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DOE OSTI2025

Flexibility Options: A Proposed Product for Managing Imbalance Risk

The presence of variable renewable energy resources with uncertain outputs in day-ahead electricity markets results in additional balancing needs in real-time. Addressing those needs cost-effectively and reliably within a competitive market with unbundled products is challenging as both the demand for and the availability of flexibility depends on day-ahead energy schedules. Existing approaches for reserve procurement usually rely either on oversimplified demand curves that do not consider how system conditions that particular day affect the value of flexibility, or on bilateral trading of hedging instruments that are not co-optimized with day-ahead schedules. This article proposes a new product, ‘Flexibility Options', to address these two limitations. The demand for this product is endogenously determined in the day-ahead market and it is met cost-effectively by considering real-time supply curves for product providers, which are co-optimized with the energy supply. As we illustrate with numerical examples and mathematical analysis, the product addresses the hedging needs of participants with imbalances cost-effectively, provides a less intermittent revenue stream for participants with flexible outputs, promotes value-driven pricing of flexibility, and ensures that the system operator is revenue-neutral. This article provides a comprehensive design that can be further tested and applied in large-scale systems.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2025

Final Technical Report of a Feasibility Investigation of a Hydropower Flexibility Upgrade Kit

The project studied the feasibility of a concept for a flexibility upgrade kit called h-Dynamyk to improve the flexibility of U.S. hydropower plants and assessed its potential impact on the U.S. hydropower industry. This concept addresses the growing need for grid flexibility amid rising renewable energy adoption, such as wind and solar, which often introduce intermittency. The upgrade kit is intended to address challenges posed by aging turbine designs in meeting modern grid demands for flexibility services like frequency response, voltage control, spinning reserve, and black-start capabilities. Key features of the h-Dynamyk kit include siphon turbine assemblies, medium-voltage variable frequency drives (VFDs), and smart controls integrated with plant systems to optimize operations and extend equipment life. This nine-month discovery project successfully achieved its objectives by defining a baseline design and performance metrics for the h-Dynamyk flexibility upgrade kit, analyzing this baseline, and incorporating lessons learned from this analysis into a modified set of metrics and recommendations for future design and testing, which were further guided by field site studies.

13 HYDRO ENERGY↗

DOE OSTI2024

Energy Storage Improves Power Plant Flexibility and Economic Performance

Most existing coal-fired power plants were designed for sustained operation at full load to maximize efficiency, reliability, and revenue, as well as to operate air pollution control devices at design conditions. Depending on plant type and design, these plants can adjust output within a fixed range in response to plant operating or market conditions. The need for flexibility driven by increased penetration of variable and non-dispatchable power generation, such as wind and solar, is shifting the traditional mission profile of thermoelectric power plants in three ways: more frequent shutdowns when market or grid conditions warrant, more aggressive load ramp rates (rate of output change), and a lower minimum sustainable load, which provides a wider operating range and helps avoid costly plant shutdowns. Recent studies have shown that the flexibility of a coal-fired power plant can be improved by energy storage. The objective of this work was to analyze a set of energy storage options and determine their impact on the flexibility and economics of a representative coal-fired power plant. The effect of three energy storage systems integrated with a coal power plant on plant flexibility and economics was investigated. The results obtained in this project show that energy storage systems integrated with a thermal power plant improve plant flexibility and participation in the energy and ancillary services markets, which improves plant financial performance.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2024

Learning-Based Building Flexibility Estimation and Control to Improve Microgrid Economics and Resilience: Preprint

This paper proposes a learning-based building flexibility estimation and control framework to improve system economics and resilience. A data-driven building load flexibility model consisting of weather forecasting and estimating load consumption is proposed to quantify building heating, ventilation, and air conditioning (HVAC) load flexibility. A reinforcement learning-based microgrid controller is proposed to dispatch distributed generators, distributed energy resources, and build HVAC loads while taking flexibility information as one of the inputs. Simulation analysis is conducted on the model of a real microgrid in California. The effectiveness of the proposed learning-based building flexibility estimation and control in reducing microgrid energy costs and improving the sustainability of critical loads is demonstrated.

building load flexibility↗

DOE OSTI2026

Estimating Flexibility Envelopes for Residential Customers From Utility Smart Meter Data: Preprint

Demand response from residential customers has significant potential to support power system operations, but accurate flexibility estimation is challenging due to the limited resolution of advanced metering infrastructure (AMI) data. Most utility AMI measurements are recorded at hourly intervals, with only a small portion at higher resolutions, and even fewer households have appliance-level energy usage data. To address this issue, this paper proposes a two-stage long short-term memory (LSTM) framework for estimating household flexibility envelopes from low-resolution AMI data. In the first stage, the heating, ventilating, and air-conditioning (HVAC) load and non-HVAC loads are estimated by using a model trained on a small set of households with appliance-level profiles. These estimated data are then used to compute the upper- and lower-flexibility bounds, which are subsequently down-sampled to lower-resolution data. In the second stage, these flexibility bounds serve as training inputs for another LSTM model, enabling direct prediction of flexibility envelopes for households with only hourly AMI data. This method is validated using Pecan Street data from two different areas, and the results demonstrate its applicability and effectiveness.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

A Diazo Linker Ligand Promotes Flexibility and Induced Fit Binding in a Microporous Copper Coordination Network

Abstract Flexible organic linkers represent an intuitive and effective strategy to design flexible metal–organic materials. We report herein a systematic study concerning the effect of varying the central bond of mixed pyridyl‐benzoate linkers, L, upon the flexibility of three isostructuralkddtopology microporous coordination networks (CNs) of formula ML 2 :X‐kdd‐1‐Cu,1= L = (E)‐4‐(pyridin‐4‐yldiazenyl)benzoate;X‐kdd‐2‐Cu,2= L = (E)‐4‐(2‐(pyridin‐4‐yl)vinyl)benzoate; the previously reportedX‐kdd‐3‐Cu,3= L = 4‐(pyridin‐4‐ylethynyl)benzoate. As revealed by single crystal x‐ray diffraction (SCXRD) and gas sorption studies,X‐kdd‐1‐Cu, exhibited gate‐opening during CO 2 and hydrocarbon (C2 and C8) sorption experiments whereas the other two CNs did not. Insight into these phase transformations was gained from in situ variable‐pressure and variable temperature powder X‐ray diffraction (PXRD), SCXRD, and modeling. Rotation of ligand1around the diazo bond, torsion angle changes between phenyl and carboxylate moieties, and deformation of the Cu‐based rod building blocks enabled activatedX‐kdd‐1‐Cuto form new phases with C8 isomers and CH 2 Cl 2 , CH 2 Cl 2 inducing contraction of the activated phase. Computational studies suggest that1enables flexibility thanks to its lower barrier of deformation versus2or3. This study teaches that diazo moieties could offer a general strategy to enhance the flexibility of CNs.

Chemistry↗

DOE OSTI2026

A practical control strategy for demand flexibility with ensured occupant comfort in grid-interactive efficient buildings

This study proposes a practical and simplified demand response (DR) control strategy from the perspective of grid-interactive efficient buildings (GEBs), aiming to secure demand flexibility while ensuring occupant thermal comfort. Focusing on summer on-peak periods, a linear demand response (LDR) strategy that integrates cooling setpoint adjustment and lighting dimming was designed, and its performance was quantitatively evaluated. A case study was conducted using EnergyPlus-based simulations for a U.S. DOE small office prototype building under summer on-peak weather conditions. Compared with a conventional rapid demand response (RDR) strategy, the proposed LDR approach gradually reduced electrical loads while maintaining occupant thermal comfort indices, including predicted mean vote (PMV) and predicted percentage of dissatisfied (PPD), within acceptable comfort ranges. Quantitative analysis of demand flexibility using the grid-interactive impact index (GII) and the flexibility strength index (FSI) showed that the LDR strategy provided approximately 12.5% demand flexibility during DR periods and achieved an electricity cost reduction of about 8.8%. In addition, the results of the part-load ratio (PLR)-based cooling system performance analysis showed that, in the on-peak period, the LDR strategy exhibited improved cooling performance compared with the baseline. Overall, this study shows the potential of a practical DR control strategy that can simultaneously achieve occupant comfort and demand flexibility without relying on complex advanced control technologies.

Jung, Dong Eun↗

DOE OSTI2024

Flexible MOFs as Pressure-Tunable Filters for Hydrocarbon Separation

Metal–organic frameworks (MOFs) hold significant promise for separating gas mixtures, especially hydrocarbons. While the main focus in the field is the development of new adsorbents for specific separations of binary mixtures, a preferable situation would be using a single framework for separating various species. This has been achieved in some flexible MOFs, where ternary mixtures can be separated at different temperatures. Here, we propose a simple yet fascinating way of utilizing the flexibility of MOFs to create tunable filters as a function of external pressure. We thus replace the more costly temperature-driven tunability with a cost-efficient external-pressure tunability. As a proof-of-concept, we select the CaMOF flexible framework for C6 hydrocarbon separation, however, our results are applicable to other flexible framework and gas molecules. Furthermore, our findings provide mechanistic insight and guidelines to engineer separation filters by designing flexible pores with critical sizes that can be effectively manipulated by external pressure.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Insights Into Seismicity Associated With Flexibly Operating Enhanced Geothermal System From Real‐Time Distributed Acoustic Sensing

Enhanced Geothermal Systems (EGS) have the capacity to broaden the accessible resource pool for geothermal power generation. Traditionally viewed as a “baseload” resource, their flexible operation might also enable dispatchable load‐following generation and long‐term energy storage, aligning them with the evolving landscape of decarbonized electricity systems. However, increasing permeability and extracting energy during EGS operations can induce microseismic events; for many prior EGS efforts, some associated seismicity has been observed. While energetically beneficial, the flexibility of EGS operations prompts our inquiry into whether new types of operations will yield previously unseen seismicity patterns. We demonstrate the use of distributed acoustic sensing (DAS) with real‐time edge computing to monitor seismicity during a pilot test of a cyclically operated EGS facility at the Blue Mountain geothermal field. Our focus lies in uncovering seismicity insights from the real‐time microseismic catalog, particularly during load‐following dispatchability tests simulating flexible EGS operation. Here, we find that variations in pore pressure consistently correlate with seismicity, and that controlling pressure cycles during flexible operations appears to constrain microseismic activity during subsequent cycles. The spatio‐temporal evolution of microseismic clouds recorded during cyclic injection cycles fits diffusive models over our available observation period. Additionally, seismicity elevation lags behind pore pressure increases, likely due to pressure diffusion to the fracture system boundary. Through real‐time monitoring, we offer novel insights into seismicity associated with flexibly operating EGS. Our findings suggest that leveraging DAS and edge computing can inform EGS operations and help mitigate induced seismicity.

Chamarczuk, Michal [Rice Univ., Houston, TX (Unite↗

DOE OSTI2025

Mechanically flexible mid-wave infrared imagers using black phosphorus ink films

The mid-wave infrared (MWIR) spectral range (λ = 3–8 μm) enables important sensing and imaging applications, including non-invasive bioimaging, night vision, and autonomous navigation. Commercial MWIR photodetectors are limited to rigid imagers based on heteroepitaxial materials. There is an emerging need for mechanically flexible MWIR imagers to broaden their functionality and practicality. Recently, photodetectors using van der Waals (vdW) black phosphorus (BP) flakes have demonstrated highly sensitive room-temperature photodetection. Additionally, vdW materials are solution-processable, facilitating scalable processing and flexible device fabrication. In this work, we present flexible MWIR imagers consisting of photodiodes fabricated on thin plastic substrates using BP ink films. We demonstrate mechanically robust responsivity up to 2.5-mm bending radii and after 5000 bending cycles. Leveraging this flexibility, we achieve full-azimuthal imaging, detecting directional light sources with precision. These results establish a scalable approach for large-area, conformable MWIR imaging and pave the way for integration with flexible electronics.

Wijaya, Theodorus Jonathan↗

DOE OSTI2025

Ambient mechanosynthesis of flexible two-dimensional covalent organic frameworks

We present the first ambient mechanosynthesis of 16 flexible covalent organic frameworks (COFs) within an hour. Notably, one representative COF exhibited a high iodine uptake capacity of ∼4.3 g g −1 from aqueous solutions and 5.97 g g −1 from vapor. Flexible two-dimensional covalent organic frameworks (2D COFs) constructed from nonplanar building blocks represent an emerging paradigm in COF design. Nevertheless, the prevailing solvothermal synthesis suffers from low time efficiency, environmental unfriendliness, and cumbersome protocols. Here, we address these challenges by developing the first ambient mechanosynthesis of a diverse library of flexible 2D COFs. Sixteen distinct triazine-cored Schiff-base COFs, including five as-yet-unreported ones, were rapidly synthesized via ball milling using 2,4,6-tris(4-aminophenoxy)-1,3,5-triazine (TPT-NH 2 ) and 2,4,6-tris(4-formylphenoxy)-1,3,5-triazine (TPT-CHO) as building blocks. Notably, the representative COF, MC-flexible-COF-1, was synthesized in as little as one hour under mechanosynthesis conditions, whereas it remained unattainable via the traditional solvothermal method, despite prolonged heating and extensive solvent screening. The highly dynamic nature of the imine linkage was unequivocally demonstrated through mechanochemical “scrambling” experiments using molecular model compounds. Furthermore, MC-flexible-COF-1 exhibited a high iodine uptake capacity of ∼4.30 g g −1 from aqueous solutions and 5.97 g g −1 from the vapor phase. This work underscores the immense potential of mechanochemistry as a powerful and sustainable tool for the rapid synthesis of advanced 2D COFs, including those inaccessible via conventional solution-based methods.

Nailwal, Yogendra↗

DOE OSTI2024

Concrete Thermal Energy Storage Enabling Flexible Operation without Coal Plant Cycling

The work described in this report is responsive to the Office of Fossil Energy program “Energy Storage for Fossil Power Generation.” The pilot plant built as a result of this project demonstrated the feasibility and performance of a concrete thermal energy storage (CTES) system integrated with a supercritical coal power plant. The 10 MWh electrical (>25 MWh thermal) CTES unit, developed by Storworks Power, was designed to enable flexible operation of coal plants without cycling damage. The project's key technical achievements showcase a significant advancement in energy storage technology. A modular CTES system using 42 “Bolderblocs” units was successfully designed and constructed at Alabama Power’s Plant Gaston Unit 5, with each block containing embedded stainless-steel coils in specialized, cost-effective high-temperature concrete. The system interfaced seamlessly with the plant's 3500 psig (241 barg), 1000°F (538°C) supercritical steam, demonstrating operational flexibility. Over 86 full cycles, the CTES exhibited rapid charging and discharging capabilities, effectively mimicking steam turbine feed conditions and handling varying load profiles and storage durations. Performance validation confirmed the system's ability to consistently meet design target steam conditions of 75 bar-a and ~400°C for nominal baseline discharge. The concrete material withstood repeated thermal cycling without degradation, validating earlier lab-scale tests. Integration of balance of plant components, including a condensate management system with storage tank and air-cooled condenser, minimized plant interfaces and water consumption. A robust control scheme ensured safe, automated operation across various scenarios. Key learnings from the project were invaluable: 1. Initial concrete drying and commissioning procedures were refined for future deployments, enhancing efficiency in subsequent installations. 2. System flexibility exceeded expectations, with rapid response to changing conditions. 3. Design improvements were identified including optimized insulation and piping that will enhance overall system efficiency in future deployments 4. Full cycle thermal roundtrip efficiencies exceeded 88%. While the roundtrip electrical efficiency was somewhat limited by known challenges using input steam, such constraints may be mitigated by swapping steam for hot air as thermal input. 5. A summary of key performance parameters for the pilot test and predicted performance of a full scale commercial system with specified improvements determined from the pilot are shown in Section 8. The project faced challenges, including COVID-19 delays and host plant availability constraints. However, these were overcome through adaptive planning and execution. The successful management of these obstacles demonstrated the resilience and adaptability of the project team and the robustness of the CTES technology. This successful pilot demonstrates the potential for CTES to enhance coal plant flexibility, supporting grid stability as renewable penetration increases. The validated design and operational data provide a solid foundation for scaling up to utility-scale implementations, potentially transforming how thermal plants operate in evolving energy landscapes. The system's ability to rapidly respond to changing grid conditions while maintaining high efficiency makes it a promising solution for balancing intermittent renewable energy sources. Furthermore, the project highlighted the potential for even greater efficiencies in future iterations. The use of air as an input medium could potentially eliminate the limitations observed with steam input, opening new possibilities for energy storage applications beyond coal plant integration. In conclusion, this pilot project not only achieved its primary goals but also uncovered additional benefits and potential applications of the CTES technology. It represents a significant step forward in addressing the challenges of grid stability and flexibility in an increasingly renewable-driven energy landscape.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2025

The influence of wind veer and drivetrain flexibility on fatigue loading for large floating wind turbines

To reduce costs, offshore wind turbines are expected to be designed with significantly increased rotor diameters. Larger turbines become more flexible and span a larger portion of the atmospheric boundary layer. With these changes, the validity of traditional modeling assumptions should be investigated. This work challenges two common assumptions: (1) that the drivetrain can be considered rigid (except in torsion) and does not couple with the rotor and tower and 2) that wind directional change with height (veer) does not greatly influence the fatigue damage in the tower, blades and drivetrain. Two large semi-submersible floating wind turbines are considered: a 15 and a 22 MW reference turbine. Both use direct-drive generators. Aero-hydro-servo-elastic simulations are performed using OpenFAST, with drivetrain bending flexibility and main bearing response implemented in the coupled analysis. The turbines are subjected to a set of load cases at below-, near- and above-rated mean wind speeds, assembled based on the 3 km Norwegian reanalysis (NORA3) hourly wind and wave hindcast data for Utsira Nord, off the coast of Norway. In each load case, conditions with and without veer are simulated to evaluate the influence of veer on damage equivalent loads (DELs) of the turbine tower, blades and main bearings. Further, these load cases are applied to evaluate the influence of drivetrain flexibility on aero-elastic turbine response. The results indicate that, depending on the veer gradient, mean wind speed, operating regime and turbine size, veer can be very important for tower-top DELs and the fluctuations of main bearing radial loads, while main bearing and blade-root flapwise DELs are less affected. Considering these specific load cases and turbine models, drivetrain flexibility is found to significantly influence tower-top DELs of the largest turbine: the tower-top fore-aft and torsional damage equivalent moments of the 22 MW turbine are reduced by more than 20 % at near-rated wind speeds when the drivetrain is modeled as flexible.

17 WIND ENERGY↗

DOE OSTI2024

Exploring Multidimensional Spatial-Temporal Hydropower Operational Flexibilities by Modeling and Optimizing Water-Constrained Cascading Hydroelectric Systems

Because of unique characteristics such as clean and cost-competitive electricity as well as fast-ramping and storage abilities, the power industry continues to evolve its operation strategies for cascading hydroelectric (CHE) systems for providing enhanced values to the grid, especially under the deeper renewable resource integration. However, existing operation practices of CHEs predate the integration of renewables, which could prohibit the effective utilization of their inherent flexibilities in delivering maximum financial benefits and providing valuable grid services to the power system and electricity market operations. Indeed, modeling and optimizing these resource-limited while flexible CHE assets with uncertainties and imperfect information across multiple spatial-temporal dimensions present significant challenges. To facilitate CHE facility operators in effectively coordinating water usage and hydropower plant operations across multiple timescales, this project aims to fill the existing gaps by developing a suite of accurate water inflow (WI) forecast models as well as enhanced CHE modeling and optimization approaches with proper consideration of their unique characteristics, which would help explore their multidimensional spatial-temporal operational flexibility potentials. The developed approaches could better align reservoir operation strategies with variability and uncertainty of future water availability. They can also promote more effective utilization of multidimensional spatial-temporal hydropower operational flexibility potentials by designing long-term evacuation plans of reservoirs and short-term operation of CHEs, along with their coordination with other types of renewables. The project leverages various resources to facilitate the research and development activities, including actual characteristics data of CHE systems and a library of current and future cases of Portland General Electric (PGE). These realistic data enable the project team to study how to maximize the value of CHEs under current and future portfolios and evaluate opportunities to improve operation practices.

13 HYDRO ENERGY↗

DOE OSTI2024

Occupant-driven end use load models for demand response and flexibility service participation of residential grid-interactive buildings

As demand response becomes increasingly used as a tool to support improved grid flexibility, it is important to consider that there are many potential types of energy end uses that may be used to support such flexibility. Residential appliances, often accounting for 30 % or more of residential energy use, are a currently untapped source of demand flexibility, particularly when aggregated together across homes. To date there has been very limited analysis of residential appliances for use as grid-interactive loads. As such, this research uses disaggregated energy end use data for 564 households, to model the electricity demand flexibility potential of the use of residential dishwashers, clothes washers, clothes dryers, ovens, and ranges (oven + stovetop) on both weekdays and weekends. This includes both at the building level, as well as aggregated to the grid level, specifically the Midcontinent Independent System Operator (MISO) region. This study was divided into two parts. Part 1 focuses on determining appliance-level loads, and Part 2, which involves aggregation to the grid. Findings suggest that among the studied appliances, clothes dryers provide the greatest demand reduction potential for most times of the day, followed by dishwashers and clothes washers. The maximum potential reduction for clothes dryers is found to be approximately at 11:00 a.m. and this potential sustains throughout most of the daytime period. When considering the willingness of households to participate, based on a survey of households in the Midwest region, clothes dryers still have the most potential for demand reduction. The availability of appliances for load modulation on weekdays and weekends indicates similar load reduction potential for all appliances. Overall, the results of this study suggest that there is an opportunity for shifting appliance usage to optimize grid efficiency and enhance demand response strategies.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2025

Flexibility of oxygen sublattice and hydrogen bond length predict proton mobility in ternary metal oxides

Discovery of fast proton conductors is important for advancing clean energy technologies. This requires a better understanding of proton migration mechanisms. While structural and chemical traits of ternary metal oxides have been related to proton migration barriers, lattice dynamical effects have not been resolved quantitatively. Here, in this work, we introduce a phonon-based dynamic descriptor, termed ‘‘thermal O…O fluctuation,’’ quantifying the flexibility of donor-acceptor oxide-ion pairs. This enables direct comparison of O-sublattice flexibility across diverse metal oxides. Using regression models, we ranked physical descriptors as predictors of proton mobility, finding that H-bond length and thermal O…O fluctuation were the strongest descriptors. Further analysis revealed a critical O…O spacing of 2.4 A˚ at the transition state, which is easier to reach by more flexible donor-acceptor pairs, enabling facile proton transfer. Our results demonstrate oxygen sublattice flexibility as a dynamic descriptor and provide guiding principles for enhancing proton mobility in ternary metal oxides.

diffusivity↗

DOE OSTI2025

Harnessing nanoscale densification for controlling gas selectivity in flexible zeolitic imidazolate frameworks

Flexible metal-organic frameworks (MOFs) are promising for gas separation due to their molecular recognition capabilities. However, gate-opening behavior in certain flexible MOFs can reduce gas selectivity, enabling simultaneous adsorption of multiple gases. We introduce a binder-free, pressure-free densification process to enhance gas selectivity in flexible zeolitic imidazolate frameworks (ZIF-7 and ZIF-9) by optimizing nanoparticle packing. Unlike powders, the densified ZIF-7 and ZIF-9 retain rhombohedral crystal structures after solvent removal, confirmed via synchrotron powder X-ray diffraction. This process modifies adsorption behavior by introducing a diffusion barrier, enabling diffusivity-driven kinetic separation and enhanced CO2/hydrocarbon selectivity. At 0.5 bar, ZIF-7 mono shows 2×, 4×, and 9.5× higher CO 2 selectivity over C 2 H 2 , C 2 H 4 , and C 2 H 6 , respectively, versus ZIF-7 pwd . ZIF-9 mono similarly shows 6.5×, 3×, and 39× improvements over ZIF-9 pwd . Both monoliths outperform powders in ternary gas mixtures. This study provides a novel strategy to control gate opening and enhance gas selectivity in flexible MOFs for practical separation applications.

CO2/hydrocarbon separation↗

DOE OSTI2024

A Distributionally Robust Optimization Framework for Stochastic Assessment of Power System Flexibility in Economic Dispatch

Given the complexity of power systems, particularly the high-dimensional variability of net loads, accurately depicting the entire operational range of net loads poses a challenge. To address this, recent methodologies have sought to gauge the maximum range of net load uncertainty across all buses. In this paper, we consider the stochastic nature of the net load and introduce a distributionally robust optimization framework that assesses system flexibility stochastically, accommodating a minimal extent of system violations. We verify the proposed method by solving the flexibility of the economic dispatch problem on four distinct IEEE standard test systems. Compared to traditional deterministic flexibility evaluations, our approach consistently yields less conservative flexibility outcomes.

distributionally robust optimization↗