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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Modular supply chain optimization considering demand uncertainty to manage risk

Supply chain under demand uncertainty has been a challenging problem due to increased competition and market volatility in modern markets. Flexibility in planning decisions makes modular manufacturing a promising way to address this problem. We report the problem of multiperiod process and supply chain network design is considered under demand uncertainty. A mixed integer two-stage stochastic programming problem is formulated with integer variables indicating the process design and continuous variables to represent the material flow in the supply chain. The problem is solved using a rolling horizon approach. Benders decomposition is used to reduce the computational complexity of the optimization problem. To promote risk-averse decisions, a downside risk measure is incorporated in the model. The results demonstrate the several advantages of modular designs in meeting product demands. A pareto-optimal curve for minimizing the objectives of expected cost and downside risk is obtained.

42 ENGINEERING↗
DOE OSTI2021

Data-driven optimization of mixed-integer bi-level multi-follower integrated planning and scheduling problems under demand uncertainty

The coordination of interconnected elements across the different layers of the supply chain is essential for all industrial processes and the key to optimal decision-making. Yet, the modeling and optimization of such interdependent systems are still burdensome. Here we address the simultaneous modeling and optimization of medium-term planning and short-term scheduling problems under demand uncertainty using mixed-integer bi-level multi-follower programming and data-driven optimization. Bi-level multi-follower programs model the natural hierarchy between different layers of supply chain management holistically, while scenario analysis and data-driven optimization allow us to retrieve the guaranteed feasible solutions of the integrated formulation under various demand considerations. We address the data-driven optimization of this challenging class of problems using the DOMINO framework, which was initially developed to solve single-leader single-follower bi-level optimization problems to guaranteed feasibility. This framework is extended to solve single-leader multi-follower stochastic formulations and its performance is characterized by well-known single and multi-product process scheduling case studies. Through our data-driven algorithmic approach, we present guaranteed feasible solutions to linear and nonlinear mixed-integer bi-level formulations of simultaneous planning and scheduling problems and further characterize the effects of the scheduling level complexity on the solution performance, which spans over several hundred continuous and binary variables, and thousands of constraints.

42 ENGINEERING↗
DOE OSTI2022

A reforecasting-based dynamic reserve estimation for variable renewable generation and demand uncertainty

The installed capacity of renewables-based energy sources has been increasing in traditional power systems. In order to accommodate the increased variability and uncertainty associated with the deeper penetration of renewable sources like solar and wind, adjusted amounts of dynamic reserve are needed. Although probabilistic dynamic reserve estimation methods have been previously developed, most of them consider the uncertainty to be represented by parametric density functions that tend to perform poorly under extreme events and, moreover, neglect uncertainty introduced by the forecasting model itself. Toward addressing these limitations, this work presents, for the first time, a dynamic reserve estimation method for flexibility that incorporates nonparametric density estimation and a machine learning based reforecasting to provide a day-ahead prediction of the mean and spread of uncertainty around the base forecast. The prediction is, in turn, used to estimate the up and down reserve relative to the base forecast. Here, the present method takes various endogenous and exogenous features, including the calendar variables, as input to estimate the day-ahead reserve. Using a combination of reforecasting and dynamic reserve estimation techniques, the method is shown to adjust better to the dynamic nature of reserve requirements providing only what is needed to accommodate the expected deviations. Considering California Independent System Operator (CAISO) solar, wind and load data over an 18 month period, up to 67% reduction in the amount of reserve capacity needed for a one day reserve and reserve penalty for solar uncertainty is demonstrated. Additionally, the risk of reserve insufficiency in meeting the net demand is reduced by 20% with the proposed method.

14 SOLAR ENERGY↗
NASA NTRS2018

Required Time of Arrival as a Control Mechanism to Mitigate Uncertainty in Arrival Traffic Demand Management

The objective of this study is to explore the use of Required Time of Arrival (RTA) capability on the flight deck as a control mechanism on arrival traffic management to improve traffic delivery accuracy by mitigating the effect of traffic demand uncertainty. The uncertainties are caused by various factors, such as departure error due to the difference between scheduled departure and the actual take-off time. A simulation study was conducted using the Multi Aircraft Control System (MACS) software, a comprehensive research platform developed in the Airspace Operations Laboratory (AOL) at NASA Ames Research Center. The Crossing Time (CT) performance (i.e. the difference between target crossing time and actual crossing time) of the RTA for uncertainty mitigation during cruise phase was evaluated under the influence of varying two main factors: wind severity (heavy wind vs. mild wind), and wind error (1 hour, 2 hours, and 5 hours wind forecast errors). To examine the CT performance improvement made by the RTA, the comparison to the CT of the aircraft that were not assigned with RTA (Non-RTA) under the influence of the selected factors was also made. The Newark Liberty International Airport (EWR) was chosen for this study. A total 66 inbound traffic to the EWR (34 of them were airborne when the simulation was initiated, 32 were pre-departures at that time) was simulated, where the pre-scripted departure error was assigned to each pre-departure (61 conform to their Expected Departure Clearance Time, which is +-300 seconds of their scheduled departure time). The results of the study show that the delivery accuracy improvement can be achieved by assigning RTA, regardless of the influence of the selected two factors (the wind severity and the wind information inaccuracy). Across all wind variances, 66.9 (265 out of 396) of the CT performance of the RTA assigned aircraft was within +- 60 seconds (i.e. target tolerance range) and 88.9 (352 out of 396) aircraft met +-300 seconds marginal tolerance range, while only 33.6 (133 out of 396) of the Non-RTA assigned aircrafts CT performance achieved the target tolerance range and 75.5 (299 out of 396) stayed within the marginal. Examination of the impact of different error sources i.e. departure error, wind severity, and wind error suggest that although large departure errors can significantly impact the CT performance, the impacts of wind severity and errors were modest relative the targeted +- 60 second conformance range.

required time of arrival (RTA)↗
DOE OSTI2024

FORCE Update 2024

The Framework for Optimization of Resources and Economics (FORCE) tool suite is the U.S. Department of Energy’s Nuclear Integrated Energy Systems (IES) Program flagship tool suite for technoeconomic IES analysis of IES. This tool suite is useful for analysis designed to evaluate and improve the technoeconomics of energy production systems, particularly for systems including nuclear technology. In this report, we document the development activity for the FORCE tool suite to extend its capabilities as performed during fiscal year 2024. In addition to reliability and accessibility, capability is one of the three standards guiding the development of the FORCE tool suite and the software codes that are its constituent parts. Extending the capabilities of the FORCE tool suite allows analysis both within the IES program as well as industry, university, and laboratory partners to perform analysis with more accuracy, insight, and impactful narrative. Four areas of capability development were the focus of activity this year: economic parameter uncertainty quantification, multiresolution analysis, components-to-optimization workflow automation, and statespace construction workflows for real-time optimal control. In economic parameter uncertainty quantification, the ability of HERON to capture risk due to scenarios (weather and energy demand uncertainty) was expanded to also include uncertainties in financial parameters such as capital cost or operation and maintenance costs. By including these sources of uncertainty, which are sometimes very large compared with scenario uncertainty, HERON is better able to capture the risk posed by investment in various IES technology. Because of this, analysts can also consider the reduction in risks that can be realized by choice of some technologies. In multiresolution analysis, development activity extended on work completed previously. In fiscal year 2023, methods for decomposing time series signals, such as demand, solar and wind availability, and price profiles, were analyzed and down-selected to those most effective at splitting signals into different resolutions. These resolutions allow considering the influence of different energy demand and supply behaviors across different time scales. For example, energy demand might be divided into seasonal, weekly, and hourly profiles. In fiscal year 2024, this preliminary work was extended and implemented within the Risk Analysis Virtual Environment (RAVEN) risk and uncertainty analysis platform, which is used throughout the FORCE framework. This development of the “multi-resolution time series analysis” (MR-TSA) module in RAVEN allows training synthetic history generators on complex time series. These synthetic history generators can then be used in HERON for generating scenarios that represent possible market and weather scenarios that can be analyzed on different time scales. We envision completing this work in the future, implementing multiresolution dispatch optimization strategies that can make the most beneficial use of these stratified time histories. In components-to-optimization workflow development, workflows for translating user inputs of components into algorithms for algebraic optimization were selected and implemented. Similar algorithms within the Holistic Energy Resource Optimization Network (HERON) were separated from the main code base of HERON and gathered with the components-to-optimization workflows in the new Dispatch Optimization Variable Engine (DOVE) software library. This modularization allows FORCE users to analyze dispatch optimization and energy system duty cycles independently of HERON, which previously was a burdensome task. Additionally, these dispatch optimization algorithms, set up in an independent library, can now be used across all software applications within FORCE, especially including the real-time optimal control software Optimization of Real-time Capacity Allocation (ORCA). Allowing FORCE software to share dispatch optimization algorithms within a single library allows for improved software maintenance and reliability. In statespace characterization workflow development, alternative workflows for optimizing dispatch with additional technical accuracy was the focus, particularly to improve the real-time optimization decision making in ORCA. Using algorithms and workflows initially developed for the Feasible Actuator Range Modifier (FARM), workflows for determining the statespace representation of IES were identified and demonstrated. The resulting dispatch optimization required a more robust optimization algorithm than that originally used in HERON (and moved to DOVE), which required adding an alternate workflow to DOVE that can more accurately match the behavior of physical systems using a partial differential equation representation. In conclusion, capability developments in the FORCE tool suite in fiscal year 2024 have improved the ability of the FORCE tool suite to perform

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2025

Two-Stage Distributionally Robust Conic Linear Programming over 1-Wasserstein Balls

Here, this paper studies two-stage distributionally robust conic linear programming under constraint uncertainty over type-1 Wasserstein balls. We present optimality conditions for the dual of the worst-case expectation problem, which characterizes worst-case uncertain parameters for its inner maximization problem. This condition offers an alternative proof, a counterexample, and an extension to previous works. Additionally, the condition highlights the potential advantage of a specific distance metric for out-of-sample performance, as exemplified in a numerical study on a facility location problem with demand uncertainty. Furthermore, cutting-plane-based algorithms, equipped with a unified scenario generation framework, are proposed for addressing both unbounded support and second-stage dual feasible regions, with a finite convergence proof under less stringent assumptions.

Wasserstein↗
DOE OSTI2025

Marine energy supported multi-energy system planning and operation optimization for sustainable coastal community

The growing need for sustainable energy solutions in coastal areas necessitates the development of integrated systems that leverage abundant marine resources. In this study, a standalone Marine Energy Supported Multi-Energy System (MRE-MES) is designed for sustainable coastal community development, utilizing renewable marine resources, including offshore wind, wave, and solar energy, to address the energy needs of electricity, heat, freshwater, and hydrogen. The proposed MRE-MES incorporates a co-optimization model that simultaneously balances capacity planning and operational efficiency to minimize costs and environmental impacts. The system is tested under different renewable energy penetration levels and demand uncertainties, using a two-stage stochastic programming to account for variability in renewable resources and consumption needs. The experimental results indicate that in the optimal system capacity configuration, the percentage of total renewable energy generation is around 80 %, with or without capacity limitation constraints on PV, water tank, and hydrogen storage. Compared to the worst-case scenario in Monte Carlo experiments, two-stage stochastic optimization results in a more robust decision that effectively mitigates the risks posed by future uncertain demand conditions. In conclusion, the findings highlight the viability of marine energy for providing a resilient, comprehensive energy solution to coastal communities.

Capacity planning↗
DOE OSTI2025

Life cycle greenhouse gas emissions and carbon intensity of U.S. fuel use and projection for the next 10 years-based on built capacity and expansion plans

The U.S. Inflation Reduction Act of 2022 supports biofuel production expansion through the 45Z clean fuel production tax credit, replacing previous 40A and 40B credits. This follows on the Renewable Fuel Standard from the Energy Policy Act of 2005 and its expansion in 2007. States like California, Oregon, and Washington also offer clean fuel credits. Meanwhile, federal agencies, including the U.S. Department of Energy, have advanced alternative fuel technologies through research and development funding. The surging interest in the biofuel industry has spurred the demand for biofuel supplies in the markets, although achieving profitability for advanced biofuels and low-carbon e-fuels remains challenging. This study aims to track U.S. alternative fuel production capacity expansion plans over the next 10 years and estimate impacts on greenhouse gas (GHG) emissions. By tracking built capacity and industry announcements of planned expansion, this study complements other studies which use models to predict changes in energy technologies and the associated GHG implications. Modeled projections of future technologies are often criticized for over or underestimating the cost and potential role of new technologies. The study focuses on sustainable aviation fuel, renewable diesel, ethanol, biodiesel, and renewable natural gas. Using facility-level data, we conducted a bottom-up analysis linking biofuel production pathways with corresponding pathways and parameterizations in the Argonne R&D GREET model. Results indicate that biofuel capacity could reach 3.8 exajoules in 2035, potentially reducing U.S. GHG emissions by 179 million tonnes, including the full life cycle. This corresponds to a 20% reduction in transportation and 5% in industry sector emissions by 2035, or a 3.6% reduction in economy-wide emissions. Overall, this study shows that while biofuel production capacity in the U.S. is expanding, the capacities remain limited compared to fuel demand. Uncertainty regarding the durability and extension of incentives may be dampening the pace of growth. Meanwhile, demonstrating the commercial potential for alternative fuels and climbing the learning curve for new technologies could lead to an increased pace of expansion in later years. This study offers insights for bioenergy stakeholders, highlighting biofuel technologies' contribution to U.S. energy system and emissions reduction over time based on producers' plans.

Biofuel Producers↗
NASA NTRS2016

Comparison of Different Control Schemes for Strategic Departure Metering

Airports and their terminal airspaces are key choke points in the air transportation system causing major delays and adding to pollution. A solution aimed at mitigating these chokepoints integrates the scheduling of runway operations, flight release from the gates and ramp into the airport movement area, and merging with other traffic competing for downstream airspace points. Within this integrated concept, we present a simulation-based analysis of the departure metering process, which delays the release of flights into the airport movement area while balancing two competing objectives: (1) maintaining large enough queues at the airport resources to maximize throughput and (2) absorbing excess delays at the gates or in ramp areas to save on fuel consumption, emissions, noise, and passenger discomfort. Three metering strategies are compared which respectively attempt to control the number of flights that (1) left the gate but did not take off, (2) left the ramp but did not take off, and (3) spent their unimpeded transit time to the runway but did not take off. It was observed that under deterministic and demand uncertainty conditions, the first strategy performed better than the other two strategies in terms of maintaining the runway throughput while transferring a significant average delay of two minutes to the gate. On the other hand, under uncertainties of flight transit time and runway service rate, all the strategies struggled to delay flights at the gate without a significant impact on the runway throughput.

air traffic management↗
DOE OSTI2025

Optimal Power Management for Large-Scale Battery Energy Storage Systems via Bayesian Inference

Large-scale battery energy storage systems (BESS) have found ever-increasing use across industry and society to accelerate clean energy transition and improve energy supply reliability and resilience. However, their optimal power management poses significant challenges: the underlying high-dimensional nonlinear nonconvex optimization lacks computational tractability in real-world implementation, and the uncertainty of the exogenous power demand makes exact optimization difficult. This paper presents a new solution framework to address these bottlenecks. The solution pivots on introducing power-sharing ratios to specify each cell’s power quota from the output power demand. To find the optimal power-sharing ratios, we formulate a nonlinear model predictive control (NMPC) problem to achieve power-loss-minimizing BESS operation while complying with safety, cell balancing, and power supply-demand constraints. We then propose a parameterized control policy for the power-sharing ratios, which utilizes only three parameters, to reduce the computational demand in solving the NMPC problem. This policy parameterization allows us to translate the NMPC problem into a Bayesian inference problem for the sake of 1) computational tractability, and 2) overcoming the nonconvexity of the optimization problem. We leverage the ensemble Kalman inversion technique to solve the parameter estimation problem. Concurrently, a low-level control loop is developed to seamlessly integrate our proposed approach with the BESS to ensure practical implementation. This low-level controller receives the optimal power-sharing ratios, generates output power references for the cells, and maintains a balance between power supply and demand despite uncertainty in output power. We conduct extensive simulations and experiments on a 20-cell prototype to validate the proposed approach.

Battery energy storage systems (BESSs)↗
DOE OSTI2022

Partner with a Third-Party Delivery Service or Not? A Prediction-and-Decision Tool for Restaurants Facing Takeout Demand Surges During a Pandemic

Amidst the COVID-19 pandemic, restaurants become more reliant on no-contact pick-up or delivery ways for serving customers. As a result, they need to make tactical planning decisions such as whether to partner with online platforms, to form their own delivery team, or both. In this paper, we develop an integrated prediction-decision model to analyze the profit of combining the two approaches and to decide the needed number of drivers under stochastic demand. We first use the susceptible-infected-recovered (SIR) model to forecast future infected cases in a given region and then construct an autoregressive-moving-average (ARMA) regression model to predict food-ordering demand. Using predicted demand samples, we formulate a stochastic integer program to optimize food delivery plans. We conduct numerical studies using COVID-19 data and food-ordering demand data collected from local restaurants in Nuevo Leon, Mexico, from April to October 2020, to show results for helping restaurants build contingency plans under rapid market changes. Our method can be used under unexpected demand surges, various infection/vaccination status, and demand patterns. Here, our results show that a restaurant can benefit from partnering with third-party delivery platforms when (i) the subscription fee is low, (ii) customers can flexibly decide whether to order from platforms or from restaurants directly, (iii) customers require more efficient delivery, (iv) average delivery distance is long, or (v) demand variance is high.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Robust vehicle routing under uncertainty via branch-price-and-cut

Here, this paper contemplates how branch-price-and-cut solvers can be employed along with the robust optimization paradigm to address parametric uncertainty in the context of vehicle routing problems. In this setting, given postulated uncertainty sets for customer demands and vehicle travel times, one aims to identify a set of cost-effective routes for vehicles to traverse, such that the vehicle capacities and customer time window constraints are respected under any anticipated demand and travel time realization, respectively. To tackle such problems, we propose a novel approach that combines cutting-plane techniques with an advanced branch-price-and-cut algorithm. Specifically, we use deterministic pricing procedures to generate "partially robust" vehicle routes and then utilize robust versions of rounded capacity inequalities and infeasible path elimination constraints to guarantee complete robust feasibility of routing designs against demand and travel time uncertainty. In contrast to recent approaches that modify the pricing algorithm, our approach is both modular and versatile. It permits the use of advanced branch-price-and-cut technologies without significant modification, while it can admit a variety of uncertainty sets that are commonly used in robust optimization but could not be previously employed in a branch-price-and-cut setting.

42 ENGINEERING↗
DOE OSTI2023

Multi-layered Energy Management Framework for Extreme Fast Charging Stations Considering Demand Charges, Battery Degradation, and Forecast Uncertainties

To achieve a cost-effective and expeditious charging experience for extreme fast charging station (XFCS) owners and electric vehicle (EV) users, the optimal operation of XFCS is crucial. It is however challenging to simultaneously manage the profit from energy arbitrage, the cost of demand charges, and the degradation of a battery energy storage system (BESS) under uncertainties. This paper, therefore, proposes a multi-layered multi-time scale energy flow management framework for an XFCS by considering long- and short-term forecast uncertainties, monthly demand charges reduction, and BESS life degradation. In the proposed approach, an upper scheduling layer (USL) ensures the overall operation economy and yields optimal scheduling of the energy resources on a rolling horizon basis, thereby considering the long-term forecast errors. A lower dispatch layer (LDL) takes the short-term forecast errors into account during the real-time operation of the XFCS. Per the latest research, monthly demand charges can be as high as 90% of the total monthly bills for EV fast charging stations; to this end, this paper takes the first attempt at the reduction of demand charges cost by considering the trade-off between the energy cost and monthly demand charges. Contrasting literature, this work allocates an energy reserve in the BESS stored energy to deal with the impact of short-term forecast errors on the optimized real-time operation of the XFCS. Moreover, degradation modeling considers the trade-off between short-term benefits and long-term BESS life degradation. As a result, case studies and a comparative analysis prove the efficacy of the proposed framework.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

A Comprehensive Scheduling Framework using SP-ADMM for Residential Demand Response with Weather and Consumer Uncertainties

This paper presents a comprehensive scheduling framework for residential demand response (DR) programs considering both the day-ahead and real-time electricity markets. In the first stage, residential customers determine the operating status of their responsive devices such as heating, ventilation, and air conditioning (HVAC) systems and electric water heaters (EWHs), while the distribution system operator (DSO) computes the amount of electricity to be purchased in the day-ahead electricity market. In the second stage, the DSO purchases insufficient (or sells surplus) electricity in the real-time electricity market to maintain the supply-demand balance. Due to its computational complexity and data privacy issues, the proposed model cannot be directly solved in a centralized manner, especially with a large number of uncertain scenarios. Therefore, this paper proposes a combination of stochastic programming (SP) and the alternating direction method of multipliers (ADMM) algorithm, called SP-ADMM, to decompose the original model and then solve each sub-problem in a distributed manner while considering multiple uncertain scenarios. The simulation study is performed on the IEEE 33-bus system including 121 residential houses. Here, the results demonstrate the effectiveness of the proposed approach for large-scale residential DR applications under weather and consumer uncertainties.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Optimal Demand Response Incorporating Distribution LMP with PV Generation Uncertainty

The utilization of aggregated demand-side flexibility via demand response (DR) has become a promising pathway for the integration of renewable energy resources in power systems. Nowadays, there are several management strategies for DR such as the price-based transactive control strategies. However, many of such existing price-based control strategies neglect the physics and operational constraints of the underlying distribution networks when computing the price, raising concerns regarding their theoretical and practical values. This paper studies this issue and investigates optimal DR (ODR) by incorporating the distribution locational marginal price (DLMP). In particular, we discuss DR in connection with DLMPs and propose a multiperiod bilevel optimization problem to find the ODR strategy. Here, the objective is to minimize the peak load, load fluctuation, and payments of load aggregators. In addition, a robust bilevel ODR model is formulated to provide a robust ODR strategy while minimizing operating costs under the worst-case realization of uncertainties; this mitigates the impact of forecasting errors on renewable energy resources. Then, we propose an efficient solution approach by employing the Karush-Kuhn-Tucker conditions and strong duality. Simulation results are presented to illustrate the mutual impacts of the interaction between DR and DLMP and the benefits of the robust ODR strategy.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Evaluating grid stress and reliability in future electricity grids across a range of demand, generation mix, and weather trends

The reliability of power grids in the future will depend on how system planners account for the integration of new technologies, extreme weather events, and uncertainties in demand growth from increased electrification and data centers. This study introduces an open-source, multisectoral, multiscale modeling framework that projects grid stress and reliability trends between 2020 and 2055 in the Western Interconnection of the United States. The framework integrates global to national energy-water-land dynamics with power plant siting and hourly grid operations modeling. We analyze future wholesale electricity price shocks and unserved energy events across eight scenarios spanning a range of population growth and economic change, generation mixes, and weather conditions. Our results show future grids with high percentage of non-renewable generation and strong economic growth are characterized by higher reliability and lower wholesale electricity prices than lower growth scenarios because of larger reliance on dispatchable generators and lower fossil fuel extraction costs. Scenarios with high percentage of renewable resources have lower median but more volatile wholesale electricity prices as well as more frequent and severe unserved energy events compared to scenarios relying more on dispatchable generators. These events occur because higher proportion of solar and wind energy causes net demand curves to deepen during midday (duck curves get progressively severe), exacerbating the challenge of meeting demand during summer evening peaks. This study suggests that robust and co-optimized transmission and energy storage planning could help maintain low wholesale electricity prices and high reliability levels in future electricity grids across uncertainties in generation mixes.

Electric grid reliability↗