Results for “dynamical systems” — Page 17

DOE OSTI2021

Deep learning of parameterized equations with applications to uncertainty quantification

We propose a learning algorithm for discovering unknown parameterized dynamical systems by using observational data of the state variables. Our method is built upon and extends the recent work of discovering unknown dynamical systems, in particular those using deep neural network (DNN). We propose a DNN structure, largely based upon the residual network (ResNet), to not only learn the unknown form of the governing equation but also take into account the random effect embedded in the system, which is generated by the random parameters. Once the DNN model is successfully constructed, it is able to produce system prediction over longer term and for arbitrary parameter values. For uncertainty quantification, it allows us to conduct uncertainty analysis by evaluating solution statistics over the parameter space.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Koopman-based Differentiable Predictive Control for the Dynamics-Aware Economic Dispatch Problem

The dynamics-aware economic dispatch (DED) problem embeds low-level generator dynamics and operational constraints to enable near real-time scheduling of generation units in a power network. DED produces a more dynamic supervisory control policy than traditional economic dispatch (T-ED) that reduces overall generation costs. However, the incorporation of differential equations that govern the system dynamics makes DED an optimization problem that is computationally prohibitive to solve. In this work, we present a new data-driven approach based on differentiable programming to efficiently obtain offline parametric solutions to the underlying DED problem. In particular, we employ the recently proposed differentiable predictive control (DPC) for offline learning of explicit neural control policies based on identified Koopman operator (KO) model of the system dynamics. We demonstrate the high solution quality and five orders of magnitude computational-time savings of the DPC method over the original optimization-based DED approach on a 9-bus test power grid network.

King, Ethan↗

DOE OSTI2023

Impact of Transportation Electrification on the System's Dynamic Frequency Response

Transportation electrification is an integral component of the energy decarbonization transition. This paper investigates the impact of distributed energy resources (DERs), including distributed photovoltaics (DPV) and electric vehicles (EVs), in the primary frequency response of the power grid. Increasing DER adoption poses challenges to maintaining grid frequency stability. However, DERs' ability to provide fast frequency regulation services-primary frequency response (PFR) and secondary frequency response (SFR)-can be exploited to recover the frequency after an N-1 contingency event in the system. This paper also investigates the importance of a droop control strategy through dynamic models of DPV and EV to provide the primary frequency regulation services following the contingency event. A dynamic EV model, based on the PVD1 model Western Electricity Coordinating Council (WECC) introduced, has been used for the simulation. Further, DERs' primary frequency response is studied for five different cases of DER penetration levels after the system is exposed to the generator trip. Additionally, different frequency regulation capacities of EVs are analyzed. The studies show that an increment in DERs capacity providing effective PFR can improve the system frequency nadir and stabilize the frequency faster after the generation trip contingency.

distributed energy resources↗

DOE OSTI2023

Impact of Transportation Electrification on the System's Dynamic Frequency Response: Preprint

Transportation electrification is an integral component of the energy decarbonization transition. This paper investigates the impact of distributed energy resources (DERs), including distributed photovoltaics (DPV) and electric vehicles (EVs), in the primary frequency response of the power grid. Increasing DER adoption poses challenges to maintaining grid frequency stability. However, DERs' ability to provide fast frequency regulation services-primary frequency response (PFR) and secondary frequency response (SFR)-can be exploited to recover the frequency after an N-1 contingency event in the system. This paper also investigates the importance of a droop control strategy through dynamic models of DPV and EV to provide the primary frequency regulation services following the contingency event. A dynamic EV model, based on the PVDl model Western Electricity Coordinating Council (WECC) introduced, has been used for the simulation. Further, DERs' primary frequency response is studied for five different cases of DER penetration levels after the system is exposed to the generator trip. Additionally, different frequency regulation capacities of EVs are analyzed. The studies show that an increment in DERs capacity providing effective PFR can improve the system frequency nadir and stabilize the frequency faster after the generation trip contingency.

ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2026

SODAs: sparse optimization for the discovery of differential and algebraic equations

Differential-algebraic equations (DAEs) integrate ordinary differential equations (ODEs) with algebraic constraints, providing a fundamental framework for developing models of dynamical systems characterized by time-scale separation, conservation laws and physical constraints. While sparse optimization has revolutionized model development by allowing data-driven discovery of parsimonious models from a library of possible equations, existing approaches for dynamical systems assume DAEs can be reduced to ODEs by eliminating variables before model discovery. This assumption limits the applicability of such methods for DAE systems with unknown constraints and time scales. We introduce sparse optimization for differential-algebraic systems (SODAs), a data-driven method for the identification of DAEs in their explicit form. By discovering the algebraic and dynamic components sequentially without prior identification of the algebraic variables, this approach leads to a sequence of convex optimization problems. It has the advantage of discovering interpretable models that preserve the structure of the underlying physical system. To this end, SODAs improves since SODAs is singular numerical stability when handling high correlations between library terms, caused by near-perfect algebraic relationships, by iteratively refining the conditioning of the candidate library. We demonstrate the performance of our method on biological, mechanical and electrical systems, showcasing its robustness to noise in both simulated time series and real-time experimental data.

DAE↗

DOE OSTI2020

The Adjoint Petrov–Galerkin method for non-linear model reduction

Here, we formulate a new projection-based reduced-order modeling technique for non-linear dynamical systems. The proposed technique, which we refer to as the Adjoint Petrov–Galerkin (APG) method, is derived by decomposing the generalized coordinates of a dynamical system into a resolved coarse-scale set and an unresolved fine-scale set. A Markovian finite memory assumption within the Mori–Zwanzig formalism is then used to develop a reduced-order representation of the coarse scales. This procedure leads to a closed reduced-order model that displays commonalities with the adjoint stabilization method used in finite elements. The formulation is shown to be equivalent to a Petrov–Galerkin method with a non-linear, time-varying test basis, thus sharing some similarities with the Least-Squares Petrov–Galerkin method. Theoretical analysis examining a priori error bounds and computational cost is presented. Numerical experiments on the compressible Navier–Stokes equations demonstrate that the proposed method can lead to improvements in numerical accuracy, robustness, and computational efficiency over the Galerkin method on problems of practical interest. Improvements in numerical accuracy and computational efficiency over the Least-Squares Petrov–Galerkin method are observed in most cases.

42 ENGINEERING↗

DOE OSTI2025

Machine Learned Empirical Numerical Integrator from Simulated Data

Recently, a number of state-of-the-art surrogate machine learning (ML) models have been designed for global weather and climate prediction, which have been trained using reanalysis data products. Reanalysis data products are constructed using numerical model simulations that combine numerical integration of partial differential equations and parameterization schemes. These products are typically only archived and made available using coarsened spatial and temporal resolutions. This study explores the impact of the numerical generation methods used to produce the training datasets and the temporal resolution of those datasets on machine learning surrogate models. Using the nonlinear vector autoregression (NVAR) machine as an explainable ML technique, simple dynamical systems are emulated with ML models trained on data produced by three classical numerical integration schemes. NVAR is validated as a skillful ML method, capable of producing accurate predictions and, more importantly, reconstructing both the underlying dynamics and the numerical integration scheme used to generate the training data. However, the machine fails to generalize predictions on unseen test data generated by different numerical integration schemes, despite the underlying dynamical system being the same. This result provides a word of caution for the growing field of machine learning emulation of weather and climate dynamics. Furthermore, we illustrate using NVAR that training on temporally coarsened data may increase the required complexity of ML models and potentially introduce new numerical challenges. Finally, we discover that empirical integration schemes with arbitrary time-stepping sizes can be constructed directly from the data, which implies a potential for the development of empirical numerical integration schemes.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Recent Development of Frequency Estimation Methods for Future Smart Grid

The frequency estimated by the Phasor Measurement Unit (PMU) is a critical index of power system status and supports many smart grid applications. The future smart grid features high penetration of renewables and more fast-moving power electronics inverters but raises challenges to the reliable frequency estimation. This article presents three methods to address these challenges. First, an enhanced zero-crossing algorithm was developed to track the fast-changing frequency in system dynamics. Second, we propose a technology that can tolerate the system transient and suppress the outliers. Third, an algorithm was developed to export high time-resolution frequency estimations with minimum computational effort. All of the proposed methods are realized in hardware and compared with classical frequency estimation methods. The testing results indicate that the proposed methods have excellent performance. They can be used in future PMUs and provide reliable and high time resolution data for smart grid applications.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

A New Simple-to-Configure Self-Perturbing Multivariable Extremum-Seeking Controller

This paper presents a new stochastic relay-based extremum-seeking controller (ESC) for multi-input-single-output (MISO) systems. The algorithm was developed with the goal of simplifying configuration to enable easier deployment to real-world problems. A solution is developed first for a static map and then adapted for a general class of dynamic systems. The number of configurable parameters is one per input channel for the static case and only one additional parameter is needed for the dynamic version. The problem of gradient identifiability is solved via the use of stochastic relay gains and a simple stability proof for the static case is presented. Simulation tests demonstrate the performance of the strategy for optimizing both static and dynamic systems.

Salsbury, Timothy [BATTELLE (PACIFIC NW LAB)]↗

DOE OSTI2022

Dynamic, Adaptive, Systems and Materials: Complex, Simple and Emergent Behaviors

This program has been funded by DoE/BES for twenty years. It has moved into and out of various subjects as it has developed, but it has retained its focus on complexity and complex systems. The project has evolved in the following way: Self-Assembly and Biomimetic Self-Assembly: All self-assembling systems depend upon a minimum of two types of interaction: a repulsion and an attraction. For the familiar molecular systems, attractive interactions are typically hydrogen bonds and electrostatic interactions. Repulsive interactions include steric effects, hydrophobic effects (in biological systems), and charge-charge repulsion. We have expanded this repertoire to include surface interactions, magnetic interactions, and others. I list these systems in the order in which we have explored them: i) A key emphasis in current work is in understanding how the movement of ions in a magnetic field (the Lorentz effect) interacts with catalytic systems. We have demonstrated that an acceleration in rate of reduction of CO 2 to CO can be accomplished by applying an external magnetic field. This acceleration is largely due to the application of the Lorentz effect on mass transport at the catalyst’s surface. ii) We have also extensively explored the influence of electrostatics, as exhibited in self-assembling systems, by tribocharging. iii) Another key system involves surface tension effects; examples include interactions between heavy particles floating at a liquid-air interface, and interacting by changes in surface area; interactions of bubbles and bubble rafts, behaviors of bubble trains in microfluidic networks, and behaviors of microorganisms in constraining environments. iv) This work has intentionally de-emphasized biological systems; but it does include some work on protein-ligand interactions and interactions among microorganisms. v) We have also explored applications of some of these effects, these explorations include bubble rafts as diffraction gratings, exploration of the structures that can be obtained by tribocharging and uses of these structures in exploring nucleation and melting of crystals. vi) Although not a major focus of this work, several other topics have emerged and offer opportunities for future work. These include the behavior of bubble trains and bubble rafts in microfluidic systems. A particularly interesting example is the formation of bubble trains that repeat in the alteration of large and small bubbles according to rules we do not presently understand, but are uniquely large-period oscillating systems. These systems offer a new route into understanding the instabilities of the type represented by oscillations. vii) We have also begun exploratory projects on magnetic levitation (especially to determine molecular density), and information storage (in molecules). Magnetic Levitation: Self-assembling and biomimetic systems require both attraction and repulsion. We have used electrostatics (tribocharging), interfacial free-energies (surface tension and related forces) and others. Potential uses include reconfigurable diffraction gratings and liquid lenses; exploration of mechanisms in tribocharging; tunneling in EGaIn junctions; and bubble trains (especially in micro-fluidic systems). Examples of systems representing these topics is included in the following papers: Complexity: Disks rotating at a water-air interface; Benard-Marangoni effects; Vortex-Crystals from spinning magnetic disks (Marangoni effects); EGaIn Electrode to study quantum tunneling; Self-Assembly of electrostatically-charged metallic spheres (electrets); Dynamically reconfigurable lens; Using computational designs of ligands for enzymes; Electrostatic self-assembly by tribocharging; Monodisperse bubble trains in microchannel systems; Inverted dripping faucet; Flames; Printing of micro-organisms to regenerate the “ink” of printing device; Using micro-organisms to move loads (“microoxen”); Motion of bacterial swarms near surfaces; Making monodisperse particles in microfluidic systems; Coding/decoding of information stored in droplet trains in microfluidic networks; Magnetic levitation; and Information storage. i) Tribocharging. The change in focus of this work on electrets from the fundamentals of charging to applications of these materials in studying self-assembly using electrostatic interactions. ii) Bubbles in Microchannels. The realization that systems of bubbles in microchannels represented a major opportunity to study complexity in a very tractable system, and the development of a semi-quantitative theory of this subject. iii) Flames. The growth of “flames” remains an exploratory subject for the research, although their currently relatively little active work involving it ongoing. iv) Systems with Microorganisms. The removal of work in biological systems from this project. Based on work supported in this program, we now have a significant project on the development of microfluidic tools for studying C. elegans (a nematode), but this work was not appropriate for a program focused on complexity, and we developed separate support for it. (It is, however, an example of successful seeding of a new area by BES.) The work on electrets has gone through a period in which a part of the program was the subject of a MURI; the focus of this work was to develop materials that did not charge electrostatically on friction or contact. The MURI is now over, and the work on dynamic self-assembly (supported by BES) is the major focus. “Flames” has also enjoyed synergistic support, in terms of a project supported by DARPA on flame suppression (in the absence of extinguishing agents, using acoustic and electrostatic interactions). This work was helpful in understanding some of the basics of flames, but is entirely distinct from the BES focus in complexity. A growing interest is in the Lorentz effect. The Lorentz effect is the force exerted on charged particles (electrons, ions, charged molecules) when they move through a perpendicular magnetic field. The Lorentz effect is almost ubiquitous in modern technology: examples of applications include electric motors, dynamos, cathode ray tubes, many batteries, and most systems that control electrical currents with magnetic forces. We have begun to explore the Lorentz effect in electrochemical systems and heterogeneous catalytic systems involving charged organic species and inorganic ions. This work is still at an early stage, but initial studies that Lorentz effects can be large when ions move through magnetic fields, or magnetic fields move in the presence of ions.

36 MATERIALS SCIENCE↗

DOE OSTI2022

McMillan map and nonlinear Twiss parameters

In this article we consider two dynamical systems: the McMillan sextupole and octupole integrable mappings originally introduced by Edwin McMillan; the second one is also known as canonical McMillan map. Both of them are simplest symmetric McMillan maps with only one intrinsic parameter, the trace of the Jacobian at the fixed point. While these dynamical systems have numerous of applications and are used in many areas of math and physics, some of their dynamical properties have not been described yet. We fulfill the gap and provide complete description of all stable trajectories including parametrization of invariant curves, Pioncaré rotation numbers and canonical action-angle variables. In the second part we relate these maps with general chaotic map in McMillan-Turaev form. We show that McMillan sextupole and octupole mappings are first order approximations of dynamics around the fixed point, in a similar way as linear map and quadratic invariant (Courant-Snyder invariant in accelerator physics) is the zeroth order approximation (known as linearization). Finally we suggest the new formalism of nonlinear Twiss parameters which incorporate dependence of rotation number as a function of amplitude, in contrast to e.g. betatron phase advance used in accelerator physics which is independent of amplitude. Specifically in application to accelerator physics this new formalism is capable of predicting dynamical aperture around 1-st, 2-nd, 3-rd and 4-th order resonances for flat beams, which is critical for beam injection/extraction.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Structured Neural Network Modeling for Developing Digital Twins Models of Hydropower Generation Units

Dynamic modeling is a key part in the development of digital twin (DT) for dynamic systems. This is true for hydropower systems, where whole system modeling including penstock, turbine and generators, etc is important in realizing actuate modeling for the real systems. On the other hand, in response to the large variations of the power demand due to increased penetration of renewables such as wind and solar, hydropower systems are now required to operate in a large power generation range. This situation triggers the nonlinear characteristics of the generation unit with respect to its models. As such, it is imperative to use data driven modeling such as neural networks to learn the nonlinear dynamics of the hydropower generation unit. To achieve this objective, this study constructs a modeling and learning algorithm integrated with multiple structured neural network models for the modeling of turbine shaft speed, penstock pressure, and generator power output based on the generator power control setpoint, field current, and field voltage. In addition, the study uses the hydropower data from Tacoma Public Utilities to train and validate the proposed neural network algorithm. The results have shown that this structured neural network modeling approach can learn the system dynamics effectively by using the real-time data collected from the hydropower system with the desired modeling results.

Wang, Hong↗

DOE OSTI2023

Targeting tissues via dynamic human systems modeling in generative design

Drug discovery is a complex, costly process with high failure rates. A successful drug should bind to a target, be deliverable to an intended site of activity, and promote a desired pharmacological effect without causing toxicity. Typically, these factors are evaluated in series over the course of a pipeline where the number of candidates is sequentially whittled down from a very large initial pool. One promise of AI-driven discovery is the opportunity to evaluate multiple facets of drug performance in parallel. However, despite ML-driven advancements, current models for pharmacological property prediction are exclusively trained to predict molecular properties, ignoring important, dynamic biodistribution and bioactivity effects. Here, we present our progress towards incorporating quantitative systems physiology models into an AI-enabled drug design and molecular generation pipeline. Within a genetic algorithm, we include human-relevant physiologically based pharmacokinetic (PBPK) models. These PBPK models leverage properties that are predicted by a fine-tuned molecular language model. Together, these models will aid in capturing the mapping between molecules and therapeutic outcomes that is necessary to accelerate the drug discovery process.

Fox, Zach↗

DOE OSTI2023

Towards a Circular Economy for PET Bottles in the US

The United States generates the most plastic waste of any country. Along with that GHG emissions from the global plastic economy are expected to increase to 15% of the global carbon budget by 2050. It is imperative that plastic recycling is made a reality to reduce both plastic pollution in the environment and GHG emissions. A portfolio of end-of-life strategies must be implemented to minimize environmental impacts and retain valuable plastic material, but it is challenging to compare options that generate products with different utility and lifetime. Plastic use reduction, reuse and recycling are thus increasingly important, but making informed policy and research decisions within this space can be challenging given the diverse range of available solutions. The novel analysis framework, Plastic Parallel Pathways Platform (4P) has been equipped with consequential life cycle assessment, techno-economic analysis, and a plastic circularity indicator to estimate the greenhouse gas (GHG) emissions, circularity, and cost of polyethylene terephthalate (PET) down-cycling to lower-quality resin, closed-loop recycling to food-grade PET bottles, up-cycling to fiber-reinforced plastic (FRP), and conversion to non-plastic products (electricity, oil) on a United States economy-wide basis. Integrating system dynamics into this robust plastics model that already incorporates techno-economics, circularity, and environmental impacts will enable identification of key bottlenecks between manufacturers, waste sorters, and reclaimers that currently prevent rapid decarbonization of the plastics economy. System dynamics (SD) explore the evolution of activities and technologies based on changed macro parameters such as plastic demand and supply, market shifts, and cross-sectoral interactions. This project particularly aims to explore the interplay between, waste collection, plastic waste sorting, recycling, and manufacturing, as well as the effect of plastic bale quality and plastic reuse initiatives on the surrounding process stages. This functionality will facilitate combinatory analysis in which a portfolio of end-of-life pathways are assessed simultaneously, with the exact makeup of that portfolio affected by parameters such as technology scales, resource constraints, and waste mitigation efforts. Integrating SD with the 4P framework enables analyzing the effect of increased revenue and reinvestment into improving process efficiencies, sorting and collection quantities. Through that, market effects of increased recycled resin availability can be studied for the plastics systems model for the US. The results will help identify technical or economic bottlenecks that currently limit efforts to decarbonize the U.S. plastics economy.

circular economy↗

DOE OSTI2024

Towards a Circular Economy for PET Bottles in the U.S. - 4P Model

The United States generates the most plastic waste of any country. Along with that GHG emissions from the global plastic economy are expected to increase to 15% of the global carbon budget by 2050. It is imperative that plastic recycling is made a reality to reduce both plastic pollution in the environment and GHG emissions. A portfolio of end-of-life strategies must be implemented to minimize environmental impacts and retain valuable plastic material, but it is challenging to compare options that generate products with different utility and lifetime. Plastic use reduction, reuse and recycling are thus increasingly important, but making informed policy and research decisions within this space can be challenging given the diverse range of available solutions. The novel analysis framework, Plastic Parallel Pathways Platform (4P) has been equipped with consequential life cycle assessment, techno-economic analysis, and a plastic circularity indicator to estimate the greenhouse gas (GHG) emissions, circularity, and cost of polyethylene terephthalate (PET) down-cycling to lower-quality resin, closed-loop recycling to food-grade PET bottles, up-cycling to fiber-reinforced plastic (FRP), and conversion to non-plastic products (electricity, oil) on a United States economy-wide basis. Integrating system dynamics into this robust plastics model that already incorporates techno-economics, circularity, and environmental impacts will enable identification of key bottlenecks between manufacturers, waste sorters, and reclaimers that currently prevent rapid decarbonization of the plastics economy. System dynamics (SD) explore the evolution of activities and technologies based on changed macro parameters such as plastic demand and supply, market shifts, and cross-sectoral interactions. This project particularly aims to explore the interplay between, waste collection, plastic waste sorting, recycling, and manufacturing, as well as the effect of plastic bale quality and plastic reuse initiatives on the surrounding process stages. This functionality will facilitate combinatory analysis in which a portfolio of end-of-life pathways are assessed simultaneously, with the exact makeup of that portfolio affected by parameters such as technology scales, resource constraints, and waste mitigation efforts. Integrating SD with the 4P framework enables analyzing the effect of increased revenue and reinvestment into improving process efficiencies, sorting and collection quantities. Through that, market effects of increased recycled resin availability can be studied for the plastics systems model for the US. The results will help identify technical or economic bottlenecks that currently limit efforts to decarbonize the U.S. plastics economy.

carbon↗

DOE OSTI2024

Towards a Circular Economy for PET Bottles in the U.S. - 4P Framework

The United States generates the most plastic waste of any country. Along with that GHG emissions from the global plastic economy are expected to increase to 15% of the global carbon budget by 2050. It is imperative that plastic recycling is made a reality to reduce both plastic pollution in the environment and GHG emissions. A portfolio of end-of-life strategies must be implemented to minimize environmental impacts and retain valuable plastic material, but it is challenging to compare options that generate products with different utility and lifetime. Plastic use reduction, reuse and recycling are thus increasingly important, but making informed policy and research decisions within this space can be challenging given the diverse range of available solutions. The novel analysis framework, Plastic Parallel Pathways Platform (4P) has been equipped with consequential life cycle assessment, techno-economic analysis, and a plastic circularity indicator to estimate the greenhouse gas (GHG) emissions, circularity, and cost of polyethylene terephthalate (PET) down-cycling to lower-quality resin, closed-loop recycling to food-grade PET bottles, up-cycling to fiber-reinforced plastic (FRP), and conversion to non-plastic products (electricity, oil) on a United States economy-wide basis. Integrating system dynamics into this robust plastics model that already incorporates techno-economics, circularity, and environmental impacts will enable identification of key bottlenecks between manufacturers, waste sorters, and reclaimers that currently prevent rapid decarbonization of the plastics economy. System dynamics (SD) explore the evolution of activities and technologies based on changed macro parameters such as plastic demand and supply, market shifts, and cross-sectoral interactions. This project particularly aims to explore the interplay between, waste collection, plastic waste sorting, recycling, and manufacturing, as well as the effect of plastic bale quality and plastic reuse initiatives on the surrounding process stages. This functionality will facilitate combinatory analysis in which a portfolio of end-of-life pathways are assessed simultaneously, with the exact makeup of that portfolio affected by parameters such as technology scales, resource constraints, and waste mitigation efforts. Integrating SD with the 4P framework enables analyzing the effect of increased revenue and reinvestment into improving process efficiencies, sorting and collection quantities. Through that, market effects of increased recycled resin availability can be studied for the plastics systems model for the US. The results will help identify technical or economic bottlenecks that currently limit efforts to decarbonize the U.S. plastics economy.

circular economy↗

DOE OSTI2025

Existing Methods for Grid Strength Assessment and Role of Hydropower in Future Grids

The power system is undergoing rapid evolution with increasing penetration of inverter-based resources (IBRs), large loads, microgrids, and power electronic devices. Ensuring reliable and stable operation of the modern power grid is a multi-faceted challenge that requires detailed understanding of this complex system. Dynamic stability is a major concern in maintaining the security of power grids as the generation mixes and large loads transitions to include high shares of power electronic devices. The operation of IBRs in regions with low system strength and higher grid impedances has been found to be the main reason behind many of the power system instabilities that manifest themselves in various types of oscillations and interactions that, if not properly addressed and damped, can jeopardize the reliable operation of the power system. Weak grid conditions compound such stability problems, particularly when many IBRs operate in proximity to and connect to weak power grids. Therefore, it is important to assess grid strength for planning, integration and operation of IBRs for a given power system. In this report, we aim to understand and classify existing methodologies for grid strength assessment, along with their limitations and future needs. Further, we aim to utilize the huge untapped potential in utilizing hydro energy resources in addressing some of the pertinent challenges of grid strength and reliable operation of modern power systems. Hydropower, historically valued for its flexibility and dispatchability, now faces new constraints due to reduced share of synchronous machines in the generation mix and seasonal variability of available water resources. Yet, these same plants present untapped potential beyond energy generation - notably, as providers of critical grid services. This report explores how hydropower plants, particularly through operation as synchronous condensers, can play a pivotal role in strengthening the grid amid evolving system dynamics.

13 HYDRO ENERGY↗

DOE OSTI2023

Evolution of Robustness in Growing Random Networks

Networks are widely used to model the interaction between individual dynamic systems. In many instances, the total number of units and interaction coupling are not fixed in time, and instead constantly evolve. In networks, this means that the number of nodes and edges both change over time. Various properties of coupled dynamic systems, such as their robustness against noise, essentially depend on the structure of the interaction network. Therefore, it is of considerable interest to predict how these properties are affected when the network grows as well as their relationship to the growth mechanism. Here, we focus on the time evolution of a network’s Kirchhoff index. We derive closed-form expressions for its variation in various scenarios, including the addition of both edges and nodes. For the latter case, we investigate the evolution where single nodes with one or two edges connecting to existing nodes are added recursively to a network. In both cases, we derive the relations between the properties of the nodes to which the new node connects along with the global evolution of network robustness. In particular, we show how different scalings of the Kirchhoff index can be obtained as a function of the number of nodes. We illustrate and confirm this theory via numerical simulations of randomly growing networks.

97 MATHEMATICS AND COMPUTING↗