic modeling

Previous approaches to dispatching nuclear integrated energy systems (NIES) have focused on the profitability and flexibility of these systems to operate on energy grids with highly variable pricing. However, due to the complexity involved in modeling and designing these systems, there has been less emphasis on ensuring that these dispatch strategies are physically achievable. It is imperative to develop methods that allow the system to remain within the desired NIES operating conditions and perform this based on realistic limited forecasted information. This research employs next generation artificial intelligence, namely deep reinforcement learning (DRL), and a dynamic system model written in Modelica to find a safe and profitable dispatch strategy for a solar nuclear hybrid design. The DRL agent is shown to find a novel dispatch strategy that manages both power ramping and power levels while respecting operational limits. This DRL-based dispatch is compared to other dispatching strategies including an optimal design solution from mixed integer linear programming (MILP). It is found that incorporating the physics of such a tightly coupled NIES limits the profitability of the MILP-based dispatch strategy. As a result, the MILP solution overestimates the design’s generated revenue. In contrast, DRL significantly reduces the number of breaches of safe operational conditions during energy arbitrage while maintaining profitability. Furthermore, this work paves the way for a more detailed assessment of NIES profitability and could be used to aid operator decisions on future NIES projects.

14 - SOLAR ENERGY↗
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↗
NASA NTRSDate not supplied

Aerial Vehicle Routing and Scheduling for UAS Traffic Management: A Monte Carlo Tree Search Approach

Numerous unmanned aircraft systems operating at low altitudes to deliver goods and services may one day become ubiquitous in our cities. In the Unmanned Aircraft Systems (UAS) Traffic Management (UTM) framework, such a concept is envisioned, where aerial vehicles operate beyond visual line of sight (BVLOS) within specifically reserved and time stamped “corridors” in the airspace. For example, these corridors or operational intent volumes can connect an aerial vehicle’s origin site to its destination site for package delivery operations. There may also be more than one corridor available for an aerial vehicle to choose from and often different corridors may intersect with one another. Thus, it is imperative to ensure flight trajectories belonging to different aerial vehicles are not in conflict. Per the UTM CONOPs, we assume that a vehicle almost always stays inside its corridor or operational volume. This work provides a framework for strategic deconfliction of UTM or package delivery drones, where we schedule the departure time of all vehicles subject to various temporal constraints (including the corridor deconfliction at the intersections). We present the “multi-route weighted package delivery problem” which serves as an exemplifying model for strategic deconfliction in UTM. In the multi-route weighted package delivery problem, a graph network is given which consists of a set of depots (source) and drop-off (destination) nodes, with multiple routes (defined as a sequence of waypoints) connecting the depots to drop-off nodes. In addition, routes are weighted by the associated ground risk and total travel distance for package delivery. The goal is for a known set of aerial vehicles to depart from the depots, choose a route and take off time, while avoiding conflicts with other aerial vehicles, and minimizing both risk and distance traveled. We provide a mixed integer linear programming (MILP) formulation of the problem, as well as a heuristic solution based on Monte Carlo Tree Search (MCTS) – a method used in game theory and artificial intelligence – to overcome limitations inherent to optimal solvers. Computational results show the advantages of using MCTS over the MILP formulation; the former can provide a sub-optimal solution quickly, and may sometimes even reach an optimal solution, whereas the latter may not even produce a solution in reasonable time. Furthermore, results from both the MILP formulation and MCTS methods were validated using a preliminary agent-based simulator implementing the UTM concept of operations. Thus, the MCTS method can be seen as a scalable solution to the complex multi-route weighted package delivery problem and may possibly be extended to similar complex optimization problems.

Kenny Chour↗
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

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 OSTI2023

Designing a GIS-based supply chain for producing carinata-based sustainable aviation fuel in Georgia, USA

Carinata is a potential crop for sustainable aviation fuel (SAF) production in the southern USA. However, as a novel crop, the cost-effectiveness and environmental feasibility of carinata feedstock are unknown, and there are questions about the optimal supply chain configuration for carinata-based SAF production. This study aims to design a supply chain model for carinata-based SAF production by optimizing the location of farms and facilities (e.g. storage units, crushing mills, biorefineries) for a minimum transportation cost under a set of supply and demand conditions. An integrated mixed-integer linear programming (MILP) model was combined with geographical information system (GIS) analysis to design a spatially explicit supply chain configuration. The GIS-based network analysis considered all of the counties in Georgia to set the candidate locations of carinata farms and facilities, and determined minimum cost and emission routes between those counties and the airport using existing transportation networks and modes (e.g. road, rail and pipeline). The MILP model determined the final selection of the farms and the number of facilities and their locations over those minimum-cost routes. With this supply chain configuration, the minimum price of SAF was $\$$0.92 L –1 , which is $\$$0.44 higher than conventional aviation fuel (CAF). The associated carbon intensity of SAF was estimated at 940.7 g CO 2 e L –1 , a reduction of 66% relative to the carbon intensity of equivalent CAF. The study found that a carbon tax (or subsidy) of $\$$230.48 t CO 2 e –1 would be needed to overcome the cost differential with CAF and promote carinata-based SAF in Georgia.

09 BIOMASS FUELS↗
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 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↗