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At least 55 records · Page 3

Research Highlight - Dispatch Optimization, System Design and Cost Benefit Analysis of a Nuclear Reactor with Molten Salt Thermal Storage

We highlight our work from our previous publication titled "Dispatch Optimization, System Design, and Cost Benefit Analysis of a Nuclear Reactor with Molten Salt Thermal Storage" published in MDPI Energies 2022 (doi.org/10.3390/en15103599). Variable renewable energy availability has increased the volatility in energy prices in most markets. Nuclear power plants, with a large ratio of capital to variable costs, have historically operated as base load energy suppliers but the need for more flexible operation is increasing. We simulate the techno-economic performance of a 950 MWt nuclear power plant, based on the Westinghouse lead-cooled fast reactor, coupled with molten salt thermal storage as a method for flexible energy dispatch. We use the System Advisor Model to model the nuclear reactor thermal power input and power cycle operating modes. We combine this robust engineering model with a mixed-integer linear program model for optimized dispatch scheduling. We then simulate the coupled nuclear and thermal storage system under different market scenarios with varying price volatility. We find that the coupled plant outperforms the base plant under markets where energy price peaks fluctuate by a factor of two or more about the mean price. We show that a calculated power purchase agreement price for the plant improves by up to 10% when operating under California energy market conditions. Sensitivity analysis on the thermal storage cost shows that the optimal design remains unchanged even when doubling costs.

97 MATHEMATICS AND COMPUTING↗

Evaluating Nationwide Supply Chain for Circularity of PET and Olefin Plastics

PET (Polyethylene Terephthalate, #1) and olefin plastics including HDPE (High Density Polyethylene, #2), LDPE/LLDPE (Low Density/Linear Low-Density Polyethylene, #4) and PP (Polypropylene, #5) together comprise nearly 80% of the U.S. plastic market. Due to their high market share and extensive application in packaging these polymers have better potential for circularity than other polymer types. To understand the potential of future scenarios with higher recycling rates, supply chain scenarios for PET and olefin plastic packaging need to be analyzed with increased availability and collection of plastics. Currently there exists a knowledge gap to understand the circular supply chain on a national level. Performing a nationwide analysis introduces certain challenges such as variability in the plastic mix of the recycling stream in different municipalities, lack of collection of some types of plastics, regional differences in cost and estimating a national supply curve based on state level access rate and participation rate. Currently, a limited number of Plastic Reclaimers recycle the nation’s collected plastic involving transportation over long distances surpassing state boundaries. Modeling a nationwide scenario instead of regional/state based scenario will facilitate transportation beyond state boundaries for the development of a circular economy. A Mixed-integer Linear Programming model was developed, to identify the optimal location and capacity of the Material Recovery Facilities (MRFs) nationwide subject to maximizing the profit margin of the industrial entities within the model. We considered three different scenarios including the base case scenario (S1) collecting 2.27 million metric tons/year as well as two additional scenarios with available plastic supply of 1.8 times (S2) and 2.2 times (S3) of the base case scenario. The model identified 166, 275 and 319 counties as potential MRF locations for scenarios S1, S2 and S3 respectively. Compared to the existing number of counties having MRFs in the US, the model results indicated a reduction of 38% of MRFs for S1. For S2 and S3, the number of counties with MRFs increased 3% and 20% respectively compared to counties currently with MRFs. The average profit remains constant between $180-$181/ton regardless of the increased plastic collection.

54 - ENVIRONMENTAL SCIENCES/GLOBAL CLIMATE CHANGE ↗

Optimization for Bioenergy Systems

The Sustainable Aviation Fuel (SAF) Grand Challenge (Langholtz, 2024 ) seeks to generate 35 billion gallons of SAF each year by 2050, with corn stover, an agricultural byproduct, playing a key role as a feedstock. This study develops an optimization framework to enhance the quality and quantity of corn stover while ensuring economic and environmental viability. Using the Decision Support System for Agrotechnology Transfer (DSSAT) crop model, we simulate the effects of cover crops on rotation yield, soil moisture balance, and nitrogen cycling across diverse climates and soils. The model outputs, including yield data and soil quality changes, inform a Mixed-Integer Linear Programming (MILP) optimization model. This model aims to maximize economic and environmental returns by incorporating production costs, direct and indirect income, and environmental incentives. The optimization model evaluates 280 agriculture management plans composed of various crop management strategies, including corn stover removal rates, cover crop adoption, and fertilization practices. It seeks to identify the optimal combination of crop and tillage decisions for each subfield, maximizing profits while enhancing soil carbon sequestration and reducing greenhouse gas emissions. Outputs include detailed subfield locations, optimal management plans, and profits per hectare and per acre, allowing for comparison with literature values on farm profits. This study provides a robust optimization framework supporting the SAF Grand Challenge by proposing economically viable and environmentally sustainable strategies for corn stover utilization. The findings highlight corn stover's potential as a sustainable feedstock for SAF production, offering practical solutions to enhance its quality and quantity while maintaining soil health. Idaho is used as a case study to demonstrate the framework's applicability and effectiveness in real-world scenarios. Langholtz, M. H., Davis, M., Hellwinckel, C., De La Torre Ugarte, D., Efroymson, R., Jacobson, R., Milbrandt, A., Coleman, A., Davis, R., Kline, K. L., Badgett, A., Curran, S., Schmidt, E., Theiss, T., Fried, J., English, B., Lambert, L., Cook, H., Field, J., ... Walker, L. (2024). 2023 Billion-Ton Report: An Assessment of U.S. Renewable Carbon Resources. https://doi.org/10.2172/2441098 DSSAT Foundation. (2025). Decision Support System for Agrotechnology Transfer (DSSAT). Retrieved from https://dssat.net/

09 - BIOMASS FUELS↗

Optimal Operation of Residential High Performance Water Heater for Reduction of Electricity Cost and Peak Demand Through Field Validation

Water heating accounts for about 18% of a typical US home’s energy use. Modern water heaters have enabled control options through APIs, offering customers the opportunity to reduce their energy cost and peak demand by dynamically adjusting settings. A water heater’s capacity to store energy using its storage tank makes it an asset for peak demand reduction and energy cost savings. For this reason, a mixed-integer linear programming model is proposed to minimize the energy cost of a high-performance water heater while also reducing the peak demand of the residential household under a time-of-use utility rate by dynamically changing the water heater’s running mode. Specifically, a multi-objective optimization model is formulated to determine the mode settings of the water heater considering hot water use, time-of-use rate, and peak demand limit of the residential household. The mode settings are associated with different dead bands of water temperature for triggering on/off action of the heat pump and heating element. A 66-gal hybrid electric high performance water heater was used for numerical simulation and practical experiments. The simulation results were well aligned with measurements of practical experiments, validating the soundness of the thermodynamic model. In addition, reductions of energy cost, enabling affordability, and reducing peak demand are demonstrated. The research team also developed a software framework with dashboards to automatically and continuously monitor and manage devices.

Liu, Guodong [ORNL] (ORCID:0000000213498608)↗

Near-Optimal Solutions for Day-Ahead Unit Commitment

Given the difficulty and the time pressure of solving unit commitment problems, near -optimal solutions (those with 0.1 or 0.001% optimality gaps) are often used in practice. The choice in which of the near -optimal solutions is used, however, is random. We investigate the impact of solution choice on the revenues obtained by generator owners across a variety of pricing schemes and problem instances.

market-clearing↗

Stochastic Unit Commitment: Model Reduction via Learning

As weather-dependent renewable generation increases its share in the generation mix of most electric energy systems, a stochastic unit commitment becomes the natural day-ahead scheduling tool. However, such a tool is generally computationally intractable if a detailed uncertainty description is considered. Taking this into account, we proposed a learning method to make the stochastic unit commitment problem tractable. Here, recent advances in statistical learning and machine learning to address optimization problems can be advantageously applied to the rather intractable stochastic unit commitment problem. Considering these advances, we explore simple learning techniques to drastically reduce the size of a stochastic unit commitment problem without significantly altering its optimal solution. The considered stochastic unit commitment problem is formulated as a two-stage stochastic programming problem. The first stage represents commitment decisions, while the second one represents the operation conditions under different scenarios. Taking into account historical solved instances (or proxies for them), we reduce the size (measured by numbers of constraints and variables) of the stochastic unit commitment problem by (i) fixing unchanged binary variables and by (ii) eliminating inactive inequality constraints. Our numerical results show that the reduced problem generally requires significantly less time to solve while obtaining high-quality solutions, which are very close to or indistinguishable from the one obtained by solving the original problem. We use an Illinois 200-bus system to illustrate and characterize the performance of the proposed problem-reduction method.

42 ENGINEERING↗

Enhancing power grid resilience to winter storms via generator winterization with equity considerations

Here we develop two-stage stochastic programming models for generator winterization that enhance power grid resilience while incorporating social equity. The first stage in our models captures the investment decisions for generator winterization, and the second stage captures the operation of a degraded power grid, with the objective of minimizing load shed and social inequity. To incorporate equity into our models, we propose a concept called adverse effect probability that captures the disproportionate effects of power outages on communities with varying vulnerability levels. Grid operations are modeled using DC power flow, and equity is captured through mean or maximum adverse effects experienced by communities. We apply our models to a synthetic Texas power grid, using winter storm scenarios created from the generator outage data from the 2021 Texas winter storm. Our extensive numerical experiments show that more equitable outcomes, in the sense of reducing adverse effects experienced by vulnerable communities during power outages, are achievable with no impact on total load shed through investing in winterization of generators in different locations and capacities.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Optimizing mixed cool thermal storage systems across a connected community

A high level of electric demand flexibility must be integrated into our building infrastructure to enable greater renewable energy penetration in the grid. In the U.S., 9% of electricity generated is used to cool buildings in a periodic manner, making this end-use an ideal target for active management through cool thermal energy storage (CTES) technologies. Historic uses for CTES are designed around central chilled water plants, but these systems cool less than 25% of U.S. commercial floorspace. Emerging technologies are under development to serve the many smaller distributed cooling systems, such as rooftop units (RTUs), and have the potential to add CTES to an additional 66% of cooled commercial floorspace. However, these unitary thermal storage systems (UTSS) lack the modeling and analysis tools to evaluate them in the future interactive grid context. Here, this study develops the modeling and optimization tools necessary to simultaneously examine central and distributed ice storage systems within the multi-building, connected community context. An integrated simulation-optimization workflow is created to allow for rapid customized analysis. Results demonstrate the energy and flexibility tradeoffs of various implementations.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

A Decomposition-Based Learn-To-Optimize Approach with Feasibility Layer Assistance for Sub-Hourly Unit Commitment

Sub-hourly unit commitment (UC) with 15-min intervals is gaining significant attention as a way to respond rapidly to the fluctuations in electricity supply and demand introduced by renewable resources. However, the increased temporal resolution and complex inter-temporal dependencies pose substantial computational challenges for traditional optimization methods. To this end, this paper explores a decomposition-based learn-to-optimize approach. Building on recent advances in machine learning, our method revisits the long- overlooked Lagrangian relaxation framework, which is a classical decomposition technique that enables tractable subproblem solving. These smaller subproblems are inherently well-suited for machine learning, as their reduced dimensionality and structural regularity allow predictive models to efficiently learn and generalize solution patterns. We thus propose a generic predictive model, which embeds Gated Recurrent Units (GRUs) and Attention in the encoder-decoder structure, and integrate a rule-based feasibility layer to capture temporal dependencies, reduce training effort, and improve feasibility w.r.t. unit-level constraints. Our method has been validated on the IEEE 118-bus system, demonstrating promising performance in solving sub-hourly UC problems efficiently and feasibly.

97 MATHEMATICS AND COMPUTING↗

Integrated Transmission-Distribution Multi-Period Switching for Wildfire Risk Mitigation: Improving Speed and Scalability with Distributed Optimization: Preprint

With increasingly severe wildfire conditions driven by climate change, utilities must manage the risk of wildfire ignitions from electric power lines. During "public safety power shutoff'" events, utilities de-energize power lines to reduce wildfire ignition risk, which may result in load shedding. Distributed energy resources provide flexibility that can help support the system to reduce load shedding when lines are de-energized. We investigate a coordinated transmission-distribution optimization problem that balances wildfire risk mitigation and load shedding. We model distribution systems that include battery energy storage systems which may support loads when transmission lines are de-energized. This multi-period integrated transmission-distribution optimal switching problem jointly optimizes line switching decisions, the generators' setpoints, load shedding, and the batteries' states of charge, resulting in significant computational challenges. To improve scalability, we decompose the problem over both space and time and apply a distributed optimization algorithm. Using a large-scale synthetic California test case with realistic distribution models and real wildfire risk data, we show that distributed optimization can solve large-scale multi-period switching problems that are otherwise intractable for centralized solvers. We also discuss challenges and future directions for improving the distributed algorithm's convergence performance as the number of time periods increases.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Extreme-scale EV charging infrastructure planning for last-mile delivery using high-performance parallel computing

Here, this paper addresses stochastic charger location and allocation problems under queue congestion for last-mile delivery using electric vehicles (EVs). The objective is to decide where to open charging stations and how many chargers of each type to install, subject to budgetary and waiting-time constraints. We formulate the problem as a mixed-integer non-linear program, where each station-charger pair is modeled as a multiserver queue with stochastic arrivals and service times to capture the notion of waiting in fleet operations. The model is extremely large, with billions of variables and constraints for a typical metropolitan area; even loading the model in solver memory is difficult, let alone solving it. To address this challenge, we develop a Lagrangian-based dual decomposition framework that decomposes the problem by station and leverages parallelization on high-performance computing systems, where the subproblems are solved by using a cutting plane method and their solutions are collected at the master level. We also develop a three-step rounding heuristic to transform the fractional subproblem solutions into feasible integral solutions. Computational experiments on data from the Chicago metropolitan area with hundreds of thousands of households and thousands of candidate stations show that our approach produces high-quality solutions in cases where existing exact methods cannot even load the model in memory. We also analyze various policy scenarios, demonstrating that combining existing depots with newly built stations under multiagency collaboration substantially reduces costs and congestion. These findings offer a scalable and efficient framework for developing sustainable large-scale EV charging networks.

Capacity allocation↗

A matheuristic for design and dispatch of a utility-connected distributed energy system

Modeling distributed power generation systems often requires complicated mathematical expressions that present challenges for commercial optimization solvers. Here, this paper presents a matheuristic to solve a mixed-integer optimization model that informs decisions regarding the design and dispatch of a utility-connected microgrid. We deploy a genetic algorithm to search the system design space and a linear program to solve the economic dispatch problem. The model is a component of a web tool that requires solutions within a few minutes. Our method yields objective function values within 5% of an exogenously produced optimal in fewer than 30 seconds for 90% of our test cases compared to only 10% of our test cases by a traditional optimization solver in the same amount of time.

24 POWER TRANSMISSION AND DISTRIBUTION↗

McCormick envelopes in mixed-integer PDE-constrained optimization

McCormick envelopes are a standard tool for deriving convex relaxations of optimization problems that involve polynomial terms. Such McCormick relaxations provide lower bounds, for example, in branch-and-bound procedures for mixed-integer nonlinear programs but have not gained much attention in PDE-constrained optimization so far. This lack of attention may be due to the distributed nature of such problems, which on the one hand leads to infinitely many linear constraints (generally state constraints that may be difficult to handle) in addition to the state equation for a pointwise formulation of the McCormick envelopes and renders bound-tightening procedures that successively improve the resulting convex relaxations computationally intractable. We analyze McCormick envelopes for a model problem class that is governed by a semilinear PDE involving a bilinearity and integrality constraints. We approximate the nonlinearity and in turn the McCormick envelopes by averaging the involved terms over the cells of a partition of the computational domain on which the PDE is defined. This yields convex relaxations that underestimate the original problem up to an a priori error estimate that depends on the mesh size of the discretization. These approximate McCormick relaxations can be improved by means of an optimization-based bound-tightening procedure. We show that their minimizers converge to minimizers to a limit problem with a pointwise formulation of the McCormick envelopes when driving the mesh size to zero. We provide a computational example, for which we certify all of our imposed assumptions. The results point to both the potential of the methodology and the gaps in the research that need to be closed. Our methodology provides a framework first for obtaining pointwise underestimators for nonconvexities and second for approximating them with finitely many linear inequalities in an infinite-dimensional setting.

Approximations and Expansions↗

A bilevel multistage stochastic self-scheduling model with indivisibilities for trading in the continuous intraday electricity market

In this paper, we study the profit maximization problem of a virtual power plant trading in the continuous intraday electricity market. Our virtual power plant model is compatible with renewable, and thermal assets, covering a range of virtual power plants currently participating in energy markets. We model the trading problem as a bilevel multistage stochastic program. The upper level of the problem accounts for the profit maximization of the virtual power plant with explicit modeling of the technical constraints of the operational status of the thermal power plant including minimum start-up and shut-down times, ramp-up and ramp-down rates, and minimum generation level. The upper level also decides which continuous and indivisible (fill-or-kill) orders are submitted to the market. The lower-level problem accounts for the clearing of the continuous intraday market, i.e., matching of buy and sell orders. Because of the presence of fill-or-kill orders, the lower-level problem is mixed-integer, which prevents its direct conversion to a single-level problem using duality. In order to solve this challenging problem, we develop a convex-hull extended formulation for the lower-level problem, apply duality theory to obtain a single-level stochastic equivalent formulation, and employ McCormick envelopes to turn the problem into a multistage stochastic mixed-integer linear problem, which we solve using the stochastic dual dynamic integer programming algorithm. We conduct numerical experiments and analyze the optimal trading behavior of a virtual power plant trading in an ideal continuous market without arbitrage.

Bilevel multistage stochastic programming problem↗

Relaxations of the steady optimal gas flow problem for a non-Ideal gas

Natural gas ranks second in U.S. primary energy consumption. Because most production sites are remote, gas must be transported through pipeline networks equipped with compressors, valves, and other components. For both economic efficiency and system reliability, it is desirable to operate these networks optimally. The governing physics across pipeline components entails nonlinear, non-convex equality and inequality constraints, and the most general steady-flow operations problem is a Mixed-Integer Nonlinear Program (MINLP).This work focuses on one such steady-flow problem-the Optimal Gas Flow (OGF) for a natural gas pipeline network-which minimizes production cost subject to the steady-flow physics. For day-to-day operations, the ability to quickly compute a globally optimal solution and a strong lower bound for varying demand profiles is crucial. A promising strategy is to build tight relaxations of the OGF’s nonlinear constraints. However, many nonlinearities arising from non-ideal equations of state either lack relaxations or have relaxations that do not scale to realistic network sizes. We address this gap by combining recent advances in polyhedral relaxations for univariate functions to construct tight, computationally efficient relaxations of the OGF with a non-ideal equation of state. These relaxations solve within seconds on a standard laptop. In conclusion, we demonstrate their quality through extensive numerical experiments on very large-scale test networks from the literature and find that the proposed approach proves optimality in 92% of tested instances.

03 NATURAL GAS↗