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At least 235 records · Page 13

Hydration of divalent lanthanides, Sm 2+ and Eu 2+ : A molecular dynamics study with polarizable AMOEBA force field

The chemistry of divalent lanthanides, Ln 2+ , is a growing sub-field of heavy element chemistry owing to new synthetic approaches. However, some theoretical aspects of these unusual cations are currently underdeveloped, especially as they relate to their dynamic properties in solution. In this study, we address the hydration of two of the classical Ln 2+ cations, Sm 2+ and Eu 2+ , using atomic multipole optimized energetic for biomolecular applications (AMOEBA) force fields. These cations have not been parameterized to date with AMOEBA, and few studies are available because of their instability with respect to oxidation in aqueous media. Coordination numbers (CN's) of 8.2 and 8.1 respectively for Sm 2+ and Eu 2+ , and 8.8 for both Sm 3+ and Eu 3+ have been obtained and are in good agreement with the few available AIMD and X-ray absorption fine structures studies. The decreased CN of Ln 2+ compared with Ln 3+ arises from progressive water exchange events that indicates the gradual stabilization of 8-coordinate structures with respect to 9-coordinate geometries. Moreover, the effects of the chloride counter anions on the coordination of Ln 2+ cations have been studied at different chloride concentrations in this work. Lastly, water exchange times of Ln 2+ cations have been calculated to provide a comprehensive understanding of the behavior of Eu 2+ and Sm 2+ in aqueous chloride media.

AMOEBA force field parameterization↗

Microscopic insights into the solvation of polyethylene glycol chains in water: A machine learning potential approach

Polyethylene glycol (PEG) is a structurally simple, nontoxic, and water-soluble polymer widely utilized in medical and pharmaceutical applications. Notably, when a PEG chain is immersed in water, the surrounding water molecules play a key role in driving conformational changes of this macromolecule. In this study, we explore the solvation behavior of PEG under mechanical strain using molecular dynamics simulations, with an interatomic potential obtained from machine learning. Our focus is on the transition from the favored coil-like conformation to an extended one under external force. Through analyses of radial distribution functions, hydrogen bonding, and solvation dynamics, we uncover how mechanical stretching influences the local hydration environment. Furthermore, we disentangle the enthalpic and entropic contributions to the conformational stability of PEG in water. Surprisingly, our neural network potential model identifies dewetting of PEG C-atoms, and not water H-bonding with PEG O-atoms, as the main enthalpic driving force for the coiling of PEG in water.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modeling phonons in nanomaterials

The vibrational properties of nanomaterials play fundamentally important roles in determining their stability and various functionalities, from rippling of otherwise flat two-dimensional (2D) monolayers to the extreme thermal transport behaviors observed in one-dimensional (1D) and 2D carbon-based systems. Here we discuss modeling efforts to understand how phonons in lower dimensional materials differ from those in bulk, and how these behaviors manifest in their unusual properties. In particular, this chapter gives a heavy focus to calculations of phonon dynamics, interactions, and lattice thermal transport in 1D chains and nanotubes, 2D monolayers, and van der Waals coupled bulk materials from first principles methods. This chapter will discuss important phonon calculation details related to nanomaterials with examples and discussions providing both historical and modern perspectives.

Lindsay, Lucas↗

Small-Signal Stability of Grid-Forming Inverters Using Current-Limiting and Frequency Stabilization

This paper presents a small-signal stability analysis of grid-forming (GFM) inverters under current-limiting conditions. It examines how adjustments in virtual impedance angles, implemented through advanced current-limiting and frequency stabilization techniques, influence small-signal stability. This paper studies a GFM inverter control integrating a fictitious power technique stabilizing primary control by adding a virtual power term and a hybrid current limiter integrating virtual impedance in the anti-wind-up feedback with current reference saturation limiting. A small-signal model is developed to assess the impact of virtual impedance angles on GFM inverter dynamics during grid disturbances, such as voltage drops. The findings indicate that although increasing the virtual impedance angle (to make it more inductive) enhances large-signal stability and voltage support during faults, it can induce oscillations and lead to instability if the angle exceeds certain thresholds. Based on the small-signal models, this paper provides design considerations for the current-limiter impedances to ensure reliable GFM inverter behavior under grid disturbances while maintaining small-signal stability.

current limiting↗

Electromagnetic Transient Simulation of Large-Scale Inverter-Based Resources With High-Granularity

The power grid is undergoing a significant transformation with the rapid increase in inverter-based resources (IBRs), including large-scale photovoltaic (PV) plants. Ensuring reliable and resilient grid operation in this new paradigm necessitates high-granularity electromagnetic transient (EMT) modeling that accurately captures the behavior of individual inverters and their interactions within IBR plants. Central to this approach is the detailed representation of both the IBR plant’s collector system and the dynamics of individual inverters. To achieve this, a high-granularity EMT model of a large-scale PV plant has been developed using advanced simulation algorithms, including matrix splitting and the Schur complement. These proposed techniques significantly enhance simulation speed, numerical stability, and accuracy while improving the modularity and efficiency of the collector system’s representation. The effectiveness of the proposed methods is validated through simulations of a representative large-scale PV plant consisting of 125 individual PV inverters, 25 IBR unit transformers, and a 52-bus collector system.

Choi, Jongchan [Oak Ridge National Laboratory (ORN↗

Adaptive critic design-based reinforcement learning approach in controlling virtual inertia-based grid-connected inverters

In this report, an adaptive critic design (ACD) approach is proposed to control the phase and voltage of a grid-connected virtual synchronous generator (VSG). The penetration of fast responding inertia-less power converters significantly affect the stability of the power system, especially weak systems such as micro grids. The concept of virtual inertia addresses this concern by virtually emulating the behavior of a synchronous generator. However, the conventional VSG is designed based on two conditions: (i) fixed operating point and (ii) inductive grid connections. The performance of VSGs in low-voltage semi-resistive microgrids is far from optimal. To overcome the aforementioned concerns, a heuristic dynamic programing (HDP) approach is proposed to optimally control grid-connected VSGs. The neural-network-based inherence of the HDP enables the proposed technique to adapt to any impedance angle. The HDP controller includes two subnetworks: (i) the action network that controls the system optimally and (ii) the critic network, which evaluates the effectiveness of the action network. The simulation and experimental results are provided to evaluate the effectiveness of the proposed technique. As shown, the HDP-based approach illustrates a better performance in comparison with the conventional PI-based VSG in various operating conditions.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Locking water molecules via ternary O–H⋯O intramolecular hydrogen bonds in perhydroxylated closo -dodecaborate

A multitude of applications related to perhydroxylated closo-dodecaborate B 12 (OH) 12 2− in the condensed phase are inseparable from the fundamental mechanisms underlying the high water orientation selectivity based on the base B 12 (OH) 12 2− . Herein, we directly compare the structural evolution of water clusters, ranging from monomer to hexamer, oriented by functional groups in the bases B 12 H 12 2− , B 12 H 11 OH 2− and B 12 (OH) 12 2− using multiple theoretical methods. A significant revelation is made regarding B 12 (OH) 12 2− : each additional water molecule is locked into the intramolecular hydrogen bond B–O–H ternary ring in an embedded form. This new pattern of water cluster growth suggests that B–(H–O)⋯H–O interactions prevail over the competition from water–hydrogen bonds (O⋯H–O), distinguishing it from the behavior observed in B 12 H 12 2− and B 12 H 11 OH 2− bases, in which competition arises from a mixed competing model involving dihydrogen bonds (B–H⋯H–O), conventional hydrogen bonds (B–(H–O)⋯H–O) and water hydrogen bonds (O⋯H–O). Through aqueous solvation and ab initio molecular dynamics analysis, we further demonstrate the largest water clusters in the first hydrated shell with exceptional thermodynamic stability around B 12 (OH) 12 2− . These findings provide a solid scientific foundation for the design of boron cluster chemistry incorporating hydroxyl-group-modified borate salts with potential implications for various applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

First-principles investigation of structure-property relationships in stable and metastable MXenes

Understanding the structure–property relationships in layered transition-metal carbides or nitrides, known as MXenes, is of critical importance for their rational design, synthesis, and application. However, the vast chemical and structural diversity of MXenes, stemming from their wide range of M and X elements, surface terminations, and different atomic coordination environments, makes it challenging to clearly understand these structure–property relationships. Here, in this work, we perform first-principles density functional theory (DFT) calculations and molecular dynamics (MD) simulations to comprehensively investigate the stability and a variety of physical properties of MXenes with different coordination environments. Using Ti- and Mo-based carbide MXenes as model systems, energetic calculations reveal that Ti-based MXenes are most stable in octahedral coordination, whereas Mo-based MXenes preferentially adopt prismatic coordination. This fundamental difference in preferred atomic coordination gives rise to markedly distinct properties between these two systems as a function of the fraction of octahedral and prismatic sites. For instance, the in-plane stiffness of Ti-based MXenes increases as octahedral coordination becomes dominant, but it decreases in the Mo-based MXenes under the same conditions. Additional stability analyses based on mechanical, lattice-dynamical, and temperature-dependent thermodynamic properties demonstrate that many metastable MXenes not only satisfy the strict stability criteria but can also undergo phase transitions among different structures and even become stabilized at elevated temperatures. Although surface terminations, such as F and O atoms, do not alter the energetic ordering or the overall stiffness trends among stable and metastable MXenes, they influence other material properties. For instance, O termination can induce semiconducting behavior in both stable and metastable Ti 2 ⁢CO 2 MXenes. This study significantly advances the fundamental understanding of structure–property relationships in MXenes and provides valuable guidance for developing coordination-based design principles to precisely engineer MXenes with improved properties.

Oyeniran, Noah [University of Alabama, Tuscaloosa,↗

Impact analysis of DERs on bulk power system stability through the parameterization of aggregated DER_a model for real feeders

With an ever increasing percentage of distributed energy resources (DERs) connected behind the meter in the distribution system, it is becoming increasingly important to equip transmission planners with the visibility of DER dynamic performance in distribution system. Not having visibility of the disconnection of DERs with the occurrence of transmission events, could result in an erroneous view of the stability of bulk power system. Here, in this paper, a parameterized aggregated model (DER_a) serves as a representation of the distribution-level dynamics of real residential feeders, which is used for analysis of bulk power system stability. The parameters are obtained by executing dynamic Monte Carlo simulations. Faults are then induced at the substation level causing the DERs to trip which subsequently enables the parameterization of the low and high voltage breakpoints (v l0 , v l1 , v h0 , and v h1 ) of the DER_a model’s partial voltage trip block. These parameters are then utilized to study the effectiveness of the DER_a model to represent the behavior of the aggregated DERs’ response and their impact on the bulk power system. The case study shows the ability of the positive-sequence DER_a model to provide an accurate estimation of DERs that are susceptible to trip due to 3-$\phi$ and 1-$\phi$ faults of transmission.

14 SOLAR ENERGY↗

Transformation and twinning induced plasticity in metastable Ti-Mo alloys under high strain rate deformation

The development of metastable titanium (Ti) alloys provides an unprecedented opportunity to expand their use in plasticity and damage critical applications like protective structures. However, such applications require knowledge of quasi-static to dynamic mechanical behavior, which is currently lacking. Here we perform in-situ, ultrafast synchrotron x-ray diffraction during high strain rate (Kolsky) pressure bar testing in tension and post-mortem electron microscopy to study TRansformation Induced Plasticity (TRIP) and TWinning Induced Plasticity (TWIP) in metastable Ti-Mo alloys. Two alloys, namely Ti-12Mo and Ti-15Mo (wt.%), were selected for study having different β -phase chemical stabilities. TWIP was observed in both Ti-12Mo and Ti-15Mo by in-situ synchrotron diffraction during high strain rate testing. Post-mortem microstructural characterization also revealed the presence of TRIP in Ti-12Mo. TWIP in Ti-15Mo was found to under-perform in terms of total elongation compared to TRIP/TWIP in Ti-12Mo. Ti-12Mo exhibited an average elongation of 17% compared to only 12% for Ti-15Mo with deformation at 1000 s -1 . In conclusion, TRIP resulted in significantly finer microstructure evolution and alleviated local strain accumulations in Ti-12Mo, suggesting TRIP can be used to tune available strength/ductility combinations in metastable Ti alloys under high strain rate deformation conditions.

36 MATERIALS SCIENCE↗

Edge localized mode characteristics and divertor heat flux during stationary and transient phase for CFETR hybrid scenario

The study of edge localized mode (ELM) behavior, stationary heat flux and transient heat flux during the ELM crash phase is performed for a China Fusion Engineering Test Reactor (CFETR) 1 GW hybrid mode operation scenario ($R$ = 7.2 m, ${B_{\text{T}}}$ = 6.5 T, ${I_{\text{p}}}$ = 13.78 MA). Modeling and simulation start with a scenario obtained by multi-code integrated modeling on the one modeling framework for integrated tasks framework. Linear stability and nonlinear simulations of ELM dynamics are carried out using the BOUT++ six-field reduced magnetohydrodynamic module, which show a much smaller ELM energy loss (Δ ELM ~ 0.13%) compared to that of a Type-I ELM. Parametric analysis of the weak linear growth rate and small ELM energy loss characteristics shed light on physics corresponding to a grassy ELM regime for CFETR 1 GW hybrid scenario. The transient heat flux on the divertor target during this small ELM phase is investigated using BOUT++. Here we found that upstream radial transport in the scrape-off-layer (SOL) induced by small ELMs is weak, which keeps it in the drift-dominated region. However, the heat flux width is still broadened to ${\lambda _{\text{q}}}$ = 4.64 mm by the increase of separatrix temperature during ELM nonlinear evolution. The impact of transient peak heat load and ELM energy fluence on tungsten melting and net erosion rate of divertor target is evaluated for the first-time using physics-based transport that connects the pedestal with the SOL. Energy fluence caused by a single ELM pulse is below the tungsten melting limit, while tungsten erosion would exceed the material requirements. We conclude that external mitigation methods, such as divertor detachment and advanced divertor geometry are likely needed for the steady state operation of CFETR.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Nucleation of Dislocations in 3.9 nm Nanocrystals at High Pressure

As circuitry approaches single nanometer length scales, it has become important to predict the stability of single nanometer-sized metals. The behavior of metals at larger scales can be predicted based on the behavior of dislocations, but it is unclear if dislocations can form and be sustained at single nanometer dimensions. Here, we report the formation of dislocations within individual 3.9 nm Au nanocrystals under nonhydrostatic pressure in a diamond anvil cell. We used a combination of x-ray diffraction, optical absorbance spectroscopy, and molecular dynamics simulation to characterize the defects that are formed, which were found to be surface-nucleated partial dislocations. These results indicate that dislocations are still active at single nanometer length scales and can lead to permanent plasticity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Amphiphilic Baskets for Supramolecular Nanoarchitectures at Interfaces: Inverted Monolayer Formation on Water

Interfacial chemistry of molecular baskets remains poorly understood despite their promise for supramolecular applications of detection and sequestration of toxic molecules including those of illicit drugs, organophosphorus compounds, and anticancer agents. We present a fundamental investigation of the interfacial behavior of three amphiphilic supramolecular baskets (ASB 4, 8, and 12), having increasingly longer yet linear alkyl chains at the top of their bowl-shaped cavity. The studies were completed at the air−water interface to elucidate surface activity, interfacial stability, self-assembly, and monolayer organization that drive inverted monolayer formation, in which the molecular arms orient toward the aqueous phase in a configuration opposite to that typically observed for lipids. Herein, surface pressure−area isotherms of ASB 4, 8, 12, deposited on a water surface, were performed in tandem with nonequilibrium relaxation experiments to quantify surface activity, thermodynamic stability, and monolayer compressibility of the baskets’ monolayer assembly. Brewster angle microscopy enabled direct visualization of morphological evolution, aggregation, and packing at the interface. We show that systematic extension of the hydrocarbon arms, from four to 12 methylene groups, progressively modifies intermolecular packing, drives distinct two-dimensional aggregation pathways, and increases number densities at the air−water interface. Atomistic molecular dynamics simulations corroborate many of these experimentally observed trends and provide mechanistic detail on the cooperative roles of basket topology and interfacial concentration in regulating the hydration structure and dynamics within the cavities generated by surface-adsorbing baskets, consistent with observed variations in surface activity and packing. Our results establish how the topology of these unique supramolecules and their concentration govern interfacial organization and offer a rational framework for designing amphiphiles with predictable behavior at soft interfaces.

Hydrocarbons↗

Examination of the Radiolytic Stability of the GENIORS Solvent

The INL radiolysis test loop system has been employed to evaluate the effects of gamma radiolysis the stability and performance of the GENIORS solvent extraction process. This report describes details and results of the experiments performed and documents completion of milestone M3FT-21IN030101024 “Testing of Radiolytic Stability of m-TDDGA Based Solvent at INL”. The purpose of the proposed dynamic irradiation tests to be performed is to evaluate the radiolytic stability of the GENIORS process solvent for An/Ln recovery under process-like conditions. Recent research efforts within the European Union GENIORS project have focused upon demonstrating additional process improvements. These improvements include simplification of the solvent composition, use of reagents composed of only C, H, O, and N atoms (the CHON principle), identification of a diglycolamide derivative with more favorable Pu loading behavior, and use of an aqueous soluble stripping reagent that is not sulfonated. As a result, a new solvent utilizing dimethyl-N,N,N’,N’-tetradecyl-diglycolamide (cis-mTDDGA) as the An/Ln extractant and the aqueous soluble 2,6-bis[1-(propan-1-ol)-1,2,3-triazol-4yl]-pyridine (PTD) as the An/Ln stripping reagent was proposed. The impact of gamma radiolysis upon the efficacy of the GENIORS process solvent was evaluated by determining the americium, europium, and cerium distribution ratios as a function of absorbed dose. The measured distribution ratios demonstrated that the GENIORS solvent did undergo radiolytic degradation. However, at absorbed doses corresponding to realistic process conditions, the extraction and stripping performance of the solvent remains acceptable. Compositional analysis of the irradiated solvent revealed a decrease in the concentration of cis-mTDDGA, which is consistent with the observed changes in metal distribution ratios as a function of absorbed dose.

38 - RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCL↗

Colloidal Behavior of Plutonium Oxide in Concentrated Electrolyte Solutions

The Hanford Site in Washington State manages legacy high-level radioactive waste streams that display major chemistry and engineering challenges, including the high salt levels and pH values that correspond to conditions under which many classical concepts describing chemical reactivity cannot be applied. One particular challenge that needs to be tackled at Hanford is that Pu concentrations, [Pu], in the soluble phases of the tank wastes are higher than expected based on the solubility of crystalline PuO2, which is widely accepted to be caused by the formation of PuO2 colloid, consisting of nano- to submicron-sized particles (PuO2 NPs). Fundamental research underpinning the behavior of PuO2 NPs under conditions not only relevant to the Hanford tank waste but at high ionic strength in general is needed to reliably predict the chemical reactivity of PuO2 NPs and develop engineering solutions to safely and efficiently process high-level radioactive waste into forms suitable for long-term storage. In this work, we study the behavior of PuO2 NPs (particle size ~100 nm) under high ionic strength conditions by reacting it with highly concentrated (up to 5 M) salt solutions. We explore different electrolyte compositions to elucidate the impact of different anions (NO3-, Cl-, ClO4-, SO42-, C2O42-, CO32-) on the stability of PuO2 NP in the acidic and alkaline pH regime. PuO2 NP aggregation and precipitation as function electrolyte concentration is tracked by a combination of liquid scintillation counting, dynamic light scattering for determination of particle size distributions, and zeta potentials as a proxy for particle charge. At acidic pH, electrolytes containing non-coordinating anions, such as NaNO3, NaCl, and NaClO4 mostly stabilize PuO2 NPs over a large electrolyte concentration range, showing only subtle differences in their reactivity. Other electrolyte anions show a more pronounced effect on the PuO2 NP stability: SO42-, binds directly to the particles’ surface, reverses the particle charge, and precipitates the PuO2 NPs efficiently even at intermediate sulfate concentrations (>0.1 M). In contrast, C2O42- is found to lead to high [Pu] in solution, in the milli-molar range, even at mildly acidic pH (~4). Thermodynamic modeling of the dissolved Pu concentrations using PHREEQC is unable to predict the observed [Pu] in the acidic pH regime, supporting the influence of colloids in maintaining elevated [Pu]. It is noteworthy that the current thermodynamic databases do not include constants for colloidal Pu phases and cannot accurately predict many of the high ionic strength solutions relevant to this work. The mechanisms and models responsible for these observations will need further investigation in the future. At high pH values (~12), PuO2 NPs exhibits classical sol-gel chemistry, meaning that upon destabilization of the colloidal sol, for example by addition of concentrated NaOH, highly porous and viscid PuO2 coagulates are formed that consist of a three-dimensional network likely held together by physical interactions. The PuO2 NP coagulate shows no significant reversibility of the aggregation when contacted with concentrated brines; however, PuO2 NPs can be efficiently resuspended in solution by addition of diluted electrolytes, alkaline solutions containing high amounts of carbonate, or simple addition of water. Especially carbonate is shown to stabilize PuO2 NPs in solution at high pH, characterized by stable colloidal suspensions that are resistant against sedimentation during centrifugation. Thermodynamic modeling of the carbonate system was able to predict an increasing dissolved Pu concentration with increasing carbonate concentration. However, the model was profoundly sensitive to the fixed redox potential and does not include any thermodynamic constants for colloidal Pu species.

Neumann, Julia↗

Data-driven modeling and control of an X-ray bimorph adaptive mirror

Adaptive X-ray mirrors are being adopted on high-coherent-flux synchrotron and X-ray free-electron laser beamlines where dynamic phase control and aberration compensation are necessary to preserve wavefront quality from source to sample, yet challenging to achieve. Additional difficulties arise from the inability to continuously probe the wavefront in this context, which demands methods of control that require little to no feedback. In this work, a data-driven approach to the control of adaptive X-ray optics with piezo-bimorph actuators is demonstrated. This approach approximates the non-linear system dynamics with a discrete-time model using random mirror shapes and interferometric measurements as training data. For mirrors of this type, prior states and voltage inputs affect the shape-change trajectory, and therefore must be included in the model. Without the need for assumed physical models of the mirror's behavior, the generality of the neural network structure accommodates drift, creep and hysteresis, and enables a control algorithm that achieves shape control and stability below 2 nm RMS. Using a prototype mirror and ex situ metrology, it is shown that the accuracy of our trained model enables open-loop shape control across a diverse set of states and that the control algorithm achieves shape error magnitudes that fall within diffraction-limited performance.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Stabilizing a strongly nonlinear structure through shaker dynamics in fixed frequency voltage control tests

Bifurcations are commonly encountered during force controlled swept and stepped sine testing of nonlinear structures, which generally leads to the so-called jump-down or jump-up phenomena between stable solutions. There are various experimental closed-loop control algorithms, such as control-based continuation and phase-locked loop, to stabilize dynamical systems through these bifurcations, but they generally rely on specialized control algorithms that are not readily available with many commercial data acquisition software packages. A recent method was developed to experimentally apply sequential continuation using the shaker voltage that can be readily deployed using commercially available software. By utilizing the stabilizing effects of electrodynamic shakers and the force dropout phenomena in fixed frequency voltage control sine tests, this approach has been demonstrated to stabilize the unstable branch of a nonlinear system with three branches, allowing for three multivalued solutions to be identified within a specific frequency bandwidth near resonance. Recent testing on a strongly nonlinear system with vibro-impact nonlinearity has revealed jumping behavior when performing sequential continuation along the voltage parameter, like the jump phenomena seen during more traditional force controlled swept and stepped sine testing. Here, this paper investigates the stabilizing effects of an electrodynamic shaker on strongly nonlinear structures in fixed frequency voltage control tests using both numerical and experimental methods. The harmonic balance method is applied to the coupled shaker-structure system with an electromechanical model to simulate the fixed voltage control tests and predict the stabilization for different parameters of the model. The simulated results are leveraged to inform the design of a set of experiments to demonstrate the stabilization characteristics on a fixture-pylon assembly with a vibro-impact nonlinearity. Through numerical simulation and experimental testing on two different strongly nonlinear systems, the various parameters that influence the stability of the coupled shaker-structure are revealed to better understand the performance of fixed frequency voltage control tests.

42 ENGINEERING↗

Demand Response Under Stochastic, Price-Dependent User Behavior

This letter focuses on price-based demand response (DR) implemented through dynamic adjustments of electricity prices. It extends existing DR models to a stochastic framework in which customer response is represented by price-dependent random variables, leveraging models and tools from the theory of stochastic optimization with decision-dependent distributions. The inherent epistemic uncertainty in the customers' responses renders open-loop, model-based DR strategies impractical. We propose a stochastic, feedback-based pricing strategy to compensate for estimation errors and uncertainty in customer response, establish theoretical results demonstrating the stability and near-optimality of the proposed approach, and validate its effectiveness through numerical simulations.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗