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DOE OSTI2022

Revenue prediction for integrated renewable energy and energy storage system using machine learning techniques

Revenue estimation for integrated renewable energy and energy storage systems is important to support plant owners or operators’ decisions in battery sizing selection that leads to maximized financial performances. A common approach to optimizing revenues of a hybrid hydro and energy storage system is using mixed-integer linear programming (MILP). Although MILP models can provide accurate production cost estimations, they are typically very computationally expensive. To provide a fast yet accurate first-step information to hydropower plant owners or operators who consider integrating energy storage systems, we propose an innovative approach to predicting optimal revenues of an integrated energy generation and storage system. In this study, we examined the performance of two prediction techniques: Generalized Additive Models (GAMs) and machine learning (ML) models developed based on artificial neural networks (ANN). Predictive equations and models are generated based on optimized solutions from a market participation optimization model, the Conventional Hydropower Energy and Environmental Resource System (CHEERS) model. The two predicting techniques reduce the computational time to evaluate annual revenue for one set of battery configurations from 3 h to 1 to 4 min per run while also being implementable with significantly less data. The model validation prediction errors of developed GAMs and ML models are generally below 5%; for model testing predictions, the ML models consistently outperform the regression equations in terms of root mean square errors. This new approach allows plant owners, operators, or potential investors to quickly access multiple battery configurations under different energy generation and market scenarios. This new revenue prediction method will therefore help reduce the barriers, and thereby promoting the deployment of battery hybridization with existing renewable energy sources.

13 HYDRO ENERGY↗

DOE OSTI2022

Rolling Optimization of Transmission Network Recovery and Load Restoration Considering Hybrid Wind-Storage System and Cold Load Pickup

A common solution to deal with the stochasticity introduced by fast-ramping wind power integration is to equip wind farms (WFs) with energy storage systems (ESSs) to formulate hybrid WF-ESSs. In addition to leveling off wind power fluctuations during normal operations, a hybrid WF-ESS can be a flexible power source to accumulate the power system restoration. In this paper, we propose a rolling optimization model for transmission network recovery and load restoration considering the contributions of WF-ESSs. The proposed model is formulated as a mixed integer linear programming problem that simultaneously optimizes the amount and location of restorable load blocks as well as the restoration lines. The cold load pickup features of interrupted loads considering the outage duration are modeled in detail. A chance-constrained method is employed to deal with the uncertainty of wind power, and a rolling horizon-based framework is adopted to reduce the influence of forecast error. Case studies are conducted on both New England 39-bus system and part of a provincial power system in China. The results show that the load restoration process can be significantly accelerated by employing the proposed method and contributions of hybrid WF-ESSs to power system restoration are validated.

chance-constrained optimization↗

DOE OSTI2022

A scalable planning framework of energy storage systems under frequency dynamics constraints

As the penetration of renewables increases in power systems, the declining system inertia can cause frequency stability issues. Battery energy storage systems (BESSs) respond fast and therefore can relieve the low inertia difficulty but need to be appropriately sized considering the associated cost. This paper presents a novel stochastic optimization model for economically planning BESS capacity while considering the spatial–temporal correlation of wind generation and generator outages under frequency stability constraints, which include the rate-of-change of frequency (RoCoF), frequency nadir (FN), and quasi-steady-state (QSS) frequency. A set of new FN constraints that can be easily linearized is developed. To account for renewable uncertainties, a realistic uncertainty modeling approach, Random Field, is adopted to generate wind generation scenarios by considering both spatial and temporal evolutions of wind speed profiles. The ESS sizing is formulated as a mixed-integer linear programming problem and solved by using a scalable decomposition-and-coordination approach, Surrogate Absolute Value Lagrangian Relaxation (SAVLR). To further improve the scalability and reduce computational burdens, a rolling-horizon-based update is developed and incorporated into SAVLR for providing a practical solution to the long-term planning of very large-scale power systems. Finally, a modified IEEE 118-bus system and the Polish system are used to validate the effectiveness and scalability of the model and solution methodology.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Exploring the benefits of utilizing small modular device for sustainable and flexible shale gas water management

Growing shale gas extraction in recent years has triggered wide discussions on the associated freshwater requirement and wastewater management. Many optimization approaches have been developed for shale gas water management; however, most of the studies assumed permanent utilization of wastewater treatment facilities with fixed capacities. Considering the rapidly declining characteristics of shale gas wastewater production, these treatment facilities could remain largely underutilized after the first few months/years of production, making them less economically attractive. To maximize the capacity utilization of treatment facilities and further improve the economic performance of shale gas development, this study develops a systematic optimization framework, where the capacity strategy of conventional treatment facilities and utilization of the recent concept of modular manufacturing are both considered for flexible shale gas water management. The proposed mixed-integer linear programming (MILP) model simultaneously optimizes the design and planning of integrated shale gas and water supply chain, with a focus on capacity planning for both large-scale conventional treatment facilities and small-scale modular devices. A series of Marcellus-based case studies are performed to illustrate the applicability of the proposed model and provide general insights into the trade-offs between the multiple types of treatment facilities. The optimization results reveal that the combinatorial utilization of conventional facilities and modular devices for wastewater treatment (66% by conventional facilities and 34% by modular devices) brings 9.3% more reused water for other well development and 6.2% savings in water-related costs, compared to flexible management of only conventional facilities. Furthermore, this work suggests that taking modular device as auxiliary equipment for shale gas water management is most beneficial to increase the capacity utilization of treatment facilities and achieve a more economic and sustainable shale gas production system.

04 OIL SHALES AND TAR SANDS↗

DOE OSTI2020

Piecewise polyhedral formulations for a multilinear term

Herein, we present a mixed-integer linear programming (MILP) formulation of a piecewise, polyhedral relaxation (PPR) of a multilinear term using its convex-hull representation. Based on the PPR’s solution, we also present a MILP formulation whose solutions are feasible for nonconvex, multilinear equations. We then present computational results showing the effectiveness of proposed formulations on standard benchmark nonlinear programs (NLPs) with multilinear terms and compare with a traditional formulation that is built using recursive bilinear groupings of multilinear terms.

42 ENGINEERING↗

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 OSTI2021

Risk-averse optimization for resilience enhancement of complex engineering systems under uncertainties

With the growth of complexity and extent, large scale interconnected network systems, e.g., transportation networks or infrastructure networks, become more vulnerable to external disturbances. Hence, managing potential disruptive events during the design, operating, and recovery phase of an engineered system and therefore improving the system’s resilience is an important yet challenging task. Here, to ensure system resilience after the occurrence of failure events, this study proposes a mixed-integer linear programming (MILP) based restoration framework using heterogeneous dispatchable agents. The scenario-based stochastic optimization (SO) technique is adopted to deal with the inherent uncertainties imposed on the recovery process from nature. Moreover, different from conventional SO using deterministic equivalent formulations, the CVaR risk measure is implemented for this study because of the temporal sparsity of the decision making in applications such as the recovery from extreme events. The resulting restoration framework involves a large-scale MILP problem and thus an adequate decomposition technique i.e. modified Lagrangian dual decomposition, is also employed to achieve tractable computational complexity. Case study results based on the IEEE 37-bus test feeder demonstrate the benefits of using the proposed framework for resilience improvement as well as the advantages of adopting SO formulations.

42 ENGINEERING↗

DOE OSTI2021

Stochastic pre-event preparation for enhancing resilience of distribution systems

Extreme weather events are the common causes for power supply interruptions and power outages in electrical distribution systems. Improving the distribution system and enhancing its resilience is becoming crucial due to the increased frequency of extreme weather events. Preparation and allocation of multiple flexible resources, such as mobile resources, fuel resources, and labor resources before extreme weather events can mitigate the effects of extreme weather events and enhance the resilience of power distribution systems. Here, in this paper, a two-stage stochastic mixed-integer linear programming (SMILP) is proposed to optimize the preparation and resource allocation process for upcoming extreme weather events, which leads to faster and more efficient post-event restoration. The objective of the proposed two-stage SMILP is to maximize the served load and minimize the operating cost of flexible resources. The first stage in the optimization problem selects the amounts and locations of different resources. The second stage considers the operational constraints of the distribution system and repair crew scheduling constraints. The proposed stochastic pre-event preparation model is solved by a scenario decomposition method, Progressive Hedging (PH), to ease the computational complexity introduced by a large number of scenarios. Furthermore, to show the impact of solar photovoltaic (PV) generation on system resilience, three types of PV systems are considered during a power outage and the resilience improvements with different PV penetration levels are compared. Numerical results from simulations on a large-scale (more than 10,000 nodes) distribution feeder have been used to validate the effectiveness and scalability of the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Supply chain optimization of sustainable aviation fuel from carinata in the Southeastern United States

We report carinata is a purpose-grown oilseed feedstock for renewable fuels, including sustainable aviation fuel (SAF) that can replace conventional aviation fuel (CAF). Given carinata is a new crop in the Southeastern United States, it is crucial to analyze its sustainability from a supply chain perspective. This study developed a mixed-integer linear programming (MILP) model and simulated it for 20 years, starting from a farm (county-level data) and ending at the airport. About 2.06 million ha in Alabama, Florida, and Georgia combined were found suitable for carinata production. Given the three-year rotation period, about 0.69 million hectares can be cultivated annually, approximately 65% of which was in Georgia. About 2.4% of the combined SAF annual demand of four major airports (about 210 thousand t) in the study area is satisfied at that level of carinata cultivation. However, all available SAF was supplied to the Atlanta airport as this decision minimizes the supply chain cost. A total of 1343 storage units, one oil extraction mill, and one biorefinery were needed to meet the overall demand. We found that SW Georgia is the top supplier of carinata seeds. The unit cost of production and carbon intensity were estimated to be $\$$0.89 L -1 (or $\$$26.79 GJ -1 ) and 0.91 kg CO 2 e L -1 (or 27.28 kg CO 2 e GJ -1 ), respectively. This carbon intensity of carinata-based SAF was 67.8% lower than that of CAF. With variations included in SAF demand, yield, and soil carbon sequestration, carbon savings remained between 66.5% and 67.8%. Given the GHG advantage of SAF over CAF, there is justification for subsidies required to make SAF competitive.

10 SYNTHETIC FUELS↗

DOE OSTI2024

Techno-economic analysis and network design for CO 2 conversion to jet fuels in the United States

The conversion of carbon dioxide (CO 2 ) into jet fuel holds significant potential for reducing CO 2 emissions, providing an alternative to carbon-based resources, and offering a renewable means of energy storage. The objective of this study is to conduct a techno-economic analysis and optimize the supply chain network for converting CO 2 to jet fuel in the United States, aiming to minimize total costs while assessing the environmental and economic feasibility of two CO 2 conversion pathways. This first pathway is based on Fischer-Tropsch synthesis (FTS), and the other one is based on the valorization and upgrading of light methanol (MeOH). Incorporating spatial and techno-economic data, a mixed-integer linear programming model was developed to select source plants and conversion pathways, locations of conversion refinery sites, and the amount of captured CO 2 across the United States. The optimal results indicate that the FTS pathway is adopted at all selected refineries when the hydrogen price is 1000 dollars/t and the operating cost, mainly electricity used in conversion, is reduced to 5 % of its current level. Under this scenario, the total annual profit is 8 billion dollars, and the net carbon emissions are -88,783,284 tons. The sensitivity analyses reveal that the prices of electricity and hydrogen significantly contribute to total production costs. The CO 2 recycle percentage of the FTS pathway influences the choice of applied pathways at refineries. Additionally, a higher conversion rate holds a substantial promise for reducing the total production cost and can make the MeOH pathway a viable choice.

10 SYNTHETIC FUELS↗

DOE OSTI2021

A systems engineering framework for the optimization of food supply chains under circular economy considerations

The current linear “take-make-waste-extractive” model leads to the depletion of natural resources and environmental degradation. Circular Economy (CE) aims to address these impacts by building supply chains that are restorative, regenerative, and environmentally benign. This can be achieved through the re-utilization of products and materials, the extensive usage of renewable energy sources, and ultimately by closing any open material loops. Such a transition towards environmental, economic and social advancements requires analytical tools for quantitative evaluation of the alternative pathways. Here, in this work, we present a novel CE system engineering framework and decision-making tool for the modeling and optimization of food supply chains. First, the alternative pathways for the production of the desired product and the valorization of wastes and by-products are identified. Then, a Resource-Task-Network representation that captures all these pathways is utilized, based on which a mixed-integer linear programming model is developed. This approach allows the holistic modeling and optimization of the entire food supply chain, taking into account any of its special characteristics, potential constraints as well as different objectives. Considering that typically CE introduces multiple, often conflicting objectives, we deploy here a multi-objective optimization strategy for trade-off analysis. A representative case study for the supply chain of coffee is discussed, illustrating the steps and the applicability of the framework. Single and multi-objective optimization formulations under five different coffee-product demand scenarios are presented. The production of instant coffee as the only final product is shown to be the least energy and environmental efficient scenario. On the contrary, the production solely of whole beans sets a hypothetical upper bound on the optimal energy and environmental utilization. In both problems presented, the amount of energy generated is significant due to the utilization of waste generated for the production of excess energy.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2021

Real time operation of high-capacity electric vehicle ridesharing fleets

We study the feasibility of using electric vehicles in online, high-capacity ridepooling systems. Prior work has shown that online algorithms perform well for centrally-controlled, high-capacity ridepool systems. First, we propose a mixed integer linear program to expand past algorithms on ridepooling to electric vehicle fleets with the objective of scheduling vehicle charging to maintain sufficient fleet sizes at various times of day. Then we show a faster, scalable algorithm with similar performance that is practical for full-scale systems. Furthermore, our contributions reinforce the importance of having knowledge and estimates of future demand even when operating in the online setting.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2024

Redesigning large-scale multimodal transit networks with shared autonomous mobility services

Here, this study addresses a large-scale multimodal transit network design problem, with Shared Autonomous Mobility Services (SAMS) as both transit feeders and an origin-to-destination mode. The framework captures spatial demand and modal characteristics, considers intermodal transfers and express services, determines transit infrastructure investment and path flows, and generates transit routes. A system-optimal multimodal transit network is designed with minimum total door-to-door generalized costs of users and operators, satisfying transit origin-destination demand within a pre-set infrastructure budget. Firstly, the geography, demand, and modes in each zone are characterized with continuous approximation. The decisions of network link investment and multimodal path flows in zonal connection optimization are formulated as a minimum-cost multi-commodity network flow (MCNF) problem and solved efficiently with a mixed-integer linear programming (MILP) solver. Subsequently, the route generation problem is solved by expanding the MCNF formulation to minimize intramodal transfers. The model is illustrated through a set of experiments with the Chicago network comprised of 50 zones and seven modes, under three scenarios. The computational results present savings in traveler journey time and operator cost demonstrating the potential benefits of collaboration between multimodal transit systems and SAMS.

Autonomous vehicles↗

DOE OSTI2024

Heuristic solutions to the single depot electric vehicle scheduling problem with next day operability constraints

This study focuses on the single depot electric vehicle scheduling problem (SDEVSP) within the broader context of the vehicle scheduling problem (VSP). By developing an effective scheduling model using mixed-integer linear programming, we generate bus blocks that accommodate electric vehicles (EVs), ensuring successful completion of each block while considering recharging requirements between blocks and during off-hours. Next day operability constraints are also incorporated, allowing for seamless repetition of blocks on subsequent days. The SDEVSP is known to be computationally complex, deriving optimal solutions unattainable for large-scale problems within reasonable timeframes. To address this, we propose a two-step solution approach: first solving the single depot VSP, and then addressing the block chaining problem (BCP) using the blocks generated in the first step. The BCP focuses on optimizing block combinations to facilitate recharging between consecutive blocks, considering operational constraints. Further, a case study conducted reveals that nearly 100% electrification for Chicago, IL and Austin, TX transit buses is viable yet requires 1.6 EVs at 150-mile range per diesel vehicle.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2023

Phase-based design of CO 2 capture, transport, and storage infrastructure via SimCCS 3.0

The design of optimal infrastructure is essential for the deployment of commercial and large-scale carbon capture and storage (CCS) technology. During the design process, it is important to consider CO 2 capture and storage locations and CO 2 transportation pipelines to minimize the total project cost. SimCCS, first introduced in 2009, is an integrated open-source tool to optimize CCS infrastructure. The core CCS infrastructure design problem in SimCCS is structured as a mixed-integer linear programming problem by selecting the optimal pipeline routes, searching CO 2 source capture and storage locations, and determining the corresponding CO 2 amounts to meet desired capture targets. Multiple important and practical features have been developed to the latest version of SimCCS, SimCCS 3.0 . One of these features is phase-based modeling which enables users to dynamically design the CCS infrastructure. We demonstrate the phased-based modeling capability using two CCS infrastructure optimization case studies. The results from these case studies reveal that the phase-based modeling capability in SimCCS is particularly useful to optimize the dynamic deployment of CCS projects.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Multi-Attribute Subset Selection enables prediction of representative phenotypes across microbial populations

The interpretation of complex biological datasets requires the identification of representative variables that describe the data without critical information loss. This is particularly important in the analysis of large phenotypic datasets (phenomics). Here we introduce Multi-Attribute Subset Selection (MASS), an algorithm which separates a matrix of phenotypes (e.g., yield across microbial species and environmental conditions) into predictor and response sets of conditions. Using mixed integer linear programming, MASS expresses the response conditions as a linear combination of the predictor conditions, while simultaneously searching for the optimally descriptive set of predictors. We apply the algorithm to three microbial datasets and identify environmental conditions that predict phenotypes under other conditions, providing biologically interpretable axes for strain discrimination. MASS could be used to reduce the number of experiments needed to identify species or to map their metabolic capabilities. The generality of the algorithm allows addressing subset selection problems in areas beyond biology.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2026

Stochastic Microgrid Scheduling With Chance‐Constrained Resilience Consideration

Traditionally, it is assumed that microgrids transition seamlessly from grid‐connected operation to islanded mode in the event of sudden main grid outages. In reality, the islanding process, especially unintentional islanding, is rarely seamless. Instead, it is subject to voltage and frequency fluctuations caused by the instantaneous disconnection of the point of common coupling (PCC) switch, variations in loads and renewable generation output and even the protection tripping of distributed energy resources (DERs). To mitigate these fluctuations and facilitate a smooth islanding process, we propose a stochastic microgrid scheduling model that incorporates chance‐constrained resilience measures. Specifically, the resilience measure is defined as the probability of successful islanding (PSI), that is, the probability that a microgrid can mitigate the generation‐demand imbalance caused by the disconnection of the PCC switch, variations in load and renewable generation and DER tripping. This measure is modelled using chance constraints. Unlike existing reliability and resilience indices, which typically neglect the possibility of microgrid/DER failure under extreme events and assume their survival while primarily focussing on reducing impact duration or magnitude, the proposed PSI‐based framework explicitly addresses microgrid and DER survival during the islanding transition. The formulated nonlinear chance constraints are approximated using a multiinterval approach and equivalently represented as a mixed‐integer linear programming (MILP) formulation. Case study results validate the proposed method, showing that the PSI estimation error is reduced to less than 8%, compared to approximately 28% with existing methods. Various sensitivity analyses on the DER tripping rate and PSI settings were performed to validate the robustness of the proposed method. In particular, the necessity of accounting for DER tripping in the PSI calculation was demonstrated.

chance constrained optimization↗

DOE OSTI2021

A two-stage service restoration method for electric power distribution systems

Improving the reliability of power distribution systems is critically important for both utilities and customers. This calls for an efficient service restoration module within a distribution management system to support the implementation of self-healing smart grid networks. Although the emerging smart grid technologies, including distributed generators (DGs) and remote-controlled switches, enhance the self-healing capability and allow faster recovery, they still pose additional complexity to the service restoration problem, especially under cold load pickup (CLPU) conditions. Herein, a novel two-stage restoration framework is proposed to generate a restoration solutions with a sequence of control actions. The first stage generates a restoration plan that supports both the traditional service restoration using feeder reconfiguration and the grid-forming DG-assisted intentional islanding methods. The second stage generates an optimal sequence of switching operations to bring the outaged system quickly to the final restored configuration. The problem is formulated as a mixed-integer linear program that incorporates system connectivity, operating constraints, and the CLPU models. It is demonstrated that on using a multi-feeder test case, the proposed framework is effective in utilizing all available resources to quickly restore the service and generate an optimal sequence of switching actions to be used by the operator to reach the desired optimal configuration.

24 POWER TRANSMISSION AND DISTRIBUTION↗