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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 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Numerical and experimental investigation of the flame kernel growth in a methane/air mixture near the lean flammability limit

Lean combustion has the potential to improve the thermal efficiency of spark-ignition engines, but it faces the significant challenge of increased cycle-to-cycle variation due to low mixture reactivity and unstable flame dynamics. Computational fluid dynamics (CFD) employing predictive models can guide engine design and optimize operating strategies for lean combustion. However, ignition and combustion models have rarely been validated at fuel-lean conditions, and a fundamental understanding of the early flame kernel growth process is also lacking for a successful sub-model development. Here, the present study develops a numerical simulation framework used to investigate early flame kernel growth in methane/air mixtures. A nanosecond-pulsed discharge (NPD) approach is employed to effectively decouple the flame kernel growth from the electrical discharge due to their difference in timescales, and equivalence ratios near the experimentally measured lean flammability limit (LFL) are selected to focus on challenging mixture conditions. Three numerical investigations, such as the choice of turbulence modeling, grid size, and grid control strategies, are examined to match both LFL and flame kernel structure measured from experiments. It is demonstrated that a quasi-direct numerical simulation (QDNS) with a fixed grid embedding of 10 μm can predict the LFL as φ CFD =0.61 and match the displacement speed of the kernel’s boundary marked in schlieren images. To predict the LFL and flame kernel shape, a fine grid (Δ≤12.5 μm) is needed to capture the consumption of formaldehyde (CH 2 O) in kernel’s reaction branches attached to the anode, and adaptive mesh refinement is replaced with the fixed embedding due to loss of simulation accuracy. Also, it is found that a large-eddy simulation (LES) using the Dynamic Structure model is not suitable for the NPD-induced flame kernel simulation because artificial sub-grid turbulent kinetic energy induced by shock dynamics alters the flow velocity calculation, resulting in divergence of LES from QDNS. Lastly, the simulation well matches the experimental data for the flame kernel evolution in three mixture conditions (φ = 0.7, 0.61, 0.55), showing toroidal flame kernel expansion and flame kernel growth/extinction.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2026

Spatial Correlations of the Poisson Model for Radiation Transport

Characterizing the relationship between bulk physical properties and mixing in randomly heterogeneous media is a central challenge across many areas of science and engineering. A benchmark model for such studies is the Poisson model, a random tessellation of space by a Poisson process of hyperplanes. In radiation transport studies, the lack of exact expressions for the Poisson model’s spatial multipoint functions has led to approximate methods being used, introducing unquantified sources of error. Here, we recently introduced an exact solution for the Poisson model’s multipoint functions and closely related conditional probability functions (CPFs), providing a new opportunity to understand and reduce these sources of error. In this paper, we enable a more rigorous investigation of radiation transport in stochastic media by applying the recently introduced exact solution for the Poisson model’s CPFs. This paper consists of three main contributions. First, we introduce a unified framework for CPFs of the Poisson model, encompassing the recently introduced exact CPFs as well as the previously introduced atomic mix, nearest-neighbor, and combination CPFs. This framework also includes existing pruning techniques for the approximate CPFs, such as angular exclusion, as well as a novel form of angular exclusion suitable for the exact CPFs. Second, we use the exact CPFs to characterize the spatial regions where each approximate three-point CPF is most accurate, thereby explaining the observed hierarchy of accuracy among the approximate models. Finally, we evaluate material transmittance, reflectance, and flux in a three-dimensional test problem using conditional point sampling, demonstrating the relationship between CPF accuracy and transport simulation accuracy.

Poisson model↗
DOE OSTI2021

Autoignition and preliminary heat release of gasoline surrogates and their blends with ethanol at engine-relevant conditions: Experiments and comprehensive kinetic modeling

This work utilizes a rapid compression machine (RCM) to experimentally quantify autoignition and preliminary heat release characteristics for blends of 0 to 30% ethanol by volume into two surrogates (FGF-LLNL and FGF-KAUST) that represent a full boiling range gasoline (FACE-F). Experimental conditions cover pressures from 15 to 100 bar, temperatures from 700 to 1000 K, and diluted/stoichiometric and undiluted/lean fuel loading conditions representative of boosted spark-ignition and advanced compression ignition engines, respectively. Direct comparison is made with previously reported results for FACE-F/E0–E30 blends. Here, a detailed gasoline surrogate chemistry model is also proposed, and chemical kinetic modeling is undertaken using the proposed model to generate chemical insights into the compositional effects and ethanol blending effects.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Modeling a Sodium Heat Pipe Experiment at SPHERE Using Sockeye

The Single Primary Heat Extraction and Rejection Emulator (SPHERE) facility at Idaho Na- tional Laboratory was recently utilized to generate data for the startup and steady operation of a high-performance, sodium heat pipe over the course of 1000 hours, as a test of detrimental, long-term effects of heat pipe operation. The setup consists of a single, sodium heat pipe enclosed in a stainless-steel vacuum chamber, heated radiatively via a cylindrical ceramic fiber heater configuration and cooled via a water-cooled calorimeter. Measurements include temperatures at several axial locations along the outer surface of the heat pipe, the power provided to the heaters, and the heat removal rate of the calorimeter. In this work, this data is utilized to validate heat pipe models in the heat pipe application Sockeye, which is based upon the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework. Sockeye provides various heat pipe models at an engineering scale appropriate for the multiphysics simulation of microreactors, which may feature several hundred heat pipes. This work details models of this experiment in SPHERE using various heat pipe models with Sockeye, including heat conduction-based models and compressible flow models of the heat pipe interior. These models are compared to the experimental data to assess the accuracy of several aspects of heat pipe modeling, including frozen startup, the effect of non-condensable gases, and the coupling of the heat pipe to its environment.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Modeling a Sodium Heat Pipe Experiment at SPHERE Using Sockeye

The Single Primary Heat Extraction and Rejection Emulator (SPHERE) facility at Idaho National Laboratory was recently utilized to generate data for the startup and steady operation of a high-performance, sodium heat pipe over the course of 1,000 hours to test the detrimental, long-term effects of heat pipe operation. The setup consisted of a single, sodium heat pipe enclosed in a stainless-steel vacuum chamber, heated radiatively via a cylindrical ceramic-fiber heater configuration and cooled via a water-cooled calorimeter. Measurements included temperatures at several axial locations along the outer surface of the heat pipe, the power provided to the heaters, and the heat removal rate of the calorimeter. In this work, we use this data to validate heat pipe models in Sockeye, a heat pipe application based on the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework. Sockeye provides various heat pipe models at an engineering scale appropriate for the multiphysics simulation of microreactors, which may feature several hundred heat pipes. This work details models of this experiment at SPHERE using various heat pipe models with Sockeye, including heat-conduction-based and compressible flow models of the heat pipe interior.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Development and evaluation of a skeletal mechanism for EHN additized gasoline mixtures in large Eddy simulations of HCCI combustion

Advanced Low Temperature Combustion modes, such as the Sandia proposed Additive-Mixing Fuel Injection (AMFI), can unlock significant potential to boost fuel conversion efficiency and ultimately improve the energy conversion of internal combustion engines. This is a novel improved combustion process that is enabled by supplying small (<5%) variable amounts of autoignition improver to the fuel to enhance the engine operation and control. Common, diesel-fuel ignition-quality enhancing additive, 2-ethylexyl nitrate (EHN), is doped into gasoline to enable Sandia LTGC + AMFI combustion. This manuscript focuses on the development of a reduced sub-mechanism for EHN chemical kinetics at engine relevant conditions that is implemented into a skeletal mechanism for chemical kinetic studies of gasoline surrogate fuels. The mechanism validation utilized zero-dimensional numerical simulations and comparison to shock tube ignition-delay data of pure and EHN-doped n-heptane. Additional validation is presented with Homogeneous Charge Compression-Ignition (HCCI) engine data of pure and EHN-doped research-grade E10 gasoline. Then, the mechanism was deployed in a 3-D computational fluid dynamics (CFD) using Large Eddy Simulations (LES) to model the HCCI engine experiments of 0.4% vol EHN additized E10 gasoline at several equivalence ratios. Simulations showed a very good performance of the mechanism, and the model accurately reproduced (a) the ignition point, (b) combustion phasing, (c) combustion duration, and (d) the peak of the heat release rates of the engine experiments. The results show that EHN promotes Low-Temperature Heat Release, ultimately driving the gasoline to autoignite at thermodynamic conditions where the fuel would not otherwise ignite. Overall, this work demonstrates a viable reduced chemical-kinetic mechanism for EHN and shows that it can be combined with a skeletal gasoline mechanism for CFD-LES analysis of well-mixed LTGC that matches well with experimental results. The CFD-LES analysis also shows the spatial distribution of EHN-fuel interactions that control the autoignition throughout the combustion chamber.

Guleria, Gaurav↗
DOE OSTI2025

Design and Demonstration of a NH3-Fueled Two-Stroke Uniflow Engine for Greenhouse Gas Reduction

The maritime shipping industry is growing increasingly interested in both low and non-carbon-containing fuels to meet future greenhouse gas emission targets. Specifically of interest is ammonia, as it has a relatively high volumetric energy density compared to other future fuels, such as hydrogen, making it more economical to transport. The robust engine architecture of low-speed two-stroke marine engines makes them an ideal candidate for ammonia fuel, overcoming many of the issues surrounding its poor ignitability and low flame speed. If emissions and fueling system challenges can be addressed, retrofits of current low-speed two-stroke dual-fuel engines represent a viable pathway for bringing ammonia engines to market. This study explores these technical hurdles by describing the design, analysis, and experimental validation of a single cylinder research engine converted to operate on ammonia fuel. The engine is a reduced-scale uniflow two-stroke marine engine with two previous hardware configurations available – diesel and high-pressure CNG dual-fuel. A concept study was used to evaluate possible ammonia-fueled engine architectures and the associated tradeoffs and design considerations. With the chosen architecture, low-pressure dual fuel, 1D and 3D analysis tools were used to inform hardware selection and to determine hardware configurations which minimized ammonia-slip. In addition to these considerations the hardware and engine configuration were designed to provide a versatile and robust testing platform. This includes options to test both gaseous and liquid ammonia injection, as well as a wide range of performance parameters such as AFR, swirl, valve timing, SOI, and many others. Design constraints imposed by the existing engine hardware necessitated an iterative loop between design and analysis toolsets, ultimately converging on a final design for the ammonia-conversion hardware. The engine was rebuilt with the new hardware and evaluated in an engine test cell. A new control strategy developed and flashed onto a prototyping electronic control unit allowed for full control over all engine parameters. An initial calibration was developed, providing test data for validation of the engine 1D and 3D models. The impact of the design choices on engine operability and the ability to meet program targets is discussed as well as opportunities for further optimization of the ammonia-conversion hardware, informed by the validated models.

Kaul, Brian [ORNL] (ORCID:0000000184813620)↗
DOE OSTI2020

Grimsel Test Site - A Successful International Underground Research Laboratory for Many Decades - 20429

For more than 35 years, Nagra and its partners from around the world have been conducting underground research projects at the Grimsel Test Site (GTS, www.grimsel.com) to contribute to the development and confirmation of safe geological disposal concepts and for the characterization of suitable host rock formations. Over the years, the results of this internationally recognized research program have been, and continue to be, incorporated directly into exploration programs, modelling, safety, and engineering feasibility studies on options for deep geological repositories. Each project of the GTS program involves field-testing, laboratory studies, design and modelling tasks, and integrates all scientific and technical aspects. Each project phase is planned with a duration of three to five years to facilitate practical and administrative aspects and allow flexibility for updating the overall project plans with the latest findings. Scientific and engineering interaction among the different projects is ensured via an international steering committee meeting. Hosting an IAEA level C radiation- controlled zone, which allows use of radionuclides, including actinides such as thorium, uranium, neptunium, plutonium and americium, in in-situ experiments is one of the reasons why GTS also developed as a center of excellence for work with radioactive tracers under realistic in-situ boundary conditions. Last year, a new five-year program (2019 to 2023) started which includes projects with a planning horizon of decades. The new five-year program includes a new phase of in-situ experiments using radionuclides such as migration experiments in the Colloid Formation and Migration project (CFM), the Long-Term Diffusion experiment (LTD) and the newly established C-14 and I-129 Migration in cement project (CIM). The 'High Temperature effects on Bentonite' (HotBENT) project is starting in the current phase and is studying the effects of elevated temperatures (>175 deg. C) on bentonite materials. As a generic underground research laboratory (URL) it is expected that the GTS will provide in the coming years a platform for international collaboration, knowledge development and knowledge transfer for the next generation of scientists and engineers in the area of radioactive waste disposal and geosciences. A key role regarding knowledge transfer and training is provided by the well-established Grimsel Training Center (GTC), which (beside many URL related issues) also covers many general aspects of radioactive waste management. In this paper we provide an overview of the current program at the GTS, focusing on the experiments that study the migration of radionuclides through engineered barrier materials and the geosphere. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

Numerical modeling of hydrogen mixing in a direct-injection engine fueled with gaseous hydrogen

Hydrogen is considered as one of the most promising options to achieve effective decarbonization of the energy and transportation sectors. As such, it has recently been receiving increasing attention because of its promising potential as an energy carrier for advanced energy and propulsion systems. With a focus on internal combustion engines, direct injection (DI) of gaseous hydrogen during the compression stroke offers great potential for high engine efficiency and specific power while reducing the risk of backfiring and pre-ignition issues. Therefore, many experimental and numerical efforts have recently been dedicated to understanding the physical and chemical behaviors of hydrogen in engine during mixing and combustion. This study focuses on computational fluid dynamics (CFD) modeling of the hydrogen DI process in a hydrogen optical research engine. Under the conditions studied, gaseous hydrogen is injected into the combustion chamber via a centrally located single-hole injector at a pressure of 100 bar. Two configurations, namely low-and high-tumble, are investigated to understand the impact of different in-cylinder flow patterns on the fuel-air mixture preparation. Simulations are carried out using the commercial CFD software CONVERGE. Here, the in-cylinder turbulence is modeled with an unsteady Reynolds-averaged Navier-Stokes (URANS) formulation closed by the renormalization group (RNG) k-ε model. Several numerical methods and model constants, including but not limited to turbulent Schmidt number, are evaluated. The numerical results are systematically compared against experimental measurements of velocity and hydrogen concentration fields on the vertical center plane to assess the performance of the CFD model, unveil the physics of hydrogen mixing, and establish best practices for modeling hydrogen DI under relatively high injection pressure conditions.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2023

Fuel-air mixing in motored CFR engine at research octane number (RON) relevant condition

This paper presents a three-dimensional (3-D) computational fluid dynamics (CFD) study of a motored cooperative fuel research (CFR) engine at research octane number (RON) relevant condition. The boundary conditions for 3-D simulations were generated with a one-dimensional GT-Power model. For the first time in literature, a carburetor was added to a virtual CFR engine model with 3-D CFD. Therefore, the proposed setup can simulate the fuel and thermal stratifications inside the engine cylinder with realistic detail. The transient simulations in this work were performed within the Reynolds-averaged Navier-Stokes (RANS) framework with a Realizable k-ε turbulence model. Major conclusions from the present work are: (1) The in-cylinder flow of the CFR engine is swirl-dominated due to the existence of the intake valve shroud. (2) There is a significant amount of liquid droplets entering the cylinder during the intake stroke. The maximum instantaneous amount of liquid for 50% PRF 87 (containing 87% iso-octane and 13% n-heptane (v/v)) and 50% ethanol mixture is indicated to be around 26% of total injected fuel mass. (3) The heat of vaporization (HoV) of the fuel is responsible for creating both temperature and charge stratification inside the cylinder.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2021

Biological Carbon Sequestration for Climate and Soil Health

The United States recently launched the Net Zero World Initiative on decarbonization. As temperatures and sea levels rise, strong action is needed to mitigate high atmospheric CO 2 levels. In response to this need, a joint workshop between the US Department of Energy’s Oak Ridge National Laboratory (ORNL) and Lawrence Berkeley National Laboratory (LBNL) was convened to assess the challenges and opportunities within biological carbon (C) capture. The virtual workshop on Biological Carbon Sequestration for Climate and Soil Health focused on three aspects of biological C capture research: natural systems, engineered systems, and modeling. For this workshop, the scope of natural systems included unmanaged (e.g., grasslands, wetlands, natural forests) and managed (e.g., agricultural lands, commercial forests, forest biofuels) ecosystems. The engineered systems group covered topics in genetically modified plants and microbes, synthetic microbiomes, and altered plant–microbe interactions for enhancing C capture, storage, and utilization. The modeling group focused on computational tools and data collection to predict and assess the effectiveness of new biocarbon sequestration advances. Participant expertise included plant and microbial systems biology, synthetic biology, soil biogeochemistry, and techno-economic analysis. Together, participants outlined key scientific advances in support of biological C capture and storage. Among the major findings of the meeting were the need to better measure C flux within natural, agricultural, and fabricated ecosystems for experimentation; better understand the role of soil composition, plant roots, and the rhizosphere (i.e., the soil surrounding the plant root) in the underground storage of organic C; and design plant–microbe systems for maximal C storage.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

An Improved CRISPR Interference Tool to Engineer Rhodococcus opacus

Rhodococcus opacus is a non-model bacterium that is well suited for valorizing lignin. Despite recent advances in our systems-level understanding of its versatile metabolism, studies of its gene functions at a single gene level are still lagging. Elucidating gene functions in non-model organisms is challenging due to limited genetic engineering tools that are convenient to use. To address this issue, we developed a simple gene repression system based on CRISPR interference (CRISPRi). This gene repression system uses a T 7 RNA polymerase system to express a small guide RNA, demonstrating improved repression compared to the previously demonstrated CRISPRi system (i.e., the maximum repression efficiency improved from 58% to 85%). Additionally, our cloning strategy allows for building multiple CRISPRi plasmids in parallel without any PCR step, facilitating the engineering of this GC-rich organism. Using the improved CRISPRi system, we confirmed the annotated roles of four metabolic pathway genes, which had been identified by our previous transcriptomic analysis to be related to the consumption of benzoate, vanillate, catechol, and acetate. Furthermore, we showed our tool’s utility by demonstrating the inducible accumulation of muconate that is a precursor of adipic acid, an important monomer for nylon production. While the maximum muconate yield obtained using our tool was 30% of the yield obtained using gene knockout, our tool showed its inducibility and partial repressibility. In conclusion, our CRISPRi tool will be useful to facilitate functional studies of this non-model organism and engineer this promising microbial chassis for lignin valorization.

09 BIOMASS FUELS↗
DOE OSTI2023

Tencoder: tensor-product encoder-decoder architecture for predicting solutions of PDEs with variable boundary data

It is widely hoped that artificial intelligence will boost data-driven surrogate models in science and engineering. However, fundamental spatial aspects of AI surrogate models remain under-studied. We investigate the ability of neural-network surrogate models to predict solutions to PDEs under variable boundary values. We do not wish to retrain the model when the boundary values change but to make them inputs to the model and infer the solution of the PDE under those boundary conditions. Such a capability is essential to making AI-based surrogate models practically useful. While simple feedforward networks are used for one-dimensional (1D) Poisson equation, an encoder-decoder architecture with a tensor-product layer is developed for the two-dimensional Poisson equation posed on a rectangular domain. We show that it is indeed possible to infer solutions to PDEs from variable boundary data using neural networks in this relatively simple setting, and point to future directions.

Kashi, Aditya↗
DOE OSTI2021

Addressing Human and Organizational Factors In Nuclear Industry Modernization: A Sociotechnically-Based Strategic Framework

The modernization of nuclear power plants will require an advanced concept of operations, involving an integrated set of tightly coupled systems in which all stakeholders act in a coordinated manner. For this modernization effort to be enabled, we developed a human and organizational factors approach, based on a broad sociotechnical framework. Starting from core human factors principles, we conducted a literature review of the methods and approaches relevant to the modernization problem. These included core disciplines such as cognitive systems engineering, systems theoretic accident modeling and processes (STAMP), human systems integration, resilience engineering, and macroergonomics but also related topics of safety culture and organizational change. From this literature, we developed a conceptual framework centered around the work system with its four interacting components: people, technology, process, and governance. In an effective work system, these four components are jointly optimized according to three systems criteria: efficiency, effectiveness, and safety. System failure may result from excessive emphasis on any one criterion. The actual work of attaining joint optimization in a given work system can be accomplished by utilizing three high level functions: knowledge elicitation, knowledge representation, and cross-functional integration. We illustrated the utility of this approach by applying it to practical problems and case studies. The complete report is available in [1]; this paper is a description of our approach and report contents.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2021

Multidimensional Numerical Modeling of Combustion Dynamics in a Non-Premixed Rotating Detonation Engine With Adaptive Mesh Refinement

In the present work, a novel computational fluid dynamics (CFD) methodology was developed to simulate full-scale non-premixed rotating detonation engines (RDEs). A unique feature of the modeling approach was the incorporation of adaptive mesh refinement (AMR) to achieve a good trade-off between model accuracy and computational expense. Here, unsteady Reynolds-averaged Navier–Stokes (RANS) simulations were performed for an Air Force Research Laboratory (AFRL) non-premixed RDE configuration with hydrogen as fuel and air as the oxidizer. The finite-rate chemistry model, along with a ten-species detailed kinetic mechanism, was employed to describe the H 2 -Air combustion chemistry. Three distinct operating conditions were simulated, corresponding to the same global equivalence ratio of unity but different fuel/air mass flowrates. For all conditions, the capability of the model to capture essential detonation wave dynamics was assessed. An exhaustive verification and validation study was performed against experimental data in terms of a number of waves, wave frequency, wave height, reactant fill height, oblique shock angle, axial pressure distribution in the channel, and fuel/air plenum pressure. The CFD model was demonstrated to accurately predict the sensitivity of these wave characteristics to the operating conditions, both qualitatively and quantitatively. A comprehensive heat release analysis was also conducted to quantify detonative versus deflagrative burning for the three simulated cases. The present CFD model offers a potential capability to perform rapid design space exploration and/or performance optimization studies for realistic full-scale RDE configurations.

42 ENGINEERING↗
DOE OSTI2023

Validation of IMEP on Alcator C-Mod and JET-ILW ELMy H-mode plasmas

Abstract The recently developed integrated model based on engineering parameters (IMEP) (Luda et al 2020 Nucl. Fusion 61 126048; Luda et al 2021 Nucl. Fusion 60 036023), so far validated on ASDEX Upgrade, has been tested on a database of 3 Alcator C-Mod and 55 JET-ILW ELMy (type I) H-mode stationary phases. The empirical pedestal transport model included in IMEP, consisting now of imposing a fixed value of R < ∇ T e > / T e , t o p = − 82.5 , allows an accurate prediction of the pedestal top temperature (when the pedestal top density is fixed to the experimental measurements) across these three machines with different sizes, when the pedestal is peeling–ballooning (PB) limited. Cases far from the ideal PB boundary, corresponding to high edge Spitzer resistivity, are instead strongly overpredicted by IMEP. A comparison between the predictions of Europed and IMEP for a subset of JET-ILW cases shows that IMEP can more accurately reproduce the experimental pedestal width. This allows IMEP to better capture profile effects on the pedestal stability, and therefore to correctly describe the negative effect of fueling on the pedestal pressure for PB limited cases. A strong correlation between the separatrix density and the fueling rate has been identified for a subset of JET-ILW cases, when taking into account different divertor configurations. Overall, these promising results encourage further developments of integrated models to obtain reliable predictions of pedestal and global confinement using only engineering parameters for present and future machines.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Convex Optimization of Integrated Power-Gas Energy Flow Model With Applications to Probabilistic Energy Flow

Energy flow calculation is a fundamental problem of the integrated power and gas system (IPGS) operation and planning. However, the nonlinear gas flow model introduces major challenges to the energy flow calculation. In this paper, we propose a tractably convex optimization model to solve the energy flow problem in IPGSs. It is demonstrated that the proposed optimization model has the same optimal solution as the original nonlinear steady energy flow model. Also, piecewise linearization is adopted to tightly linearize the nonlinear objective function of the model, which transforms the formulated convex optimization into a linear program one. Thus, the computation complexity of the proposed energy flow model is significantly reduced as compared with the existing methods. In addition, the proposed model can be extended to probabilistic energy flow estimation. Extensive case studies are conducted to validate the effectiveness of the proposed energy flow model using three IPGSs.

42 ENGINEERING↗