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Tightest Mixed-Integer Programming Formulations for Quadratic SCUC Optimization

In this project, we developed new, tighter Mixed-Integer Programming (MIP) formulations for the combined Alternating Current (AC) Security-Constrained Unit Commitment (SCUC) and Security-Constrained Optimal Power Flow (SCOPF). The work addresses a critical challenge in power system operations: efficiently determining which generation units to commit and how to optimally dispatch them while maintaining network reliability constraints for both normal and contingency scenarios. Our efforts: 1. Advance the Understanding of SCUC/SCOPF Modeling: By introducing tighter MIP formulations and leveraging cutting-edge optimization tools (Julia/JuMP, PowerModels.jl), this project has pushed forward the state of the art in efficient power systems scheduling. 2. Enhance Technical and Economic Feasibility: The methods developed provide more accurate and potentially faster solutions to large-scale, realistic scheduling and dispatch problems in electric power systems, which can translate into improved reliability and potentially lower costs for grid operations. 3. Benefit to the Public: Greater efficiency in power system operations leads to cost savings for utilities and end-users. Improved reliability and integration of advanced modeling approaches can facilitate the adoption of clean energy resources and better accommodate uncertainties in renewable generation. Because this technology could impact bulk power markets and reliability, these innovations have far-reaching public benefits in terms of cost savings, reliability, and sustainability.

24 POWER TRANSMISSION AND DISTRIBUTION

ARPA-E Grid Optimization (GO) Competition Challenge 2

The ARPA-E Grid Optimization (GO) Competition Challenge 2, from 2020 to 2021, expanded upon the problem posed in Challenge 1 by adding adjustable transformer tap ratios, phase shifting transformers, switchable shunts, price-responsive demand, ramp rate constrained generators and loads, and fast-start unit commitment. Furthermore, Challenge 2 was a maximization problem while Challenge 1 was a minimization problem. Specifically, the economic surplus, defined as the benefit of serving load minus the cost of generation, is being maximized. It was expected that the objective value of a given solution should be positive, representing economic gain, but negative objectives from poor solutions were possible. The two code submission feature of Challenge 1 was maintained. Additionally, Divisions 3 and 4 within the competition permitted on/off switching of transmission lines (Divisions 1 and 2 did not). After the initial release of the Problem Formulation on 7/20/2020, ARPA-E Director Lane Genatowski announced Challenge 2 on 9/12/2020. The final May 31, 2021, version of the Problem Formulation was 97 pages long with 299 equations. The Challenge proceeded with 2 non-prize Events and 2 prize Events. Teams receiving Challenge 1 FOA awards and prize money were required to use the prize money to fund their Challenge 2 efforts (Georgia Institute of Technology, Global Optimal Technology, Inc., Lawrence Livermore National Laboratory, Lehigh University, Northwestern University, Artelys, Columbia, Pearl Street Technologies, Pennsylvania State University, and University of Colorado Boulder). For more information on the competition and challenge 2 see the "GO Competition Challenge 2 Information" resource below. Challenge 1 and Challenge 3 information can be found in the resources linked below.

ACOPF

Power generation-cooling water Nexus: Impacts of cooling water shortage on power system operation - a simulation case study in Illinois, U.S

Cooling water shortage, frequently attributed to drought and heat waves, poses a significant threat to the operations of thermoelectric power plants and further poses a challenge for the entire power system and environmental stakeholders. Recognizing the critical nexus between power generation and cooling water availability and the potential ability of power generations to adjust generation schedules during cooling water shortages, this paper introduces a security-constrained unit commitment and economic dispatch model considering water-energy nexus. In specific, the model is augmented with a unit-level cooling water requirement (CWR) model and multi-level cooling water availability (CWA) constraints. The unit-level CWR model quantifies the cooling water withdrawal per MWh of power generation, taking into account factors such as thermoelectric generation technologies, cooling system technologies, and environmental parameters. The multi-level CWA constraints incorporate pump-level, plant-level, watershed-level, and forced minimum power constraints, utilizing data derived from actual-based cooling water shortage scenarios. Using a simulation case study in Illinois, United States, this research examines the reliability, economic, and environmental implications of cooling water shortages on power system operations. The results show that Illinois may experience 10-15% daily load curtailment and severe congestion between certain regions from the east to central during cooling water shortages, while once-through and wet-tower units experience a 52% and 17% reduction in power generation. In conclusion, overall cooling water withdrawal decreases by 24-38% as severity intensifies.

Cooling water shortage

Sparow-Examples

SAND2026-16701O SPAROW-Examples software provides a repository of stochastic programming examples designed to demonstrate Sandia's SPAROW optimization library. This resource helps users learn to develop complex applications with SPAROW by offering reference implementations that can be used to test and enhance new optimization solvers. The library offers a diverse range of simple and complex exemplars, including those related to power grid applications such as unit commitment and expansion planning. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Hart, William [Sandia National Lab. (SNL-CA), Live

A VSC-HVDC-Assisted Black-Start Strategy in Bulk Power Systems a Case Study in San Diego

With the worldwide growth in deploying high-voltage direct current (HVDC) transmission systems, their ability to facilitate black-start (BS) restoration has been a research topic of interest. In this context, voltage source converter (VSC)-HVDC is regarded as a BS resource, and this paper proposes a VSC-HVDC-assisted parallel BS restoration strategy in bulk power systems. The proposed strategy consists of two stages: 1) determination of the VSC and generator startup sequence and 2) load restoration simulation. In the first stage, the entire blackout system is sectionalized into multiple subsystems. Each subsystem includes a VSC-HVDC station or traditional BS unit, it independently determines its generator startup timeline and the energization timelines for buses and lines. The second stage involves load restoration, conceptualized as a modified unit commitment problem, with the timelines established in the first stage work as critical inputs. The proposed BS restoration strategy is tested on the San Diego power system to simulate the 2011 Southwest blackout. The simulation results validate the effectiveness of using VSC-HVDC links as a BS resource which not only speeds up the restoration process but also reduces both energy and economic losses.

24 POWER TRANSMISSION AND DISTRIBUTION

Optimal Economic Dispatch and Load-Following Strategies for Nuclear Integrated Energy Systems

The need for distributed and adaptable energy resources that can handle the growing unpredictability in both supply and demand is rising as the power system continues to modernize. In order to satisfy those needs and maintain grid resilience, nuclear power plants can dynamically control their output, despite typically being used as baseload generators. By incorporating energy storage and renewable energy sources, nuclear integrated energy systems are designed to satisfy the electrical and thermal demands of different end-user applications while ensuring flexible power operation. These systems generate revenue by participating in both wholesale and ancillary services electricity markets, as well as commodity markets for various byproducts generated from coupled industrial processes. This study addresses the economic dispatch efficiency of a tightly coupled nuclear integrated energy system comprising a gigawatt-scale light water reactor, commercialized in the U.S., a high-temperature steam electrolysis unit, a district heating network, and specified electrical loads. To demonstrate the nuclear power plant’s flexibility within the day-ahead unit commitment and economic dispatch framework, while maintaining equilibrium even during periods of refueling outages, this paper develops a mixed-integer linear programming framework that models the subsystems and components of its nuclear steam supply system. A systematic comparative analysis of flexible versus baseload nuclear power plant operation under varying levels of renewable energy integration indicates that flexible operation enhances system profitability by more than 18% while also increasing energy storage utilization, improving reactor responsiveness to load fluctuations, and allowing for greater participation across numerous electricity markets.

29 ENERGY PLANNING, POLICY, AND ECONOMY

Analytical Models of Frequency and Voltage in Large-Scale All-Inverter Power Systems

Low-order frequency response models for power systems have a decades-long history in optimization and control problems such as unit commitment, economic dispatch, and wide-area control. With a few exceptions, these models are built upon the Newtonian mechanics of synchronous generators, assuming that the frequency dynamics across a system are approximately homogeneous, and assume the dynamics of nodal voltages for most operating conditions are negligible, and thus are not directly computed at all buses. As a result, the use of system frequency models results in the systematic underestimation of frequency minimum nadir and maximum RoCoF, and provides no insight into the reactive power-voltage dynamics. This paper proposes a low-order model of both frequency and voltage response in grid-forming inverter-dominated power systems. The proposed model accounts for spatial-temporal variations in frequency and voltage behavior across a system and as a result, demonstrates the heterogeneity of frequency response in future renewable power systems. Electromagnetic transient (EMT) simulations are used to validate the utility, accuracy, and computational efficiency of these models, setting the basis for them to serve as fast, scalable alternatives to EMT simulation, especially when dealing with very large-scale systems, for both planning and operational studies.

24 POWER TRANSMISSION AND DISTRIBUTION

A Review of Quantum Computing Technologies in Power System Optimization

As modern power grids increasingly integrate variable renewable generation, distributed energy resources, and energy storage systems, classical optimization techniques are facing unprecedented challenges. This review examines the emerging application of quantum computing to overcome these challenges in power system optimization, including optimal power flow (OPF), unit commitment (UC), economic dispatch (ED), and intelligent switching and topology optimization (IS-TO). Recent research has introduced various quantum methodologies—such as gate-based, annealing-based, variational algorithms, and quantum-inspired algorithms—to address the combinatorial complexity inherent in grid reconfiguration and energy management. The review summaries the quantum algorithms, quantum devices and the power system test cases, highlighting hybrid quantum–classical strategies that leverage the complementary strengths of both paradigms. Some quantum advantages have been observed, including theoretical speedup, accurate simulation results, scalable qubit usage, efficient QUBO mapping. In particular, the review emphasizes the importance of integrating quantum optimization techniques with classical control frameworks, these hybrid approaches demonstrate the potential to improve real-time grid management and operational reliability. A significant portion of the analysis is devoted to the practical limitations of current quantum devices. Present-day quantum hardware, operating in the noisy intermediate-scale quantum (NISQ) era, remains highly sensitive to noise and limited in qubit connectivity, which constrains the scale and accuracy of implemented algorithms. The review delves into specific challenges such as the need for qubit-efficient encoding techniques and error mitigation strategies that are critical for handling real-world grid optimization problems. In addition, the work draws attention to the performance discrepancies between theoretical quantum speedups and experimental validations, underscoring the importance of rigorous benchmark studies using representative power grid test cases. In summary, this review highlights both the promise and limitations of quantum computing for power system optimization. It provides a comprehensive overview of the state-of-the-art technologies, categorizes recent advancements in algorithm design, and discusses practical considerations for implementation, and serves as an informative resource on current research. Future research directions include developing robust hybrid frameworks, advancing qubit-efficient formulations, and scaling up experimental demonstrations to confirm the theoretical advantages of quantum methods in large-scale power system operations.

24 POWER TRANSMISSION AND DISTRIBUTION

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

A Model for Hybrid Systems for Production Cost Modeling Studies Considering Ancillary Services

This paper introduces a model for simulating hybrid plants participating in energy and ancillary services for bulk power system studies. The model considers a hybrid plant comprised of a renewable energy source, a thermal power unit, a storage unit, fixed power loads, or any combination of these technologies. The model focuses on Production Cost Modeling (PCM) studies under the assumption of centralized dispatch. We present an example case study to illustrate the use of the model in a single-stage production cost model similar to those conducted by planning agencies. We explore the allocation of behind-the-meter ancillary services products and total energy participation to hybrid plant sub-assets and the resulting impacts on the system's ancillary service allocation. The model is implemented and simulated in a unit commitment problem in the RTS test system, which was modified to include a hybrid plant asset.

ancillary services

Improved Evaluation of Large Network Matrices for Linear Power Flow Within Optimization Problems

This work presents methods for evaluating the Power Transfer Distribution Factor (PTDF) and Line Outage Distribution Factor (LODF) matrices by employing sparse linear algebra for large-scale computing applications. These matrices play a critical role in many power system applications, such as the Unit Commitment Problem (UC), pre- and post-contingency power flow analysis, and transmission expansion. These matrices are typically dense, which means they require a significant amount of time and memory to be computed for large networks. However, by analyzing the structure of the matrices and their computation method, it is possible to use reduced memory methods based on sparse matrix operations. This paper shows that sparse linear algebra algorithms are faster and require less memory and time than traditional dense approaches. Additionally, we explore the effect of matrix sparsification by eliminating trailing digits on power flow calculations.

large scale

IM3 Projected U.S. Western Interconnection Grid Stress Dataset

This dataset provides projected grid stress and reliability results (including all model inputs and outputs from GO WEST and TEP) for Integrated Multisector, Multiscale Modeling (IM3) Phase 2 simulations across eight different scenarios for the U.S. Western Interconnection through 2055. The scenarios include combinations of two Shared Socioeconomic Pathways (SSP3 and SSP5) with four high-resolution climate projections specific to the United States from a set of Thermodynamic Global Warming (TGW) simulations. These climate projections include "hotter" and "cooler" variants for two Representative Concentration Pathways (RCP4.5 and RCP8.5). The resulting eight simulations are: rcp45cooler_ssp3 rcp45cooler_ssp5 rcp45hotter_ssp3 rcp45hotter_ssp5 rcp85cooler_ssp3 rcp85cooler_ssp5 rcp85hotter_ssp3 rcp85hotter_ssp5 GO WEST is an open-source power grid modeling framework for the U.S. Western Interconnection, which allows users to tailor the model depending on their research study and science questions. It covers 28 balancing authorities (BAs) and 12 states in U.S. Western Interconnection. GO WEST allows users to select different number of nodes and come up with a simplified network by utilizing 10,000 nodal topology of the U.S. Western Interconnection (ACTIVSg10k). Users can select different number of nodes, mathematical formulations (linear programming vs. mixed-integer linear programming), transmission line limit scaling factors, and hurdle rate scaling factors. GO WEST offers a unit commitment and economic dispatch (UC/ED) module to simulate grid operations on an hourly scale. In this sense, users can calibrate and validate their model versions by comparing model outputs to historical datasets. TEP is an open-source transmission capacity expansion model, built on the GO WEST framework. It utilizes linear programming to optimize transmission capacity addition investment on existing lines within the GO WEST framework. The TEP model only increases the thermal capacity of existing transmission lines and does not add new lines to the system, which leaves the topology preserved. In order to use TEP model, users need to create scenarios with the GO WEST framework. Please refer to README file for a detailed description of the dataset including individual files and references.

Capacity Expansion Model

Effect of wind turbine generator model and siting on wind power changes out of large WECS arrays

Methods of reducing the WECS generation change through selection of the wind turbine model for each site, selection of an appropriate siting configuration, and wind array controls are discussed. An analysis of wind generation change from an echelon and a farm for passage of a thunderstorm is presented. Reduction of the wind generation change over ten minutes is shown to reduce the increase in spinning reserve, unloadable generation and load following requirements on unit commitment when significant WECS generation is present and the farm penetration constraint is satisfied. Controls on the blade pitch angle of all wind turbines in an array or a battery control are shown to reduce both the wind generation change out of an array and the effective farm penetration in anticipation of a storm so that the farm penetration constraint may be satisfied.

Schleuter, R. A.

Impact of Hydrological Data on Power System Operational Studies: Preprint

Hydropower is expected to play an important role in maintaining grid reliability and flexibility as the share of of variable renewable energy increases. While the current hydropower operational models have been studied and used widely, they haven't been updated for decades to meet new performance standards. For example, current steady state and dynamic models often neglect hydrological conditions, which may lead to unrealistic expectations when relying on hydropower for energy and ancillary services. To study this impact, a multi-timescale hydrological model was created by leveraging the National Renewable Energy Laboratory-developed Multi-timescale Integrated Dynamics and Scheduling (MIDAS) tool. Using MIDAS, we compare the impact of considering hydrological conditions in a day-ahead unit commitment (DAUC) schedule on the reduced 240-bus Western Interconnect (WI) test system under winter and summer case studies. We show that neglecting current hydrological conditions of hydropower plants in power system models can lead to an overestimation of hydropower capabilities, which could lead to power balancing issues. For example, power system DAUC simulation results of our reduced test system show that in the case where hydrological conditions are not considered in the model, an approximate 31% overestimation of hydropower capabilities occurs in the summer case and approximately 60% occurs in the winter case compared to what is available. Additionally, results show an underestimation of WI day-ahead power system generation costs by approximately $54M - $80M in the weekly summer scenario and $116M - $126M in the weekly winter scenario. This analysis helps to underscore the importance of considering hydrological data in power system operational studies.

ENERGY PLANNING, POLICY, AND ECONOMY,HYDRO ENERGY

Practical Implementation of GPU-based Computing at the Grid Edge for Resilience Scenarios

This paper presents a practical implementation of GPU-accelerated computing at the grid edge to enhance power system resilience through next-generation smart meters. Advanced Metering Infrastructure (AMI) systems rely predominantly on centralized processing architectures, which limit real-time response capabilities during grid disturbances. This work proposes the integration of GPU-enabled computational platforms directly within smart meter to enable local execution support for power system analytics, fault detection algorithms, and optimization routines. The proposed framework uses the Julia programming language to leverage highperformance parallel computing capabilities while maintaining code portability and development efficiency. We use two experimental scenarios to benchmark the computational feasibility of this approach: sparse linear system solutions representative of power flow analyses, and multi-stage production cost simulations incorporating unit commitment and economic dispatch operations. Results demonstrate that computationally intensive power system algorithms, such as those supporting resilience scenario calculations, can be effectively executed at the distribution edge using commercially available embedded GPU hardware. Keywords—GPU acceleration, edge computing, smart meters, grid resilience, AMI, resilience.

De Souza, Reubun [School of Electrical Engineering

Analysis of Proposed 2007-2008 Revisions to the Lightning Launch Commit Criteria for United States Space Launches

Ascending space vehicles are vulnerable to both natural and triggered lightning. Launches under the jurisdiction of the United States are generally subject to a set of rules called the Lightning Launch Commit Criteria (LLCC) (Krider etal., 1999; Krider etal., 2006). The LLCC protect both the vehicle and the public by assuring that the launch does not take place in conditions posing a significant risk of a lightning strike to the ascending vehicle. Such a strike could destroy the vehicle and its payload, thus causing failure of the mission while releasing both toxic materials and debris. To assure safety, the LLCC are conservative and sometimes they may seriously limit the ability of the launch operator to fly as scheduled even when conditions are benign. In order to safely reduce the number of launch scrubs and delays attributable to the LLCC, the Airborne Field Mill (ABFM II) program was undertaken in 2000 - 2001. The effort was directed to collecting detailed high-quality data on the electrical, microphysical, radar and meteorological properties of thunderstorm-associated clouds. Details may be found in Dye et al., 2007. The expectation was that this additional knowledge would provide a better physical basis for the LLCC and allow them to be revised to be less restrictive while remaining at least as safe. That expectation was fulfilled, leading to significant revisions to the LLCC in 2003 and 2005. The 2005 revisions included the application of a new radar-derived quantity called the Volume Averaged Height Integrated Radar Reflectivity (VAHIRR) in the rules governing flight through anvil clouds. VAHIRR is the product of the volume averaged radar reflectivity times the radardetermined cloud thickness. The reflectivity average extends horizontally 5 km west, east, south and north of a point along the flight track and vertically from the 0 C isotherm to the top of the radar cloud. This region is defined as the "Specified Volume". See Dye et al., 2006 and Merceret et al., 2006 for a more thorough description of VAHIRR. The units are dBZ km (not dBZ per kilometer) and the threshold is 10 dBZ km. It is safe to fly through an anvil cloud for which VAHIRR is below this threshold everywhere along the flight track as long as (1) the entire cloud within 5 nmi. (9.26 km) of the flight track is colder than 0 C, (2) the points at which VAHIRR must be evaluated are at least 20 km from any active convective cores and recent lightning, and (3) the radar return is not being attenuated within the Specified Volume around those points.

Dye, James E.

Analysis of Proposed 2007-2008 Revisions to the Lightning Launch Commit Criteria for United States Space Launches

Ascending space vehicles are vulnerable to both natural and triggered lightning. Launches under the jurisdiction of the United States are generally subject to a set of rules called the Lightning Launch Commit Criteria (LLCC). The LLCC protect both the vehicle and the public by assuring that the launch does not take place in conditions posing a significant risk of a lightning strike to the ascending vehicle. Such a strike could destroy the vehicle and its payload, thus causing failure of the mission while releasing both toxic materials and debris. To assure safety, the LLCC are conservative and sometimes they may seriously limit the ability of the launch operator to fly as scheduled even when conditions are benign. In order to safely reduce the number of launch scrubs and delays attributable to the LLCC, the Airborne Field Mill (ABFM) program was undertaken in 2000 - 2001. The effort was directed to collecting detailed high-quality data on the electrical, microphysical, radar and meteorological properties of thunderstorm-associated clouds. The expectation was that this additional knowledge would provide a better physical basis for the LLCC and allow them to be revised to be both safer and less restrictive. That expectation was fulfilled, leading to significant revisions to the LLCC in 2003 and 2005. The 2005 revisions included the application of a new radar-derived quantity called the Volume Averaged Height Integrated Radar Reflectivity (VAHIRR) in the rules governing flight through anvil clouds. Analysis of the ABFM data has continued, and two additional revisions to the LLCC were proposed in late 2006 for adoption in 2007 or 2008. One proposal was to apply the VAHIRR concept to debris clouds, and the other was to reduce the "stand-off distances" in the rules for anvil and/or debris clouds. The stand-off distance is the clearance (out side of the cloud) required between the flight path of the vehicle and the edge of a cloud that it is not permissible to fly through. This paper will discuss these proposed changes in the LLCC and the scientific rationale for adopting or rejecting them based on ABFM data.

Dye, J. E.

Commercial development of space - A national commitment

The United States is currently in a unique position. It has all the assets required to lead the world in commercial space development. It has the transportation: the Shuttle and a family of expendable launch vehicles. Space Station Freedom is forthcoming. It has the extrepreneurial spirit, coupled with a strong university system and lending institutions with financial capacity necessary for entrepreneurial activities. But, there are a number of actions that the government should take to improve the climate and prospects for greater commercial development of space. This paper outlines some of the steps that NASA is taking to incentivize the private sector to apply its resources and talents to commercial space endeavors.

Rose, James T.