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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 505 records · Page 28

Variability in Wind Energy Generation across the Contiguous United States

ERA5 provides high-resolution, high-quality hourly wind speeds at 100 m and is a unique resource for quantifying temporal variability in likely wind-derived power production across the United States. Gross capacity factors (CF) in seven independent system operators (ISOs) are estimated using the location and rated power of each wind turbine, a simplified power curve, and ERA5 output from 1979 to 2018. Excluding the California ISO, the marginal probability of a calm (zero power production) is less than 0.1 in any ERA5 grid cell. When a calm occurs, the mean co-occurrence across wind-turbine-containing grid cells ranges from 0.38 to 0.39 for ISOs in the Midwest and central plains [Midcontinent (or Midwest) ISO (MISO), Southwest Power Pool (SPP), and the Electric Reliability Council of Texas (ERCOT) region], increasing to 0.54–0.58 for ISOs in the eastern United States [Pennsylvania–New Jersey–Maryland interconnection (PJM), New York ISO (NYISO), and New England ISO (NEISO)]. Periods with low gross CF have a median duration of ≤6 h, except in California, and are most likely during summer. Additionally, gross CF exhibit highest variance at periods of 1 day in ERCOT and SPP; on synoptic scales in MISO, NEISO, and NYISO; and on interannual time scales in PJM. This implies differences in optimal strategies for ensuring resilience of supply. Theoretical scenarios show adding wind energy capacity near existing wind farms is advantageous even in areas with high existing installed capacity (IC), while expanding into areas with lower IC is more beneficial to reducing ramps and the probability of gross CF falling below 20%. These results emphasize the benefits of large balancing areas and aggregation in reducing wind power variability and the likelihood of wind droughts.

17 WIND ENERGY↗

Optimal resource allocation for flexible-grid entanglement distribution networks

We use a genetic algorithm (GA) as a design aid for determining the optimal provisioning of entangled photon spectrum in flex-grid quantum networks with arbitrary numbers of channels and users. After introducing a general model for entanglement distribution based on frequency-polarization hyperentangled biphotons, we derive upper bounds on fidelity and entangled bit rate for networks comprising one-to-one user connections. Simple conditions based on user detector quality and link efficiencies are found that determine whether entanglement is possible. We successfully apply a GA to find optimal resource allocations in four different representative network scenarios and validate features of our model experimentally in a quantum local area network in deployed fiber. Our results show promise for the rapid design of large-scale entanglement distribution networks.

97 MATHEMATICS AND COMPUTING↗

Cyber Secure Sensor Network for Fossil Fuel Power Generation Assets Monitoring

The energy sector is undergoing digital transformation which is to say more and more power generation assets have become automated and connected to the internet. The connected sensors can tap into plants to monitor the health of assets and manage fleets remotely. These are just some of the benefits digitalization is bringing to the power industry. Within a power plant, control systems are no longer concerned with one system or one piece of equipment, but rather whole fleet of assets inter-connected with smart sensors which have the function of continuously monitoring and transmitting real-time operational data to operators. These connected systems will form a part of the industrial internet of things (IIoT). The big data scenarios provide benefits of performing system prognostics and optimization which is a key selling point of power plant digitalization.

20 FOSSIL-FUELED POWER PLANTS↗

Adiabatic diesel engine component development: Reference engine for on-highway applications

The main objectives were to select an advanced low heat rejection diesel reference engine (ADRE) and to carry out systems analysis and design. The ADRE concept selection consisted of: (1) rated point performance optimization; (2) study of various exhaust energy recovery scenarios; (3) components, systems and engine configuration studies; and (4) life cycle cost estimates of the ADRE economic worth. The resulting ADRE design proposed a reciprocator with many advanced features for the 1995 technology demonstration time frame. These included ceramic air gap insulated hot section structural components, high temperature tribology treatments, nonmechanical (camless) valve actuation systems, and elimination of the cylinder head gasket. ADRE system analysis and design resulted in more definition of the engine systems. These systems include: (1) electro-hydraulic valve actuation, (2) electronic common rail injection system; (3) engine electronic control; (4) power transfer for accessory drives and exhaust energy recovery systems; and (5) truck installation. Tribology and performance assessments were also carried out. Finite element and probability of survival analyses were undertaken for the ceramic low heat rejection component.

Hakim, Nabil S.↗

Optimization techniques applied to passive measures for in-orbit spacecraft survivability

Spacecraft designers have always been concerned about the effects of meteoroid impacts on mission safety. The engineering solution to this problem has generally been to erect a bumper or shield placed outboard from the spacecraft wall to disrupt/deflect the incoming projectiles. Spacecraft designers have a number of tools at their disposal to aid in the design process. These include hypervelocity impact testing, analytic impact predictors, and hydrodynamic codes. Analytic impact predictors generally provide the best quick-look estimate of design tradeoffs. The most complete way to determine the characteristics of an analytic impact predictor is through optimization of the protective structures design problem formulated with the predictor of interest. Space Station Freedom protective structures design insight is provided through the coupling of design/material requirements, hypervelocity impact phenomenology, meteoroid and space debris environment sensitivities, optimization techniques and operations research strategies, and mission scenarios. Major results are presented.

Mog, Robert A.↗

Optimization techniques applied to passive measures for in-orbit spacecraft survivability

The purpose of this research is to provide Space Station Freedom protective structures design insight through the coupling of design/material requirements, hypervelocity impact phenomenology, meteoroid and space debris environment sensitivities, optimization techniques and operations research strategies, and mission scenarios. The goals of the research are: (1) to develop a Monte Carlo simulation tool which will provide top level insight for Space Station protective structures designers; (2) to develop advanced shielding concepts relevant to Space Station Freedom using unique multiple bumper approaches; and (3) to investigate projectile shape effects on protective structures design.

Mog, Robert A.↗

Notes on SAW Tag Interrogation Techniques

We consider the problem of interrogating a single SAW RFID tag with a known ID and known range in the presence of multiple interfering tags under the following assumptions: (1) The RF propagation environment is well approximated as a simple delay channel with geometric power-decay constant alpha >/= 2. (2) The interfering tag IDs are unknown but well approximated as independent, identically distributed random samples from a probability distribution of tag ID waveforms with known second-order properties, and the tag of interest is drawn independently from the same distribution. (3) The ranges of the interfering tags are unknown but well approximated as independent, identically distributed realizations of a random variable rho with a known probability distribution f(sub rho) , and the tag ranges are independent of the tag ID waveforms. In particular, we model the tag waveforms as random impulse responses from a wide-sense-stationary, uncorrelated-scattering (WSSUS) fading channel with known bandwidth and scattering function. A brief discussion of the properties of such channels and the notation used to describe them in this document is given in the Appendix. Under these assumptions, we derive the expression for the output signal-to-noise ratio (SNR) for an arbitrary combination of transmitted interrogation signal and linear receiver filter. Based on this expression, we derive the optimal interrogator configuration (i.e., transmitted signal/receiver filter combination) in the two extreme noise/interference regimes, i.e., noise-limited and interference-limited, under the additional assumption that the coherence bandwidth of the tags is much smaller than the total tag bandwidth. Finally, we evaluate the performance of both optimal interrogators over a broad range of operating scenarios using both numerical simulation based on the assumed model and Monte Carlo simulation based on a small sample of measured tag waveforms. The performance evaluation results not only provide guidelines for proper interrogator design, but also provide some insight on the validity of the assumed signal model. It should be noted that the assumption that the impulse response of the tag of interest is known precisely implies that the temperature and range of the tag are also known precisely, which is generally not the case in practice. However, analyzing interrogator performance under this simplifying assumption is much more straightforward and still provides a great deal of insight into the nature of the problem.

Barton, Richard J.↗

NASA's Soil Moisture Active and Passive (SMAP) Mission

The Soil Moisture Active-Passive (SMAP) Mission is one of the first Earth observation satellites being formulated by NASA in response to the 2007 National Research Council s Decadal Survey. SMAP will make global measurements of soil moisture at the Earth's land surface and its freeze-thaw state. These measurements will allow significantly improved estimates of water, energy and carbon transfers between the land and atmosphere. Soil moisture measurements are also of great importance in assessing flooding and monitoring drought. Knowledge gained from SMAP observations can help mitigate these natural hazards, resulting in potentially great economic and social benefits. SMAP observations of soil moisture and freeze/thaw timing over the boreal latitudes will also reduce a major uncertainty in quantifying the global carbon balance and help to resolve an apparent missing carbon sink over land. The SMAP mission concept will utilize an L-band radar and radiometer sharing a rotating 6-meter mesh reflector antenna flying in a 680 km polar orbit with an 8-day exact ground track repeat aboard a 3-axis stabilized spacecraft to provide high-resolution and high-accuracy global maps of soil moisture and freeze/thaw state every two to three days. In addition, the SMAP project will use these surface observations with advanced modeling and data assimilation to provide estimates of deeper root-zone soil moisture and net ecosystem exchange of carbon. SMAP recently completed its Phase A Mission Concept Study Phase for NASA and transitioned into Phase B (Formulation and Detailed Design). A number of significant accomplishments occurred during this initial phase of mission development. The SMAP project held several open meetings to solicit community feedback on possible science algorithms, prepared preliminary draft Algorithm Theoretical Basis Documents (ATBDs) for each mission science product, and established a prototype algorithm testbed to enable testing and evaluation of the performance of candidate algorithms. SMAP conducted an Applications Workshop in September 2009 to coordinate with potential application users interested in the mission data. A draft Applications Plan describing the Project s planned outreach to potential applications users has been prepared and will be updated during Phase B. SMAP made a significant evaluation of the potential terrestrial radio frequency interference (RFI) source environment and established radiometer and radar flight hardware and ground processing mitigation approaches. SMAP finalized its science orbit and orbit injection approach to optimize launch mass and prepared launch and commissioning scenarios and timeline. A science data communications approach was developed to maximize available science data volume to improve science margins while maintaining moderately short data product latencies to support many potential applications using existing ground assets and with minimum impact to the flight system. SMAP developed rigid multi-body and flexible body dynamics and control models and system designs for the 6-meter rotating instrument reflector-boom assembly (RBA) and flight system to confirm pointing and control performance, and devised strategies to efficiently implement on-orbit balancing if needed. Industry partners were selected for the spin mechanism assembly (SMA) and RBA. Preliminary designs for the radar and radiometer were initiated, including constructing breadboards of key assemblies.

Kellogg, Kent↗

Crop and Substrate Tests with Single Use Rooting "Pillows" for the VEGGIE Plant Growth Hardware

VEGGIE is a small plant production chamber built by ORBITEC. This chamber can be collapsed for easy stowage and deployed in orbit. It is designed for gravity independent operation, and provides 0.17 square m of crop growth area with three primary subsystems: an LED light panel, extendable transparent Teflon bellows to enclose the plants, and a wicking reservoir. VEGGIE would provide the capability for astronauts to grow fresh foods for dietary supplementation. Initial planting concepts tested with the VEGGIE included direct seeding or plug placement on the reservoir surface. These options had issues of salt accumulation and eventual toxicity if the reservoir was filled with nutrient solution, and hardware reuse was limited due to sanitation. In response a rooting packet or "pillow" concept was developed: single-use bags of media containing time release fertilizer with a wicking surface contacting the VEGGIE reservoir. Pillows being tested are small electrostatic bags with a Nitex nylon mesh side, each holding 100 mL of dry media. Six pillows fit in one VEGGIE unit; however pillow size could vary depending on crop selected. Seeds can be planted directly in pillows and planted pillows can be hydrated in space as desired. Our goals were to define optimal media and crops for an ISS mission scenario. Plant tests in pillows were performed in a controlled environment chamber set to habitat-relevant conditions, and capillary reservoir analogs were utilized. Media tested within pillows included: a commercial peat-based potting mix, arcillite (calcined clay), perlite: vermiculite, and peat-based: arcillite blends. Testing included 15 types of leafy greens, snow pea, radish, and herbs. Media performance was crop dependent, but generally plants showed the greatest growth in the peat-based: arcillite mixes. Crops with the best performance in pillows were identified, and testing is underway with select leafy greens examining plant and microbial load response to repeated harvest. We plan to use findings from previous flight testing with media to evaluate the effects of capillary flow from the reservoir to pillows in microgravity.

Massa, Gioia↗

Arbitrage and Capacity Firming in Coordination with Day-Ahead Bidding of a Hybrid PV Plant

A hybrid PV plant (HPP) combines a photovoltaic (PV) plant with a battery energy storage system (BESS), which is considered a promising step towards the future of renewable power plants by the U.S. Department of Energy. When the renewable penetration reaches a significant level, a hybrid PV plant can bid in as a controllable thermal plant in the future electricity market. In this study, a bidding and BESS scheduling model is proposed for the HPP. The robust optimization (RO) technique has been utilized to identify the worst-case scenario of uncertainties during the bidding process. To address the overly conservative issue of the single-stage RO, we have decoupled the BESS schedule for arbitrage and PV capacity firming by a two-stage RO formulation. By comparing the output of single-stage RO and two-stage RO, the two-stage RO bids and schedules in a more aggressive manner, which increases the income of HPP. Also, the penalty of under-generation is considered in our model so that the day-ahead bidding decision and arbitrage schedules can be adjusted based on the potential UNDER-GENERATION penalty. Because the proposed model is non-convex and contains multi-stages, the Column-and-Constraint Generation (C&CG) algorithm is applied to the model as the solution. The proposed model has shown better economic performance compared to a state-of-art single-stage bidding method in case studies.

BESS scheduling↗

Incorporation of market signals for the optimal design of post combustion carbon capture systems

Recent studies have shown that fossil generators equipped with post-combustion carbon capture (PCC) systems are needed to reduce the cost of deep decarbonization. Such generators need to be flexible and responsive to grid conditions, particularly in a high variable renewable energy (VRE) environment. In this work, we evaluate the net present value (NPV) of retrofitting an existing natural gas combined cycle (NGCC) unit with a flexible PCC system while incorporating market signals from a high VRE grid. We use our industrial partner’s NGCC configuration as representative of existing NGCC units and Svante’s rapid-temperature swing adsorption (TSA) for PCC. Because of its ability to rapidly startup/shutdown and ramp-up/ramp-down, the chosen capture technology is very attractive for load-following operations. For a given set of market signals, we formulate a two-stage stochastic multi-period optimization problem, under the price-taker assumption, to simultaneously optimize the design of the capture system and operation of the entire plant. Rigorous models for the NGCC unit, PCC system, and compression system are developed using commercial process simulators and validated with either plant or vendor data. For computational tractability, we develop surrogate/reduced-order models for use in the optimization problem. The surrogate model for the NGCC plant is constructed by linearizing the rigorous dynamic model at 75% load, while data-driven nonlinear surrogate models for the capture and compression systems are constructed using simulation data from the rigorous models. The optimization problem, formulated as a mixed integer bilinear program, is implemented in the IDAES® integrated platform and solved to global optimality using Gurobi 9.5. Using this formulation, we determine the profitability of retrofitting an existing NGCC unit with the chosen capture system for multiple regions in the U.S. under two scenarios with different carbon prices. Importantly, the results show that the optimal decision strongly depends on the region and on the carbon price, thereby demonstrating the importance of the inclusion of market signals in the design process.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

A preconditioning technique for Schur complement systems arising in stochastic optimization

Deterministic sample average approximations of stochastic programming problems with recourse are suitable for a scenario-based parallelization. In this paper the parallelization is obtained by using an interior-point method and a Schur complement mechanism for the interior-point linear systems. However, the direct linear solves involving the dense Schur complement matrix are expensive, and adversely affect the scalability of this approach. We address this issue by proposing a stochastic preconditioner for the Schur complement matrix and by using Krylov iterative methods for the solution of the dense linear systems. The stochastic preconditioner is built based on a subset of existing scenarios and can be assembled and factorized on a separate process before the computation of the Schur complement matrix finishes on the remaining processes. The expensive factorization of the Schur complement is removed from the parallel execution flow and the scaling of the optimization solver is considerably improved with this approach. The spectral analysis indicates an exponentially fast convergence in probability to 1 of the eigenvalues of the preconditioned matrix with the number of scenarios incorporated in the preconditioner. Numerical experiments performed on the relaxation of a unit commitment problem show good performance, in terms of both the accuracy of the solution and the execution time.

99 GENERAL AND MISCELLANEOUS↗

Scalable Truck Charging Demand Simulation for Cost-Optimized Infrastructure Planning

This project developed a scalable, high-resolution model to simulate medium- and heavy-duty (MHD) electric truck charging demand and assess its impact on grid infrastructure. Using generative modeling, simulation, and cost optimization, the project delivered an end-to-end software pipeline and a library of 96 real-world scenarios for the Dallas–Houston megaregion. We demonstrated a modular architecture for transportation and grid modeling, implemented cost-optimized infrastructure planning methods, and quantified grid capital, operational, and environmental costs across a wide range of truck electrification scenarios. The results have been adopted by major utility stakeholders and contributed to regional planning efforts.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DEEP Solar: Data DrivEn Modeling and Analytics for Enhanced System Layer ImPlementation

Realizing the SETO 2030 mission of reducing solar energy costs to 3-5 c/kWh will require innovative enabling research on effective, cost-efficient integration of local PV within distribution systems. However, the intermittent and variable nature of PVs compels operators to impose conservative hosting capacity constraints. Given the extremely high variability of (intermittent and unpredictable) solar energy generation, relaxing the capacity constraints (which are currently around 15%) and achieving 100% or greater integration of renewables will require a fundamental transformation of the power grid via the utilization of exponentially larger amounts of AMI enabled fine-grained data. To address the challenges in increasing the penetration of renewable energy based DERs, this project envisions an Enhanced System Layer (ESL) at the distribution network level that is reliable, cost-effective and scalable to millions of Distributed Energy Resources (DERs)/devices. This includes developing: 1) Transformative and highly scalable machine learning based predictive analytics tools that plug into distribution system planning and provide real-time situational awareness at the distribution level for short and long-term operational planning. The tools will be built using novel data-driven energy models of millions of active nodes with AMI, 2) Adaptive stochastic analysis and optimization algorithms for real-time grid operations, 3) Dynamic Scenario Analysis using parallel Cloudenabled implementations with < 1 minute computational cycle times.

14 SOLAR ENERGY↗

A Cutting Surface Algorithm for Semi-Infinite Convex Programming with an Application to Moment Robust Optimization

In this paper, we present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. Moments of arbitrary order, as well as nonpolynomial moments, can be included in the formulation. We show that this gives rise to a hierarchy of optimization problems with decreasing levels of risk-aversion, with classic robust optimization at one end of the spectrum and stochastic programming at the other. Although our primary motivation is to solve distributionally robust optimization problems with moment uncertainty, the cutting surface method for general semi-infinite convex programs is also of independent interest. The proposed method is applicable to problems with nondifferentiable semi-infinite constraints indexed by an infinite dimensional index set. Examples comparing the cutting surface algorithm to the central cutting plane algorithm of Kortanek and No demonstrate the potential of our algorithm even in the solution of traditional semi-infinite convex programming problems, whose constraints are differentiable, and are indexed by an index set of low dimension. After the rate of convergence analysis of the cutting surface algorithm, we extend the authors' moment matching scenario generation algorithm to a probabilistic algorithm that finds optimal probability distributions subject to moment constraints. The combination of this distribution optimization method and the central cutting surface algorithm yields a solution to a family of distributionally robust optimization problems that are considerably more general than the ones proposed to date.

97 MATHEMATICS AND COMPUTING↗

Study of Storage Requirements and Costs for Shaping Renewables and Nuclear Energy (FY23 Summary Report)

To decarbonize electricity generation primarily by using wind and solar resources, it is likely that additional low (or zero) carbon dioxide (CO 2 ) alternatives will be required for ensuring a reliable electricity supply. This study extends the work and modeling framework that we consolidated in FY 2022, by assessing the zero-CO 2 pathways of a Texas power system in which the availability of variable renewable energy (VRE), nuclear energy, and energy storage types (i.e., battery and thermal energy storage [TES]) are considered the sole resources available for expansion. Using the Risk Analysis Virtual Environment (RAVEN) and Holistic Energy Resource Optimization Network (HERON) frameworks, this study investigates the market of two nuclear energy technologies (i.e., large light-water reactors [LWRs] and LWR-type small modular reactors [SMRs]) under two plausible storage coupling scenarios (i.e., electric coupling and direct thermal coupling). We also explore optimal environments for nuclear energy deployment, and identify key performance characteristics that make nuclear energy economically viable in areas with significant intermittent energy sources. Our analysis encompasses 24 cases. We model the least-cost grid systems, highlight the potential for a coupled LWR-TES approach, and utilize SMRs to achieve deep decarbonization in an affordable, technically feasible manner. We also examine seasonal variations in balancing electricity supply and demand, and account for varying performance, costs, and grid constraints. Overall, the findings of our modeling afford valuable insights for supporting future technology investment decisions in the energy sector.

25 ENERGY STORAGE↗

Optimal well placement and brine extraction for pressure management during CO 2 sequestration

Large-scale pressure increases resulting from carbon dioxide (CO 2 ) injection in the subsurface can potentially impact caprock integrity, induce reactivation of critically stressed faults, and drive CO 2 or brine through conductive features into shallow groundwater. Pressure management involving the extraction of native fluids from storage formations can be used to reduce such pressure increases. However, dealing with large volumes of extracted brine can be technically challenging and expensive. Selection of optimal well locations and pumping rates are critical for maximizing CO 2 storage and minimizing brine extraction during geologic CO 2 sequestration (GCS). Robust and efficient computerized algorithms combining reservoir models and optimization methods are needed to make proper decisions on well placement and pumping rates. This work presents a constrained differential evolution (CDE) algorithm for solving global optimization problems involving pressure management of GCS projects. Application of the CDE optimization methodology was demonstrated for a hypothetical CO 2 storage scenario in a deep sandstone reservoir in the Southern San Joaquin Basin in California, USA. Industrial-scale storage of CO 2 would generate significant pressure buildup in this formation, which in turn would raise concerns about induced seismicity due to presence of multiple faults surrounding the injection site. Through the CDE optimization algorithm coupled to a vertically-averaged reservoir simulator, we successfully estimated optimal solutions for brine extraction wells in the reservoir that would limit the local pressure along the faults to a prescribed threshold. Multiple realizations of the reservoir permeability field were created to understand the impact of reservoir heterogeneity on optimization results. Our results indicate that the reservoir slope and heterogeneity have significant impact on optimum extraction rates. Reservoir heterogeneity is also a significant factor for extraction well locations, suggesting that in practice decisions about extraction well placement through optimization should be made at later project stages when data from a few years of CO 2 injection have allowed iterative updating and refining of the reservoir forward models. Although the study focused on optimization of brine extraction, the CDE optimization methodology presented in this paper has also potential to solve other complex optimization problems related to GCS, such as increasing storage efficiency by enhancing injectivity and capillary and dissolution trapping.

58 GEOSCIENCES↗

Determining spatially varying profit‐maximizing management practices for miscanthus and switchgrass production in the rainfed United States

Abstract Determining optimal management practices for the profitable production of perennial energy crops is critical for scaling up production beyond experimental levels. Although many experimental field studies have examined the effects of management practices on the performance of miscanthus and switchgrass, there are no recommendations for economically optimal nitrogen (N) application rates and how they should vary spatially and with the age of the energy crop as well as on optimal rotation age of the energy crop to maximize profits. We develop a modeling framework to determine economically optimal crop management decisions and simulate the variability under various scenarios for miscanthus and switchgrass production across 2287 counties in the rainfed United States. We find that profit‐maximizing N recommendations for these crops vary across maturity stages and regions and can increase the landowner's profits compared with a uniform N rate across ages and regions. We also find that the optimal rotation for these crops is shorter than the productive physical lifespan (15–20 and 10 years for miscanthus and switchgrass, respectively). Specifically, the N rate that maximizes the economic returns is negligible for miscanthus and 111 kg ha −1 for switchgrass production at age 2. The mean profit‐maximizing N rate increases with age for miscanthus, peaking at 151 kg ha −1 at age 11 before declining to 114 kg ha −1 at the optimal rotation age of 13 years while that for switchgrass is 150 kg ha −1 for middle‐aged stands and declines to 114 kg ha −1 at the optimal rotation of 8–9 years. We find that miscanthus is the most profitable energy crop in the northern region of the rainfed United States while switchgrass is most profitable in the south of the rainfed United States. Our findings are useful for improving assessments of the profitability of energy crops and guiding future management decisions by landowners.

54 ENVIRONMENTAL SCIENCES↗