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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Cybersecurity for Electric Vehicle Charging Infrastructure

As the U.S. electrifies the transportation sector, cyberattacks targeting vehicle charging could impact several critical infrastructure sectors including power systems, manufacturing, medical services, and agriculture. This is a growing area of concern as charging stations increase power delivery capabilities and must communicate to authorize charging, sequence the charging process, and manage load (grid operators, vehicles, OEM vendors, charging network operators, etc.). The research challenges are numerous and complicated because there are many end users, stakeholders, and software and equipment vendors interests involved. Poorly implemented electric vehicle supply equipment (EVSE), electric vehicle (EV), or grid operator communication systems could be a significant risk to EV adoption because the political, social, and financial impact of cyberattacks — or public perception of such — would ripple across the industry and produce lasting effects. Unfortunately, there is currently no comprehensive EVSE cybersecurity approach and limited best practices have been adopted by the EV/EVSE industry. There is an incomplete industry understanding of the attack surface, interconnected assets, and unsecured inter faces. Comprehensive cybersecurity recommendations founded on sound research are necessary to secure EV charging infrastructure. This project provided the power, security, and automotive industry with a strong technical basis for securing this infrastructure by developing threat models, determining technology gaps, and identifying or developing effective countermeasures. Specifically, the team created a cybersecurity threat model and performed a technical risk assessment of EVSE assets across multiple manufacturers and vendors, so that automotive, charging, and utility stakeholders could better protect customers, vehicles, and power systems in the face of new cyber threats.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Securing Vehicle Charging Infrastructure

As the US electrifies the transportation sector, cyber attacks targeting vehicle charging could bring consequences to electrical system infrastructure. This is a growing area of concern as charging stations increase power delivery and must communicate to a range of entities to authorize charging, sequence the charging process, and manage load (grid operators, vehicles, OEM vendors, charging network operators, etc.). The research challenges are numerous and are complicated because there are many end users, stakeholders, and software and equipment vendors interests involved. Poorly implemented electric vehicle supply equipment (EVSE), electric vehicle (EV), or grid communication system cybersecurity could be a significant risk to EV adoption because the political, social, and financial impact of cyberattacks - or public perception of such - ripples across the industry and has lasting and devastating effects. Unfortunately, there is no comprehensive EVSE cybersecurity approach and limited best practices have been adopted by the EV/EVSE industry. There is an incomplete industry understanding of the attack surface, interconnected assets, and unsecured interfaces. Thus, comprehensive cybersecurity recommendations founded on sound research are necessary to secure EV charging infrastructure. This project is providing the power, security, and automotive industry with a strong technical basis for securing this infrastructure by developing threat models, determining technology gaps, and identifying or developing effective countermeasures. Specifically, the team is creating a cybersecurity threat model and performing a technical risk assessment of EVSE assets, so that automotive, charging, and utility stakeholders can better protect customers, vehicles, and power systems in the face of new cyber threats.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2020

A neural network for determination of latent dimensionality in Nonnegative Matrix Factorization

Non-negative Matrix Factorization (NMF) has proven to be a powerful unsupervised learning method for uncovering hidden features in complex and noisy datasets with applications in data mining, text recognition, dimension reduction, face recognition, anomaly detection, blind source separation, and many other fields. An important input for NMF is the latent dimensionality of the data, that is, the number of hidden features, K, present in the explored dataset. Unfortunately, and this quantity is rarely known a priori. The existing methods for determining latent dimensionality, such as Automatic Relevance Determination (ARD), are mostly heuristic and utilize different characteristics to estimate the number of hidden features. However, all of them require human presence to make a final determination of K. Here we utilize a supervised machine learning approach in combination with a recent method for model determination, called NMFk, to determine the number of hidden features automatically. NMFk performs a set of NMF simulations on an ensemble of matrices, obtained by bootstrapping the initial dataset, and estimates which K produces stable groups of latent features that reconstruct the initial dataset well. We then train a Multi-Layter Perceptron (MLP) classifier network to determine the correct number of latent features utilizing the statistics and characteristics of the NMF solution, obtained from NMFk. In order to train the MLP classifier, a training set of 58,660 matrices with predetermined latent features were factorized with NMFk. The MLP classifier in conjunction with NMFk maintains a greater than 95% success rate when applied to a held out test set. Additionally, when applied to two well-known benchmark datasets, the swimmer and MIT face data, NMFk/MLP correctly recovers the established number of hidden features. Finally, we compare the accuracy of our method to the ARD, AIC and Stability-based methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A novel transformation of the ice sheet Stokes equations and some of its properties and applications

We introduce a novel transformation of the Stokes equations into a form closely resembling the shallow Blatter–Pattyn equations. The two forms differ by only a few additional terms, while their variational formulations differ only by a single term in each horizontal direction. Specifically, the variational formulation of the Blatter–Pattyn model drops the vertical velocity in the second invariant of the strain rate tensor. Here we make use of the new transformation in two ways. First, we consider incorporating the transformed equations into a code that can be very easily converted from a Stokes to a Blatter–Pattyn model, and vice versa, by switching these terms on or off. This may be generalized so that the Stokes model is switched on adaptively only where the Blatter–Pattyn model loses accuracy. Second, the key role played by the vertical velocity in the Blatter–Pattyn approximation motivates new approximations. Two examples are presented. These require a mesh that enables the discrete continuity equation to be invertible for the vertical velocity in terms of the horizontal velocity components. Examples of such meshes, such as the first-order P1–E0 mesh and the second-order P2–E1 mesh, are given in both 2D and 3D. However, the transformed Stokes model has the same type of gravity forcing as the Blatter–Pattyn model, determined by the ice surface slope, thereby forgoing some of the mesh generality of the traditional formulation of the Stokes model.

58 GEOSCIENCES↗
DOE OSTI2020

Distributed non-negative matrix factorization with determination of the number of latent features

The holistic analysis and understanding of the latent (that is, not directly observable) variables and patterns buried in large datasets is crucial for data-driven science, decision making and emergency response. Such exploratory analyses require devising unsupervised learning methods for data mining and extraction of the latent features, and non-negative matrix factorization (NMF) is one of the prominent such methods. NMF is based on compute-intense non-convex constrained minimization, which, for large datasets requires fast and distributed algorithms. However, current parallel implementations of NMF fail to estimate the number of latent features. In practice, identifying these features is both difficult and significant for pattern recognition and latent feature analysis, especially for large dense matrices. Here, we introduce a distributed NMF algorithm coupled with distributed custom clustering followed by a stability analysis on dense data, which we call DnMFk, to determine the number of latent variables. The results on synthetic data and the classical Swimmer data set demonstrate the accuracy of model determination while scaling nearly linearly across multiple processors for large data. Further, we employ DnMFk to determine the number of hidden features from a terabyte matrix.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Control-oriented core-SOL-divertor model to address integrated burn and divertor control challenges in ITER

The real-time regulation of a burning plasma’s temperature and density, or burn control, will be necessary to produce high fusion power in future tokamaks like ITER. This is made more challenging due to the plasma’s nonlinear characteristics and the interdependence between the core-plasma and edge-plasma regions. For example, a raising plasma temperature leads to increasing reactivity and therefore to more alpha-particle heating, which further increases temperature. Furthermore, a raise of the fusion power increases the heat flow through the scrape-off-layer (SOL), which can compromise the integrity of the divertor without proper safeguards. For control design, a model-based approach is attractive because it can directly incorporate the nonlinear, coupled, burning-plasma dynamics into the design. To facilitate this design approach, a control-oriented core-SOL-divertor (CSD) model is presented in this work. In this CSD model, a core-plasma model captures the nonlinear dynamics of the core’s density and temperature, and a SOL-divertor model defines the plasma conditions at the separatrix and divertor including the heat load on the target plates. The core-plasma and SOL-divertor models are coupled through the exchange of various variables. In particular, the SOL-divertor model yields the separatrix temperature and the influx of recycled particles into the core-plasma. Further, these variables influence the power and particle balances captured by the core-plasma model. In return, the core-plasma model determines the intensity of the heat and particles fluxes across the separatrix, and this outflow strongly impacts the SOL-divertor model. Therefore, the power and density of the core-plasma, which can be readily modulated through external heating systems and pellet injection, can be viewed as control knobs for the SOL-divertor region in addition to the gas puffing. In simulations of the CSD model, it is demonstrated how external actuation can be utilized to meet burn control and divertor control objectives simultaneously.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

A new method for predicting hurricane rapid intensification based on co-occurring environmental parameters

Abstract Tropical cyclones (TCs) that undergo Rapid Intensification (RI) can pose serious socioeconomic threats and can potentially result in major damaging impacts along coastal areas. Considering the complexity of various physical mechanisms that play a role in RI and its relatively low probability of occurrence, predicting RI remains a major operational challenge. In this study, we propose a simple deterministic binary classification model based on the co-occurrence of environmental parameters (MCE) to predict an RI event. More specifically, the model determines the possibility of RI based on a simple count of the number of environmental predictors deemed favorable and unfavorable. We compare our model results to logistic regression (LR) and decision tree (DT) models, well-trained using the same set of environmental predictors. Results reveal that at an RI threshold of 30 kt, the MCE exhibits a critical success index score of 0.233 which is 14% higher than DT and LR model performances. When tested at multiple RI thresholds, the MCE displays relatively higher skill scores across multiple metrics. By simultaneously evaluating the favorability of predictors, the MCE is able to comparatively reduce the number of false alarms predicted when certain predictors are unfavorable toward RI. Interpreting these model results to gain a physical understanding of how co-occurring environmental parameters can affect RI, we highlight future directions for using models based on the MCE approach to understand and predict TC RI as well as other meteorological extremes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Composition and Pressure Effects on Partitioning of Ferrous Iron in Iron-Rich Lower Mantle Heterogeneities

Both seismic observations of dense low shear velocity regions and models of magma ocean crystallization and mantle dynamics support enrichment of iron in Earth’s lowermost mantle. Physical properties of iron-rich lower mantle heterogeneities in the modern Earth depend on distribution of iron between coexisting lower mantle phases (Mg,Fe)O magnesiowüstite, (Mg,Fe)SiO3 bridgmanite, and (Mg,Fe)SiO3 post-perovskite. The partitioning of iron between these phases was investigated in synthetic ferrous-iron-rich olivine compositions (Mg0.55Fe0.45)2SiO4 and (Mg0.28Fe0.72)2SiO4 at lower mantle conditions ranging from 33–128 GPa and 1900–3000 K in the laser-heated diamond anvil cell. The resulting phase assemblages were characterized by a combination of in situ X-ray diffraction and ex situ transmission electron microscopy. The exchange coefficient between bridgmanite and magnesiowüstite decreases with pressure and bulk Fe# and increases with temperature. Thermodynamic modeling determines that incorporation and partitioning of iron in bridgmanite are explained well by excess volume associated with Mg-Fe exchange. Partitioning results are used to model compositions and densities of mantle phase assemblages as a function of pressure, FeO-content and SiO2-content. Unlike average mantle compositions, iron-rich compositions in the mantle exhibit negative dependence of density on SiO2-content at all mantle depths, an important finding for interpretation of deep lower mantle structures.

Dorfman, Susannah M. (ORCID:0000000239689592)↗
DOE OSTI2023

Impact of Blast Overpressure on the Pharmacokinetics of Various Antibiotics in Sprague Dawley Rats

ABSTRACT Introduction Combat injuries are complex and multimodal. Most injuries to the extremities occur because of explosive devices such as improvised explosive devices. Blast exposure dramatically increases the risk of infection in combat wounds, and there is limited available information on the best antibiotic treatments for these injuries. We previously demonstrated that mice exposed to blast displayed a delayed clearance of cefazolin from the plasma and liver; further semi-mechanistic modeling determined that cefazolin concentrations in the skin of these mice were reduced. Our objective was to investigate the effects of blast on the pharmacokinetics of antibiotics of different types used for the treatment of combat wounds in the rat model. Materials and Methods Male Sprague Dawley rats were exposed to blast overpressure followed by injection of a bolus of animal equivalent doses of an antibiotic (cefazolin, cefepime, ertapenem, or clindamycin) into the tail vein at 1-hour post-blast exposure. Blood was collected at predetermined time points via repeated sampling from the tail vein. Animals were also euthanized at predetermined time points, at which time liver, kidney, skin, and blood via cardiac puncture were collected. Antibiotic concentrations were determined by ultra-performance liquid chromatography–tandem mass spectrometry. Results Blast-exposed rats exhibited a similar rate of clearance compared to non-blasted rats in the blood, liver, kidney, and skin, which is inconsistent with the data regarding cefazolin in blast-exposed mice. Conclusions Our results in rats do not recapitulate our previous observation of delayed cefazolin clearance in mice following the blast overpressure exposure. Although using rats permitted us to collect multiple blood samples from the same animals, rats may not be a suitable model for measuring the pharmacokinetics of antibiotics following blast. The interpretation of the results may be challenging because of variation in data among rat subjects in the same sample groups.

General & Internal Medicine↗
DOE OSTI2023

Analysis of Uncertainty Impacts on Emissions and Fuel Economy Evaluation for Chassis Dynamometer Testing

This study illustrates a methodology for quantifying the uncertainties encountered in the measurement of tailpipe emissions and in the fuel consumption measurements for light-duty conventional vehicles tested on a four-wheel drive chassis dynamometer. The study leverages high-fidelity experimental data collected over three standard drive cycles, UDDS, HWY and US06, intended to simulate a wide range of operating conditions. Here, a method is developed to estimate the measurement uncertainties in fuel consumption for a test cycle, which occur due to the accumulation of measurement uncertainties propagated through the system. The uncertainty determination model uses statistical analysis and standard propagation techniques to evaluate and combine the uncertainties introduced from various sources (including the vehicle, chassis dynamometer, driver, and instrumentation). The analysis also examines three different experimental methods for determining the fuel consumption: 1) carbon mass balance, 2) volumetric fuel scale and 3) gravimetric fuel scale, and takes into consideration the properties of the instrumentation used. The results show that the most significant influence on the determination of the emissions comes from the concentration measurement, and similarly the biggest impact on the total fuel consumption uncertainty comes from the uncertainty in the determination of the carbon dioxide mass, due to the large presence of this pollutant in the overall emissions. It was found that the fuel consumption uncertainties are in the range of ±1-2% for all three methods analyzed, with the lowest values being obtained for measurements performed using the gravimetric method for all three drive cycles considered.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2025

Incorporating geological structure into sensitivity analysis of subsurface contaminant transport

Simulating subsurface contaminant transport at the kilometer-scale often entails modeling reactive flow and transport within and through complex geologic structures. These structures are typically meshed by hand and as a result geologic structure is usually represented by one or a few deterministically generated geological models for uncertainty studies of flow and transport in the subsurface. Uncertainty in geologic structure can have a significant impact on contaminant transport. In this study, the impact of geologic structure on contaminant tracer transport in a shale formation is investigated for a simplified generic deep geologic repository for permanent disposal of spent nuclear fuel. An open-source modeling framework is used to perform a sensitivity analysis study on transport of two tracers from a generic spent nuclear fuel repository with uncertain location of the interfaces between the stratum of the geologic structure. The automated workflow uses sampled realizations of the geological structural model in addition to uncertain flow parameters in a nested sensitivity analysis. Concentration of the tracers at observation points within, in line with, and downstream of the repository are used as the quantities of interest for determining model sensitivity to input parameters and geological realization. Finally, the results of the study indicate that the location of strata interfaces in the geological structure has a first-order impact on tracer transport in the example shale formation, and that this impact may be greater than that of the uncertain flow parameters.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

Integrating deep neural networks with full-waveform inversion: Reparameterization, regularization, and uncertainty quantification

Full-waveform inversion (FWI) is an accurate imaging approach for modeling the velocity structure by minimizing the misfit between recorded and predicted seismic waveforms. However, the strong nonlinearity of FWI resulting from fitting oscillatory waveforms can trap the optimization in local minima. We have adopted a neural-network-based full-waveform inversion (NNFWI) method that integrates deep neural networks with FWI by representing the velocity model with a generative neural network. Neural networks can naturally introduce spatial correlations as regularization to the generated velocity model, which suppresses noise in the gradients and mitigates local minima. Furthermore, the velocity model generated by neural networks is input to the same partial differential equation (PDE) solvers used in conventional FWI. The gradients of the neural networks and PDEs are calculated using automatic differentiation, which back propagates gradients through the acoustic PDEs and neural network layers to update the weights of the generative neural network. Experiments on 1D velocity models, the Marmousi model, and the 2004 BP model determine that NNFWI can mitigate local minima, especially for imaging high-contrast features such as salt bodies, and it significantly improves the inversion in the presence of noise. Adding dropout layers to the neural network model also allows analyzing the uncertainty of the inversion results through Monte Carlo dropout. NNFWI opens a new pathway to combine deep learning and FWI for exploiting the characteristics of deep neural networks and the high accuracy of PDE solvers. Because NNFWI does not require extra training data and optimization loops, it provides an attractive and straightforward alternative to conventional FWI.

58 GEOSCIENCES↗
DOE OSTI2022

Bayesian time-varying occupancy model for West Nile virus in Ontario, Canada

Occupancy models determine the true presence or absence of a species by adjusting for imperfect detection in surveys. They often assume that species presences can be detected only if sites are occupied during a sampling season. We extended these models to estimate occupancy rates that vary throughout a sampling season as well as account for spatial dependence among sites. For these methods, we constructed a fast Gibbs sampler with the Pólya-Gamma augmentation strategy to conduct inference on covariate effects. We applied these methods to evaluate how environmental conditions and surveillance practices are associated with the presence of West Nile virus in mosquito traps across Ontario, Canada from 2002 to 2017. We found that urban land cover and warm temperatures drove viral occupancy, whereas viral testing on pools with higher proportions of Culex mosquitoes was more likely to result in a positive test for West Nile virus. Models with time-varying occupancy effects achieved much lower Watanabe-Akaike information criteria than models without such effects. Our final model had strong predictive performance on test data that included some of the most extreme seasons, demonstrating the promise of these methods in the study of pathogens spread by mosquito vectors.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

The Role of Phytoplankton Biomacromolecules in Controlling Ocean Surface Roughness

Satellite altimetric data routinely map sea surface topography by measuring the ocean return signal. One source of altimeter measurement contamination occurs when the radar ocean backscatter becomes unusually large, a situation termed a Sigma-0 bloom. Past research suggests Sigma-0 blooms are associated with weak wind and natural surface slick conditions where capillary waves at the air–sea interface are suppressed. To date, no explicit connection between these conditions and Sigma-0 bloom presence has been provided. Using a series of simplified equations, our reduced model determines capillary wave heights from estimates of planktonic carbon concentrations and regional wind speed. Our results suggest that the radar signal reflection increases as capillary wave height decreases. This relationship depends on surfactant concentration, surfactant composition, and wind speed. Model sensitivity analysis indicates that the interface reflectivity depends on biological activity and wind speed. Our proposed simplified model provides a method to identify potential Sigma-0 bloom regions. We conclude that because of the demonstrated impact of biological surfactants on ocean roughness, it is necessary to consider the biological activity, i.e., phytoplankton bloom events, when interpreting signals from radar altimetry and when developing ocean hydrology models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

ACDC (Automated Campbell Diagram Code) [SWR-26-042]

This application provides a web-based graphical user interface to generating Campbell Diagrams and visualizing mode shapes for OpenFAST turbine models. Determining the aeroelastic stability and dynamic characteristics of wind turbines is a critical step in turbine design and analysis. Historically, extracting natural frequencies and mode shapes from OpenFAST—the industry-standard whole-turbine simulation code—has been a fragmented and tedious process. It required manual model configuration, command-line linearization execution, and complex post-processing via proprietary scripts to handle rotating-frame dynamics. To address these workflow bottlenecks, we present the Automated Campbell Diagram Code (ACDC), an open-source graphical software tool developed by the National Laboratory of the Rockies (NLR) under the DOE-funded Distributed Wind Aeroelastic Modeling (dWAM) project. ACDC streamlines the end-to-end linearization and stability analysis workflow into a single, intuitive cross-platform application. The software guides users through OpenFAST model configuration, definition of operating points, and the automated execution of steady-state trim and linearization simulations. Under the hood, ACDC automates the complex mathematical post-processing steps required for rotating systems, including Multi-Blade Coordinate (MBC) transformations, eigenanalysis, and advanced modal tracking utilizing the Modal Assurance Criterion (MAC) and spectral clustering. Finally, ACDC processes these results to automatically generate Campbell diagrams and features a robust 3D visualization engine to animate full-system mode shapes. By eliminating the reliance on external post-processing environments and manual data manipulation, ACDC significantly accelerates dynamic analysis and lowers the barrier to entry for wind energy researchers and engineers.

Summerville, Brent [National Laboratory of the Roc↗
DOE OSTI2021

Insights for Canadian electricity generation planning from an integrated assessment model: Should we be more cautious about hydropower cost overruns?

Hydropower accounts for approximately 60% of electricity generation in Canada, with growth expected in the coming decades as part of renewable energy transitions; however, frequent cost overruns threaten the viability of this growth. Here, using the integrated assessment model GCAM, we develop an endogenous representation of hydropower for Canada that accounts for market dynamics, thus permitting analysis of hydropower competition with other electricity generation technologies, both with and without cost overruns. Results show that modelling hydropower resources endogenously increases Canadian hydropower deployment relative to an assumption of fixed hydropower production, from 417 to 495 TWh annually by 2050. In scenarios that apply cost overruns at historical levels, hydropower loses market share to more easily scalable technologies like wind power. When including high cost overrun assumptions, the model determines that hydropower falls from about 73% to 65% of Canadian electricity generation by 2050, while wind power increases from about 8% to 11%. Countries may be better able to achieve electrification and renewable energy targets at lower cost by avoiding large-scale, overrun-prone hydropower and nuclear generation projects. Model results support that cost overruns are important considerations for policy decisions related to electricity sector development in Canada and elsewhere.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2022

Spatiotemporal Metabolic Network Models Reveal Complex Autotroph-Heterotroph Biofilm Interactions Governed by Photon Incidences

Autotroph-heterotroph interactions are ubiquitous in natural environment and play a key role in controlling various essential ecosystem functions, such as production and utilization of organic matter, cycling of nitrogen, sulfur, and other chemical elements. Understanding how these biofilm metabolic interactions are constrained in space and time remains challenging because fully predictive models designed for this purpose are currently limited. Toward filling this gap, here we developed community metabolic network models for two autotroph-heterotroph biofilm consortia (termed UCC-A and UCC-O), which share a suite of common heterotrophic members but have a single distinct photoautotrophic cyanobacterium (Phormidesmis priestleyi str. ANA and Phormidium sp. OSCR) that provides organic carbon and nitrogen sources to support the growth of heterotrophic partners. After determining model parameters by data fitting using the spatiotemporal distributions of microbial abundances, we comparatively analyzed the resulting biofilm models to examine any fundamental differences in microbial interactions between the two consortia under the variation of key environmental variables: CO2 and photon levels. The UCC-A model predicted generally expected responses, i.e., the autotroph population increased in response to elevated levels of CO2 and photon, followed by increase in the heterotroph population. In contrast, the UCC-O model showed somewhat complicated dynamics, e.g., higher photon incidence rates resulted in the increase in autotroph population but decrease in heterotroph population due to the lowered provision of glucose from the autotroph. A further analysis showed that species coexistence was governed by the photon incidences rather than the carbon availability for UCC-O, which was the opposite for UCC-A.

Phalak, Poonam↗
DOE OSTI2021

Coordinated Optimization and Control of Residential Solid State Power Substations in Electrical Distribution Network

This paper proposes a computationally efficient mixed integer linear programming (MILP) model for the coordinated optimization of solid-state power substations (SSPSs) in a feeder considering the full unbalanced three-phase structure of the distribution grid and its characteristics. The proposed model determines the optimal real and reactive power of each SSPS at the point of common coupling (PCC) that minimizes the operating cost and maximizes the system performance, e.g., voltage regulation and phase balancing. To improve the computational efficiency, an inscribed octagon is introduced to approximate the quadratic capacity constraints of components. Numerical simulation results show the effectiveness of the proposed model and significant improvements in voltage profiles and power imbalance between phases.

Liu, Guodong↗