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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 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Development of Scalable Reactive Transport Framework for PFAS

Research on PFAS chemicals is extensive and covers all aspects, including analytical quantification, determination of properties, toxicology, ex situ treatment, and in situ remediation. PFAS chemicals are very stable and thus persistent/recalcitrant in the environment. Although there are many unknowns about PFAS chemicals, degradation pathways, reaction rates, etc., many different sorption, oxidation, reduction, biological, and innovative treatment approaches are being developed. Sorption with activated carbon is currently the only fully available in situ treatment technology for PFAS-impacted groundwater. Given the wide array of PFAS chemicals and transformation products, remediation may need multi-step treatment trains to fully address the PFAS contamination. The work here provides kinetic reaction modules that represent an initial cut at functionality representing PFAS migration and reaction in groundwater aquifer flow and transport models. One reaction kinetics module provides a method to model kinetically limited adsorption using a mass transfer model. The second reaction module represents biological transformation of 8:2 FTOH and daughter species, illustrating how a complex reaction pathway network can be represented. Both reaction modules allow for spatially variable parameter values so that a variety of remediation approaches (e.g., a PRB or volumetric treatment or variations in geochemical conditions) can be simulated. The intent with these PFAS reaction modules is to provide tools for practitioners to aid in the selection, design, and assessment of potential in situ PFAS remediation strategies. It is anticipated that, as PFAS remediation technologies and scientific understanding advances, these modules would be refined or replaced to match new knowledge.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Tuning metal-support interactions in nickel–zeolite catalysts leads to enhanced stability during dry reforming of methane

Ni-based catalysts are highly reactive for dry reforming of methane (DRM) but they are prone to rapid deactivation due to sintering and/or coking. In this study, we present a straightforward approach for anchoring dispersed Ni sites with strengthened metal-support interactions, which leads to Ni active sites embedded in dealuminated Beta zeolite with superior stability and rates for DRM. The process involves solid-state grinding of dealuminated Beta zeolites and nickel nitrate, followed by calcination under finely controlled gas flow conditions. By combining in situ X-ray absorption spectroscopy and ab initio simulations, it is elucidated that the efficient removal of byproducts during catalyst synthesis is conducted to strengthen Ni–Si interactions that suppress coking and sintering after 100 h of time-on-stream. Transient isotopic kinetic experiments shed light on the differences in intrinsic turnover frequency of Ni species and explain performance trends. This work constructs a fundamental understanding regarding the implication of facile synthesis protocols on metal-support interaction in zeolite-supported Ni sites, and it lays the needed foundations on how these interactions can be tuned for outstanding DRM performance.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Local Power-Voltage Sensitivity and Thevenin Impedance Estimation from Phasor Measurements

This paper describes how to use voltage phasor measurements to produce a sensitivity matrix that describes how real and reactive power injections at a node on a distribution network affect the local voltage magnitude and angle. Rather than estimating the sensitivity directly, the voltage phasor measurements and power commands/measurements are used to estimate the unbalanced, three-phase Thevenin impedance. The Thevenin impedance estimation is conducted using recursive least squares on temporal difference measurements. The Thevenin impedance and voltage phasor measurement are then used to build the local power-voltage sensitivity matrix with the closed form expression for the Jacobian of the power flow manifold. Hardware-in-the-loop simulations with phasor measurement units providing real phasor measurements are used to evaluate the recursive temporal difference Thevenin impedance estimation and Thevenin-based power-voltage sensitivity methods.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

A Geo‐Structurally Based Correction Factor for Apparent Dissolution Rates in Fractured Media

Abstract Field measurements of apparent geochemical weathering reaction rates in subsurface fractured porous media are known to deviate from laboratory measurements by multiple orders of magnitude. To date, there is no geologically based explanation for this discrepancy that can be used to predict reaction rates in field systems. Proposed correction factors are typically based on ad hoc characterizations related to geochemical kinetic models. Through a series of high‐fidelity reactive transport simulations of mineral dissolution within explicit 3D discrete fracture networks, we are able to link the geo‐structural attributes with reactive transport observations. We develop a correction factor to linear transition state theory for the prediction of the apparent dissolution rate based on measurable geological properties. The modified rate law shows excellent agreement with numerical simulations, indicating that geological structure could be a primary reason for the discrepancy between laboratory and field observations of apparent dissolution rates in fractured media.

58 GEOSCIENCES↗
DOE OSTI2021

Modelling Nuclear Thermal Propulsion Reactor Startup Transients

The National Aeronautics and Space Administration (NASA) has set the goal of a manned mission to Mars by the year 2030 [1] and charged the national academy of sci- ences "to identify primary technical and programmatic chal- lenges, merits, and risks for maturing space nuclear propulsion technologies of interest to a future human Mars exploration mission" [2]. One relevant technology, nuclear thermal propul- sion (NTP), has notable advantages over traditional chemical rockets; most important among them is the ability to produce larger specific impulse on the order of 900s. The reduction of mission time is crucial for a manned mission to Mars to reduce the risk for the crew. Due to its higher specific impulse, NTP satisfies this need and is pursued as one technology to get humans to Mars [3, 4]. The construction of an NTP sys- tem has to negotiate several challenges laid out in Ref. [2]; one of these challenges is the need to startup the NTP sys- tem from essentially cold conditions to full power within one minute. This paper focuses on studying the neutronics and thermal-hydraulics behavior of a simplified NTP model dur- ing prescribed reactivity insertions and mass flow rate (MFR) ramps. It is the goal of this paper to investigate startup, peak material temperatures, and average specific impulse for a low enriched Uranium (LEU), ceramic and metal material (CER- MET) NTP system when varying reactivity insertion and MFR ramps.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2023

Atomistic insight into the effects of electrostatic fields on hydrocarbon reaction kinetics

Reactive Molecular Dynamics (MD) and Density Functional Theory (DFT) computations are performed to provide insight into the effects of external electrostatic fields on hydrocarbon reaction kinetics. By comparing the results from MD and DFT, the suitability of the MD method in modeling electrodynamics is first assessed. Results show that the electric field-induced polarization predicted by the MD charge equilibration method is in good agreement with various DFT charge partitioning schemes. Then, the effects of oriented external electric fields on the transition pathways of non-redox reactions are investigated. Results on the minimum energy path suggest that electric fields can cause catalysis or inhibition of oxidation reactions, whereas pyrolysis reactions are not affected due to the weaker electronegativity of the hydrogen and carbon atoms. MD simulations of isolated reactions show that the reaction kinetics is also affected by applied external Lorentz forces and interatomic Coulomb forces since they can increase or decrease the energy of collision depending on the molecular conformation. In addition, electric fields can affect the kinetics of polar species and force them to align in the direction of field lines. These effects are attributed to energy transfer via intermolecular collisions and stabilization under the external Lorentz force. The kinetics of apolar species is not significantly affected mainly due to the weak induced dipole moment even under strong electric fields. The dynamics and reaction rates of species are studied by means of large-scale combustion simulations of n-dodecane and oxygen mixtures. Results show that under strong electric fields, the fuel, oxidizer, and most product molecules experience translational and rotational acceleration mainly due to close charge transfer along with a reduction in their vibrational energy due to stabilization. This study will serve as a basis to improve the current methods used in MD and to develop novel methodologies for the modeling of macroscale reacting flows under external electrostatic fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Elucidating Norrish type I reactive pathways by ultrafast X-ray absorption spectroscopy

Norrish type I reactions selectively cleave carbon–carbon bonds directly adjacent to carbonyl groups. Despite their broad use in combination with aromatic carbonyls for additive manufacturing and dental UV curing applications, the nature of the photochemically active state and its population mechanism remain insufficiently understood. Detailed mechanistic insight requires mapping of the photoexcited population flow involving internal conversion and intersystem crossing. We present a time-domain study of gas phase acetophenone as a prototypical aromatic carbonyl combining soft X-ray time-resolved near-edge X-ray absorption fine structure (TR-NEXAFS) spectroscopy at the oxygen K-edge with ab initio multiple spawning (AIMS) simulations. Exploiting the specific sensitivity of TR-NEXAFS spectroscopy to states with nπ* character, we observe population transfer from the initially excited 1 ππ* state to the 1 nπ* state with a time constant of (0.13 ± 0.02) ps after an initial induction period of (0.12 ± 0.02) ps without population transfer, in quantitative agreement with the AIMS simulations. The population in the 1 nπ* state subsequently decays via intersystem crossing, likely mediated by a 3 ππ* state, within (3.17 ± 0.66) ps to a long-lived 3 nπ* state, which is presumed to be active towards Norrish type I chemistry.

Graßl, Martin [SLAC National Accelerator Laborator↗
DOE OSTI2020

Feasibility of using reactive silicate particles with temperature-responsive coatings to enhance the security of geologic carbon storage

The large-scale deployment of geologic carbon storage will require minimizing the risk of CO 2 leakage. Here we report on a novel strategy to seal leakage pathways by injecting functionalized reactive calcium silicate (CaSiO 3 ) particles. The particles consist of a mineral silicate core within a temperature-sensitive Poly(N,N-dimethylaminoethyl methacrylate) coating that limits contact between the core and the surrounding CO 2 (aq) above a switching temperature making them relatively unreactive deep in the subsurface. If the CO 2 leaks to shallower depths and cooler temperatures, the coatings would extend and enable the silicate core to react with CO 2(aq) to form solid carbonate precipitates that reduce the permeability of the fracture or flow path. A combined laboratory- and simulation-based investigation was conducted to explore key early-stage research questions related to the feasibility of this leakage management strategy. Sand columns were injected with either coated or uncoated CaSiO 3 particles and the permeability was measured before and after exposure to CO 2 . Experiments were conducted at 35 °C and 70 °C, a range that spans the switching temperature for the coatings. Results show that at the cooler temperature the coating effectively enabled reaction and permeability reduction. At higher temperatures, the coated particles limited mineral carbonation and the permeability decrease was minimal compared to columns with uncoated particles. Here, the morphology and location of the precipitates provides insight about permeability evolution. Model simulations of 2D radial particle transport from an injection point provided insight into the effects of particle size, coating properties, and concentrations of particles in several representative rock formations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Catalytic Resonance Theory: Forecasting the Flow of Programmable Catalytic Loops

Chemical transformations on catalyst surfaces occur through series and parallel reaction pathways. These complex networks and their behavior can be most simply evaluated through a three-species surface reaction loop (A* to B* to C* to A*) that is internal to the overall chemical reaction. Application of an oscillating dynamic catalyst to this reactive loop has been shown to exhibit one of three types of behavior: (1) a positive net flux of molecules about the loop in the clockwise direction, (2) a negative net flux of molecules about the loop in the counterclockwise direction, or (3) negligible flux of molecules about the loop at the limit cycle of reaction. Three-species surface loops were simulated with microkinetic modeling to assess the reaction loop behavior resulting from a catalytic surface oscillating between two or more catalyst surface energy states. Selected input parameters for the simulations spanned an 11-dimensional parameter space using 127 688 different parameter combinations. Their converged limit cycle solutions were analyzed for their loop turnover frequencies, the majority of which were found to be approximately zero. Classification and regression machine learning models were trained to predict the sign and magnitude of the loop turnover frequency and successfully performed above accessible baselines. Notably, the classification models exhibited a baseline weighted F1 score of 0.49, whereas trained models achieved weighted F1 scores of 0.94 and 0.96 when trained on the parameters used to define the simulations and derived rate constants, respectively. The trained models successfully predicted catalytic loop behavior, and interpretation of these models revealed all input parameters to be important for the prediction and performance of each model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Solar Thermochemical Carbon Dioxide Splitting Using Ceria and Iron Aluminate Foam Devices and Simulation of a Plant System for Demonstration

An international research project has been undertaken to integrate a unique solar thermal processing reactor system with ceria and iron aluminate as active redox materials for CO2 splitting. Experimental investigations for CO2 splitting were conducted using a solar simulator and tube furnace at Niigata University, followed by demonstrations using a high-flux solar furnace (HFSF) at the National Renewable Energy Laboratory (NREL) in Golden, CO. Each experimental setup consisted of foam devices composed of reticulated porous ceramic (RPC). The RPC has a full ceria or iron aluminate body. It fabricated using the replica method and subjected to a two-step redox reaction, which iteratively separated a stream of CO2 into O2 and CO. Reactivity was evaluated using CO production per mass of the reactive material. The tubular furnace yielded a CO production of 6.41 mL/g at a reduction temperature of 1600degrees C, showcasing a higher CO production rate and total amount than those obtained from experiments conducted with solar simulators and solar furnace setups. For iron aluminate RPC, the productivity was measured as 3.57 mL/g using HFSF at a reduction temperature of 1450degrees C. These results are somewhat higher than those of the previous experiment at lower reduction temperatures of 1400degrees C-1500degrees C. Additionally, the production of CO in the case of ceria RPC was compared with the steady flow model simulation, which assumed chemical equilibrium at various levels of oxygen partial pressure during the reduction process. On the basis of these results, this study proposes a solar fuel system with an open receiver that uses a high-temperature heat transfer fluid.

carbon dioxide thermochemical splitting↗
DOE OSTI2021

Visual Tool for Assessing Stability of DER Configurations on Three-Phase Radial Networks

Here, we present a method and tool for evaluating the placement of Distributed Energy Resources (DER) on distribution circuits in order to control voltages and power flows. Our previous work described Phasor-Based Control (PBC), a novel control framework where DERs inject real and reactive power to track voltage magnitude and phase angle targets. Here, we employ linearized power flow equations and integral controllers to develop a linear state space model for PBC acting on a three-phase unbalanced network. We use this model to evaluate whether a given inverter-based DER configuration admits a stable set of controller gains, which cannot be done by analyzing controllability nor by using the Lyapunov equation. Instead, we sample over a parameter space to identify a stable set of controller gains. Our stability analysis requires only a line impedance model and does not entail simulating the system or solving an optimization problem. We incorporate this assessment into a publicly available visualization tool and demonstrate three processes for evaluating many control configurations on the IEEE 123-node test feeder (123NF).

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Balanced Fast-SpaciMS capillary configurations provide practically noninvasive channel-average measurements in catalytic monoliths

Spatially resolved capillary-inlet mass spectrometry (SpaciMS) provides a detailed picture of the spatiotemporal evolution of reaction network in catalytic monoliths. In the present work, we combine the SpaciMS experiments with a newly developed non-isothermal 3D CFD model for heterogeneously catalyzed reactive flows, including diffusion and permeation through the coated catalyst and channel wall. We explore how the capillary size and sampling rate can be balanced to minimize the impact on probed-channel conversions and provide species concentration measurements representative of the free channel average. In all studied configurations, the balanced sampling-rate fraction is noticeably higher than the corresponding capillary occlusion fraction. For a typical 350-micron capillary that occupies 11% of the channel cross- section, the balanced sampling rate represents 43% of the channel flow. Furthermore, the present work shows that together, a balanced SpaciMS configuration and numerical simulation provide accurate channel-averaged information of a monolithic catalyst under realistic operation conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Comprehensive parametric study of CO 2 sequestration in deep saline aquifers

Carbon dioxide injection in deep saline aquifers is a key method for permanently sequestering anthropogenic CO 2 . Here this study employs a reactive transport model to explore mineral precipitation/dissolution and its impact on reservoir properties in deep saline aquifers. We also assess capillary pressure and relative permeability hysteresis on various CO 2 trapping mechanisms. Results from this study reveal the significant influence of initial brine composition on mineral precipitation/dissolution. The dissolution and precipitation of minerals have different effects around the wellbores compared to the overall reservoir. Additionally, salt concentration (Ca ++ and Mg ++ ) and quartz surface area affect CO 2 mineralization, while Na + impacts halite precipitation, altering flow properties. The effect of capillary pressure is significant, as including the capillary pressure in the simulation case resulted in significantly improved CO 2 trapping, achieving almost total dissolution of the injected CO 2 in around 300 years. This study offers novel insights into the interactions of reservoir minerals, brine properties, and the injected CO 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Reactive transport modeling of the Aquifer Thermal Energy Storage (ATES) system at Stockton University, New Jersey during seasonal operations

Hydrogeochemical processes associated with Aquifer Thermal Energy Storage (ATES) operations can often impact the system performance owing to mineral precipitation either at the wellbore or in the aquifer owing to changes in temperature and fluid disequilibria. Although failure of ATES systems due to mineral precipitation ("fouling") is common, predictive reactive-transport models have rarely been applied to plan their design and operation. Here, the objective of this study is to develop a reactive-transport model by coupling thermal, hydrological, and chemical (THC) processes to evaluate effects of introduced atmospheric oxygen on water chemistry, mineral precipitation/dissolution, porosity, and permeability changes associated with an ATES system at Stockton University (New Jersey, USA). The THC model builds on a Thermal-Hydrological-Mechanical (THM) model of the site that evaluated system failure owing to possible fracturing in the caprock or around the wellbore. The causes of the system failure are not known – potential causes include hydraulic fracturing owing to elevated pump pressures that took place, a flow pathway created by one of the boreholes, or a pre-existing natural hydrologic connection between the upper unconfined aquifer and the ATES aquifer, any of which could have led to oxygenated water entering the reservoir and causing the observed Fe-oxide fouling on well screens. The THC model is used to evaluate some of the hypotheses and observations regarding system failure owing to geochemical processes. The reactive-transport code TOUGHREACT V4 was used to model the THC processes during seasonal heating and cooling operations at the Stockton ATES site over 6 years of operation. In the THC simulations, the primary effects on geochemistry were observed when the injection water is saturated with atmospheric oxygen. Simulations show greater precipitation of goethite near the cold wells as compared to the warm wells. Although volume fractions of Fe-hydroxides were relatively small, the model was aimed at processes in the aquifer at the scale of meters and larger rather than at the scale of mm or cm (i.e., a well screen). Kaolinite is the dominant precipitating phase, also around the cold wells. Illite dissolves near the cold wells and precipitates near the warm wells. There is a net decrease in the porosity near the cold wells and increase near the warm wells, although a slight amount of thermal contraction near the cold wells and expansion near the warm wells is responsible for a significant proportion of the porosity change. Owing to the coarse discretization of the numerical grid near the wells (compared to the screen thickness) the magnitude of permeability changes at the wellbore are likely underestimated. The reactive transport model in this study can be used for characterization of aquifers, optimizing the operational parameters (temperature, pressure, pH etc.), and planning of mitigation strategies for ATES systems.

15 GEOTHERMAL ENERGY↗
DOE OSTI2024

Direct numerical simulations of turbulent premixed cool flames: Global and local flame dynamics analysis

The cool flame dynamics, especially in turbulent flows, is of great interest for both practical application and fundamental research. Here, in this study, a series of direct numerical simulations of turbulent premixed n-C 7 H 16 /O 2 /O 3 /N 2 cool flames are performed, with the focus on the influence of turbulence intensity (u'/S L , where S L is the laminar flame speed) on the flame structure as well as the global and local cool flame dynamics. It is found that the cool flame front is considerably wrinkled by turbulence at high u'/S L , leading to significantly thickened turbulent cool flame brush and largely altered local reactivity compared with the reference laminar flame. However, the turbulent flame structure in the temperature space is found to be insensitive to u'/S L . Besides, with increasing u'/S L , the normalized turbulent cool flame speed (S L /S L ) is monotonically increased, attributed to substantial augmentation on the flame surface area (A T /A L ), while the stretching factor (I 0 ) remains almost constant and is smaller than 1. The underlying mechanisms for such variations are revealed through local flame dynamics analysis. Specifically, the local flame displacement speed S d is found to be strongly negatively correlated with flame curvature; meanwhile, such negative correlation and the probability distribution function (PDF) of flame curvature are barely influenced by u'/S L , leading to a weak dependence of I 0 on u'/S L . In contrast, the PDF of the tangential strain rate is found to span a much wider range and shift to the positive side as u'/S L increases, suggesting that the enhanced tangential strain rate is the main cause for the increase in surface area of the turbulent premixed cool flame. Finally, the influence of equivalence ratio on above findings is found to be insignificant, indicating that although the local reactivity of turbulent premixed cool flames is altered due to the differential diffusion, the resultant flame- stretch interaction is insensitive to the equivalence ratio. This study presents some unique cool flame dynamics that are distinct from hot flames, which can help improve the understanding and modeling of turbulent cool flames.

Cool flames↗
DOE OSTI2019

Effect of natural fractures on determining closure pressure

Abstract In Utah FORGE reservoir, eight pressure transient tests (microhydraulic fracturing and DFIT™) show natural fracture/pressure-dependent leakoff. This behavior may lead to misinterpretation of the closure pressure (proxy for minimum principal stress). The closure pressures obtained from DFIT™ (or microhydraulic fracturing) testing may reflect shear failure along natural fractures or discontinuities rather than tensile failure and lead to inaccurate estimates of the minimum principal stress. In pressure tests conducted at the Utah FORGE site showed that reactivation or opening of natural fractures intersecting the wellbore and were suggested by multiple closure events in DFIT™ tests. In addition, comparisons between the pre- and post-well-tests FMI logs show that there are populations of induced fracture and reactivated natural fractures which are mostly vertical and sub-vertical. In this study, DFIT™ (or microhydraulic fracturing) test analysis and numerical simulations were used to suggest that hydraulic shearing of critically stressed natural fractures can contribute to multiple closure signatures and possibly lead to incorrect determination of the minimum principal stress. As other authors have previously advocated, the DFIT™ test analyses and numerical simulations suggest that better estimations of minimum principal stress may be derived by injecting at relatively high rate and pressure and insuring that tensile breakdown is reached. In addition, extended shut-in period is required to determine accurate reservoir characteristics and fluid flow regime.

Nadimi, S.↗
DOE OSTI2024

Impact of K-factor on Short Circuit Program Convergence for Inverter-Based Resources during Faults

Classical short-circuit programs that linearize the power network are no longer applicable for inverter based resources (IBRs), necessitating an iterative approach. Phasor domain programs can model the IBRs using an iterative approach considering nonlinear fault responses. In phasor domain models, the IBR can be modeled as a voltage controlled current source (VCCS) in tabular form with positive, negative, and zero sequence information for balanced and unbalance short-circuit faults. In the VCCS modeling of the IBR, positive and negative incremental reactive current, also known as the k-factor, plays an important role in short circuit program convergence. In this work, a few approaches: conventional VCCS modeling with a k-factor of 2, conventional VCCS modeling with a k-factor of 2 with modified pre-fault voltages, VCCS characteristics based on the power flow solution with a k-factor of 2, and VCCS characteristics based on the power flow solution with a k-factor of 1 are investigated for short circuit program convergence under higher IBR penetration. The IEEE 39 bus New England Test System is taken as the test system, and simulations are carried out in PSS®CAPE 15.0.26 simulation software. Simulation results demonstrate that IBR penetration is higher for the VCCS model, which corresponds to the power flow solution with k-factor 1, compared to other approaches.

42 ENGINEERING↗
DOE OSTI2024

Chapter 7: Learning Stable Local Volt/Var Controllers in Distribution Grids

This chapter describes a framework to synthesize provably stable local Volt/Var controllers for distributed energy resources (DERs) in power distribution grids (DGs). The goal is to control the reactive power injections of DERs to improve the system performance as quantified by a generic optimal reactive power flow (ORPF) problem. To achieve this, we jointly design for each DER the control function, which prescribes the reactive power update rule, and the equilibrium function, which approximates the ORPF solutions from local measurements of voltages and powers. We provide conditions on the equilibrium functions and the control parameters ensuring the stability of the closed-loop system. In particular, we discuss the trade-offs between each set of conditions accounting for practical considerations, like fully exploiting the DERs' generation capabilities and reducing the optimality gap. These conditions are then translated into learning constraints on the neural networks' parameters that are enforced in the training phase. We validate our framework with numerical simulations on the IEEE 37-bus network and through a comparison with an optimized version of standard piece wise linear control rules.

closed-loop asymptotic stability↗