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At least 631 records · Page 35

An OpenStreetMaps based tool to study the energy demand and emissions impact of electrification of medium and heavy-duty freight trucks

In this paper, we present the mathematical formulation of an OpenStreetMaps (OSM) based tool that compares the costs and emissions of long-haul medium and heavy-duty (M&HD) electric and diesel freight trucks, and determines the spatial distribution of added energy demand due to M&HD EVs. The optimization utilizes a combination of information on routes from OSM, utility rate design data across the United States, and freight volume data, to determine these values. In order to deal with the computational complexity of this problem, we formulate the problem as a convex optimization problem that is scalable to a large geographic area. In our analysis, we further evaluate various scenarios of utility rate design (energy charges) and EV penetration rate across different geographic regions and their impact on the operating cost and emissions of the freight trucks. Our approach determines the net emissions reduction benefits of freight electrification by considering the primary energy source in different regions. Such analysis will provide insights to policy makers in designing utility rates for electric vehicle supply equipment (EVSE) operators depending upon the specific geographic region and to electric utilities in deciding infrastructure upgrades based on the spatial distribution of the added energy demand of M&HD EVs. To showcase the results, a case study for the U.S. state of Texas is conducted.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

A data-driven approach to real-time vertical position estimation for NSTX-U vertical stability control

In this paper, a database of 77 996 plasma equilibrium reconstructions from 727 discharges during the initial operation of the NSTX-U spherical tokamak is analyzed to develop a statistically robust model of the plasma vertical position for real-time control. A variety of regression models are developed and tested, ranging in complexity from linear models to deep neural networks, and including input signals ranging from the four pairs of flux loops used historically on NSTX-U up to the full set of 389 real-time signals available to the plasma control system. A linear model based on 140 real-time magnetics signals is found to offer excellent accuracy, with a coefficient of determination R 2 = 0.906. The robustness of this model to limited training data, new operating scenarios, and signal errors is tested, and a procedure is demonstrated to tune the model parameters to optimize its robustness. A time-dependent plasma equilibrium solver, TokaMaker, is used to simulate vertical stability control in NSTX-U, demonstrating that it should be possible to iteratively tune the parameters of a linear vertical position model to stabilize both positive and negative triangularity plasmas in future experiments.

magnetic diagnostics↗

Improving Robustness of Spectrogram Classifiers with Neural Stochastic Differential Equations

Signal analysis and classification is fraught with high levels of noise and perturbation. Computer-vision-based deep learning models applied to spectrograms have proven useful in the field of signal classification and detection; however, these methods aren't designed to handle the low signal-to-noise ratios inherent within non-vision signal processing tasks. While they are powerful, they are currently not the method of choice in the inherently noisy and dynamic critical infrastructure domain, such as smart-grid sensing, anomaly detection, and non-intrusive load monitoring. Currently, these models can be brittle, which makes them susceptible to noisy input. This also means they have sub-optimal stability of explanation outputs. Experts and technicians using these models to make decisions in real world scenarios need assurance that a model is performing as it is supposed to. The classification or prediction outputs it generates should be sound and grounded, not likely to change in the presence of shifting noise landscapes. In this work, we explore the idea of Neural Stochastic Differential Equations (NSDE's) to improve the robustness of models trained to classify time series data and the effect of NSDE's on the explainability of outputs. We then test the effectiveness of these approaches by applying them to a non-intrusive load monitoring (NILM) dataset that consists of simulated harmonic signals injected into a real building.

Brogan, Joel↗

Preprocessing for Unintended Conducted Emissions Classification with ResNet

Characterization of Unintended Conducted Emissions (UCE) from electronic devices is important when diagnosing electromagnetic interference, performing nonintrusive load monitoring (NILM) of power systems, and monitoring electronic device health, among other applications. Prior work has demonstrated that UCE analysis can serve as a diagnostic tool for energy efficiency investigations and detailed load analysis. While explaining the feature selection of deep networks with certainty is often not fully comprehensive, or in other applications, quite lacking, additional tools/methods for further corroboration and confirmation can help further the understanding of the researcher. This is true especially in the subject application of the study in this paper. Often the focus of such efforts is the selected features themselves, and there is not as much understanding gained about the noise in the collected data. If selected feature and noise characteristics are known, it can be used to further shape the design of the deep network or associated preprocessing. This is additionally difficult when the available data are limited, as in the case which the authors investigated in this study. Here, the authors present a novel work (which is a proposed complementary portion of the overall solution to the deep network classification explainability problem for this application) by applying a systematic progression of preprocessing and a deep neural network (ResNet architecture) to classify UCE data obtained via current transformers. By using a methodical application of preprocessing techniques prior to a deep classifier, hypotheses can be produced concerning what features the deep network deems important relative to what it perceives as noise. For instance, it is hypothesized in this particular study as a result of execution of the proposed method and periodic inspection of the classifier output that the UCE spectral features are relatively close to each other or to the interferers, as systematically reducing the beta parameter of the Kaiser window produced progressively better classification performance, but only to a point, as going below the Beta of eight produced decreased classifier performance, as well as the hypothesis that further spectral feature resolution was not as important to the classifier as rejection of the leakage from a spectrally distant interference. This can be very important in unpredictable low-FNR applications, where knowing the difference between features and noise is difficult. As a side-benefit, much was learned regarding the best preprocessing to use with the selected deep network for the UCE collected from these low power consumer devices obtained via current transformers. Baseline rectangular windowed FFT preprocessing provided a 62% classification increase versus using raw samples. After performing a more optimal preprocessing, more than 90% classification accuracy was achieved across 18 low-power consumer devices for scenarios in which the in-band features-to-noise ratio (FNR) was very poor.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

A Survey of Mathematical Structures for Lunar Networks

To sustain the current and increasing accessibility of space, a scalable communications infrastructure (i.e. the Solar System Internet, SSI) is necessary. The goal of this paper is to begin the discovery of the fundamental underlying mathematical structure of space networks to help the research community harness these structures for algorithm development and optimization. To ensure the applicability of the research, the approaches are considered through the lens of simulated scenarios inspired by the Artemis Back-to-the-Moon mission set for 2024. We note that any approach to an SSI must fit under the umbrella of Delay Tolerant Networking (DTN), due to celestial mobility, high link latencies, high variance in link latencies, disconnections, lack of end-to-end paths, and so on. These difficulties are exacerbated by the fact that the underlying structure of a space network is a time-evolving network and may experience multiple discontinuities in its topology. In this paper we propose several novel approaches to a mathematical foundation for Delay Tolerant Networking Theory that fall outside the traditional scope of temporal network theory. These techniques include methods from Topological Data Analysis, Dynamic Graph Analysis, Applied Algebraic Geometry, Probability Theory, and Game Theory. Some of these methods include tools adapted to the study of dynamic metric spaces, such as zigzag persistent homology and their higher parameter analogs. We find that several of these methods target desired engineering outcomes such as discovery and automatic sub-netting. While each approach is theoretical, they are also algorithmic in nature and offer immediate practical applications. The paper concludes with comparisons of the various methods along with suggestions for future work.

Delay tolerant networking↗

Science Target Prioritization Framework for Remote Sensing

Behind the scenes of a remote sensing mission there are complex decision making and planning operations. Streamlining these operations, with a quantitative scientific value framework, aids efficient and optimized science data collection.While there have been previous efforts to quantify the science value for specific science scenarios, our work aims to develop a general framework which can be applied across different scenarios. We describe a pipeline of processes which combines model forecast and observation data, in computational forms, as dictated by the mission objectives set forth by subject matter experts. The framework is described with use cases involving the monitoring of nitrogen dioxide (NO2) concentrations over the Gulf of Mexico and methane concentrations over interior Alaska.

Remote Sensing↗

Storm-DEPART (Damage Estimate Prediction and Recovery Tool)

Storm-DEPART (Damage Estimate Prediction and Restoration Tool): Each year hurricanes and tropical storms in the United States damage critical infrastructure assets, disrupt the services they provide, and cause millions to billions of dollars in economic impacts due to extended recovery times. The Storm-DEPART tool and analytical output enable more impactful data-driven decision-making capabilities and strengthen national-level disaster preparedness, response, and recovery. Storm-DEPART, built through multi-month collaboration between Entergy and INL, combines Entergy’s critical infrastructure inventory data with weather forecasts to predict damages to Electric utility’s assets due to natural disasters and the estimated recovery support needed, including time, materials, and resource allocation. In the event of an approaching hurricane, this innovative solution can assess potential damage to power generation capacity, transmission grids, distribution networks, and communications assets from wind bands, storm surge, and flooding. With more effective predictions, Entergy can more efficiently allocate resources to mitigate impacts and optimize recovery for customers. Storm-DEPART also allows Electric utilities the ability to apply a planning scenario and model expected damage to better inform infrastructure restoration needs leading to enhance system resiliency. The technology is fully transferrable to other electric utilities with the same damage estimating challenges. The INL team is working on the evolution of Storm-DEPART to include ice event damage prediction framework.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Storm-DEPART (Damage Estimate Prediction and Recovery Tool)

Storm-DEPART (Damage Estimate Prediction and Restoration Tool): Each year hurricanes and tropical storms in the United States damage critical infrastructure assets, disrupt the services they provide, and cause millions to billions of dollars in economic impacts due to extended recovery times. The Storm-DEPART tool and analytical output enable more impactful data-driven decision-making capabilities and strengthen national-level disaster preparedness, response, and recovery. Storm-DEPART, built through multi-month collaboration between Entergy and INL, combines Entergy’s critical infrastructure inventory data with weather forecasts to predict damages to Electric utility’s assets due to natural disasters and the estimated recovery support needed, including time, materials, and resource allocation. In the event of an approaching hurricane, this innovative solution can assess potential damage to power generation capacity, transmission grids, distribution networks, and communications assets from wind bands, storm surge, and flooding. With more effective predictions, Entergy can more efficiently allocate resources to mitigate impacts and optimize recovery for customers. Storm-DEPART also allows Electric utilities the ability to apply a planning scenario and model expected damage to better inform infrastructure restoration needs leading to enhance system resiliency. The technology is fully transferrable to other electric utilities with the same damage estimating challenges. The INL team is working on the evolution of Storm-DEPART to include ice event damage prediction framework.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Modeling and analyzing parasitic parameters in high frequency converters

This research focuses on electromagnetic interference (EMI) / electromagnetic compatibility (EMC) design and analysis in power electronics systems. To limit the EMI under the standards, different methods and strategies are investigated. Parasitic parameters of high frequency (HF) transformer are analyzed using a novel analytical method, finite element method (FEM), and experimental measurements for different structures and windings arrangements. Also, the magnetic field, electric field, electric displacement, and electric potential distribution are simulated and analyzed. Moreover, a high voltage system is considered and analyzed to improve the EMC. The EMI propagation paths are analyzed. The EMI noise level of the system is obtained and compared to the IEC61800-3 standard. To improve the EMC, the parasitic parameters of the transformer, as the main path of EMI circulation, are analyzed and optimized to block the propagation. Furthermore, the geometry structure of the HF transformer is optimized to lower the parasitics in the system. Three pareto-optimal techniques are investigated for the optimization. The models and results are verified by 3D-FEM and experimental results for several given scenarios. Furthermore, the EMC modeling and conducted EMI analysis are developed for a system including an AC-DC-DC power supply (rectifier and dual active bridge (DAB) converter). Moreover, the common mode (CM) EMI noise propagation through the system is discussed and the noise sources and effect of components on the noise are analyzed. Additionally, the CM impedance of different parts of the system and the noise levels are discussed. Finally, EMI attenuation techniques were applied to the system.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Contrasting Time-Frequency Representations for Unknown Waveform Detection

In real-world applications like spectrum management and interference detection, dealing with unseen electromagnetic waveforms is critical. Although some methods attempt to simulate open set data using generator models, they face challenges in generating synthetic samples for open set while simultaneously selecting an optimal discriminator for accurate classification. This results in difficulties capturing distinctive features across classes, especially in dynamic scenarios where new classes emerge. To detect unseen waveforms, we propose combining time and frequency domain features with cosine similarity loss to enhance feature distinctiveness and enabling more accurate predictions. This approach efficiently captures more comprehensive information than single-domain representations or approaches without cosine loss. Additionally, our model avoids generic feature vectors by extracting class-specific features during training, resulting in improved class representation. The experiment results show that this combined feature approach with cosine loss outperforms single-domain models and improves accuracy by 10\% over models without cosine loss.

99 - GENERAL AND MISCELLANEOUS↗

Access and limits of RMP ELM suppression with n = 1 fields in DIII-D

This work reports on DIII-D experiments aimed at extending resonant magnetic perturbation (RMP) suppression of edge localized modes (ELMs) to n = 1 fields, where n is the toroidal mode number. Modeling of the 3D ideal MHD plasma response to the RMPs using the GPEC code is used to quantify edge and core resonant fluxes, guiding experimental strategies to increase plasma resilience against core error field penetration, optimize multicoil phasing, and explore higher q 95 operation. In DIII-D, ELM mitigation is regularly observed across a wide range of n = 1 RMP scenarios. A ∼100 ms phase of complete ELM suppression was achieved at q 95 ∼ 3.9 using an odd-parity coil configuration. The suppressed phase exhibited clear signatures of RMP ELM suppression, including the elimination of Dα spikes, increased pedestal rotation, enhanced magnetic response, and elevated broadband density turbulence. An optimized coil configuration for edge-to-core resonant flux did show increased edge resonance indicated by increased density pumpout, but did not yield RMP ELM suppression. At q 95 ∼ 5.1, a bifurcation to a grassy-like ELM regime occurred, while large type-I ELMs persisted. These results demonstrate progress in experimental access to n = 1 RMP ELM suppression in DIII-D, motivating further study for robust access. This work also highlights the potential role of 3D edge stability as well as rational surface alignment in RMP ELM suppression access, which has important implications for the use of low-n RMPs in future reactor-scale devices.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Grad–Shafranov equilibria via data-free physics informed neural networks

A large number of magnetohydrodynamic (MHD) equilibrium calculations are often required for uncertainty quantification, optimization, and real-time diagnostic information, making MHD equilibrium codes vital to the field of plasma physics. In this paper, we explore a method for solving the Grad–Shafranov equation by using physics-informed neural networks (PINNs). For PINNs, we optimize neural networks by directly minimizing the residual of the partial differential equation as a loss function. We show that PINNs can accurately and effectively solve the Grad–Shafranov equation with several different boundary conditions, making it more flexible than traditional solvers. This method is flexible as it does not require any mesh and basis choice, thereby streamlining the computational process. We also explore the parameter space by varying the size of the model, the learning rate, and boundary conditions to map various tradeoffs such as between reconstruction error and computational speed. Additionally, we introduce a parameterized PINN framework, expanding the input space to include variables such as pressure, aspect ratio, elongation, and triangularity in order to handle a broader range of plasma scenarios within a single network. Parameterized PINNs could be used in future work to solve inverse problems such as shape optimization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Overview of the KSTAR experiments and future plan

The Korea Superconducting Tokamak Advanced Research (KSTAR) device has recently entered a new phase of operation following the installation of a tungsten mono-block divertor, providing a unique platform to investigate high-performance, long-pulse plasma scenarios for future reactors. The 2023–2024 experimental campaigns demonstrated significant progress in commissioning the tungsten divertor, developing plasma operation scenarios, and achieving real-time control. Comparative studies revealed increased core radiation losses and associated performance degradation relative to the carbon divertor environment. Alleviation strategies, such as optimized neutral beam injection timing, boron powder seeding, and impurity control through gas puffing, were shown to reduce tungsten accumulation and extend high-performance phases, including record H-mode operation exceeding 100 s. International collaboration enabled the first demonstration of high poloidal beta scenarios with an internal transport barrier on KSTAR. Advances in control included upgraded real-time resonant magnetic perturbation schemes and disruption forecasting. Furthermore, divertor detachment control using a new surrogate-model-based approach with real-time radiation imaging demonstrated active impurity and heat flux management. Supported by enhanced heating, current drive, and diagnostic systems, these achievements offer valuable insights into tungsten impurity behavior, transport physics, and control strategies for future reactors including ITER. Planned upgrades toward a full-tungsten wall and ITER-aligned real-time plasma control will further establish KSTAR as a leading experimental platform for developing operational scenarios required to achieve steady-state, burning plasma conditions.

KSTAR↗

Performance, Combustion and Emissions Evaluation of Liquid Phase Port-Injected LPG on a Single Cylinder Heavy-Duty Spark Ignited Engine

Liquefied petroleum gas (LPG), like many other alternative fuels, has witnessed increased adoption in the last decade, and its use is projected to rise as stricter emissions regulations continue to be applied. However, much of its use is limited to dual fuel applications, gaseous phase injection, light-duty passenger vehicle applications, or scenarios that require conversion from gasoline engines. Therefore, to address these limitations and discover the most efficient means of harnessing its full potential, more research is required in the development of optimized fuel injection equipment for liquid port and direct injection, along with the implementation of advanced combustion strategies that will improve its thermal efficiency to the levels of conventional fuels. This paper focuses on the development of a liquid phase port-injection system for LPG, the design of a reference piston, and the baseline evaluation of the performance, combustion, and emissions characteristics of a single cylinder research engine to establish a benchmark comparable to existing LPG engines. A sweep of start of injection (SOI) timing is performed by injecting liquid LPG at several closed and open intake valve timings, which demonstrates no significant variation in engine performance, but accounts for a 10% reduction in bsCO with the optimal SOI timing. Spark timing sweep demonstrates the 50% burn crank angle location related to maximum brake torque (MBT) point with a brake thermal efficiency (BTE) of ~34% for the tested load case. The effect of equivalence ratio is also presented with optimal SOI timing at MBT condition. The engine starts exhibiting knocking combustion at 140kPa intake manifold air pressure (IMAP) with a peak torque of 253Nm and a 5% reduction in brake specific fuel consumption compared to the naturally aspirated scenario.

Fosudo, Toluwalase↗

Micromobility Integrated Transit and Infrastructure for Efficiency (MITIE)

Nearly omnipresent in many cities of all sizes across the United States, micromobility vehicles-e-scooters, manual bicycles, e-bicycles, and larger seated electric scooters-are notably missing from SMART Mobility research. This project aims to expand the spectrum of modes currently being researched within SMART Mobility by exploring micromobility as an important tool toward meeting energy-efficient mobility goals. It expands on findings from SMART Mobility 1.0 that revealed preferences to reduce transportation-related expenses through use of a network of mobility-as-a-service (MaaS) and other shared mobility options, and builds on findings from a 2019 Vehicle Technology Analysis Program (VTAP) funded micromobility project conducted by our team. We will explore multiple facets of micromobility, including behavior and decision-making, the integration of micromobility within transportation infrastructure, energy estimates, and operations. Guiding research questions include: (1) What are the potential energy savings from low, medium, and high market penetration of micromobility (in passenger, multimodal, and freight domains)? (2) Which scenarios for micromobility use and related enablement of increased public transit use should be modeled/considered in the SMART 2.0 Workflow? (3) To what degree can micromobility supplement/complement transit system operations? (4) What are people's preferences towards micromobility? How do preferences vary across various sociodemographic segments? How can this knowledge inform operations? (5) What are optimal strategies to attain high user adoption and shift users toward more energy-efficient mode choices in terms of micromobility operation? How do these strategies affect energy savings, person-miles traveled, lifecycle energy use, and adoption rates? These questions will be addressed through applied research in five project emphasis areas: (1) Energy estimates of micromobility for Workflow scenarios: Expand and refine previous micromobility work to augment the Workflow approaches to modeling urban travel. (2) Multimodal connection with transit: Utilizing Mobility-Energy Productivity (MEP) tools to evaluate multimodal travel patterns enabled by micromobility, including assessing how to reduce barriers of inequity of access to mobility options and destinations. (3) Mode choice, induced demand, and infrastructure: Understanding the mode shift induced through micromobility to inform energy impact analysis. (4) Energy optimization of micromobility operations: Identification of micromobility operations parameters and development of operations scenarios to better understand present-day micromobility operations for integration into the Workflow, in partnership with BEAM and POLARIS modeling teams. (5) Micro-freight: Characterize the current state of micro-freight activities, including energy effects and geospatial analyses, to inform Workflow.

ADVANCED PROPULSION SYSTEMS,POWER TRANSMISSION AND↗

Micromobility Integrated Transit and Infrastructure for Efficiency (MITIE)

Nearly omnipresent in many cities of all sizes across the United States, micromobility vehicles-e-scooters, manual bicycles, e-bicycles, and larger seated electric scooters-are notably missing from SMART Mobility research. This project aims to expand the spectrum of modes currently being researched within SMART Mobility by exploring micromobility as an important tool toward meeting energy-efficient mobility goals. It expands on findings from SMART Mobility 1.0 that revealed preferences to reduce transportation-related expenses through use of a network of mobility-as-a-service (MaaS) and other shared mobility options, and builds on findings from a 2019 Vehicle Technology Analysis Program (VTAP) funded micromobility project conducted by our team. We will explore multiple facets of micromobility, including behavior and decision-making, the integration of micromobility within transportation infrastructure, energy estimates, and operations. Guiding research questions include: 1) what are the potential energy savings from low, medium, and high market penetration of micromobility (in passenger, multimodal, and freight domains)? 2) which scenarios for micromobility use and related enablement of increased public transit use should be modeled/considered in the SMART 2.0 Workflow? 3) to what degree can micromobility supplement/complement transit system operations? 4) what are people's preferences towards micromobility? How do preferences vary across various sociodemographic segments? How can this knowledge inform operations? 5) what are optimal strategies to attain high user adoption and shift users toward more energy-efficient mode choices in terms of micromobility operation? How do these strategies affect energy savings, person-miles traveled, lifecycle energy use, and adoption rates? These questions will be addressed through applied research in five project emphasis areas: 1) energy estimates of micromobility for Workflow scenarios: Expand and refine previous micromobility work to augment the Workflow approaches to modeling urban travel; 2) multimodal connection with transit: Utilizing Mobility-Energy Productivity (MEP) tools to evaluate multimodal travel patterns enabled by micromobility, including assessing how to reduce barriers of inequity of access to mobility options and destinations; 3) mode choice, induced demand, and infrastructure: Understanding the mode shift induced through micromobility to inform energy impact analysis; 4) energy optimization of micromobility operations: Identification of micromobility operations parameters and development of operations scenarios to better understand present-day micromobility operations for integration into the Workflow, in partnership with BEAM and POLARIS modeling teams; 5) micro-freight: Characterize the current state of micro-freight activities, including energy effects and geospatial analyses, to inform Workflow.

ADVANCED PROPULSION SYSTEMS↗

Distinguishing Charged Lepton Flavor Violation Scenarios with Inelastic 𝜇 → 𝑒 Conversion

The Mu2e and COMET experiments are expected to improve existing limits on charged lepton flavor violation (CLFV) by roughly 4 orders of magnitude. 𝜇 → 𝑒 conversion experiments are typically optimized for electrons produced without nuclear excitation, as this maximizes the electron energy and minimizes backgrounds from the free decay of the muon. Here we argue that Mu2e and COMET will be able to extract additional constraints on CLFV from inelastic 𝜇 → 𝑒 conversion, given the 27 Al target they have chosen and backgrounds they anticipate. We describe CLFV scenarios in which inelastic CLFV can induce measurable distortions in the near-endpoint spectrum of conversion electrons, including cases where certain contributing operators cannot be probed in elastic 𝜇 → 𝑒 conversion. We extend the nonrelativistic EFT treatment of elastic 𝜇 → 𝑒 conversion to include the new nuclear operators needed for the inelastic process, evaluate the associated nuclear response functions, and describe several new-physics scenarios where the inelastic process can provide additional information on CLFV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Engineering calculations for communications satellite systems planning

Computer-based techniques for optimizing communications-satellite orbit and frequency assignments are discussed. A gradient-search code was tested against a BSS scenario derived from the RARC-83 data. Improvement was obtained, but each iteration requires about 50 minutes of IBM-3081 CPU time. Gradient-search experiments on a small FSS test problem, consisting of a single service area served by 8 satellites, showed quickest convergence when the satellites were all initially placed near the center of the available orbital arc with moderate spacing. A transformation technique is proposed for investigating the surface topography of the objective function used in the gradient-search method. A new synthesis approach is based on transforming single-entry interference constraints into corresponding constraints on satellite spacings. These constraints are used with linear objective functions to formulate the co-channel orbital assignment task as a linear-programming (LP) problem or mixed integer programming (MIP) problem. Globally optimal solutions are always found with the MIP problems, but not necessarily with the LP problems. The MIP solutions can be used to evaluate the quality of the LP solutions. The initial results are very encouraging.

Reilly, C. H.↗