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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Analyzing School Bus Electrification in Richmond, Virginia

School buses are an essential component of the transportation infrastructure, serving as a lifeline for students across the globe. However, the widespread use of diesel school buses has raised concerns about the health impact on millions of students exposed to harmful emissions daily. Recognizing this issue, school districts worldwide are urgently seeking cleaner energy alternatives. Electric school buses emerge as an environmentally friendly and sustainable option, fostering a healthier environment for both students and communities. However, school bus electrification faces the challenges of high upfront cost, cumbersome charging management, and constraints from power grids. To help school bus operators address those challenges, this study presents a data-driven analysis for school bus electrification. This study considered a real-world school bus system in Richmond, VA, and developed a mathematical programming model to analyze the system design, charging strategies, and charging load profiles for the electrification scenario. The study evaluated different charging strategies based on model outcomes, aiming to optimize efficiency and effectiveness. Ultimately, this research generated electric school bus charging demand profiles under various scenarios, shedding light on the feasibility and implications of transitioning to electric-powered school buses.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2020

Synthetic residential load models for smart city energy management simulations

The ability to control tens of thousands of residential electricity customers in a coordinated manner has the potential to enact system-wide electric load changes, such as reduce congestion and peak demand, among other benefits. To quantify the potential benefits of demand-side management and other power system simulation studies (e.g. home energy management, large-scale residential demand response), synthetic load datasets that accurately characterize the system load are required. This study designs a combined top-down and bottom-up approach for modelling individual residential customers and their individual electric assets, each possessing their own characteristics, using time-varying queueing models. The aggregation of all customer loads created by the queueing models represents a known city-sized load curve to be used in simulation studies. The three presented residential queueing load models use only publicly available data. An open-source Python tool to allow researchers to generate residential load data for their studies is also provided. The simulation results presented consider the ComEd region (utility company from Chicago, IL) and demonstrate the characteristics of the three proposed residential queueing load models, the impact of the choice of model parameters, and scalability performance of the Python tool.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Experimental test of model predictive control in a variable air volume system

Model predictive control (MPC) has been widely studied as a promising approach for improving energy efficiency and operational flexibility in buildings, yet its real-world performance for commercial variable air volume (VAV) systems remains insufficiently characterized. In particular, the impacts of model mismatch on control robustness, real-time computational burden, and device-level operation are rarely evaluated using long-term field data. Here, this study presents a comprehensive experimental evaluation of MPC applied to a full-scale VAV system in Oak Ridge National Laboratory’s Flexible Research Platform-2 building with constant cooling/heating temperature setpoints and no occupancy. The study offers three key advantages over existing work: (1) it uses a representative building in a full-scale experimental test, capturing realistic system dynamics and complexity; (2) it evaluates a relatively sophisticated MPC formulation using two different optimization solvers (Gurobi and PSO), fully accounting for computational complexity and methodological diversity; and (3) it systematically assesses potential negative impacts on various building devices, benchmark against a well-established baseline, ASHRAE Guideline 36 (G36). To isolate zone- and air-handling-unit–level supervisory control effects, the supply fan was operated with a fixed static pressure setpoint under all strategies, and the trim-and-response static pressure reset in G36 was not enabled. Results show that MPC maintained thermal comfort while improving energy efficiency. Abrupt solar radiation variations degraded performance. Computation times ranged from ∼1 s (Gurobi) to ∼ 70 s (PSO). Compared with G36, MPC achieves 33% energy savings and reduces median reheat coil output by approximately a factor of 5–10 for a representative cooling day under matched weather conditions. However, it increases the maximum discomfort deviation from 0.5 to 1°C and results in a 32% increase in staging frequency. In addition, PSO-based MPC introduced damper oscillations, also affecting actuator longevity.

ASHRAE guideline 36↗
DOE OSTI2024

Modeling Framework for the Assessment of a Sustainable Hydrogen Production and Supply Chain Network in California

The cost-effective and sustainable deployment of hydrogen supply and demand networks, especially in large economic regions like California, can be challenging considering the spatial-temporal availability and variability of the different actors across the network such as production processes, distribution modes, and end-users. In this presentation, we will provide an overview and demonstration of a modeling framework used to assess the environmental, economic, and human health impacts of plausible hydrogen production and supply chain networks in California. Scenarios focus on green hydrogen production pathways using water electrolysis and biomass gasification. End-use applications included in the model are transit, medium and heavy-duty trucking, port authorities, and power and aviation companies that currently consume natural gas, diesel, and aviation fuel for their day-to-day operation. Representative locations for hydrogen production and end-use are based on recent projections of the hydrogen economy in California. All mass and energy flows, as well as estimated emissions, are based on H2A process model designs and projections of technology performance, literature review, and LBNL process, economic and life cycle modeling, and not on company data for the sake of this presentation. Human health impacts are included following methodologies developed for the University of California Irvine HyDeal project. Life cycle phases associated with hydrogen production include feedstock preparation (water and biomass), energy production and consumption (renewable, grid, and combination of renewable and grid electricity), maintenance (chemical utilization in electrolysis and natural gas combustion in gasification), carbon sequestration, hydrogen storage (compression and liquefaction), and distribution (truck and pipeline). We apply the framework utilizing California specific emission factors, financial data, and human health damages and explore the impact of network characteristics on results. Example variations include: the inclusion of policy incentives or not, different representations of the electricity grid and source, electrolysis versus gasification versus combinations of both for production, liquefaction versus compression based on producer capacity cutoffs, transportation truck versus pipeline based on existing infrastructure, and ultimate end use. Comparison of these different scenarios can help inform future projects by demonstrating the trade-offs among environmental, economic, and human health impacts. This model, automated in R, is a starting platform upon which new analysis, modeling capabilities, locations, and emission factors can be rapidly tested and integrated.

Zaki, Mohammed Tamim↗
DOE OSTI2024

ARPA-E Grid Optimization (GO) Competition Challenge 1

The ARPA-E Grid Optimization (GO) Competition Challenge 1, from 2018 to 2019, focused on the basic Security Constrained AC Optimal Power Flow problem (SCOPF) for a single time period. The Challenge utilized sets of unique datasets generated by the ARPA-E GRID DATA program. Each dataset consisted of a collection of power system network models of different sizes with associated operating scenarios (snapshots in time defining instantaneous power demand, renewable generation, generator and line availability, etc.). The datasets were of two types: Real-Time, which included starting-point information, and Online, which did not. Week-Ahead data is also provided for some cases but was not used in the Competition. Although most datasets were synthetic and generated by GRIDDATA, a few came from industry and were only used in the Final Event. All synthetic Input Data and Team Results for the GO Competition Challenge 1 for the Sandbox, Trial Events 1 to 3, and the Final Event along with problem, format, scoring and rules descriptions are available here. Data for industry scenarios will not be made public. Challenge 1, a minimization problem, required two computational steps. Solver 1 or Code 1 solved the base SCOPF problem under a strict wall clock time limit, as would be the case in industry, and reported the base case operating point as output, which was used to compute the Objective Function value that was used as the scenario score. The feasibility of the solution was provided by the Solver 2 or Code 2, which solves the power flow problem for all contingencies based on the results from Solver 1. This is not normally done in industry, so the time limits were relaxed. In fact, there were no time limits for Trial Event 1. This proved to be a mistake, with some codes running for more than 90 hours, and a time limit of 2 seconds per contingency was imposed for all other events. Entrants were free to use their own Solver 2 or use an open-source version provided by the Competition. Containers, such as Docker, were considered to improve the portability of codes, but none that could reliably support a multi-node parallel computing environment, e.g., MPI, could be found. For more information on the competition and challenge see the "GO Competition Challenge 1 Information" and "GO Competition Challenge 1 Additional Information" resources below.

ACOPF↗
DOE OSTI2022

Optimal Gas-Electric Energy System Decarbonization Planning

As energy utilities implement climate change mitigation policies, system planners require strategies for achieving affordable emissions reductions. Coordinated planning of electric power and natural gas systems will allow synergistic investments to address cross-sector operational constraints, competing uses for net-zero emissions fuels, and shifts in energy demands across energy carriers. In this study, we develop a novel optimization program that finds the cost-minimizing mix of infrastructure expansion or reduction across gas and electric systems to satisfy sector-specific emissions constraints. Alongside energy supply resources, our framework allows for central-planning of end-use equipment stocks to allow switching between gas and electric appliances upon failure or premature replacement. The proposed model is used to simulate case study scenarios for a benchmark 24-pipe gas network coupled to a 24-node power system test network. We find that electrification of greater than 80% of core gas demands is a component of the least-cost solution for modeled energy systems. Despite this substitution, the gas system is maintained to service difficult-to-electrify customers and to deliver net-zero emissions gas to electricity generators in times of peak electricity demand. Restricting electrification of gas appliances increases reliance on power- to-gas technologies and increases annual costs by 15% in 2040. Neglecting constraints on pipeline blending of hydrogen can produce a misleading result that relies on hydrogen blend fractions of greater than 50%. In all cases, we find the average costs of delivered gas increase nearly 5-fold across the decarbonization transition, highlighting the importance of future work investigating cost-allocation strategies for ensuring an equitable energy transition.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2022

Coffee supply chain planning under climate change

The growing demand but uncertain supply makes the sustainability of the coffee industry a shared concern for all participants along the coffee supply chain. This study proposed a decision-making model that comprises the cultivation management, including shade management and annual agriculture management, and the supply chain logistics. A two-stage stochastic program is presented and used within a rolling horizon scheme that periodically updates input data information to deal with uncertainty associated with future climate scenarios. The program minimizes the total expected cost of the entire supply chain of arabica coffee. The study applied the model to the real case study of arabica coffee bean supply to the U.S. market, trying to answer whether arabica coffee supply can meet the U.S. demand from 2022 to 2050 and how to best mitigate any shortage through corporate-farmer partnerships. The results show that the coffee supply will have a 3% shortage in the future; medium-level shade management and more irrigation and fertilization are possible mitigation strategies. These results demonstrate the need for all participants to adopt suitable technologies for the sustainability of global coffee supply chains together.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling

Recent advances in differentiable modeling, a genre of physics-informed machine learning that trains neural networks (NNs) together with process-based equations, have shown promise in enhancing hydrological models' accuracy, interpretability, and knowledge-discovery potential. Current differentiable models are efficient for NN-based parameter regionalization, but the simple explicit numerical schemes paired with sequential calculations (operator splitting) can incur numerical errors whose impacts on models' representation power and learned parameters are not clear. Implicit schemes, however, cannot rely on automatic differentiation to calculate gradients due to potential issues of gradient vanishing and memory demand. Here we propose a “discretize-then-optimize” adjoint method to enable differentiable implicit numerical schemes for the first time for large-scale hydrological modeling. The adjoint model demonstrates comprehensively improved performance, with Kling–Gupta efficiency coefficients, peak-flow and low-flow metrics, and evapotranspiration that moderately surpass the already-competitive explicit model. Therefore, the previous sequential-calculation approach had a detrimental impact on the model's ability to represent hydrological dynamics. Furthermore, with a structural update that describes capillary rise, the adjoint model can better describe baseflow in arid regions and also produce low flows that outperform even pure machine learning methods such as long short-term memory networks. The adjoint model rectified some parameter distortions but did not alter spatial parameter distributions, demonstrating the robustness of regionalized parameterization. Despite higher computational expenses and modest improvements, the adjoint model's success removes the barrier for complex implicit schemes to enrich differentiable modeling in hydrology.

58 GEOSCIENCES↗
DOE OSTI2022

Modeling and Analysing the Impact of Heat Pump Water Heaters on Distribution Systems Using GridLAB-D

With the constant increase in energy demand, finding ways to reduce peak load and the energy-costs factors has become more imperative. Domestic water heating showcases a significant opportunity for such applications. Water heating is the second-highest energy consumer in the residential sector across the United States. Electric Water Heaters (EWHs), in particular, constitute nearly 43% of American household water heating energy consumption. Heat Pump Water Heater (HPWH), on the other hand, are an advanced water heating technology that has recently emerged in the United States residential market. The objectives of this work are to develop a HPWH model and build a case study that evaluates various penetration levels of HPWH in providing reduced peak load and cost-effective energy savings for both utilities and customers. The HPWH model was developed and integrated within the GridLAB-D simulation environment. The model behavior was then validated against a real HPWH unit at Portland State University (PSU). The case studies incorporated five HPWH penetration levels, ranging from 20% to 100%. In each case, EWHs were replaced with HPWHs. The results showed that a high penetration level of HPWHs can reduce the energy consumption on a distribution system to 38%.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

Thermal Modeling and Limitations for Power Electronics Embedded in Medium-Voltage Cables

As next-generation energy technologies gain traction and power demand increases, the existing electrical infrastructure faces significant stress, prompting innovative solutions to enhance the grid's capacity and lifespan. This work explores the possibility of embedding medium-voltage (MV) power electronics directly inline with the cable, and the resulting thermal challenges. Since the majority of power distribution cables installed in the U.S. are passively cooled, the work focuses primarily on passive cooling, with an emphasis on the limitations of axial heat spreading within the cable. To date, literature on axial spreading of high incident heat loads on cables and cable environments is limited, typically reporting cases with <10 W of incident heat load. This work will explore the considerations, limits, and tradeoffs of cable-embedded heat loads significantly larger than the cable losses. Both external and internal effects are modeled analytically in nondimensional terms via a Biot number analysis, allowing fundamental limits and tradeoffs to be derived. The work culminates in the design and experimental validation of a cable-embedded thermal system capable of passively dissipating 300 W of heat from a coaxial SiC mosfet switch module over a length of 20 cm, thus validating the possibility of MV cable-embedded power electronics from a thermal standpoint.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Estimating the value of jointly optimized electric power generation and end use: a study of ISO-scale load shaping applied to the residential building stock

A generation-to-load simulation estimated the impact, in terms of production costs and CO2 emissions, attributable to the joint optimization of electric power generation and flexible end uses to support increasing penetrations of renewable energy. Newly conceived, evaluated, and foundational in developing a U.S. National Standard was a transaction-less yet continuous demand response system based on a day-ahead optimum load shape (OLS) designed to encourage Internet-connected devices to autonomously and voluntarily explore options to favour lowest cost generators - without requiring two-way communications, personally identifiable information, or customer opt-in. Boundary conditions used for model calibration included historical weather, residential building stock construction attributes, home appliance and device empirical operating schedules, prototypical power distribution feeder models, thermal generator heat rates, startup and ramping constraints, and fuel costs. Results of an hourly-based annual case study of Texas indicate a 1/3 reduction in production costs and a 1/5 reduction in CO2 emissions are possible.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

Integrated Dynamic Facade Control with an Agent-based Architecture for Commercial Buildings

Dynamic façades have significant technical potential to minimize heating, cooling, and lighting energy use and peak electric demand in the perimeter zone of commercial buildings, but the performance of these systems is reliant on being able to balance complex trade-offs between solar control, daylight admission, comfort, and view over the life of the installation. As the context for controllable energy-efficiency technologies grows more complex with the increased use of intermittent renewable energy resources on the grid, it has become increasingly important to look ahead towards more advanced approaches to integrated systems control in order to achieve optimum life-cycle performance at a lower cost. This study examines the feasibility of a model predictive control system for low-cost autonomous dynamic façades. A system architecture designed around lightweight, simple agents is proposed. The architecture accommodates whole building and grid level demands through its modular, hierarchical approach. Automatically-generated models for computing window heat gains, daylight illuminance, and discomfort glare are described. The open source Modelica and JModelica software tools were used to determine the optimum state of control given inputs of window heat gains and lighting loads for a 24-hour optimization horizon. Penalty functions for glare and view/ daylight quality were implemented as constraints. The control system was tested on a low-power controller (1.4 GHz single core with 2 GB of RAM) to evaluate feasibility. The target platform is a low-cost ($35/unit) embedded controller with 1.2 GHz dual-core cpu and 1 GB of RAM. Configuration and commissioning of the curtainwall unit was designed to be largely plug and play with minimal inputs required by the manufacturer through a web-based user interface. An example application was used to demonstrate optimal control of a three-zone electrochromic window for a south-facing zone. The overall approach was deemed to be promising. Further engineering is required to enable scalable, turnkey solutions.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

Loosely Conditioned Emulation of Global Climate Models With Generative Adversarial Networks

Climate models encapsulate our best understanding of the Earth system, allowing research to be conducted on its future under alternative assumptions of how human-driven climate forces are going to evolve. An important application of climate models is to provide metrics of mean and extreme climate changes, particularly under these alternative future scenarios, as these quantities drive the impacts of climate on society and natural systems. Because of the need to explore a wide range of alternative scenarios and other sources of uncertainties in a computationally efficient manner, climate models can only take us so far, as they require significant computational resources, especially when attempting to characterize extreme events, which are rare and thus demand long and numerous simulations in order to accurately represent their changing statistics. Here we use deep learning in a proof of concept that lays the foundation for emulating global climate model output for different scenarios. We train two "loosely conditioned" Generative Adversarial Networks (GANs) that emulate daily precipitation output from a fully coupled Earth system model: one GAN modeling Fall-Winter behavior and the other Spring-Summer. Our GANs are trained to produce spatiotemporal samples: 32 days of precipitation over a 64x128 regular grid discretizing the globe. We evaluate the generator with a set of related performance metrics based upon KL divergence, and find the generated samples to be nearly as well matched to the test data as the validation data is to test. We also find the generated samples to accurately estimate the mean number of dry days and mean longest dry spell in the 32 day samples. Our trained GANs can rapidly generate numerous realizations at a vastly reduced computational expense, compared to large ensembles of climate models, which greatly aids in estimating the statistics of extreme events.

climate emulation, extreme climate, impacts, machi↗
DOE OSTI2025

Entanglement maximization and mirror symmetry in two-Higgs-doublet models

We consider 2-to-2 scatterings of Higgs bosons in a CP-conserving two-Higgs-doublet model (2HDM) and study the implication of maximizing the entanglement in the flavor space, where the two doublets Φ a , a = 1, 2, can be viewed as a qubit: Φ 1 = |0⟩ and Φ 2 = |1⟩. More specifically, we compute the scattering amplitudes for Φ a Φ b → Φ c Φ d and require the outgoing flavor entanglement to be maximal for a full product basis such as the computational basis, which consists of {|00⟩, |01⟩, |10⟩, |11⟩}. In the unbroken phase and turning off the gauge interactions, entanglement maximization results in the appearance of an U(2) × U(2) global symmetry among the quartic couplings, which in general is broken softly by the mass terms. Interestingly, once the Higgs bosons acquire vacuum expectation values, maximal entanglement enforces an exact U(2) × U(2) symmetry, which is spontaneously broken to U(1) × U(1). As a byproduct, this gives rise to Higgs alignment as well as to the existence of 6 massless Nambu-Goldstone bosons. The U(2) × U(2) symmetry can be gauged to lift the massless Goldstones, while maintaining maximal entanglement demands the presence of a discrete Z 2 symmetry interchanging the two gauge sectors. The model is custodially invariant in the scalar sector, and the inclusion of fermions requires a mirror dark sector, related to the standard one by the Z 2 symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Advanced Hydropower and PSH Capacity Expansion Modeling (Final Report on HydroWIRES D1 Improvements to Capacity Expansion Modeling)

Hydropower and pumped-storage hydropower (PSH) have played a key role in providing flexible, low-carbon electricity to the U.S. electricity system for over a century. As variable generation (VG) deployment increases the demand for flexible, dispatchable generation, it is important to use all available methods for understanding how hydropower and PSH interfaces with VG in a future low-carbon grid. Capacity expansion models (CEMs) of electricity systems are often used to study future electricity scenarios, but these tools often have difficulty representing site- and technology-details of hydropower and PSH due to limited spatial, temporal, or process resolution. This report demonstrates a set of model advancements to improve hydropower and PSH representations in CEMs and other models that consider hydropower and PSH's role in electricity systems. Model advancements include new data integration to define closed-loop PSH resource availability and cost, along with site-level parameterizations of existing PSH capacity and energy storage specifications. Shifting energy across seasons for both hydropower and PSH is explored to demonstrate the potential value of long-duration storage. New representations of hydropower upgrades offer opportunities to increase dispatchability, add pumps, or independently add capacity or energy depending on what is most valuable. New model structures and data are demonstrated individually and in combination to observe their impact on model results and provide initial insights into what is most important for analysts, electricity system planners, and hydropower decision-makers to consider when assessing future roles of hydropower. Improving flexibility of existing hydropower assets has the potential to reduce CO 2 emissions through complementing VG technologies and/or improve electricity system economics by reducing the need to deploy higher-cost systems. Large-scale energy storage is also shown to provide opportunities for balancing seasonal differences in VG, particularly solar photovoltaics (PV). Initial analysis with a new closed-loop PSH resource and cost dataset also demonstrate the potential for new PSH deployment to offer new grid flexibility opportunities. Future analysis and modeling of hydropower's role in the U.S. and other electricity systems could include methodological improvements based on those discussed here along with sensitivity analysis to better represent current and future potential hydropower and PSH flexibility. Improvements to geospatial and site-level data can further improve the understanding of how hydropower and PSH can be upgraded and operated in response to future electricity system needs. This work lays the groundwork to use advanced planning models to explore the range of roles hydropower and PSH can play in the grid of the future.

13 HYDRO ENERGY↗
DOE OSTI2025

Modeling of Precipitation over Africa: Progress, Challenges, and Prospects

In recent years, there has been an increasing need for climate information across diverse sectors of society. This demand has arisen from the necessity to adapt to and mitigate the impacts of climate variability and change. Likewise, this period has seen a significant increase in our understanding of the physical processes and mechanisms that drive precipitation and its variability across different regions of Africa. By leveraging a large volume of climate model outputs, numerous studies have investigated the model representation of African precipitation as well as underlying physical processes. These studies have assessed whether the physical processes are well depicted and whether the models are fit for informing mitigation and adaptation strategies. This paper provides a review of the progress in precipitation simulation over Africa in state-of-the-science climate models and discusses the major issues and challenges that remain.

CMIP6↗
DOE OSTI2020

GNET2: an R package for constructing gene regulatory networks from transcriptomic data

Abstract Motivation The Gene Network Estimation Tool (GNET) is designed to build gene regulatory networks (GRNs) from transcriptomic gene expression data with a probabilistic graphical model. The data preprocessing, model construction and visualization modules of the original GNET software were developed on different programming platforms, which were inconvenient for users to deploy and use. Results Here, we present GNET2, an improved implementation of GNET as an integrated R package. GNET2 provides more flexibility for parameter initialization and regulatory module construction based on the core iterative modeling process of the original algorithm. The data exchange interface of GNET2 is handled within an R session automatically. Given the growing demand for regulatory network reconstruction from transcriptomic data, GNET2 offers a convenient option for GRN inference on large datasets. Availability and implementation The source code of GNET2 is available at https://github.com/jianlin-cheng/GNET2. Supplementary information Supplementary data are available at Bioinformatics online.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

Deliverable Flexible Ramping Products Considering Spatiotemporal Correlation of Wind Generation and Demand Uncertainties

Flexible ramping products (FRPs) have been implemented by several independent system operators (ISOs) to procure adequate flexible resources. Currently, system operators estimate the system level ramping requirements ignoring the spatiotemporal correlations among various uncertainty sources. This leads to overestimates/underestimates of ramping requirements. In addition, the explicit FRPs model considers only the generation ramping limitation. Other security constraints, such as the transmission limits, are not considered, which leads to deliverability issues of FRPs. To deal with these shortcomings of current FRPs models, this paper proposes a deliverable FRPs based on a distributionally-robust chance constrained multi-interval optimal power flow (DRCC-MIOPF) considering the spatiotemporal correlation of wind power and demand uncertainties endogenously. Furthermore, an asymmetrical affine policy (AAP) is proposed to leverage generation flexibility and mitigate the uncertainty in different directions. The pricing mechanism of the FRPs is proposed using a novel uncertainty-contained locational marginal price (U_LMP) which is derived from the proposed AAP-DRCC-MIOPF model. New components representing the price of FRPs are added into the traditional LMP formulation. Finally, the PJM 5-bus, IEEE 39-bus and IEEE 118-bus systems case studies validate the proposed FRPs approach. The payment of uncertain demand and wind power on FRPs are analyzed.

electricity market↗