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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,675 records · Page 93
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Design analysis of a particle-based thermal energy storage system for concentrating solar power or grid energy storage

Energy storage is becoming indispensable for expanding renewable energy integration, and it is critical to the future low-carbon energy supply. Large-capacity, grid scale energy storage can support the integration of solar and wind power and support grid resilience with the diminishing capacity of baseload fossil power plants. With the development of thermal energy storage (TES) for concentrating solar power systems, standalone TES for grid integration becomes attractive due to the declining renewable generation cost and an increasing need for energy storage. The standalone TES system introduced in this paper can play a big role in the carbon-free energy future with capacity larger than batteries and cost likely lower than other energy storage methods such as pumped storage hydropower and compressed air energy storage, both of which also have geological limitations. To this end, we describe a TES system that uses stable, inexpensive solid particles as a TES media to provide scalable, low cost energy storage. The particle-based TES has the ability to drive various thermal power cycles including conventional steam-Rankine, air Brayton turbine with combined-cycle ability, or the emerging supercritical carbon dioxide Brayton power cycle. This work describes the containment design method including a concrete silo and an internal-insulation layer for the particle-TES system. The economic analysis shows significantly low storage cost when the particle-TES is integrated with Brayton combined-cycle power generation. The paper shows the design approach of the particle-TES system and its economic potential for bulk energy storage. The advantage of the particle-TES system as a promising bulk energy storage method is its ability to economically support dispatchable renewable grid penetration for larger capacity and longer discharging hours than current battery storage technologies.

25 ENERGY STORAGE↗
DOE OSTI2026

Life cycle assessment of co-firing biomass at coal-fired power plants with carbon capture and storage toward net-zero emissions

Co-firing biomass with carbon capture and storage (BECCS) offers a technological option to decarbonize coal-fired power plants toward net-zero emissions. This study estimates the life cycle emissions of co-firing biomass at coal-fired power plants with CCS and quantifies its variability and uncertainty. Deployment of co-firing BECCS at coal-fired power plants can significantly reduce the life cycle emissions toward the net-zero target but lower the power plant performance, which vary with numerous factors, including coal type, biomass type, co-firing level, and CO 2 capture rate. The breakeven co-firing levels required for biomass at coal-fired power plants with 90 % CO 2 capture to reach net-zero emissions fall with a range roughly from 15 % to 25 % on an energy basis, depending on coal and biomass types. Increasing the CO 2 capture rate from 90 % to 95 % can lower the breakeven co-firing levels by about 5 to 8 percentage points for the biomass resources of interest, which can lower reliance on biomass resources and facilitate large-scale deployment of co-firing BECCS in fossil-rich regions but with limited biomass resources. Furthermore, findings improve the understanding of the techno-environmental performance of co-firing BECCS and inform strategic planning decisions on net-zero emissions in the coal-fired power sector.

Breakeven co-firing level↗
DOE OSTI2020

Distributed power generation via gasification of biomass and municipal solid waste: A review

The access to electricity has increased worldwide, growing from 60 million additional consumers per year in 2000-2012 to 100 million per year in 2012-2016. Despite this growth, approximately 675 million people will still lack access to electricity in 2030, indicating that electricity demand will continue to increase. Unfortunately, traditional large fossil power technologies based on coal, oil and natural gas lead to a major concern in tackling worldwide carbon dioxide emissions, and nuclear power remains unpopular due to public safety concerns. Distributed power generation utilizing CO 2 -neutral sources, such as gasification of biomass and municipal solid wastes (MSW), can play an important role in meeting the world energy demand in a sustainable way. Furthermore, this review focuses on the recent technology developments on seven power generation technologies (i.e. internal combustion engine, gas turbine, micro gas turbine, steam turbine, Stirling engine, organic rankine cycle generator, and fuel cell) suitable for distributed power applications with capability of independent operation using syngas derived from gasification of biomass and MSW. Technology selection guidelines is discussed based on criteria, including hardware modification required, size inflexibility, sensitivity to syngas contaminants, operational uncertainty, efficiency, lifetime, fast ramp up/down capability, controls and capital cost. Major challenges facing further development and commercialization of these power generation technologies are discussed.

09 BIOMASS FUELS↗
DOE OSTI2023

A comparison of the power potential for surface- and seabed-deployed tidal turbines in the San Juan Archipelago, Salish Sea, WA

The San Juan archipelago lies along the axis of tidal movement between Straits of Juan de Fuca and Strait of Georgia in the Salish Sea. The amplitude of the tidal exchange produces significant tidal currents between the islands, as well as in Rosario and Haro Straits. These are of interest as a future source of electrical power generation, given the islands’ dependence on electricity supply by a subsea cable from the mainland. Here, we evaluate the tidal current energy potential in this region through a re-analysis of measurements collected by the National Ocean Service (NOS) and a high-resolution numerical model. Given the considerable variations in water depth and vertical velocity profiles across candidate tidal energy sites, we consider the trade-offs between tidal turbines deployed from a floating platform and those anchored to the seabed. Measurement re-analysis indicates several locations that could support tidal current power generation by MW-scale turbines with an acceptable balance between turbine size, rated power, and capacity factor. Even for relatively large (30 m) turbine diameters, surface-deployed turbines would be expected to produce up to 30 % more electricity than the same turbine deployed near the seabed due to vertical shear, with this difference increasing for smaller diameter turbines. A benchmark comparison at the measurement locations with the highest power generation potential shows relatively good model fidelity, though, even with relatively high resolution, time-average power density disagreements of ± 50 % persist throughout the water column. Nonetheless, the simulation identifies several locations with power generation potential more than twice as high as locations in the measurement re-analysis. These sites were either not surveyed by NOS or excluded due to data quality issues. Altogether, these results demonstrate the complimentary of models and measurements for tidal energy site assessment and suggest that tidal currents could be an important source of electricity generation in the San Juan archipelago.

16 TIDAL AND WAVE POWER↗
DOE OSTI2026

Distributed optimization and control for autonomous distributed energy resource power dispatch and frequency regulation considering communication failures

Distributed energy resources (DERs) can significantly enhance grid flexibility by supplying power and secondary frequency regulation (SFR) services. Yet, their large number and dispersed nature limit the effectiveness of traditional centralized power dispatch and frequency control schemes, and expose the system to single-point communication failures. This paper presents a unified distributed optimization and control framework for DER power dispatch and SFR provision. A transmission-loss-aware distributed direct current optimal power flow is first formulated to optimize DER power dispatch and reserve scheduling. On top of this, a fully distributed control scheme for DER autonomous SFR provision is developed to allocate automatic generation control signals cost-effectively while ensuring robustness to communication link disruptions. The framework is validated on IEEE 14-bus and 39-bus transmission systems with large-scale distribution feeders using transmission-distribution dynamic co-simulation, demonstrating reliable and autonomous DER power dispatch and SFR provision under diverse operating conditions and communication contingencies.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Synchronization in electric power networks with inherent heterogeneity up to 100% inverter-based renewable generation

The synchronized operation of power generators is the foundation of electric power network stability and a key to the prevention of undesired power outages and blackouts. Here, we derive the conditions that guarantee synchronization in power networks with inherent generator heterogeneity when subjected to small perturbations, and perform a parametric sensitivity analysis to understand synchronization with varied types of generators. As inverter-based resources, which are the primary interfacing technology for many renewable sources of energy, have supplanted synchronous generators in ever growing numbers, the center of attention on associated integration challenges have resided primarily on the role of declining system inertia. Our results instead highlight the critical role of generator damping in achieving a stable state of synchronization. Additionally, we report the feasibility of operating interconnected electric grids with up to 100% power contribution from inverter-based renewable generation technologies. Our study has important implications as it sets the basis for the development of advanced control architectures and grid optimization methods that ensure synchronization and further pave the path towards the decarbonization of the electric power sector.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Optimal energy storage portfolio for high and ultrahigh carbon-free and renewable power systems

Achieving 100% carbon-free or renewable power systems can be facilitated by the deployment of energy storage technologies at all timescales, including short-duration, long-duration, and seasonal scales; however, most current literature focuses on cost assessments of energy storage for a given timescale or type of technology. In this work, we use an optimization framework with high spatial and temporal resolution to simultaneously assess the variable renewable power deployment and the optimal storage portfolio for seven independent system operators in the United States. Results indicate that achieving high (75–90%) and ultrahigh (>90%) energy mixes requires combining several flexibility options, including renewable curtailment, short-duration, long-duration, and seasonal storage. For instance, carbon-free and renewable energy mix targets of up to 80% are achieved with economic curtailment and a combination of short- and long-duration energy storage for the performance and cost assumptions used. After that, there is a point between 80% and 95% where seasonal storage becomes cost-competitive, depending on the specific power system. Moreover, our results indicate that storage-to-storage operation—one storage device used to charge another storage device—and the decoupling of charging and discharging storage power capacity are cost-effective options for the integration of high and ultrahigh shares of carbon-free or renewable power sources. Additionally, the results from this study show that an 85% carbon-free or renewable energy mix can be achieved at a cost of avoided CO 2 emissions of US$66.0 per tonne or less, regardless of the power system.

25 ENERGY STORAGE↗
DOE OSTI2024

Solving differential‐algebraic equations in power system dynamic analysis with quantum computing

Abstract Power system dynamics are generally modeled by high dimensional non‐linear differential‐algebraic equations (DAEs) given a large number of components forming the network. These DAEs' complexity can grow exponentially due to the increasing penetration of distributed energy resources, whereas their computation time becomes sensitive due to the increasing interconnection of the power grid with other energy systems. This paper demonstrates the use of quantum computing algorithms to solve DAEs for power system dynamic analysis. We leverage a symbolic programming framework to equivalently convert the power system's DAEs into ordinary differential equations (ODEs) using index reduction methods and then encode their data into qubits using amplitude encoding. The system non‐linearity is captured by Hamiltonian simulation with truncated Taylor expansion so that state variables can be updated by a quantum linear equation solver. Our results show that quantum computing can solve the power system's DAEs accurately with a computational complexity polynomial in the logarithm of the system dimension. We also illustrate the use of recent advanced tools in scientific machine learning for implementing complex computing concepts, that is, Taylor expansion, DAEs/ODEs transformation, and quantum computing solver with abstract representation for power engineering applications.

computational complexity↗
DOE OSTI2022

Low power implementation of high frequency SiPM readout for Cherenkov and scintillation detectors in TOF-PET

State-of-the-art (SoA) electronic readout for silicon photomultiplier (SiPM)-based scintillation detectors that demonstrate experimental limits in achievable coincidence time resolution (CTR) leverage low noise, high frequency signal processing to facilitate a single photon time response that is near the limit of the SiPMs architecture. This readout strategy can optimally exploit fast luminescence and prompt photon populations, and promising measurements show detector concepts employing this readout can greatly advance PET detector CTR, relative to SoA in clinical systems. However, the technique employs power hungry components which make the electronics chain impractical for channel-dense time-of-flight (TOF)-PET detectors. We have developed and tested a low noise and high frequency readout circuit which is performant at low power and consists of discrete elements with small footprints, making it feasible for integration into TOF-PET detector prototypes. A 3 × 3 mm 2 Broadcom SiPM with this readout chain exhibited sub-100 ps single photon time resolution at 10 mW of power consumption, with a relatively minor performance degradation to 120 ± 2 ps FWHM at 5 mW. CTR measurements with 3 × 3 × 20 mm 3 LYSO and fast LGSO scintillators demonstrated 127 ± 3 ps and 113 ± 2 ps FWHM at optimal power operation and 133 ± 2 ps and 121 ± 3 ps CTR at 5 mW. BGO crystals 3 × 3 × 20 mm 3 in size show 271 ± 5 ps FWHM CTR (1174 ± 14 ps full-width-at-tenth-maximum (FWTM)) at optimal power dissipation and 289 ± 8 ps (1296 ± 33 ps FWTM) at 5 mW. The compact and low power readout topology that achieves this performance thereby offers a platform to greatly advance PET system CTR and also opportunities to provide high performance TOF-PET at reduced material cost.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Investigation of radiated-power for low aspect ratio fusion plasmas

Investigating radiated power in fusion plasmas is of utmost importance to understand the effect of undesired impurities, such as metals, in present devices, or also desired impurities, such as noble gasses, to purposefully radiate a large fraction of power in future devices. These studies are especially important for high Z impurities which will play a crucial role in future generation fusion pilot plants. In this work, we have developed a power radiation analysis module, which is used to investigate 2D distributions of impurity densities and radiated power asymmetries caused due to both plasma rotation and the cooling rate dependence on temperature profile for the cases of experimental NSTX plasmas and designed scenarios for the spherical tokamak advanced reactor (STAR), both being low aspect ratio tokamaks. Two different atomic databases have been tested during this work to study their impact on the radiated power distribution, especially for high Z impurities. Also in PRAM, self-consistent calculations of two-dimensional electron, main ion, and impurity ion densities are carried out using one-dimensional input density, temperature, and rotation profiles. In the case of NSTX, discharges with high rotation of ∼ 170 km s, measured with charge exchange recombination spectroscopy, have been investigated. Rotation-induced charge separation, leading to an electrostatic potential, is calculated iteratively to a self-consistent solution while testing high Z impurities to observe any 2D asymmetry in the core radiated power due to centrifugal forces. The STAR design, being much larger (R = 4 m), is projected to have a much lower rotation, and is shown to have low rotation-induced asymmetries, on the order of ten percent or less, between the low field and high field sides. However, another effect not due to rotation but to the dependence of impurity cooling rates on temperature can lead to radiation peaking off-axis, near the plasma edge. This effect is noticeable for argon in NSTX, for example, but can also be enhanced for certain impurities at much higher temperatures projected for STAR (T e0 ~ 32 keV), for example for undesired tungsten or possibly desired xenon.

NSTX↗
DOE OSTI2021

Cosmic shear power spectra in practice

Cosmic shear is one of the most powerful probes of Dark Energy, targeted by several current and future galaxy surveys. Lensing shear, however, is only sampled at the positions of galaxies with measured shapes in the catalog, making its associated sky window function one of the most complicated amongst all projected cosmological probes of inhomogeneities, as well as giving rise to inhomogeneous noise. Partly for this reason, cosmic shear analyses have been mostly carried out in real-space, making use of correlation functions, as opposed to Fourier-space power spectra. Since the use of power spectra can yield complementary information and has numerical advantages over real-space pipelines, it is important to develop a complete formalism describing the standard unbiased power spectrum estimators as well as their associated uncertainties. Building on previous work, this paper contains a study of the main complications associated with estimating and interpreting shear power spectra, and presents fast and accurate methods to estimate two key quantities needed for their practical usage: the noise bias and the Gaussian covariance matrix, fully accounting for survey geometry, with some of these results also applicable to other cosmological probes. Here, we demonstrate the performance of these methods by applying them to the latest public data releases of the Hyper Suprime-Cam and the Dark Energy Survey collaborations, quantifying the presence of systematics in our measurements and the validity of the covariance matrix estimate. We make the resulting power spectra, covariance matrices, null tests and all associated data necessary for a full cosmological analysis publicly available.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Full-Shape analysis of the power spectrum and bispectrum of DESI DR1 LRG and QSO samples

We present the first joint analysis of the power spectrum and bispectrum using the Data Release 1 (DR1) of the Dark Energy Spectroscopic Instrument (DESI), focusing on Luminous Red Galaxies (LRGs) and quasars (QSOs) across a redshift range of 0.4 ≤ z ≤ 2.1. By combining the two- and three-point statistics, we are able to partially break the degeneracy between the logarithmic growth rate, f(z), and the amplitude of dark matter fluctuations, σ s8 (z), which cannot be measured separately in analyses that only involve the power spectrum. In comparison with the (fiducial) Planck ΛCDM cosmology we obtain f/f fid = {0.888 -0.089 +0.186 ,0.977 -0.220 +0.182 ,1.030 -0.085 +0.368 }, σ s8 /σ fid s8 = {1.224 -0.133 +0.091 ,1.071 -0.163 +0.278 ,1.00 0 -0.223 +0.088 } respectively for the three LRG redshift bins, corresponding to a cumulative 10.1% constraint on f, and of 8.4% on σ s8 , including the systematic error budget. Additionally, we obtain constraints for the ShapeFit compressed parameters describing the isotropic scaling parameter, α iso (z), the Alcock-Paczyński parameter, α AP (z), the combined growth of structure parameter fσ s8 (z), and the combined shape parameter m(z)+n(z). Their cumulative constraints from our joint power spectrum-bispectrum analysis are respectively σ αiso = 0.9% (9% improvement with respect to our power spectrum-only analysis); σ α AP = 2.3% (no improvement with respect to power spectrum-only analysis, which is expected given that the bispectrum monopole has no significant anisotropic signal); σ fσs8 = 5.1% (9% improvement); σ m+n = 2.3% (11% improvement). These results are fully consistent with the main DESI power spectrum analysis, demonstrating the robustness of the DESI cosmological constraints, and compatible with Planck ΛCDM cosmology.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Technological developments and accelerator improvements for the FRIB beam power ramp-up

The Facility for Rare Isotope Beams (FRIB) began operation with 1 kW beam power for scientific users in May 2022 upon completion of 8 years of project construction. The ramp-up to the ultimate beam power of 400 kW, planned over a 6-year period, will enable the facility to reach its full potential for scientific discovery in isotope science and applications. In December 2023, a record-high beam power of 10.4 kW uranium was delivered to the target. Technological developments and accelerator improvements are being made over the entire facility and are key to completion of the power ramp-up. Major technological developments entail the phased deployment of high-power beam-intercepting systems, including the charge strippers, the charge selection systems, the production target, and the beam dump, along with support systems, including non-conventional utilities (NCU) and remote handling facilities. Major accelerator improvements include renovations to aging legacy systems associated with experimental beam lines and system automation for improved operational efficiency and better machine availability. Experience must be gained to safely handle the increased radiological impacts associated with high beam power; extensive machine studies and advanced beam tuning procedures are needed to minimize uncontrolled beam losses for the desired operating conditions. This paper discusses the technological developments and accelerator improvements with emphasis on major R&D efforts.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

Dynamic land use implications of rapidly expanding and evolving wind power deployment

Abstract The expansion of wind power poses distinct and varied geographic challenges to a sustainable energy transition. However, current knowledge of its land use impacts and synergies is limited by reliance on static characterizations that overlook the role of turbine technology and plant design in mediating interactions with the environment. Here, we investigate how wind technology development and innovation have shaped landscape interactions with social and ecological systems within the United States and contribute to evolving land area requirements. This work assesses trends in key land use facets of wind power using a holistic set of metrics to establish an evidence base that researchers, technology designers, land use managers, and policymakers can use in envisioning how future wind-intensive energy systems may be jointly optimized for clean energy, social, and environmental objectives. Since 2000, we find dynamic land occupancy patterns and regional trends that are driven by advancing technology and geographic factors. Though most historical U.S. wind deployment has been confined to the temperate grassland biome in the nation’s interior, regional expansion has implicated diverse land use and cover types. A large percentage of the typical wind plant footprint (∼96% to > 99%) is not directly impacted by permanent physical infrastructure, allowing for multiple uses in the spaces between turbines. Surprisingly, turbines are commonly close to built structures. Moreover, rangeland and cropland have supported 93.4% of deployment, highlighting potential synergies with agricultural lands. Despite broadly decreasing capacity densities, offsetting technology improvements have stabilized power densities. Land use intensity, defined as the ratio of direct land usage to lifetime power generation of wind facilities, has also trended downwards. Although continued deployment on disturbed lands, and in close proximity to existing wind facilities and other infrastructure, could minimize the extent of impacts, ambitious decarbonization trajectories may predispose particular biomes to cumulative effects and risks from regional wind power saturation. Increased land-use and sustainability feedback in technology and plant design will be critical to sustainable management of wind power.

17 WIND ENERGY↗
DOE OSTI2025

Decarbonization and technology cost drivers: considerations for potential future thermoelectric water use in the power sector

The power sector is currently undergoing significant changes, driven by a combination of factors, including decarbonization and technology innovation. This study aims to assess implications of these drivers on U.S. power sector technology futures and the associated water and environmental implications for cooling thermoelectric power plants. Specifically, we evaluate four decarbonization scenarios for the contiguous United States that vary in assumptions concerning demand growth and technology costs, with technology costs driving alternative outcomes that prioritize either technologies that require low amounts of water (such as wind, solar, and battery) or high amounts of water (such as nuclear and carbon capture and storage). These scenarios are executed in a power sector capacity expansion model and compared to two reference scenarios that assume status quo with policy and cost drivers. Our analysis indicates that future U.S. thermoelectric water withdrawals could decrease by 25%–60%, but water consumption could more than triple in some scenarios. These changes are driven by a combination of retirement of some power facilities, shifts in cooling technologies, and new technology deployment. The water use patterns vary across the United States, with the eastern regions demonstrating a lot more variability in water consumption across scenarios than western regions. However, local concerns can influence these possible investments, since increased water consumption can exacerbate water scarcity, leading to conflicts among competing users and affecting regional social, environmental, and economic dynamics. Future work should consider possible costs associated with alternate water sources, as well as improve the representation of water constraints within simulations. Inclusion of extreme events and alternate modeling platforms (e.g. production cost modeling and resource adequacy) may also be warranted to further stress test the robustness of these possible technology futures. Such assessments will be critical for ensuring decarbonization and other infrastructure-oriented investments lead to a reliable and resilient power grid.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Safe Reinforcement Learning for Emergency Load Shedding of Power Systems

The paradigm shift in the electric power grid necessitates a revisit of existing control methods to ensure the grid’s security and resilience. In particular, the increased uncertainties and rapidly changing operational conditions in power systems have revealed outstanding issues in terms of either speed, adaptiveness, or scalability of the existing control methods for power systems. On the other hand, the availability of massive real-time data can provide a clearer picture of what is happening in the grid. Recently, deep reinforcement learning (RL) has been regarded and adopted as a promising approach leveraging massive data for fast and adaptive grid control. However, like most existing machine learning (ML)- based control techniques, RL control usually cannot guarantee the safety of the power systems. In this paper, we introduce a novel method for safe RL-based load shedding of power systems that can enhance the safe voltage recovery of the electric power grid after experiencing faults. Numerical simulation on the IEEE 39-bus testcase is performed to demonstrate the effectiveness of the proposed safe RL emergency control, as well as its adaptive capability to faults not seen in the training.

reinforcement learning, emergency control, power g↗
DOE OSTI2022

A 4 kV/120 A SiC Solid-State DC Circuit Breaker Powered By a Load-Independent IPT System

This article introduces a 4 kV/120 A solid-state dc circuit breaker (DCCB) based on discrete SiC mosfets. The DCCB is designed in a five-layer tower structure. Each layer consists of a circular main conduction branch and an attached gate driver. There are two primary benefits of the proposed DCCB. First, it reduces conduction loss with multiple devices in parallel. Second, it achieves an ultrafast response speed with SiC mosfets. Moreover, the gate drivers of the DCCB are powered by a domino inductive power transfer (IPT) system. It achieves the load-independent constant-voltage output characteristics, which means the outputs are immune to load variations. Additionally, an IPT system prototype is implemented to test the power transfer performance. At 500-kHz frequency, the total output power reaches 15.73 W, which is sufficient to power on five gate drivers, with a peak transfer efficiency of 75.4%. The IPT system is tested to power a 4 kV/120 A DCCB prototype. It validates that the DCCB is effective to turn off 120 A current within 3.5 μs.

42 ENGINEERING↗
DOE OSTI2021

Ensemble Learning Based Convex Approximation of Three-Phase Power Flow

Though the convex optimization has been widely used in power systems, it still cannot guarantee to yield a tight (accurate) solution to some problems. To mitigate this issue, this paper proposes an ensemble learning based convex approximation for alternating current (AC) power flow equations that differs from the existing convex relaxations. The proposed approach is based on three-phase quadratic power flow equations in rectangular coordinates. To develop this data-driven convex approximation of power flows, the polynomial regression (PR) is first deployed as a basic learner to fit convex relationships between the independent and dependent variables. Then, ensemble learning algorithms such as gradient boosting (GB) and bagging are introduced to combine learners to boost model performance. Based on the learned convex approximation of power flow, optimal power flow (OPF) is formulated as a convex quadratic programming problem. The simulation results on IEEE standard cases of both balanced and unbalanced systems show that, in the context of solving OPF, the proposed data-driven convex approximation outperforms the conventional semi-definite programming (SDP) relaxation in both accuracy and computational efficiency, especially in the cases that the conventional SDP relaxation fails

Convex approximation↗