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At least 829 records · Page 46

Practical Insights on Applying Simulation-Based Control Methods in Experimental Studies

Advanced nuclear reactors are crucial to the future of energy both in the United States and around the globe. In contrast to the current operating fleet, they are characterized as being deployable in remote locations and able to operate in semi-autonomous or autonomous fashion. This leap forward necessitates a new reactor control paradigm. Because advanced nuclear reactors are still under development in the United States, the creation of new control methods to achieve autonomous operations has been based on systems modeling and simulation. However, an important factor in successfully deploying these new control methods is the ability to seamlessly transition from simulation environments to real-world settings. Control methods tested in both simulation and experimental settings need to be investigated in the context of advanced reactor applications. This work developed a series of simple controllers for Idaho National Laboratory (INL)’s Microreactor Applications Research Validation and Evaluation (MARVEL) microreactor operating in load-following scenarios. These controllers were tested in both simulation and experimental settings, and a comparative performance analysis was performed. The simulation tests leveraged the Control and Optimization Modular Modeling Application for Nuclear Deployment (COMMAND) software developed in a previous stage of the current effort, along with the MARVEL Reactor Excursion and Leak Analysis Program (RELAP5-3D) and Monte Carlo N-Particle (MCNP) models. The experimental tests leveraged the COMMAND software, MARVEL models, and the U.S. Department of Energy Microreactor Program’s Microreactor Automated Control System (MACS). MACS was developed to serve as a control method testbed. It was customized to mirror the MARVEL microreactor, and COMMAND enabled MACS to emulate the physics of MARVEL. The load-following controller was developed using the simulation platform, with efforts to emulate real systems by introducing actuator saturation and noise. These factors were incrementally accounted for in the controller design. After finalizing the controller design, it was implemented with the experimental setup. The experimental conditions tested included an initial test under conditions similar to the final simulation test, and two additional scenarios. The first scenario introduced additional actuator saturation to account for equipment aging over time, which was unknown to the controller. The second scenario introduced sensor delay, a phenomenon anticipated with the use of remote operations or wireless communication in advanced reactors. These tests revealed several notable differences. While the controller performed well in simulation, it exhibited several limitations when transitioning to hardware. The main challenges involved maintaining the steady-state target power, as evidenced by larger error values between the true reactor power and setpoint power, as well as persistent oscillations in controlled reactor power. These issues could lead to unacceptable transient conditions in real reactor testing. Introducing actuator aging and stochastic delays in the experimental setup significantly impacted controller performance, resulting in increased overshoot and undershoot, and exacerbated error and oscillations previously mentioned. These findings underscore the importance of experimental testbeds for testing and validating control methods, as controllers developed using only theory and/or simulation may perform unexpectedly when applied to actual hardware. This research emphasizes the need for an experimental testbed for achieving such validation.

46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN↗

STOCHASTIC OPTIMAL POWER FLOW FOR REAL-TIME MANAGEMENT OF DISTRIBUTED RENEWABLE GENERATION AND DEMAND RESPONSE (Final Report)

To meet the grand challenge of a sustainable energy future, there has been a surge of interest in renewable energy. Today, the uncertainty associated with renewable resources is handled by using operating reserves. The high penetration of renewable resources, however, introduces difficult-to-control dynamics and challenges for power system operation. Decision support tools are necessary at the bulk system operational level to recognize and efficiently utilize renewable resources and distributed demand response products in concert with traditional grid resources. It is envisaged that responsive load can potentially have very significant cost advantages over either spinning or non-spinning ramping reserve. Critical decisions are made during hour(s)-ahead and real-time power system operation regarding the commitment and dispatch of generators to ensure power delivery is both reliable and economic. These decisions are typically made by a security constrained optimal flow, which determines future generator commitments, dispatches, and ensures adequate reserves are available in the event of a contingency (unexpected outage) or if future system conditions deviate from forecasts. However, security has been always based on a pre-specified subset of contingency constraints whose enforcement does not guarantee security under all possible future possibilities while also giving little or no weight to the likelihood of each contingent event or the severity of its consequences. Existing tools, which are based exclusively on deterministic optimization models, do not yield optimal operational decisions to address these new challenges, in terms of both reliability and cost-effectiveness. This project has focused on developing a stochastic optimal power flow (SOPF) framework, which integrates renewable resource uncertainty, load uncertainty, distributed storage (DS), demand response (DR) products, in a holistic manner to address the uncertainty associated with ever-increasing renewable resources, along with the inclusion of distributed demand response products in future power systems. A proof-of-concept problem was created using the Pennsylvania-Jersey-Maryland (PJM) power system network. Synthetic wind generation was added to the system to simulate 50% wind penetration. A 1-hour test of SOPF operation indicated more than 6% operational cost savings. The project continued by adding the Midwestern Independent System Operator (MISO) as a partner, with focus shifting from SOPF to Stochastic Look-Ahead Unit Commitment (SLAC). Unlike PJM, MISO is faced with significant renewable energy resources within its footprint and is challenged with substantial uncertainty in its operations. The SLAC distinguishes itself from existing tools that operators use. At best, today’s tools solve two to three cases independently, where one or two system parameters, such as forecasted load level (e.g., a low, base, and high forecast), are varied and the resulting scenarios are analyzed independently. The stochastic-based optimization of SLAC leverages statistical information from an ensemble of potential operational scenarios and their respective likelihood. The SLAC output can be translated into valuable information to the operator such as suggested commitments, optimal scheduling and dispatch of resources, reserve requirements at both locational and zonal resolutions, ramping availability and requirements, availability of demand response including operational guidance concerning the near-term and real-time coordination between distributed energy resources, and utilization of distributed storage resources. The developed SOPF/SLAC tool, a stand-alone tool compatible with existing EMSs, will provide system operators with unprecedented visibility, flexibility and predictability to these resources and operational guidance concerning the real-time coordination between DERs and DR/DS products. The game changing and practical impact of this disruptive technology will be dramatic and will usher in a new era in the electric power industry, wherein green energy concepts are fully embraced, and electric power costs are lowered throughout the nation.

42 ENGINEERING↗

Runaway electron transport in stochastic toroidal magnetic fields

Here, we study the transport and confinement properties of runaway electrons (RE) in the presence of magnetic fields with perturbations producing different levels of stochasticity. We use Kinetic Orbit Runaway Electron Code (KORC) [Carbajal et al. , Phys. Plasmas 24, 042512 (2017) and del-Castillo-Negrete et al. , Phys. Plasmas 25, 056104 (2018)] for simulating the full-orbit (FO) and guiding-center (GC) dynamics of RE in perturbed magnetic fields that exhibit magnetic islands. We extend previous works on this problem [Wingen et al. , Nucl. Fusion 46, 941 (2006); Izzo et al. , Nucl. Fusion 51, 063032 (2011); Papp et al. , Nucl. Fusion 51, 043004 (2011); V. Izzo and P. Parks, Phys. Plasmas 24, 060705 (2017); and Sommariva et al. , Nucl. Fusion 58, 016043 (2018)] by studying in detail full-orbit effects on the RE dynamics. We quantify FO effects on RE transport by performing one-to-one comparisons between FO and GC simulations. It is found that, for the magnetic field configurations considered, GC simulations predict twice the RE losses of FO simulations for 1 MeV and four times the RE losses of FO simulations for 25 MeV. Similarly, we show how different GC and FO dynamics of RE moving around magnetic islands can be, especially in the scenario where the RE Larmor radius is on the order of the size of the magnetic island. We also study the role of rotation of the magnetic islands on RE confinement, and we find that low-frequency toroidal rotation has no observable effect on RE transport in the cases considered. These results shed some light into the potential of avoidance or mitigation mechanisms based on magnetic perturbations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Simulation of Physics-Based 0-10Hz Strong Motion Using High Performance Computing Supporting Refinements to Regional Ground Motion Models for the Central Eastern US

In collaboration with the U.S. Nuclear Regulatory Commission (NRC) the LLNL has developed a computationally efficient simulation platform designed to perform physics-based ground motion simulations for crustal earthquakes in the Stable Continental Regions of Central and Eastern US (CEUS), using high-performance computing. The main objective of the earthquake simulations was to use synthetic ground motion to provide constrains to refinements of existing ergodic Ground Motion Models (GMMs), for large magnitude earthquakes and near-fault distances, for which these models are less reliable. Physics-based broadband (0-10Hz) ground motion simulations were used to estimate the near-fault ground motion amplitudes and within event and between-event variabilities associated with fault rupture characteristics. In our simulations we used a 3D regional velocity model that was based on Saikia’s 1D velocity model (1994). In simulations performed during the first stage of this project the Saikia’s velocity model demonstrated better performance in modelling high frequency regional wave propagation for the CEUS region recorded during the Mw5.0 November 7, 2016, Cushing Oklahoma (Taylor et al., 2017), and Mw5.8 September 3, 2016, Pawnee Oklahoma earthquakes. The proposed regional 3D model includes random perturbations to the 1D background model using the stochastic scheme of Pitarka and Mellors (2021). In addition, validation analysis of the rupture generator and regional wave propagation models, using comparisons with different GMMs for Mw6.5 and Mw7.0 scenario earthquakes in the CEUS region resulted in a very good match between the simulated and empirical ground motion models. For the purposes of seismic hazard assessment at the existing and planned nuclear power plants, NRC is interested in studies aimed at improving the current ground motion models (GMM) for both Stable Continental Regions (SCR) in the Central and Eastern US and Active Crustal Regions (ACR) in the Western US. Due to lack of recorded data, these improvements require synthetic data for short fault distances and large magnitude earthquakes for which the existing recorded data is not enough to uniquely constrain the GMMs. The need for simulations and strong motion data is especially critical for the CEUS region where we do not have recorded data from potentially large damaging earthquakes with moment magnitudes 6.0 and higher. In this the project, we focused on 10Hz simulations of Mw7.0 scenario earthquakes with strike slip and thrust faulting mechanisms. We used more than 50 Mw7.0 earthquake rupture scenarios to investigate the ground motion uncertainty due to unknown earthquake rupture parameters, in particular, the slip distribution, rupture velocity, and faulting mechanism, and their implication on ground motion amplification due to forward rupture directivity effects.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Ultimate compressive strength and severe plastic deformation of equilibrated single-crystalline copper nanoparticles

Mechanical properties and deformation mechanisms of defect-free copper nanoparticles are investigated by combining experiments with atomistic simulations. The compressive strength of the particles increases with decreasing size and tends to saturate near the theoretical strength in the small-size limit. In this limit, the intrinsic size dependence of the strength is governed by the stochastic nature of dislocation nucleation near the particle surface. The particle deformation process evolves from the initial strain softening to strain hardening as the particle accumulates residual damage. The normalized strength-size relation for Cu is compared with those for Au, Ni, and Pt. The lack of universal behavior among the four FCC metals is discussed. Heavily deformed Cu nanoparticles develop polycrystalline structures and change the lattice orientation from [111] to [110]. The experiments and simulations reveal the twinning mechanism of the lattice rotation leading to the new grain formation.

36 MATERIALS SCIENCE↗

Ultimate compressive strength and severe plastic deformation of equilibrated single-crystalline copper nanoparticles

Mechanical properties and deformation mechanisms of defect-free copper nanoparticles are investigated by combining experiments with atomistic simulations. The compressive strength of the particles increases with decreasing size and tends to saturate near the theoretical strength in the small-size limit. In this limit, the intrinsic size dependence of the strength is governed by the stochastic nature of dislocation nucleation near the particle surface. The particle deformation process evolves from the initial strain softening to strain hardening as the particle accumulates residual damage. The normalized strength-size relation for Cu is compared with those for Au, Ni, and Pt. The lack of universal behavior among the four FCC metals is discussed. Heavily deformed Cu nanoparticles develop polycrystalline structures and change the lattice orientation from [111] to [110]. The experiments and simulations reveal the twinning mechanism of the lattice rotation leading to the new grain formation.

36 MATERIALS SCIENCE↗

How good are learning-based control v.s. model-based control for load shifting? Investigations on a single zone building energy system

Both model predictive control (MPC) and deep reinforcement learning control (DRL) have been presented as a way to approximate the true optimality of a dynamic programming problem, and these two have shown significant operational cost saving potentials for building energy systems. Furthermore, there is still a lack of in-depth quantitative studies on their approximation levels to the true optimality, especially in the building energy domain. To fill in the gap, this paper provides a numerical framework that enables the evaluation of the optimality levels of different controllers for building energy systems. This framework is then used to comprehensively compare the optimal control performance of both MPC and DRL controllers with given computation budgets for a single zone fan coil unit system. Note the optimality is estimated based on a user-specific selection of trade-off weights among energy costs, thermal comfort and control slew rates. Compared with the best optimality we can find through expensive optimization simulations, the best DRL agent can maximally approximate the optimality by 96.54%, which outperforms the best MPC whose optimality level is 90.11%. However, due to the stochasticity, the DRL agent is only expected to approximate the optimality by 90.42%, which is almost equivalent to the best MPC. Except for Proximal Policy Optimization (PPO), all DRL agents can have a better approximation to the optimality than the best MPC, and are expected to have better approximation than the MPC with a prediction horizon of 32 steps (15 min per step). In terms of reducing energy cost and thermal discomfort, MPC can outperform the rule-based control (RBC) by 18.47%–25.44%. DRL can be expected to outperform RBC by 18.95%–25.65% ,and the best DRL control policy can outperform RBC by 20.29%–29.72%. Although the comparison of the optimality level is performed in a perfect setting, e.g., MPC assumes perfect models, and DRL assumes a perfect offline training process and online deployment process, this can shed insight on their capabilities of approximating to the original dynamic programming problem.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Stochastic reconstruction of fracture network pattern using spatial point processes

Fracture spatial patterns can strongly affect fluid flow in the subsurface. Proximity and distribution of fractures control reservoir flow behavior over various length scales. In many studies, however, simplified geometrical patterns are generated for fractures which may lead to unrealistic subsurface models. Here we introduce a new method for characterization and modeling of fracture spatial patterns based on outcrop observations. We use Ripley's K-function to characterize the arrangement of fracture barycenters and intersection points over various length scales. In addition, we use semivariograms to quantify spatial correlation in fracture intensity maps. Using this information, we develop a stochastic algorithm that generates two-dimensional fracture network realizations with spatial properties similar to those of a real fracture network measured in the field. Numerical simulation models indicate that the generated fracture realizations exhibit similar flow behaviors as that of the original fracture network. Furthermore, such modeling tools expand and improve our capability in building representative fracture models and in quantification of uncertainty in naturally and hydraulically fractured reservoirs.

58 GEOSCIENCES↗

Stochastic equilibrium Raman spectroscopy (STERS)

In this manuscript, we propose a new method for cavity- and surface-enhanced Raman spectroscopy (SERS) with improved temporal resolution in the measurement of stochastic Raman spectral fluctuations. Our approach combines Fourier spectroscopy and photon correlation to decouple the integration time from the temporal resolution. Using statistical optics Monte Carlo simulations, we establish the relationship between time resolution and Raman signal strength, revealing that typical Raman spectral fluctuations, commensurate with molecular conformational dynamics, can theoretically be resolved on micro- to millisecond timescales. The method can further extract average single-molecule dynamics from small sub-ensembles, thereby potentially mitigating challenges in achieving strictly single-molecule isolation on SERS substrates.

Cobb-Bruno, Colburn [University of California, Ber↗

Using mechanistic models and machine learning to design single-color multiplexed nascent chain tracking experiments

mRNA translation is the ubiquitous cellular process of reading messenger-RNA strands into functional proteins. Over the past decade, large strides in microscopy techniques have allowed observation of mRNA translation at a single-molecule resolution for self-consistent time-series measurements in live cells. Dubbed Nascent chain tracking (NCT), these methods have explored many temporal dynamics in mRNA translation uncaptured by other experimental methods such as ribosomal profiling, smFISH, pSILAC, BONCAT, or FUNCAT-PLA. However, NCT is currently restricted to the observation of one or two mRNA species at a time due to limits in the number of resolvable fluorescent tags. In this work, we propose a hybrid computational pipeline, where detailed mechanistic simulations produce realistic NCT videos, and machine learning is used to assess potential experimental designs for their ability to resolve multiple mRNA species using a single fluorescent color for all species. Our simulation results show that with careful application this hybrid design strategy could in principle be used to extend the number of mRNA species that could be watched simultaneously within the same cell. We present a simulated example NCT experiment with seven different mRNA species within the same simulated cell and use our ML labeling to identify these spots with 90% accuracy using only two distinct fluorescent tags. We conclude that the proposed extension to the NCT color palette should allow experimentalists to access a plethora of new experimental design possibilities, especially for cell Signaling applications requiring simultaneous study of multiple mRNAs.

59 BASIC BIOLOGICAL SCIENCES↗

Evaluation of an efficient statistical transport model for turbulent droplet dispersion in dilute combusting sprays

Evaluation of an efficient statistical transport model for turbulent droplet dispersion is made for a dilute spray of methanol droplets injected into a turbulent, axisymmnetric methane-fuelled diffusion flame burning in stagnant air. In the dispersion model, a computational parcel representing a group of physical particles (droplets) is considered to have a normal probability density function (pdf) in space. The mean is determined by Lagrangian tracking through a sequence of stochastically generated turbulent eddies and the variance is evaluated from a statistical formulation based on the linearized particle equations of motion. The basic validity of this model is established through comparison with available experimental data and with theoretical predictions using a conventional stochastic direct modeling approach. The conclusion of the evaluation is that the proposed dispersion model compares favorably with experimental data and provides a valid technique for simulating turbulent combusting sprays with significant computational savings over conventional methods.

Litchford, Ron J.↗

Anomalous Transport of High Energy Cosmic Rays in Galactic Superbubbles

High-energy cosmic rays may exhibit anomalous transport as they traverse and are accelerated by a collection of supernovae explosions in a galactic superbubble. Signatures of this anomalous transport can show up in the particles' evolution and their spectra. In a continuous-time-random- walk (CTRW) model assuming standard diffusive shock acceleration theory (DSA) for each shock encounter, and where the superbubble (an OB stars association) is idealized as a heterogeneous region of particle sources and sinks, acceleration and transport in the superbubble can be shown to be sub-diffusive. While the sub-diffusive transport can be attributed to the stochastic nature of the acceleration time according to DSA theory, the spectral break appears to be an artifact of transport in a finite medium. These CTRW simulations point to a new and intriguing phenomenon associated with the statistical nature of collective acceleration of high energy cosmic rays in galactic superbubbles.

Barghouty, Nasser F.↗

Surrogate approximation of the Grad–Shafranov free boundary problem via stochastic collocation on sparse grids

In magnetic confinement fusion devices, the equilibrium configuration of a plasma is determined by the balance between the hydrostatic pressure in the fluid and the magnetic forces generated by an array of external coils and the plasma itself. The location of the plasma is not known a priori and must be obtained as the solution to a free boundary problem. The partial differential equation that determines the behavior of the combined magnetic field depends on a set of physical parameters (location of the coils, intensity of the electric currents going through them, magnetic permeability, etc.) that are subject to uncertainty and variability. The confinement region is in turn a function of these stochastic parameters as well. In this work, we consider variations on the current intensities running through the external coils as the dominant source of uncertainty. This leads to a parameter space of dimension equal to the number of coils in the reactor. With the aid of a surrogate function built on a sparse grid in parameter space, a Monte Carlo strategy is used to explore the effect that stochasticity in the parameters has on important features of the plasma boundary such as the location of the x-point, the strike points, and shaping attributes such as triangularity and elongation. Furthermore, the use of the surrogate function reduces the time required for the Monte Carlo simulations by factors that range between 7 and over 30.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Integrated Strategies for Overcoming Resolution Limits in Electron Beam Lithography of Chemically Amplified Resists

Electron beam lithography (EBL) of chemically amplified resists (CARs) faces fundamental challenges, including stochastic electron scattering and acid diffusion, that limit resolution and reproducibility. Using SU-8 as a model CAR, this study systematically investigated complementary strategies to address these challenges, combining multipass exposure, proximity effect correction (PEC) with midrange correction factors, base quencher incorporation, and post-exposure bake (PEB) suppression. Monte Carlo simulations and calibrated PEC modeling revealed that extending the point spread function to include a midrange scattering component significantly improved critical dimension (CD) control across varying pattern densities, correcting deviations that conventional two-term PEC failed to capture. Multipass exposure, particularly 4-pass writing with a 25% offset, redistributed the dose to average stochastic beam and scattering fluctuations, reducing line-width roughness by more than 50% and yielding more uniform nanoscale features. Photoacid confinement was investigated by adding urea as a base quencher, which successfully reduced acid diffusion but introduced substantial sensitivity penalties without improving ultimate resolution or Z-factor performance, underscoring the trade-offs of chemical versus physical confinement. Suppressing PEB most directly minimized acid diffusion, resulting in improved Z-factors and reproducible 30 nm half-pitch dense line/space patterns. Overall, these results demonstrated that PEC with midrange correction, multipass strategies, quencher additives, and PEB-free processing addresses different aspects of the EBL process window and that their integration provides a comprehensive framework for managing stochastic scattering, diffusion, and chemical amplification effects. This framework advances dense nanoscale patterning in CARs and establishes guiding principles for optimizing resist design and process strategies in high-resolution EBL and potentially other advanced lithographies, such as extreme ultraviolet (EUV) lithography.

36 MATERIALS SCIENCE↗

Stochastic Models of Molecule Formation on Dust

We will present new theoretical models for the formation of molecules on dust. The growth of ice mantles and their layered structure is accounted for and compared directly to observations through simulation of the expected ice absorption spectra

Charnley, Steven↗

Real-Time KMC Simulation of Vacancy-Mediated Intermixing in Au@Ag Octahedral Core–Cubic Shell Nanocrystals with Ab Initio-Guided Kinetics

Utilization of core–shell rather than monometallic nanocrystals (NCs) facilitates fine-tuning of NC properties for applications. However, compositional evolution via intermixing can degrade these properties prompting recent experimental studies. We develop an atomistic-level stochastic model for vacancy-mediated intermixing exploiting a formalism which allows incorporation at an ab initio density functional theory level of not just the thermodynamics of vacancy formation, but also relevant diffusion barriers for a vast number of possible local environments (in the core and in the shell, at the interface, and in the intermixed phase). This facilitates a predictive treatment and comprehensive understanding of intermixing on the relevant time scale (e.g., 10 1 –10 3 s). In contrast, previous modeling at the atomistic level utilized only unrealistic generic prescriptions of barriers or employed simplified continuum treatments. For Au@Ag octahedral core–cubic shell NCs, our modeling not only captures the experimentally observed rate or time scale for intermixing of ~100 s at 450 °C for 60 nm NCs, but also elucidates the underlying rate controlling processes and the effective intermixing barrier.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Designing Monte Carlo Simulation and an Optimal Machine Learning to Optimize and Model Space Missions

This paper investigates applying artificial intelligence (AI) algorithms to attitude control system of satellites to optimally tune the controller using high performance computing. This methodology is applied to the Virtual Telescope for X-ray Observation mission, which is a precise formation of two separate spacecraft observing multiple objects in the space in the X-ray domain. The mission is divided into phases based on the instrumentation and the mission goal. To reach an stable precise formation robust to stochastic slew and slew rate (i.e., Euler angles and angular velocities) in a minimal constrained time T , consumed energy of the attitude control system, denoted as E, and root-mean-square state error of attitude control system, denoted as e, are minimized. Monte-Carlo simulation is used for the sensitivity analysis of optimization and designing a controller. Deep neural networks (DNN), Gaussian processes (GP), and support vector regression (SVR) learn this optimization as a surrogate model, while their hyperparameters are optimized in a novel approach. THETA supercomputer at Argonne Leadership Computing Facility (ALCF) is used for optimizing the hyperparameters of DNN. The surrogate model meets the requirements of the mission, and it shows a better performance over the optimization and Monte-Carlo. The optimal DNN can satisfy the mission requirements e and T while reducing E for 90% compared to the other given methods.

42 ENGINEERING↗

Risk-Constrained Reinforcement Learning for Inverter-Dominated Power System Controls

Here, this paper develops a risk-aware controller for grid-forming inverters (GFMs) to minimize large frequency oscillations in GFM inverter-dominated power systems. To tackle the high variability from loads/renewables, we incorporate a mean-variance risk constraint into the classical linear quadratic regulator (LQR) formulation for this problem. The risk constraint aims to bound the time-averaged cost of state variability and thus can improve the worst-case performance for large disturbances. The resulting risk-constrained LQR problem is solved through the dual reformulation to a minimax problem, by using a reinforcement learning (RL) method termed as stochastic gradient-descent with max-oracle (SGDmax). In particular, the zero-order policy gradient (ZOPG) approach is used to simplify the gradient estimation using simulated system trajectories. Numerical tests conducted on the IEEE 68-bus system have validated the convergence of our proposed SGDmax for GFM model and corroborate the effectiveness of the risk constraint in improving the worst-case performance while reducing the variability of the overall control cost.

Frequency control↗