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At least 379 records · Page 21

Fundamentals of Solar PV Bolted Joint Loosening and Prevention

The photovoltaic (PV) industry has long reported anecdotal accounts of systems exhibiting intermittent or chronic fastener loosening, including joints that fail to maintain preload despite multiple re-tightening attempts. These occurrences are frequently, and often incorrectly, attributed to installer errors, vibration, or loading beyond design expectations (e.g., extreme weather events). Loose fasteners have serious implications and can significantly impact solar PV systems’ performance, reliability, and safety. However, effective bolted joint design and proper assembly practices can mitigate or eliminate loosening. Until the US Department of Energy’s Solar Energy Technologies Office (SETO) funded research on fasteners and solar PV structures, there was a notable gap in understanding the causes of loosening in solar PV systems.

14 SOLAR ENERGY↗

Control co-design under uncertainty for offshore wind farms: Optimizing grid integration, energy storage, and market participation

Offshore wind farms (OWFs) are set to significantly contribute to global decarbonization efforts. Developers often use a sequential approach to optimize design variables and market participation for grid-integrated offshore wind farms. However, this method can lead to sub-optimal system performance, and uncertainties associated with renewable resources are often overlooked in decision-making. Here, this paper proposes a control co-design approach, optimizing design and control decisions for integrating OWFs into the power grid while considering energy market and primary frequency market participation. Additionally, we introduce optimal sizing solutions for energy storage systems deployed onshore to enhance revenue for OWF developers over time. This framework addresses uncertainties related to wind resources and energy prices. We analyze five U.S. west-coast offshore wind farm locations and potential interconnection points, as identified by the Bureau of Ocean Energy Management (BOEM). Results show that optimized control co-design solutions can increase market revenue by 3.2% and provide flexibility in managing wind resource uncertainties.

Control Co-design↗

Techno-Economic Analysis and Market Potential of Geological Thermal Energy Storage (GeoTES) Charged With Solar Thermal and Heat Pumps

In this project, we developed a techno-economic analysis (TEA) model that can be used to evaluate the viability of a proposed Geological Thermal Energy Storage (GeoTES) design. This MATLAB-based model integrates distinct subsystem models for the reservoir, wells, power cycle, and solar field to capture their distinct characteristics. It applies this approach in simulating GeoTES storage and dispatch operations for durations ranging from hourly to seasonal. Using cases studies based on GeoTES designs provided by industry partners - Premier Resource Management (PRM) and EarthBridge Energy - we validated the TEA model estimations of system performance and costs (such as thermal and electrical power/energy inflow and outflow, capital costs, and levelized costs of energy and storage) for both concentrating solar thermal (CST) and Carnot Battery (CB) pairings with GeoTES (CST-GeoTES and CB-GeoTES). For the CST-GeoTES case, the model was validated against the proposed system designed by PRM. It showed good agreement with PRM's estimations when well and pump costs derived from PRM's estimations were used. When GETEM-based costs were used, there was a slight overprediction due to GETEM's project/site agnostic assumption of these costs. From a sensitivity analysis perspective, the levelized cost of electricity (LCOE) of the CST-GeoTES case was most sensitive to well flow rate and the charging temperature. An optimal design scenario resulted in an LCOE of 0.11 $\$$/kWhe. CST-GeoTES can also provide a source of heat to meet seasonal demands. With 12-hour and 24-hour levelized cost of heat (LCOH) of 0.018 $\$$/kWhth and 0.022 $\$$/kWhth, respectively, CST-GeoTES could be competitive in the California market with an average industrial price of natural gas in California between 0.041-0.047 $\$$/kWhth. The levelized cost of storage (LCOS) for CST-GeoTES depends on the energy storage duration. Although the LCOS is relatively higher for shorter durations (e.g., ~0.50 $\$$/kWhe for 1 hour of storage), it is an order of magnitude lower (0.06 $\$$/kWhe) for longer storage durations and competitive with lithium-ion batteries (beyond 12 hours of storage) and molten-salt thermal energy storage (beyond 32 hours). Energy. Three options were explored and applied to the EarthBridge case study: (1) A Carnot Battery design using R125 working fluid with both hot and cold storage; (2) A Carnot Battery design using R125 working fluid with only hot storage; (3) A Carnot Battery using a commercially available heat pump with carbon dioxide (CO2) working fluid and hot storage only. The CB-GeoTES with cold storage only had a slight (round-trip) efficiency advantage over the system without (43.4% vs. 42.8%). This is because the cold storage is limited by the freezing point of water, so the cold storage is not much colder than the environment. The system using commercially available technologies was the least efficient - partly because different cycles were used in the heat pump (CO2) and heat engine (binary cycle) which leads to some inefficiencies. Using the commercially available design, the levelized cost of energy (LCOS) from the model (0.10 $\$$/kWhe) was higher than that estimated by EarthBridge (0.068 $\$$/kWhe). This is because of the low round-trip (38.7%) efficiency of the commercially available design. Sensitivity analysis reveals that the model is most sensitive to electricity price. Including electricity price in the TEA for CB-GeoTES leads to an increase in LCOS from the base value to 0.25 $\$$/kWhe. To determine storage sites suitable for GeoTES, we gathered and analyzed geological, petrophysical, and geophysical data of oil and gas reservoir and aquifers in California and Texas. We down-selected possible sites based on cut-off values for site characteristics (e.g., reservoir temperature, formation thickness, permeability, porosity, depth, and brine salinity) and preliminary costs. Using this approach, the Carrizo-Wilcox, Yegua-Jackson, and Dockum brackish aquifers in Texas were identified as having the highest suitability. Similarly, in the central California region, the White Wolf, Belridge South Tulare, and Belridge South Reef Ridge were the most suitable. Going further, we assessed the storage potential in the selected sites. To do this we developed distributions of reservoir characteristic data and applied a Monte Carlo-based analysis to account for intrinsic uncertainty in the acquired data. The analysis revealed that the Carrizo-Wilcox aquifer had the highest storage potential with a mean capacity of 554 TWhth (i.e., 63 TWhe). The estimated capacity serves as an upper limit of storage potential given that not all fields in the basin will be developed. We participated in multiple outreach activities including conference presentations, panel session discussions, and the facilitation of a GeoTES workshop at the NREL Golden campus.

15 GEOTHERMAL ENERGY↗

The DataHawk2 uncrewed aircraft system for atmospheric research

Abstract. The DataHawk2 (DH2) is a small, fixed-wing, uncrewed aircraft system, or UAS, developed at the University of Colorado (CU) primarily for taking detailed thermodynamic measurements of the atmospheric boundary layer. The DH2 weighs 1.7 kg and has a wingspan of 1.3 m, with a flight endurance of approximately 60 min, depending on configuration. In the DH2's most modern form, the aircraft carries a Vaisala RSS-421 sensor for pressure, temperature, and relative humidity measurements, two CU-developed infrared temperature sensors, and a CU-developed fine-wire array, in addition to sensors required to support autopilot function (pitot tube with pressure sensor, GPS receiver, inertial measurement unit), from which wind speed and direction can also be estimated. This paper presents a description of the DH2, including information on its design and development work, and puts the DH2 into context with respect to other contemporary UASs. Data from recent field work (MOSAiC, the Multidisciplinary drifting Observatory for the Study of Arctic Climate) is presented and compared with radiosondes deployed during that campaign to provide an overview of sensor and system performance. These data show good agreement across pressure, temperature, and relative humidity as well as across wind speed and direction. Additional examples of measurements provided by the DH2 are given from a variety of previous campaigns in locations ranging from the continental United States to Japan and northern Alaska. Finally, a look toward future system improvements and upcoming research campaign participation is given.

54 ENVIRONMENTAL SCIENCES↗

Physics-informed Deep Reinforcement Learning-based Control in Power systems

Incorporating physics information into the deep reinforcement learning (DRL) process is a promising approach for addressing the challenges faced in learning-based control design problems for physical systems. Power grid dynamics, being a physical system, adheres to specific physical laws, constraints, as well as operational and control rules. Therefore, consideration of such physics-based law improves the learning process drastically. In general, traditional grid control schemes rely on rule-based mechanisms that cannot adapt to changing operating conditions. To improve the adaptability and computation time, recent research has seen a surge of DRL-based applications in power grid control. A generic DRL-based control design imposes the system performance requirements through the design of reward functions. In some cases, some of the important physics information is injected through this reward function. However, due to the complex dynamics and large state-action space, learning an optimal DRL policy often becomes challenging. Inspired by the latest developments in general machine learning (ML) research, power system researchers have been investigating more direct ways of incorporating physics knowledge into DRL training. This chapter specifically focuses on these aspects of physics-informed DRL designs in grid control. It discusses the significance, applications, research gaps, and open problems that need to be addressed in future research.

artificial intelligence, machine learning↗

Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications

This tutorial offers a pedagogical guide to hybrid quantum processors that integrate discrete-variable (DV) qubits and continuous-variable (CV) oscillators. Aimed at computer scientists, engineers, and physicists, it provides an overview of the experimental, algorithmic, and architectural aspects of this novel and rapidly developing hardware model. Experimental realizations of this model include superconducting, trapped-ion, and neutral-atom platforms. By combining DV and CV components, hybrid oscillator-qubit processors enable a powerful new paradigm that offers complementary strengths for quantum control, error correction, computation, and simulation. Working toward the goal of a full-stack system connecting applications to CV-DV hardware, we define and formulate abstract machine models and instruction set architectures. These essential abstractions enable codesign of hardware and software, and resource estimation for exploring the potential of current and future hardware for computational and simulation tasks. Using these abstractions, we present both new and existing examples that illustrate the benefits of hybrid CV-DV processors relative to traditional DV-only hardware in computation as well as quantum simulation of physical models. Examples include algorithms for transferring states between DV and CV systems, performing the quantum Fourier transform, and simulation of lattice gauge theories. Relative to qubit-only hardware, the bosonic degrees of freedom natively available in hybrid architectures can substantially reduce the circuit complexity of simulations for physical models containing bosons. A key technique is the extension of quantum signal processing ideas to CV-DV systems. This work is intended to serve as a timely and comprehensive guide to this relatively unexplored yet promising approach to quantum computation and to provide a road map to guide future development.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Hybrid Electrochemical Hydrogen/Metal Hydride Compressor (Final Technical Report)

Various alternatives to traditional mechanical compressor systems have been considered, including MHC and EHC. Both MHCs and EHCs are solid-state systems that have no moving parts other than valves. Both are quiet and have low maintenance requirements. However, strength and material issues as well as water and heat management issues have challenged EHCs, especially, when operated at very high pressures. Similarly, low efficiency, especially, when staging is required to attain high, pressure ratios, has challenged MHCs and has made them too complex and expensive. Material degradation, due to hydrogen impurity effects, has also created issues for MHCs. One novel alternative evaluated here is to combine EHC and MHC technologies in a way to maximize their advantages and to minimize each of their challenges to improve the overall systems performance on a path to meet or exceed current DOE targets. A hybrid EH/MH compressor takes advantage of lower maintenance and operating costs as well as increased reliability associated with both the MHC and EHC technologies over traditional mechanical compressors. Neither the MHC nor the EHC have any moving parts other than valves. The hybrid system also takes advantage of the higher efficiency and lower cost of the EHC by operating at lower delivery pressures combined with the robust and simple operation of a single-stage, MH compressor at higher pressures. Both MHC and EHC technologies are scalable and can be used for a variety of hydrogen compression and delivery applications.

08 HYDROGEN↗

Maskman

SAND2025-04369O Maskman is a user-friendly tool designed to create hex masks, which are essential for optimizing application performance in high-performance computing environments. By converting a list of integers into binary and then hex masks, Maskman simplifies the process of setting application affinity. This ensures that software runs efficiently on specific nodes within a computing cluster. Ideal for researchers and developers, Maskman streamlines the preparation of inputs for HPC schedulers, enhancing resource management and improving overall system performance. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Pase, Douglas [Sandia National Lab. (SNL-CA), Live↗

Design Space Exploration of Emerging Memory Technologies for Machine Learning Applications

Memory design space exploration methods study memory systems’ performances and limitations before implementation. The computer memory design space has grown exponentially because of the enormous growth of memory types, memory controllers, and application software. Computer simulators are commonly used for memory design space exploration. However, complex memory simulations take an enormous amount of time. Hence, in this paper, we proposed a machine learning-based design space exploration method for dynamic random-access memory and non-volatile memory systems. We applied our method to the CosmoGAN and LeNet applications to predict the following six memory response parameters: (i) bandwidth, (ii) power, (iii) average latency, (iv) average total latency, (v) memory reads, and (vi) memory writes. Our experimental results show that machine learning models can predict memory response parameter values faster than simulations. We used support vector machine, random forest, and gradient boosting machine learning models. We observed that the support vector machine provides better performance for bandwidth, average latency, and average total latency. The random forest model works better for memory reads and writes. The gradient boosting model provides superior prediction performance for power. We provide a detailed discussion on learning curve characteristics, error analysis, and memory type recommendation.

Hasan, S M Shamimul↗

Multibody for Everybody (M4E): A Symbolic Dynamics Modeling Tool with Applications in Simulation, Control, and Optimization

Developing the analytical model of a multibody system is often the initial step in control and optimization. The analytical model (equations of motion) describes a system’s time evolution under specified forcing conditions. Although developing these equations is easy for simple systems, this process becomes more complex for systems composed of multiple bodies. Deriving equations of motion for complex multibody systems requires specialized expertise in multibody dynamics, is time-consuming, and is susceptible to error. To address this issue, this paper presents an open-source, easy-to-use, systematic framework to derive symbolic equations of motion in both Python and MATLAB using the joint coordinate formulation. This formulation results in a set of ordinary differential equations that use the minimum set of coordinates needed to model a system. The symbolic representation provides better insight into the influence of design parameters on system performance, facilitates sensitivity analysis and parameter studies, and supports direct implementation of control and optimization routines. The tool enables numerical simulation for specified parameter sets, is modular for straightforward integration with other tools and libraries, and allows incorporation of hydrodynamics, mooring, and other external forces. The result is a reproducible, extensible pipeline for modeling, simulation, and design of complex multibody systems. The proposed tool is versatile and can be applied to domains such as robotics, control, and design. In addition, we integrated external libraries that provide capabilities for modeling offshore systems such as underwater robots and marine energy converters.

16 TIDAL AND WAVE POWER↗

Operation and performance of the CMS silicon strip tracker with proton-proton collisions at the CERN LHC

Salient aspects of the commissioning, calibration, and performance of the CMS silicon strip tracker are discussed, drawing on experience during operation with proton-proton collisions delivered by the CERN LHC. The data were obtained with a variety of luminosities. The operating temperature of the strip tracker was changed several times during this period and results are shown as a function of temperature in several cases. Details of the system performance are presented, including occupancy, signal-to-noise ratio, Lorentz angle, and single-hit spatial resolution. Saturation effects in the APV25 readout chip preamplifier observed during early Run 2 are presented, showing the effect on various observables and the subsequent remedy. Studies of radiation effects on the strip tracker are presented both for the optical readout links and the silicon sensors. The observed effects are compared to simulation, where available, and they generally agree well with expectations.

47 OTHER INSTRUMENTATION↗

Multiscale Dynamics of Reactive Fronts in the Subsurface

Understanding and predicting flow and reactive transport in rocks (i.e. geologic porous media) is critical to many technologies at the heart of the energy transition, including CO 2 sequestration and H2 storage. However, accurate modeling and prediction of these systems is very complex because physico-chemical processes that occur at very small spatial scales, i.e. in the pores of the rocks, can dramatically control the system performance at the field scale (km). For example, precipitation reactions at the pore-scale can lead to large permeability changes at the field scale and dramatically alter the migration of stored gases. Properly accounting for multi-scale coupling effects is critical to achieve predictivity and confidence in model outputs, which then can guide design and optimization at the system-scale. This can be achieved through the development of rigorous mathematical models that can appropriately account for fine-scale effects at the large scale. The final report of the Early Career award DE-SC0019075 “Multiscale dynamics of reactive fronts in the subsurface” summarizes the mathematical, numerical and experimental advancements to study and predict reactive transport in geologic porous media across scales.

58 GEOSCIENCES↗

Quasi-optical beam tracing module development for millimeter-wave high-wavenumber collective scattering on the NSTX-U and EAST tokamaks

A Python3-based beam tracing code utilizing Quasi-Optics has been developed to track both incident and receiving beams in high-k collective millimeter wave scattering systems within magnetic fusion plasmas. In contrast to existing ray tracing codes that solely consider refraction, this beam tracing code incorporates diffraction phenomena, providing a more comprehensive calculation. Here, this enhanced capability allows for a more accurate calculation of the scattering volume and spatial resolution in high-k collective scattering systems, crucial for evaluating system performance and facilitating data analysis. Unlike Geometrical Optics, Quasi-Optics employs the complex eikonal method, representing a Gaussian beam as a collection of coupled rays to accurately preserve diffraction characteristics. The developed code is intended for application in NSTX-Upgrade and EAST high-k beam tracing analyses, targeting frequencies of 693 GHz and 270 GHz, respectively. The high-k system's primary objective is the observation of electron-scale instabilities. Employing a symplectic integrator, the code ensures numerical accuracy, assessed through the conservation of the Hamiltonian. With its precision and efficiency, the code facilitates rapid inter-shot analyses.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Comparative Investigation of Current-Source Inverters using SiC Discrete Devices and Power Modules

The purpose of this paper is to investigate the impact of the SiC device packages on the commutation performance characteristics of current-source inverters (CSIs). The parasitic components in the CSI current commutation loop between the two-phase legs and output capacitors have a significant impact on the high-frequency performance of the SiC devices. To meet the elevated current requirements of high-power CSIs, it is often necessary to connect multiple discrete devices in parallel which increases the current commutation loop length. The selection of compact high-power SiC MOSFET and Schottky diode modules instead of discrete devices can be highly desirable to reduce the loop inductance and improve the system performance and power density. Two CSI benchtop prototype units, one with SiC discrete devices and the other with power modules, have been designed and tested, and the performances of the two CSIs are compared. The CSI with SiC power modules significantly reduces the inverter volume and lowers the parasitic inductance by 60% and the voltage ripple amplitude by 20% compared to the CSI unit with discrete devices.

42 ENGINEERING↗

Platform for Remote Deployment and Training for Enhanced Building Operation Practices (Building Re-Tuning and On-going Commissioning)

While a building’s energy usage is driven largely by its design and use, building operator behavior has a strong influence on its energy consumption. This project developed and piloted a specific, data-driven coaching methodology to help operators understand how they can adjust operations and/or affect no/low-cost repairs or upgrades to their specific building HVAC systems to reduce energy consumption. Named BuildingCoach, the operational optimization method used is based on the Building Re-tuning approach developed by the Pacific Northwest National Laboratory. A building operations analytics market has matured over the past decade, though its potential to affect energy-saving changes has not been fully realized. Training operators to understand the methods for operational optimization with the explicit approach of using building-system performance data is hypothesized to create a more effective, longer lasting result in building energy efficiency, and this strategy is the fundamental premise of this project. With the support of an Industry Advisory Board, the project succeeded in developing materials and recruiting for and delivering three pilot cohorts. Deliverables included twenty-two self-paced training modules (accessed via a Learning Management System) and a web-based platform that includes access to real-time building system data and a repository for building system documentation. The project set out to have 100 participants from 50 buildings in three pilot cohorts. In the end, there were 28 participants from 17 buildings, i.e., a significant shortfall. The first two pilot cohorts had only two buildings in each, and this was partially due to difficulties in deploying the Building Operator Coaching Solution (“the BOCS”), which is technology that extracts the data from the controls network and presents it as prescribed for coaching. In the third cohort, the project team deployed the BOCS successfully to 13 buildings, the methodology was piloted as intended, and numerous opportunities for optimization were identified. The BuildingCoach business plan charts a path to an economically sustainable effort. However, even with a licensing model captured in the final version of the business plan, the scalability is still limited to keeping less than 1,000 buildings affected by 2033. Even so, there are unexplored paths to greater scalability that are being considered. CUNY BPL is working to perpetuate and grow the use of BuildingCoach. As of this writing, about twenty buildings have either been connected or will be connected with operators coached / to be coached in the NYC municipal portfolio, twelve buildings across four campuses in NY State will use BuildingCoach, a NY upstate county wishes for six or seven buildings to participate with the support of funding from NYSERDA, and others have also expressed interest. In the decades to come, there will be an increasing percentage of large and mid-sized buildings that incorporate automated system optimization (ASO), and the building operators’ role will shift to spend more time on maintenance and monitoring. Meanwhile, programs such as BuildingCoach will play a critical role in optimizing operations. And, regardless of the emergence of ASO, operators will still need to understand how their systems operate so that they can monitor them properly. Within that context, BuildingCoach is an important step towards operators’ understanding of efficient building system operations.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Analysis of Space-Conditioning Loads in Commercial Buildings

Space conditioning end-uses, which include heating, cooling, and ventilation, represent a significant fraction of commercial building energy use, with a wide variety of heating and cooling technology options available in the market. In the interest of improving the overall efficiency of heating, ventilation and air-conditioning (HVAC) technologies, governments, utilities and private sector entities have implemented a variety of market transformation policies that aim to influence consumer purchase decisions. To evaluate the costs and benefits of such programs, analysts typically postulate a hypothetical default equipment choice, and compare it to one that provides comparable service with lower energy and/or power use. The corresponding reduced operating cost provides a benefit that offsets the potential higher cost of improved efficiency. Typically, life-cycle cost or cash-flow analyses are used to quantify the net economic benefit. These analyses require the capability to assess how a given equipment design would perform across a broad range of characteristics, both of the building and of the local weather. While these assessments can be performed using customized building simulations, it is generally not practical to develop and validate detailed building simulation code to cover all the potential variations of equipment design and installation. An alternative, and somewhat simpler, approach is to solely use detailed building simulations to generate time series of heating and cooling loads in commercial buildings. These loads can then be used as input to more detailed, stand-alone engineering models that simulate HVAC system performance under different equipment designs. This approach was used to evaluate a range of high-efficiency commercial packaged air conditioner design options for the Department of Energy’s Appliance and Equipment Standards Program (DOE-EERE 2015). While there may be some loss of precision relative to full simulation, the accuracy of this approach is sufficient for practical applications of cost-benefit analysis. This report describes the development of a database of commercial building heating and cooling loads, generated using the EnergyPlus software package, a whole building energy use model supported by the Department of Energy (DOE-EERE 2020a). EnergyPlus takes as input a set of configuration files that describe the building itself (size, zoning, envelope characteristics, etc.) and the various systems within it (HVAC, lighting, water heating, etc.). This analysis uses a publicly available collection of commercial reference buildings (CRB), comprised of sixteen building types and three vintages (DOE-EERE 2020b; Deru et al 2011). Each building is simulated in eighteen different locations, covering a wide range of climatic conditions. The prototype building description files assign the type of HVAC equipment used, and capacities across climate zones.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

OpenACC Profiling Support for Clang and LLVM using Clacc and TAU

Since its launch in 2010, OpenACC has evolved into one of the most widely used portable programming models for accelerators on HPC systems today. Clacc is a project funded by the US Exascale Computing Project (ECP) to bring OpenACC support for C and C++ to the popular Clang and LLVM compiler infrastructure. In this paper, we describe Clacc's support for the OpenACC Profiling Interface, a critical component of the OpenACC specification that standardizes an interface that profiling tools and libraries can depend upon across OpenACC implementations. As part of Clacc's general strategy to build OpenACC support upon OpenMP, we describe how Clacc builds OpenACC Profiling Interface support upon an extended version of OMPT. We then describe how a major profiling and tracing toolkit within ECP, the TAU Performance System, takes advantage of this support. We also describe TAU's selective instrumentation support for OpenACC. Finally, using Clacc and TAU, we present example visualizations for several SPEC ACCEL OpenACC benchmarks running on an IBM AC922 node, and we show that the associated performance overhead is negligible.

Coti, Camille↗

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

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

closed-loop asymptotic stability↗