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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Frequency-Nadir-Constrained Unit Commitment for Low-Inertia, High-IBR Island Power Systems [Slides]

The process of energy decarbonization in island power systems is accelerated due to the swift integration of inverter-based renewable energy resources (IBRs). The unique features of such systems, including rapid frequency changes resulting from potential generation outages or imbalances due to the unpredictability of renewable power, pose a significant challenge in maintaining the frequency nadir without external support. This paper presents a unit commitment (UC) model with data-driven frequency nadir constraints, including either frequency nadir or minimum inertia requirements, helping to limit frequency deviations after significant generator outages. The constraints are formulated using a linear regression model that takes advantage of real-world, year-long generation scheduling and dynamic simulation data. The efficacy of the proposed UC model is verified through a year-long simulation in an actual island power system using historical weather data. The alternative minimum inertia constraint, derived from actual system operation assumptions, is also evaluated. Findings demonstrate that the proposed frequency nadir constraint notably improves the system's frequency nadir under high photovoltaic (PV) penetration levels, albeit with a slight increase in generation costs, when compared to the alternative minimum inertia constraint.

14 SOLAR ENERGY↗
DOE OSTI2022

Numerical algorithms for water waves with background flow over obstacles and topography

Abstract We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a periodic, multiply connected fluid domain that includes stationary obstacles and variable bottom topography. One approach is formulated in terms of the surface velocity potential while the other evolves the vortex sheet strength. Both methods employ layer potentials in the form of periodized Cauchy integrals to compute the normal velocity of the free surface, are compatible with arbitrary parameterizations of the free surface and boundaries, and allow for circulation around each obstacle, which leads to multiple-valued velocity potentials but single-valued stream functions. We prove that the resulting second-kind Fredholm integral equations are invertible, possibly after a physically motivated finite-rank correction. In an angle-arclength setting, we show how to avoid curve reconstruction errors that are incompatible with spatial periodicity. We use the proposed methods to study gravity-capillary waves generated by flow around several elliptical obstacles above a flat or variable bottom boundary. In each case, the free surface eventually self-intersects in a splash singularity or collides with a boundary. We also show how to evaluate the velocity and pressure with spectral accuracy throughout the fluid, including near the free surface and solid boundaries. To assess the accuracy of the time evolution, we monitor energy conservation and the decay of Fourier modes and compare the numerical results of the two methods to each other. We implement several solvers for the discretized linear systems and compare their performance. The fastest approach employs a graphics processing unit (GPU) to construct the matrices and carry out iterations of the generalized minimal residual method (GMRES).

Ambrose, David M.↗
DOE OSTI2024

On the Stability of Power Transmission Systems Under Persistent Inverter Attacks: A Bi-Linear Matrix Approach

We investigate the stability and robustness properties of a power transmission system under persistent deceiving attacks on inverter-interfaced energy resources. The attacks can corrupt the damping coefficients in the inverters' controllers and measurements of the frequency at the points of coupling. Leveraging tools from hybrid dynamical systems theory, we characterize a broad family of persistent (and not necessarily periodic) attacks acting on the inverters, under which the stability properties of the transmission system can be shown to not be compromised. To address potentially conservative conditions identified through conventional bounding techniques, sufficient conditions on the average activation time of the attacks are identified via Lyapunov theory, as well as the formulation and solution of a class of bilinear matrix inequalities (BMI). The results are obtained for constant and slowly time-varying loads via input-to-state stability (ISS) tools. Numerical simulations on the IEEE 39-bus test system are also presented.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Novel ceramic capacitors with ultrahigh energy density and efficiency (Final Technical Report)

Antiferroelectric ceramics are a special class of material that have shown great potential as the dielectric in electrical capacitors due to their high energy- and power-density. During each charge-discharge cycle, the ceramic undergoes transformation to a ferroelectric phase and resumes its antiferroelectric phase. The hysteresis associated with the transitions leads to a mediocre energy efficiency and service lifetime of antiferroelectric capacitors and, hence, their almost absence in commercial products. Under the support of this research project, we first formulated a universal lattice-compatibility theory that included electrostatic polarization energy along with elastic energy and thermal energy to understand the origin of the hysteresis in antiferroelectric oxides. Guided by this compatibility theory, we conducted high-throughput density functional theory (DFT) calculations to assess chemical modifiers and their effect on crystal structures of 400+ PbZrO 3 -based compositions. Down-selected compositions were experimentally validated for their suppressed hysteresis and higher energy efficiency. The verified low-hysteresis compositions were then expanded to an antiferroelectric ceramic library with nearly 500 new compositions (more than 1,500 samples) using high-throughput experiments involving ceramic synthesis and property screening. The large quantity of data generated (theory and experimental) in these tasks were processed by machine-learning techniques and identified trends were fed to the next iteration. In the end, we successfully discovered four compositions with near-zero hysteresis, yielding a world-record energy efficiency of 98.2% at an energy density of 3.0 J/cm 3 . Furthermore, our antiferroelectric ceramic capacitor reaches 79.5 million charge-discharge cycles lifetime, a factor of 80 enhancement over previous antiferroelectric ceramics with large hysteresis. These research accomplishments have not only met the milestones set in the SOPO, but also led to two patent filings, three journal publications (one of them was in Advanced Materials, impact factor 29.4), and nine oral presentations at various venues. Through the course of the project, three postdocs, four Ph.D. students, and one M.S. student were trained. In short, our project established a new methodology in searching next-generation functional ceramics on the fundamental side and discovered several high-efficiency antiferroelectric compositions for capacitors on the applied side. Once fabricated into the multilayer form for commercial applications, these ceramic capacitors can potentially enable the high temperature high power density DC-link capacitors that are critical for the next generation inverters in electric vehicles. The project also significantly contributed to the nation’s workforce development in the STEM fields.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Investigating two-dimensional adjoint QCD on the lattice

We present our investigations of SU(N) adjoint QCD in two dimensions with one Majorana fermion on the lattice. We determine the relevant parameter range for the simulations with Wilson fermions and present results for Polyakov loop, chiral condensate, and string tension. In the theory with massive fermions, all observables we checked show qualitative agreement between numerical lattice data and theory, while the massless limit is more subtle since chiral and non-invertible symmetry of the continuum theory are explicitly broken by lattice regularization. In thermal compactification, we observe N perturbative vacua for the holonomy potential at high-T with instanton events connecting them, and a unique vacuum at low-T. At finite-N, this is a cross-over and it turns to a phase transition at large-N thermodynamic limit. In circle compactification with periodic boundary conditions, we observe a unique center-symmetric minimum at any radius. In continuum, the instantons in the thermal case carry zero modes (for even N) and indeed, in the lattice simulations, we observe that chiral condensate is dominated by instanton centers, where zero modes are localized. We present lattice results on the issue of confinement vs. screening in the theory and comment on the roles of chiral symmetry and non-invertible symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Smart Inverters, Dumb Risk: Taking Control of IBR Security in the Digital Age

This presentation addresses the security challenges posed by Inverter-Based Resources (IBRs) in the modern energy landscape. The presentation highlights the vulnerabilities and risks associated with IBRs, including the potential for cyber-attacks, the impact of insecure defaults, and the systemic risks posed by supply chain dependencies. Key topics covered include: 1) The increasing digital transformation in energy systems and the associated security risks. 2) Specific vulnerabilities in IBRs, including weak passwords, hardcoded credentials, and insecure web application interfaces. 3) The implications of persistent connectivity and the strategic risks posed by foreign-manufactured components. 4) The role of regulatory frameworks, such as NERC CIP, in addressing these challenges and the limitations of current oversight. 5) Practical solutions for mitigating risks, including secure design practices, vendor risk assessments, and the importance of strong passwords and role-based access control. The presentation underscores the necessity of a comprehensive, system-of-systems approach to securing IBRs, emphasizing the need for collaboration across various stakeholders, including operators, developers, and regulators, to ensure the resilience and security of the energy grid.

24 - POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Grid-Forming Inverters: Project Demonstrations and Pilots

Power system operators around the world are pushing the limits of integrating inverter-based resources (IBRs) to very high levels, approaching 100% instantaneous penetration under certain operating conditions. This often applies to smaller power systems with very little or no ac interconnections to other neighboring regions or sometimes to fringes of large balancing areas, such as Denmark or Portugal, within the mainland European power system. These jurisdictions have identified the potential of grid-forming (GFM) technology as a key enabler to support the energy transition with very few or no synchronous generators online. Until recently, practical applications of GFM inverters were limited to microgrids and isolated grids and in smaller grid applications on the order of a few tens of megawatts (MW).

Australia↗
DOE OSTI2024

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part II: Enforcing the Lorenz Gauge Condition

In a previous paper Christlieb et al. (A particle-in-cell method for plasmas with a generalized momentum formulation, part I: Model formulation, 2024), we developed a new particle-in-cell (PIC) method for the relativistic Vlasov–Maxwell system in which the electromagnetic fields and the equations of motion for the particles were cast in terms of scalar and vector potentials through a Hamiltonian formulation. This new method evolved the potentials under the Lorenz gauge using integral equation methods. New methods to construct spatial derivatives of the potentials that converge at the same rates as the fields were also presented. The new particle method was compared against standard explicit discretizations, including the well-known FDTD-PIC method, for a range of applications involving sheaths and particle beams. Here, this paper extends this new class of methods by focusing on the enforcement the Lorenz gauge condition in both exact and approximate forms using co-located meshes. A time-consistency property of the proposed field solver for the vector potential form of Maxwell’s equations is established, which is shown to preserve the equivalence between the semi-discrete Lorenz gauge condition and the analogous semi-discrete continuity equation. Using this property, we present three methods to enforce a semi-discrete gauge condition. The first method introduces an update for the continuity equation that is consistent with the discretization of the Lorenz gauge condition. Both the finite difference and spectral implementations satisfy this discrete gauge condition to machine precision. The second approach we propose enforces a semi-discrete continuity equation using the boundary integral solution to the field equations. The potential benefit of this approach is that it eliminates spatial derivatives that appear on the particle data, namely the current density, which is often calculated by linear combinations of low-order spline basis functions. This method is ideally suited to boundary integral equation methods that invert multi-dimensional operators without dimensional splitting techniques and will be the subject of future work. The third approach introduces a gauge correcting method that makes direct use of the gauge condition to modify the scalar potential and uses local maps for both the charge and current densities. This results in a gauge error, as the maps do not enforce the continuity equation. The vector potential coming from the current density is taken to be exact, and using the Lorenz gauge, we compute a correction to the scalar potential that makes the two potentials satisfy the gauge condition. This method also enforces the gauge condition to machine precision. We demonstrate two of the proposed methods in the context of periodic domains. Problems defined on bounded domains, including those with complex geometric features remain an ongoing effort. However, this work shows that it is possible to design computationally efficient methods that can effectively enforce the Lorenz gauge condition in a non-staggered PIC formulation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A Secondary Control Framework for Microgrid Interoperability With Vendor-Agnostic Grid-Forming Units: Design, Implementation, and Demonstration via Large-Scale Hardware Setup

The reliable operation of islanded microgrids increasingly depends on secondary controls that restore voltage and frequency to nominal values and ensure accurate active and reactive power sharing. Centralized secondary control architectures achieve high accuracy through global coordination at the cost of single-point failures and limited scalability compared with decentralized/distributed approaches. But a critical gap remains in addressing the interoperability and vendor-agnostic operation of secondary controls in real-world microgrids where heterogeneous diesel generator(s) and grid-forming (GFM) inverter(s) from multiple manufacturers always coexist. Practical and vendor-agnostic interoperability guidelines for the secondary control architecture of microgrids with multiple GFM units have not yet been developed; therefore, this paper proposes an interoperable and vendor-agnostic secondary control framework that operates seamlessly across GFM units from different vendors without relying on proprietary controls and protocols, hardware, or lock-ins. The framework leverages existing communication infrastructures (e.g., Modbus TCP/IP) to enable cost-effective deployment while addressing practical challenges, such as packet loss and quantization errors. Mitigation strategies-including data averaging, situational event-triggered control, and finite-iteration execution-are introduced to enhance reliability under real-world conditions. A generalized modeling and design framework is also presented, supported by robustness analysis to demonstrate independence from vendor-specific implementations. The proposed framework is validated through a large-scale hardware demonstration using a 3-$\phi$, 480-V, 60-Hz, 713-kVA laboratory hardware microgrid involving a heterogeneous diesel generator and multiple GFM inverters, showcasing its effectiveness in achieving stable voltage and frequency restoration and accurate power sharing under practical constraints. The results highlight the framework's potential as a scalable and practical solution for next-generation microgrids requiring openness, standard framework, and interoperability.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Solar PV and BESS Plant-Level Voltage Control and Interactions: Experiments and Analysis

In real world operation, low-frequency oscillations associated with plant-level voltage control of inverter-based resources (IBRs) have been a concern of grid operators. Here, this research aims to demonstrate and analyze the effect of plant-level voltage control on system stability and potential interactions among IBRs. The experiment results of a 13.2-kV system interconnected with two IBRs—a 1-MW battery energy storage system (BESS) and a 430-kW solar photovoltaic (PV) plant—are presented. Both 0.5-Hz and 3-Hz oscillations become visible at certain conditions. The phenomenon is further explained by use of a feedback system consisting of the plant-level droop control and the effect of reactive power or var injection on voltage. The main components of the block diagram are obtained via frequency scan measurements. The analysis offers an understanding of the main contributors and other influencing factors of the 3-Hz and 0.5-Hz modes. It also reveals the role of the volt-var droop gain, the low-pass filter time constant, and the system impedance in stability.

14 SOLAR ENERGY↗
DOE OSTI2024

Holistic Small-Signal Stability Analysis for Large-Scale Inverter-Intensive Power Systems with Coupled and Full-Order Dynamics from Control Systems and Power Networks

The increasing penetration of inverter-based resources (IBRs) into the existing power systems introduces tremendous benefits for enhanced sustainability but also poses inevitable challenges in terms of insufficient inertia, potential instability, and complex network dynamics, among others. However, the additional coupling introduced by the interactions among gridfollowing (GFL) and grid-forming (GFM) IBRs and the other components (i.e., synchronous generators [SGs], loads, and network, etc.) has not been clearly explored. A holistic, scalable, and quantitative stability analysis framework with the control systems and power networks is still missing. Here, in this paper, to fill in the technical gaps, a holistic small-signal model of the entire system with both rotating generation units and IBRs is established. An extended power flow model with operation dynamics from both generator control schemes and power networks is proposed to provide the varying steady-state operating points for small-signal modeling. The proposed method is compared with MATLAB solvers, and the results show that the proposed approach has a minimum calculation time, which can be less than 12 seconds for a large-scale power system with up to 2,000 buses. Furthermore, a quantitative method is developed to identify the impacts of IBRs on system performance with emphases on the potential stability issues with GFL IBRs, additional benefits of employing GFM IBRs, the feasibility of replacing SGs with GFM IBRs, and the impact of penetration level of different kinds of generation units. Finally, a field island power system is used to verify the proposed approach, and hardware-in-the-loop (HIL) tests are provided to further demonstrate the effectiveness of the proposed analysis.

14 SOLAR ENERGY↗
DOE OSTI2022

Converter-Interfaced CHP Plant for Improved Grid-Integration, Flexibility and Resiliency

GE Research and its partner GE Renewables have proposed the use of an interface converter solution to increase the penetration of small to medium-sized CHP (1MWe to 20MWe) into distribution grids and improve their flexibility and grid support capability. Indeed, the proposed interface converter solution thanks to presence of the grid-ready inverter, allows to streamline the compliance to grid codes requirements, reduce the interconnection delays and costs and ultimately one of the main barriers for CHP adoption by commercial and industrial facilities. An additional benefit provided by the interface converter is the use of the grid-ready inverter for reactive power which eliminates the need of sizing the generator for that capability. These two benefits highly favor the economic feasibility of converter-interfaced CHP. Five user cases, each in one of the leading U.S states for CHP potential reported by the DOE in its estimation of the U.S Technical Potential of CHP, were selected to compare the economic performances of converter-interfaced CHP as compared with directly-coupled. They include a college campus in California, a hospital in New York, a water reclamation plant in Texas, a hotel in Minnesota, and a large office building in Pennsylvania. Results showed that, the presence of the interface converter allows to increase the return on investment (ROI) by 0.5 to 2 percentage points in most of the cases (4 of 5). Indeed, the interface converter by shortening the interconnection process allows to accelerate revenues while reducing interconnection costs. Added to the reduced cost of the required generator these savings trade favorably the capital cost of the converter. The analysis also showed that the profitability of the converter-interfaced CHP is highly sensitive to the energy price, interconnection delay, and converter cost. However, it appears that if the interface converter can shorten the interconnection process by at least 6 months, adopting this solution will be more economically viable than directly-coupled configuration in almost all the +23,000 sites of the U.S Technical Potential CHP. The evaluation of the benefits of a converter-interfaced CHP also showed that it enables higher ROI when coupled with other distributed energy resources (DER) such as battery energy systems (BESS) or solar photovoltaic (PV). Indeed, in those scenario, the grid-ready inverter included in the interface converter eliminates the need of separate inverters if DC-coupling is used. On the technical performance, it has been verified that the presence of the interface converter allows to reduce by 70% to 80% the CHP short-circuit contribution to grid faults. This not only reduces the mechanical and thermal stresses exposed to the CHP electrical components but also increases the grid hosting capacity which ultimately enables higher penetrations CHP. Another key benefit of the interface converter validated with hardware-in-the-loop simulations and testing is its superior capability for reactive power support. Indeed, using a power hardware testbed with two +700kW inverters configured in back-to-back, a microgrid controller and actual facilities loads it was demonstrated that the presence of the interface converter can help maintain a power factor near ~1 or regulate the voltage to ~1.0pu at the point of common coupling. This benefit can be highly valuable if in the future, due to higher penetration of renewable distributed energy resources (DER), utilities start billing demand charge based on kVA instead of kW as currently. It was also validated that converter-interfaced CHP can dispatch heat and power commands and seamlessly switch between the two modes while consistently controlling the power factor or voltage at PCC. Indeed, the power hardware testing showed that grid-connected converter-interfaced CHP can follow either the power or heat demand while maintaining a unity power factor at converter output. This research proved that the adoption of an interface converter as the solution for interconnection of CHP system into the distribution grid can greatly improve the economic feasibility of small to medium-sized CHP as well as the plant power quality, flexibility and resiliency. Additionally, it allows increased penetrations of CHP into the distribution grid, extends their grid support capability, and facilitates the integration of BESS and PV DER by streamlining their collocation within the same facilities. This ultimately provides an opportunity for commercial and small industrial facilities in the U.S to accelerate their energy transition thanks to the high energy efficiency of CHP systems and its reliable, flexible, and resilient microgrid operation when interconnected with an interface converter.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Cost-Benefit Analysis of Grid-Supportive Loads for Fast Frequency Response

Flexibility in inverter-based loads could be used to support the converter-dominated power grid by offering a rapid, autonomous, and adjustable power reserve during system transients to help maintain system stability. Based on technical potential, ancillary service (AS) value, and implementation costs, this study illustrates the cost-benefit analysis of grid-supportive loads (GSLs) for the supply of fast frequency response (FFR). The net benefit for each GSL is demonstrated using a case study and relevant data sources. The findings suggest that implementation costs for enabling GSL features are low compared to the value that grid operators get from the acquisition of responsive reserve services. The authors believe that, given the rising popularity of renewable energy sources, GSLs can be a useful tool for grid stability in low-inertia systems.

cost-benefit analysis↗
DOE OSTI2020

High Efficiency Inverted GaAs and GaInP/GaAs Solar Cells With Strain-Balanced GaInAs/GaAsP Quantum Wells

High-efficiency solar cells are essential for high-density terrestrial applications, as well as space and potentially vehicle applications. The optimum bandgap for the terrestrial spectrum lies beyond the absorption range of a traditional dual junction GaInP/GaAs cell, with the bottom GaAs cell having higher bandgap energy than necessary. Lower energy bandgaps can be achieved with multiple quantum wells (QWs), but such a pathway requires advanced management of the epitaxial growth conditions in order to be useful. Strain-balanced GaAsP/GaInAs QWs are incorporated into a single junction GaAs solar cell and a dual junction GaInP/GaAs solar cell, leading to 27.2% efficiency in the single junction device and a one-sun record 32.9% efficiency in the tandem device. Good carrier collection and low non-radiative recombination are observed in the cells with up to 80 QWs. The GaAs cells employ a rear-heterojunction architecture to boost the open-circuit voltage to over 1.04 V in the quantum well device, despite the large number of QWs.

14 SOLAR ENERGY↗
DOE OSTI2020

Na-functionalized Ir Te 2 monolayer: Suppressed charge ordering and electric field tuned topological phase transition

Two-dimensional materials with atomic thickness usually possess superior tunability by surface adsorption than their bulk counterparts, showing great promise for novel nanotechnologies. In layered transition-metal dichalcogenide IrTe 2 there exhibits complex structural distortions induced by charge ordering, resulting in difficulties for the applications of its corresponding monolayer material. Here, using first-principles calculations, we demonstrate that depositing Na on the surface of the IrTe 2 monolayer can suppress the structural distortion to form a stable NaIrTe 2 sheet. It naturally breaks the inversion symmetry to enable a Rashba-type spin splitting for potential spintronic applications. In addition, the introduced empty Na s band and the valence band of the IrTe 2 monolayer can be inverted by the application of a perpendicular electric field, achieving a quantum phase transition from normal to topological insulator. Such an electric field-controlled topological phase transition is promising for the realization of topological field-effect transistors. Furthermore, these findings not only provide a feasible approach to stabilizing the IrTe 2 monolayer, but also broaden its applications in spintronics and low-dissipation topoelectronics.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Hierarchical Control of Utility-Scale Solar PV Plants for Mitigation of Generation Variability and Ancillary Service Provision

This paper presents a hierarchical control system to mitigate the variability of solar photovoltaic (PV) power plant and provide ancillary services to the electric grid without the need for additional non-solar resources. With coordinated management of each inverter in the system, the control system commands the power plant to proactively curtail a small fraction of its instantaneous maximum power potential, which gives the plant enough headroom to ramp up production from the overall power plant, for a service such as regulation reserve. This control system is practical for continuously changing cloud cover conditions in partially cloudy days. A case study from a site in Hawaii with one-second resolution solar irradiance data is used to verify the efficacy of the proposed control system. The proposed control algorithm is subsequently compared with the alternative control technology from the literature, the grouping control algorithm; the results show that the proposed hierarchical control system is over 10 times more effective in reducing generator mileage to support power fluctuations from solar PV power plants.

14 SOLAR ENERGY↗
DOE OSTI2024

Fault Contribution of Grid-Following and Grid-Forming Inverters Considering Generic Inverter Controls and Ride-through Requirements

Gradual transformation of the synchronous generator (SG)-dominated power systems to inverter-based resource (IBR)-dominated power systems is bringing new challenges regarding power system protection. Increasing IBR’s penetration will reduce the reliability of protection coordination, originally developed for SG-dominated power systems, potentially leading to less accurate calculation or even mis-operation. Thus, new protection schemes compatible with IBR-dominated power systems should be established. Prior to establishing the protection schemes, research on the fault contribution of generic IBR models should be conducted considering interconnection requirements. This paper conducts fault current contribution analysis of generic grid-following (GFL) and grid-forming (GFM) inverters considering interconnection requirements using an electromagnetic transient (EMT) simulation tool. To do this, EMT-based generic GFL models have been developed with the ride-through requirements from IEEE-1547 standards. In addition, the major functions of the generic models are explained. Then, the fault current analysis was conducted using GFL and GFM inverters in a single-inverter-infinite-bus system and a modified IEEE 34-node system considering different grid, fault, inverter control parameters.

Kim, Jinho [BATTELLE (PACIFIC NW LAB)]↗
DOE OSTI2023

Large inflationary logarithms in a nontrivial nonlinear sigma model

Loops of inflationary gravitons are known to induce large temporal and spatial logarithms that can cause perturbation theory to break down. Nonlinear sigma models possess the same kind of derivative interactions and induce the same sorts of large logarithms, without the complicated index structure and potential gauge problem. Previous studies have examined models with zero field space curvature that can be reduced to free field theories by local, invertible field redefinitions. Here we study a model that cannot be so reduced and still shows the same sorts of large logarithms. Additionally, we compute the evolution of the background at 1-loop and 2-loop orders, and we find the 1-loop β and γ functions.

79 ASTRONOMY AND ASTROPHYSICS↗