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At least 19 records

Consensus-Based Approach for Active Power Control and Reserve Estimation in Distributed PV Systems

With the increased adoption of distributed energy resources (DER), they are expected to contribute to power system reliability services and enhance power system stability. This paper presents a distributed consensus control approach for the real-time active power reserve estimation and power management in distributed PV (photovoltaic) systems. The proposed method estimates the cumulative active power reserve from numerous PV generators using only the sparse communication network for a DER aggregator to provide active power regulation services. The real-time active power reserve estimation using the proposed approach can be used by DER aggregators to manage curtailment in distributed PV systems to maintain stipulated reserves and further to provide power system frequency regulation. Using the proposed approach, the DER aggregator only requires measurements at the feeder substation and it does not require information from individual DER units, thereby improving system resiliency. The proposed distributed consensus control method is validated on IEEE 123 testbed using PSCAD simulations.

active power reserve↗

Grid-Forming PV Inverter: Technology Development and Microgrid Applications

Presently, excluding residential backup power applications, grid-forming (GFM) inverters are commercially available for battery energy storage system (BESS) and some PV plus battery systems but not yet for stand-alone PV. This tech update investigates the control design for GFM PV inverter, especially the control required to provide active power reserve and to stabilize the dc link voltage. Subsequently, the use cases of GFM PV plants in utility-level microgrids are discussed considering fully inverter-based microgrids (i.e., with PV and BESS) as well as mixed-source microgrids (i.e., with PV and diesel generator). Scenarios where active power up-reserve from GFM PV plants is beneficial are illustrated. Moreover, requirements and specifications for GFM PV plant, especially for its active power reserve function are developed. In addition, stability of an example utility-level microgrid with two GFM PV plants and a diesel generator is analyzed to shed light on the potential unstable interaction between multiple GFM resources and the countermeasures. This research aims to advance GFM PV technology to offer more flexibility in microgrid design. With GFM PV available, depending on the level of reliability required, cost-benefit analysis, etc., the GFM BESS or diesel generator may be sized smaller while leveraging the full potential of PV generation inside the microgrid.

14 SOLAR ENERGY↗

Multi-physics Preconditioning for Thermally Activated Batteries

Thermal batteries, also known as molten-salt batteries, are single-use reserve power systems activated by pyrotechnic heat generation, which transitions the solid electrolyte into a molten state. The simulation of these batteries relies on multiphysics modeling to evaluate performance and behavior under various conditions. This paper presents advancements in scalable preconditioning strategies for the Thermally Activated Battery Simulator (TABS) tool, enabling efficient solutions to the coupled electrochemical systems that dominate computational costs in thermal battery simulations. We propose a hierarchical block Gauss-Seidel preconditioner implemented through the Teko package in Trilinos, which effectively addresses the challenges posed by tightly coupled physics, including charge transport, porous flow, and species diffusion. The preconditioner leverages scalable subblock solvers, including smoothed aggregation algebraic multigrid (SA-AMG) methods and domain-decomposition techniques, to achieve robust convergence and parallel scalability. Strong and weak scaling studies demonstrate the solver’s ability to handle problem sizes up to 51.3 million degrees of freedom on 2048 processors, achieving near sub-second setup and solve times for the end-to-end electrochemical solve. These advancements significantly improve the computational efficiency and turnaround time of thermal battery simulations, paving the way for higher-resolution models and enabling the transition from 2D axisymmetric to full 3D simulations.

25 ENERGY STORAGE↗

Regional Real-Time PV Spinning Reserve Estimator

Curtailed photovoltaic (PV) generation is a zero-marginal-cost spinning reserve that can be used for a number of active power control services. Unlike traditional spinning reserve providers, however, i.e., fossil-fueled generators, which have well-defined operating characteristics, e.g., available headroom or potential high limit (PHL), PV plants have by nature variable and uncertain operating characteristics. To ensure the effective coordination between PV plants and the system operator during an active power control event, accurate knowledge of the PV PHL is essential. It ensures that enough headroom is reserved by the PV plants to deliver the award services in real time and informs feasible dispatch decisions made by the market operator. To tackle this challenge, a novel reference-control grouping-based PV plant reserve estimation method has been proposed by the National Renewable Energy Laboratory under past projects funded by the U.S. Department of Energy Office of Energy Efficiency and Renewable Energy Solar Energy Technologies Office. The estimation method separates inverters within a plant into two groups: a control group and a reference group. While the reference group is reserved to operate at its PHL, the control group can be curtailed to provide the grid services. Real-time outputs from the reference inverters are used to estimate the PHL for the whole plant based on the ratio between capacities of the reference group and of the plant. This work further enhances the methodology by (1) improving the model accuracy through machine learning; (2) automating the reference inverter selection through correlation analysis; (3) considering estimation look-ahead windows; and (4) applying to regional spinning reserve estimation. Significant performance improvement has been observed based on real-world data collected by CAISO, Southern Company, and Terabase Energy. Compared with the original scaling method, the newly proposed machine learning-based approach reduces the estimation errors by 30% and 13% at the plant level and region level, respectively. Results obtained from this project are intended to be used by grid operators, market operators, balancing authorities, and PV plant owners and operators to facilitate PV participation in ancillary service markets. Regulators, policymakers, and system planners can also consider the results of this work in their decision-making processes. In addition to the performance improvement on the existing reference-control based grouping method, we also investigated how the variability of PV generation from a single PV inverter can be used to represent the variability of PV generation at the plant level.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Real-Time Regional PV Spinning Reserve Estimator with AGC Look-Ahead Windows

Curtailed PV generation is a zero-marginal cost spinning reserve that can be used for a number of active power control services. However, unlike the traditional spinning reserve providers, i.e., fossil-fueled generators, who have well-defined operating characteristics, e.g., available headroom or potential high limit (PHL), PV plants have by nature variable and uncertain operating characteristics. To ensure the effective coordination between PV plants and the system operator during an active power control event, accurate forecasts of the PV PHL are essential. A novel reference-control grouping based scaling method has been proposed by NREL to estimate the PV PHL in real-time. This work further enhances the methodology by: 1) improving the model accuracy through machine learning; 2) considering look-ahead windows introduced by the computation and communication latencies; 3) applying the method to regional spinning reserve estimation. A significant performance improvement, over 99% of estimation error reduction, has been observed based on real-world data collected by CAISO and PV plant operators.

potential high limit↗

Real-Time Regional PV Spinning Reserve Estimator with AGC Look-Ahead Windows: Preprint

Curtailed PV generation is a zero-marginal cost spinning reserve that can be used for a number of active power control services. However, unlike the traditional spinning reserve providers, i.e., fossil-fueled generators, who have well-defined operating characteristics, e.g., available headroom or potential high limit (PHL), PV plants have by nature variable and uncertain operating characteristics. To ensure the effective coordination between PV plants and the system operator during an active power control event, accurate forecasts of the PV PHL are essential. A novel reference-control grouping based scaling method has been proposed by NREL to estimate the PV PHL in real-time. This work further enhances the methodology by: 1) improving the model accuracy through machine learning; 2) considering look-ahead windows introduced by the computation and communication latencies; 3) applying the method to regional spinning reserve estimation. A significant performance improvement, over 1.6% of estimation error reduction, has been observed based on real-world data collected by CAISO and PV plant operators.

potential high limit↗

Creation of Synthetic Electric Grids (SPP/MISO) Supporting PERFORM (Final Report)

Over the course of the project, two “realistic but not real” synthetic transmission-level grid models over the SPP-MISO and ERCOT footprints were created to provide more realistic data and increase the reliability and resiliency of the grids under a variety of scenarios. The synthetic ERCOT transmission grid is compatible with the distribution grid developed in collaboration with NREL. All generators are based on the EIA 860 data and a column with EIA plant code and Gen ID is added to generators of both grids so that they can be easily mapped. The improvements are also made to electric grids including N-1 contingencies with some remedial actions, improving the transmission lines to avoid lines in lakes, including an HVDC line to the SPP-MISO case, providing several generator parameters and their temporal constraints that were not included in EIA 860 form, generators’ cost curves, load offer curves, adding phase shifters and tap changers with impedance correction tables, adding reactive power control and partitioning the grids into active and reactive reserve zones and determine different types of the required reserve for each zone. Hourly load time series at the bus level were generated to create scenarios for solving power flow in different loading conditions. Weather measurement information and the models of renewable generators are used to directly include the impact of weather on the grids. Based on a variety of load and weather conditions the grids are improved to accommodate different conditions. The ERCOT 7k-bus grids were also modeled for the year 2030 with predicted improvements in renewable resources. The renewable generation model was also improved with historic weather data included. The impact of electric vehicles on the ERCOT grid is also modeled.

24 POWER TRANSMISSION AND DISTRIBUTION↗

The Iowa Tribe of Kansas and Nebraska: Advancing Clean, Resilient, and Sovereign Energy (Summary Report of Communities LEAP Activities)

The Iowa Tribe of Kansas and Nebraska (ITKN) is a federally recognized Native American Tribe located along the Missouri River on the border of northeast Kansas and southeastern Nebraska. There are over 800 residents (Tribal citizens and non-Tribal) who live on the reservation, as well as more than 500 people who visit or work on the reservation on a daily basis. The ITKN faces many energy challenges, including rising service costs and dozens of power outages annually that impact resident well-being and business activities on Tribal lands. Power service issues are made more challenging by the remoteness of the reservation, which is 20 miles from the nearest town. Despite this, the ITKN has a long history of cultural and economic resilience: Local self-reliance, environmental stewardship, respecting the carrying capacity of the land, and strengthening the community are Tribal communities' traditional strengths. Long-term energy goals for the ITKN are centered around achieving energy sovereignty. Priority actions include: (1) Establishing a Tribal Utility Authority (TUA) to promote social welfare and community development.; (2) Deploying renewable community microgrids with ground-mount solar arrays and sustainable energy storage systems to advance energy sovereignty, resilience, and reliability. To advance these goals, the ITKN partnered with the U.S. Department of Energy's (DOE's) Communities LEAP (Local Energy Action Program) pilot. From August 2022 to March 2024, the ITKN community coalition collaborated with technical assistance providers at DOE's National Renewable Energy Laboratory (NREL) and Sandia National Laboratories to evaluate TUA planning needs and microgrid deployment scenarios. This final report details the Communities LEAP technical assistance process, models and analysis performed, and results.

24 POWER TRANSMISSION AND DISTRIBUTION↗

The Iowa Tribe of Kansas and Nebraska: Advancing Clean, Resilient, and Sovereign Energy

The Iowa Tribe of Kansas and Nebraska (ITKN) is a federally recognized Native American Tribe located along the Missouri River on the border of northeast Kansas and southeastern Nebraska. There are over 800 residents (Tribal citizens and non-Tribal) who live on the reservation, as well as more than 500 people who visit or work on the reservation on a daily basis. The ITKN faces many energy challenges, including rising service costs and dozens of power outages annually that impact resident well-being and business activities on Tribal lands. Power service issues are made more challenging by the remoteness of the reservation, which is 20 miles from the nearest town. Despite this, the ITKN has a long history of cultural and economic resilience: Local self-reliance, environmental stewardship, respecting the carrying capacity of the land, and strengthening the community are Tribal communities' traditional strengths. Long-term energy goals for the ITKN are centered around achieving energy sovereignty. Priority actions include: (1) Establishing a Tribal Utility Authority (TUA) to promote social welfare and community development.; (2) Deploying renewable community microgrids with ground-mount solar arrays and sustainable energy storage systems to advance energy sovereignty, resilience, and reliability. To advance these goals, the ITKN partnered with the U.S. Department of Energy's (DOE's) Communities LEAP (Local Energy Action Program) pilot. From August 2022 to March 2024, the ITKN community coalition collaborated with technical assistance providers at DOE's National Renewable Energy Laboratory (NREL) and Sandia National Laboratories to evaluate TUA planning needs and microgrid deployment scenarios. This fact sheet provides an overview of the results and outcomes from the Communities LEAP technical assistance process.

Communities Leap↗

Impact of Wildfires on Solar Generation, Reserves and Energy Prices

Wildfire seasons in the Western U.S. become more prolonged and intense in recent years bringing significant variability and uncertainty of solar generation. It greatly challenges the bulk power system and electricity market operation managed by California Independent System Operator (CAISO) as California leads both the wildfire records and the solar power integration. This study presents a screening-level analysis of the impact of wildfires on solar generation, operating reserve and energy prices applying historical real-world wildfire and market operation data. To the best of the authors knowledge, it is a first-of-its-kind study and will lay the foundation for market impact quantification and wildfire mitigation strategies design based on projected wildfire activities in future years.

electricity price↗

Radioisotope production at the Spallation Neutron Source: Design concept of isotope production target

Upon completion of the Second Target Station (STS) Project in the mid 2030s, the Spallation Neutron Source accelerator at Oak Ridge National Laboratory will deliver a 2.7 MW proton beam to the neutron production targets. In the post-STS phase, the accelerator will have a reserve beam power capacity of at least 100 kW beyond what the two neutron production targets will receive, which could potentially be ramped up to 300 kW. In this paper, a design concept for a radioisotope production target that could utilize 250 kW of the reserve beam power capacity is presented. The target consists of thorium discs encapsulated in 316L austenitic steel shells that are cooled by water. The estimated post-irradiation activity of Ac-225 and Ra-225, critical medical radioisotopes used in targeted alpha therapy cancer treatment, is calculated at the end of bombardment after a 14 day long irradiation time. Thermal and structural analyses are performed on the basis of calculated nuclear heating data. The technical feasibility of a high-power target under a 250-kW beam load with an extremely low duty factor of $3.5\cdot 10^{-6}$ is presented from thermal, structural and fatigue lifetime perspectives.

Lee, Yong Joong [ORNL] (ORCID:0000000298381723)↗

Joint scheduling of energy, fast and primary frequency response reserves in integrated transmission–distribution networks

Inverter-based distributed energy resources (DERs) connected to distribution networks (DNs) can provide fast frequency support, but their reserve deliverability depends on feeder constraints and differs from synchronous primary frequency response (PFR). Existing transmission–distribution coordination studies usually treat reserve generically or neglect feeder-level feasibility, while frequency-security scheduling studies rarely represent distribution feeders explicitly. This paper develops a bi-level day-ahead scheduling framework for integrated transmission–distribution networks that jointly clears energy, transmission-side PFR, and distribution-side fast frequency response (FFR) under exogenous hourly inertia and largest-loss inputs from an external unit commitment (UC) schedule. The transmission problem is modeled with DC-optimal power flow (OPF) and closed-form second-order cone (SOC) frequency-security constraints, whereas each DN is represented by a reserve-aware branch-flow AC-OPF so that scheduled fast reserves remain deliverable during activation. The bi-level problem is reformulated through Karush–Kuhn–Tucker (KKT) conditions into a mixed-integer SOC program, and a penalty term is used to tighten the distribution-network relaxation. In the reduced test system, lower exogenous inertia increased the required primary response from 179.64 MW to 191.08 MW, distribution-side fast response reduced total frequency-response procurement by up to 4.9%, and neglecting distribution constraints overstated the combined distribution-side energy and reserve award by up to 18%. In the expanded study, the largest case was solved in 2.02 s with a 0.00% optimality gap. Time-domain simulations kept the frequency nadir above 59.0 Hz in all tested hours. These results demonstrate the value of fast-response modeling and distribution-feasible reserve delivery in coordinated market clearing.

Noh, Seung-Gil↗

Modifications to Solar Titan-130 Combustion Systems for Efficient, High Turndown Operation

The project team of Southwest Research Institute® (SwRI®), Solar Turbines Incorporated (Solar), the Electric Power Research Institute (EPRI), the University of California, Irvine (UCI), and the Georgia Institute of Technology (Georgia Tech) investigated methods to allow higher efficiency part-load operation of a Solar Titan 130 gas turbine. The objective was to develop a low-emission combustion system capable of sustaining combustion and avoiding lean blowout during high turndown operation, which would allow the gas turbine to operate as efficiently as possible at part load. Currently, electric utility markets are beginning to experience substantial increases in renewable energy generation. Some of these renewable energy sources have highly variable output in an uncontrolled manner. In order to maintain grid stability, there is a need for power plants to ramp up power to the grid rapidly to make up for drops in renewable generation. This is often termed spinning reserve, but the size of this reserve may need to increase as renewable penetration into the electric utility market increases. Small combined heat and power (CHP) power plants provide a promising option for meeting this spinning reserve requirement. In order to operate in spinning reserve while still meeting the heat requirements for the CHP, the gas turbine needs to operate efficiently at very low loads. Efficient, high turndown operations in this engine are limited by the lean flammability limit of the premixed combustion system. This project sought enhance the lean operability range of the Titan 130 combustor. First, the project team participated in a brainstorming activity and ultimately selected two concepts to explore: fuel augmentation with hydrogen (H2) to improve the stability at lean operating conditions and modifications to the fuel nozzle to improve the emissions performance at lean operating conditions. Analytical and laboratory investigations were accomplished by UCI to investigate the efficacy of H2 addition at improving lean blow out (LBO) limits and the resulting emissions. These investigations used a variety of chemical reactor network (CRN) and CFD models, validated against laboratory data, to model the impact of H 2 and inform the experimental efforts accomplished by SwRI and Solar. Ultimately, both the CRN and CFD models yielded generally good agreement with the experimental data below a particular temperature threshold. Atmospheric tests of a full-scale T130 annular combustor were performed at SwRI facilities in San Antonio, Texas, to investigate the use of H 2 addition. For these tests, the T130 combustion system remained largely unchanged; minor modifications were performed to the fuel ducting to allow for the safe use of H 2 . The test ultimately demonstrated that the addition of H 2 to the fuel mixture significantly increased the AFR ratio at which the combustor could operate. This improvement to the LBO limit should allow for less use of compressor bleed and less throttling needed by the inlet guide vanes (IGV). This in turn could result in more efficient operation of the gas turbine at lower load points. The second modification explored in this work was a direct modification to the T130 injector. The project team hypothesized that modifications to the pilot of the T130 injector could provide lower emissions at high turn-down operations. These modifications were manufactured and explored by the team at Solar. High pressure rig tests, originally slated to occur at SwRI, were ultimately accomplished by Solar to maintain overall project budget and mitigate cost growth attributable to supply chain issues and inflation. The pressurized rig tests ultimately showed that the SwRI Project No. 18.24153 - DE-EE0008415 Page 2 Final Technical Report January 24, 2024 modifications did not significantly alter the performance of the combustion system at the high turn-down conditions; both the modified injectors and the baseline configuration exhibited elevated emissions comparted to the full-load operating condition. A final set of studies performed by EPRI investigated the benefit-cost of flexible CHP as well as a grid interconnection study for the California Independent System Operator (CAISO) grid. These studies considered: traditional CHP with no spinning reserve available for on-demand grid support, 50% flexible CHP where 50% of the machine’s capacity is consumed by on-site baseload operations while providing an additional 50% capacity for on-demand grid support, and 70% flexible CHP where 70% of capacity is consumed on-site by baseload operations and 30% is available for on-demand grid support. In all cases, the analyses showed a benefit-to-cost ratio greater than unity implying a positive net present value for all configurations. However, the traditional CHP showed the most economic benefit. These results are sensitive to several factors, many of which are not fully known and may vary over time. Thus site owners must be convinced that taking up the increased costs and risks from flexible CHP would be worth implementing. As the grid in California and across the country transition to incorporate larger renewable energy generation, flexible CHP can provide much needed operating reserves and dispatchability. Alternative fuel options, such as hydrogen blending and biofuels, may also lower carbon intensities of CHP. Flexible CHP should be examined in the evolving market to understand innovative business models, changes market rules and services, and new technologies.

20 FOSSIL-FUELED POWER PLANTS↗

Impact of Wildfires on Solar Resource Availability in California in a Changing Climate

Wildfires can emit large amounts of atmospheric particulate matters and influence not only air quality but also availability of photovoltaic (PV) generation due to scattering and absorption of solar radiation. Under anthropogenic changing climate, wildfire activity is projected to increase over western North America due to drier and warmer climate, implying increasing impact on solar resource and larger uncertainty in solar generation especially in regions with faster PV penetration. This study focuses on quantifying the impact of wildfires on aerosol optical depth (AOD) and thus solar resource over California using National Solar Radiation Database (NSRDB), developed by the National Renewable Energy Laboratory (NREL). This assessment includes historical analysis and estimation of solar resource under wildfire scenarios (2020 wildfire and an enhanced wildfire scenario based on 2020 wildfires). Historical analysis for the period of July-October 2019/2020 (low/high fire activity period) shows that the averaged global horizontal irradiance (GHI) and direct normal irradiance (DNI) are reduced by about 30 and 90 W m-2 (5.6 and 15.3%), respectively, during high fire activity period. To create AOD dataset for enhanced fire scenario, 165% increase in burn area (in around 2050) is selected based on comprehensive literature review, which is further applied to the Fire INventory from NCAR (FINN) fire emission. WRF-Chem model with the enhanced FINN emissions is used to simulate and represent a preserving spatial distribution of burned areas and wildfire-emitted aerosols. Our initial analysis suggests that the"enhanced 2020 wildfire" AOD can increase by a factor of 1.3 - 2, which can significantly reduce solar irradiance and increase uncertainty in generation and reliability of power system in extreme wildfire events under a high solar penetration scenario. Overall, this study provides an estimate of the impacts of wildfires on solar resource to make informed decisions on reserve planning, generation scheduling, and reliability investments.

aerosol optical depth↗

Planning and Operations in Electricity Markets Under System Tansformation: Key Findings

This report summarizes a set of key findings that have been developed through a set of interconnected research activities performed by five institutions between January 2020 and December 2023. The project team, comprising Argonne National Laboratory, the National Renewable Energy Laboratory, Lawrence Berkeley National Laboratory, the Electric Power Research Institute, and Johns Hopkins University, collective engaged with the North American Independent System Operators and Regional Transmission Operators (ISO/RTOs) to identify the key challenges they are facing and opportunities for the project team to provide technical assistance in several prioritized challenge areas.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Aluminum Ultra-conductors for Energy-Efficient Aerospace Busbar Applications (Abstract)

In this project, we will develop aluminum ultra-conductors with graphene additives demonstrating enhanced electrical conductivity at 90 °C compared to electric grade aluminum alloy AA1100 (43% IACS at 90 °C). While ultra-conductivity has been developed in copper and copper alloys, it is yet to be reported extensively in aluminum-based materials. This project will scale initial work done at PNNL on aluminum ultra-conductors using shear-assisted processing and extrusion (ShAPETM), a novel solid phase processing technique. Ultra-conductors are an emerging class of composites, comprised of a metal substrate with small quantities of nanocrystalline additives such as graphene or carbon nanotubes that demonstrate enhanced conductivity at relevant operating temperatures. Aluminum ultra-conductors can improve efficiency and power density while reducing the demand for copper in a wide range of applications, such as power transmission cables and electric motors. Busbars are an important component in aerospace systems that require lightweight and high-current power distribution including both future electric vertical take-off and landing (eVTOL) aircrafts and current aircraft electrical systems. We will accelerate aluminum ultra-conductor composite formulation development using combinatorial synthesis and testing methods aided by process/microstructure modeling, developed previously at PNNL. Eaton will test the properties of the ShAPE aluminum ultra-conductor feedstock (used to make the busbars) in relevant operating conditions (20 – 90 °C), predict the improvement in busbar performance when manufactured with ultra-conductors over commercial conductors (such as AA1100), and perform technoeconomic analysis to evaluate the potential for commercialization of ShAPE aluminum ultra-conductors. The project is expected to have a budget of $\$375$K, with $\$300$K in federal funding and $\$75$K in-kind cost-share contribution from Eaton over a period of performance of 24 months. Of the $\$300$K of federal funds, $\$140$K is allocated for CRADA activities that generate intellectual property (IP), and the remaining $\$160$K is reserved for modeling, material testing, characterization, travel, and reporting-related activities.

36 MATERIALS SCIENCE↗

Stochastic Strategic Participation of Active Distribution Networks With High-Penetration DERs in Wholesale Electricity Markets

With the increasing penetration of distributed energy resources (DERs), traditional distribution networks as load-serving entities in wholesale electricity markets, now evolve towards active distribution networks (ADNs) which can proactively participate in wholesale markets by optimally controlling the DERs in their networks. A stochastic bilevel optimization model is proposed in this paper for the strategic participation of ADNs and DERs to provide energy and grid services in wholesale electricity markets. The bilevel optimization model can capture the interactions between the ADN and the wholesale energy and ancillary service markets, considering the uncertainties of DERs in the ADN. In the upper-level model, the ADN makes optimal decisions on energy and reserve bidding considering the availability, uncertainties, and flexibility of DERs. The joint energy and reserve market-clearing of the independent system operator (ISO) is modeled as the lower-level problem. Using strong duality theory and Karush-Kuhn Tucker (KKT) conditions, the proposed bilevel optimization problem is reformulated as mathematical programming with equilibrium constraints (MPEC) problem and further converted into a computationally-solvable mixed-integer second-order-cone programming (MISOCP) model. The simulation results demonstrate the effectiveness of the model and the interactions between an ADN and wholesale electricity markets.

active distribution network↗