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Results for “Mixed integer optimization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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410 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Electric vehicle fast charging infrastructure planning in urban networks considering daily travel and charging behavior

Electric vehicles are a sustainable substitution to conventional vehicles. This work introduces an integrated framework for urban fast charging infrastructure to address the range anxiety issue. A mesoscopic simulation tool is developed to generate trip trajectories, and simulate charging behavior based on various trip attributes. The resulting charging demand is the key input to a mixed-integer nonlinear program that seeks charging station configuration. The model minimizes the total system cost including charging station and charger installation costs, and charging, queuing, and detouring delays. The problem is solved using a decomposition technique incorporating a commercial solver for small networks, and a heuristic algorithm for large-scale networks, in addition to the Golden Section method. The solution quality and significant superiority in the computational efficiency of the decomposition approach are confirmed in comparison with the implicit enumeration approach. Furthermore, the required infrastructure to support urban trips is explored for future market shares and technologies.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2022

Nth-plant scenario for forest resources and short rotation woody crops: Biorefineries and depots in the contiguous US

Estimating the US potential of woody material is of vital importance to ensure cost-effective supply logistics and develop a sustainable bioenergy and bioproducts industry. We analyzed a mature conversion technology for woody resources for the contiguous US that takes advantage of economies of scale: the nth-plant. Here, we developed a database to quantify the total accessible woody biomass within a distributed network of preprocessing depots and biorefineries considering both quality specifications for conversion and a target cost to compete with fossil fuels. We considered two categories of woody biomass: 1) forest residues from trees, tops and limbs produced from conventional thinning and timber harvesting operations as well as non-timber tree removal; and 2) short rotation woody crops such as poplar, willow, pine, and eucalyptus. A mixed integer linear programming model was developed to analyze scenarios with woody feedstock blends at variable biomass ash contents and cost targets at the biorefinery. When considering a target cost of 85.51 dollars/dry ton (2016$) at the biorefinery, the maximum accessible biomass from forest residues in 2040 remained constant at 106 million dry tons regardless of ash targets. Including short rotation woody crops as part of the blend increased the total accessible biomass to 153 and 195 million dry tons at ash targets of 1% and 1.75%, respectively. We concluded from our analysis that woody resources could address about 55% of EPA’s (Environmental Protection Agency) target of 16 billion gallons of cellulosic biofuel.

09 BIOMASS FUELS↗
DOE OSTI2019

OPERATIONAL TOPOLOGY ESTIMATION OF THREE PHASE UNBALANCED POWER DISTRIBUTION SYSTEMS WITH OUTAGES

Distribution grid, in general, is constructionally loopy but a radially operated network. Opening and closing of suitable tie-switches allows transition from one radial topology to another. Tie-switches ensure reliability and provide restoration paths when faults (outages) occur. The estimation of the system's current operational topology is a precursor to implementing any optimal control actions (during normal operation) or restorative actions (during outage condition). The existing literature in topology detection suffers with several limitations including: (1) computationally intensive nonlinear formulations that are not scalable for large distribution systems, (2) methods requiring exhaustive search for the correct topology by enumerating the complete topological search space, and (3) approaches requiring large volumes of time-series measurements and are not applicable for estimating continuously changing operational topology. Furthermore, the existing literature on distribution grid topology estimation cannot be extended to estimate the operational topology during outage conditions. For operational topology estimation during outages, our objective is to estimate both energized radial feeder and the outaged sections. Starting with a radial topology, these methods identify outaged feeder sections and hence, are inapplicable when the current radial operational topology is not known. In this work, we present a mathematical programming approach to estimate the operational topology of a three-phase unbalanced power distribution system under both outage and normal operating conditions. The aforementioned limitations of existing literature were countered by modeling the problem as a mixed-integer linear programming (MILP) problem which minimizes the errors in available measurements while satisfying the power flow and structural constraints of the system. Specically, a minimum weighted least absolute value estimator is proposed that uses the instantaneous line flow measurements, historical/ forecasted load data, and ping measurements from a limited set of smart meters and solves an MILP to identify the operational topology based on a linearized three-phase unbalanced power flow model. The proposed approach is tested on IEEE 123-bus feeder and 1069 bus multi-feeder test system and the numerical results prove the applicability of the proposed method to large three phase unbalanced grids with high errors in measurements. It is observed that the approach performs well even at high percentages of measurement errors.

GANDLURU NAGA, ANANDINI↗
DOE OSTI2025

An interregional optimization approach for time series aggregation in continent-scale electricity system models

Modeling electric power systems with high shares of weather-dependent resources requires tradeoffs between temporal, spatial, and operational resolution. Many studies perform time series aggregation using clustering algorithms to reduce the temporal dimension, but when modeling continent-scale electricity systems that are large enough to contain multiple independent weather systems, this approach requires large numbers of representative periods to minimize errors in regional wind and solar capacity factors. Here, a new optimization-based approach for representative period selection and weighting is introduced that minimizes regional errors in average renewable capacity factors and electricity demand. The method delivers higher regional fidelity with fewer representative periods than alternative clustering methods when applied to wind, solar, and demand profiles for the contiguous United States. When representative periods are selected from multiple weather years, the optimized method reproduces regional averages with lower error than a complete 365-day time series from any single weather year. The method identifies only representative (as opposed to outlying) periods but can be combined with an iterative "stress period" identification approach to guide efficient decision-making considering both average and high-risk weather conditions.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2018

A Heuristic Approach to the Post-disturbance and Stochastic Pre-disturbance Microgrid Formation Problem

Microgrid formation is a potential solution in post-disaster electric grid recovery efforts. Recent works propose distribution level microgrid formation models using mixed-integer linear programming techniques. However, these models can only be solved for small and medium size power systems due to their computational intractability. In this article we introduce a heuristic approach that allows to approximately solve the post-disturbance microgrid formation problem for medium to large, more realistic, instances. Furthermore, the proposed approach allows to approximately solve the pre-disturbance microgrid formation problem (a stochastic version of the post-disturbance problem), in which the aim is to allocate extra generation capacity to the network to immunize it, as best as possible, against an uncertain cascading failure. Our results are illustrated by solving versions of the problem on ten test cases with up to 3012 buses.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Security-Constrained Unit Commitment for Electricity Market: Modeling, Solution Methods, and Future Challenges

This paper summarizes the technical activities of the IEEE Task Force on Solving Large Scale Optimization Problems in Electricity Market and Power System Applications. This Task Force was established by the IEEE Technology and Innovation Subcommittee to first review the state-of-the-art of the security-constrained unit commitment (SCUC) business model, its mathematical formulation, and solution techniques in solving electricity market clearing problems. The Task Force then investigated the emerging challenges of future market clearing problems and presented efforts in building benchmark mathematical and business models.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

Designing Metabolic Division of Labor in Microbial Communities

ABSTRACT Microbes face a trade-off between being metabolically independent and relying on neighboring organisms for the supply of some essential metabolites. This balance of conflicting strategies affects microbial community structure and dynamics, with important implications for microbiome research and synthetic ecology. A “gedanken” (thought) experiment to investigate this trade-off would involve monitoring the rise of mutual dependence as the number of metabolic reactions allowed in an organism is increasingly constrained. The expectation is that below a certain number of reactions, no individual organism would be able to grow in isolation and cross-feeding partnerships and division of labor would emerge. We implemented this idealized experiment using in silico genome-scale models. In particular, we used mixed-integer linear programming to identify trade-off solutions in communities of Escherichia coli strains. The strategies that we found revealed a large space of opportunities in nuanced and nonintuitive metabolic division of labor, including, for example, splitting the tricarboxylic acid (TCA) cycle into two separate halves. The systematic computation of possible solutions in division of labor for 1-, 2-, and 3-strain consortia resulted in a rich and complex landscape. This landscape displayed a nonlinear boundary, indicating that the loss of an intracellular reaction was not necessarily compensated for by a single imported metabolite. Different regions in this landscape were associated with specific solutions and patterns of exchanged metabolites. Our approach also predicts the existence of regions in this landscape where independent bacteria are viable but are outcompeted by cross-feeding pairs, providing a possible incentive for the rise of division of labor. IMPORTANCE Understanding how microbes assemble into communities is a fundamental open issue in biology, relevant to human health, metabolic engineering, and environmental sustainability. A possible mechanism for interactions of microbes is through cross-feeding, i.e., the exchange of small molecules. These metabolic exchanges may allow different microbes to specialize in distinct tasks and evolve division of labor. To systematically explore the space of possible strategies for division of labor, we applied advanced optimization algorithms to computational models of cellular metabolism. Specifically, we searched for communities able to survive under constraints (such as a limited number of reactions) that would not be sustainable by individual species. We found that predicted consortia partition metabolic pathways in ways that would be difficult to identify manually, possibly providing a competitive advantage over individual organisms. In addition to helping understand diversity in natural microbial communities, our approach could assist in the design of synthetic consortia.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Nth-plant scenario for blended pellets of Miscanthus, Switchgrass, and Corn Stover using multi-modal transportation: Biorefineries and depots in the contiguous U.S.

The sustainability of the biofuel industry depends on the development of a mature conversion technology on a national level that can take advantage of the economies of scale: the nth-plant. Here, this study addresses the logistic challenge of mobilizing national cellulosic feedstock supplies for a sustainable bioenergy industry. A Mixed Integer Linear Programming (MILP) model was developed and updated to deliver on-spec biomass that considers both a desired quantity and quality at the biorefinery. Our supply chain analysis includes multi-modal transport (truck and rail), varying depot and biorefinery sizes, and feedstock blends of corn stover (harvested by either a two- or three-pass method), switchgrass, and miscanthus. The following US states: Illinois, Kansas, Missouri, North Carolina, Oklahoma, Georgia, and Texas were identified as key locations for producing accessible miscanthus. Based on our most optimistic scenario, using trucks as the only transportation mode in 2040 with a cost target of $\$$79/dt, corn stover, switchgrass, and miscanthus could help meet 48% of the EPA target, 173 million dry tons that translate into 7.8 billion GGE. The addition of rail transportation for biomass delivery to biorefineries could help meet 79% of the EPA target, 283 million dry tons that translate into 12.7 billion GGE.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2023

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↗
DOE OSTI2023

Piecewise linear approximation with minimum number of linear segments and minimum error: A fast approach to tighten and warm start the hierarchical mixed integer formulation

In several areas of economics and engineering, it is often necessary to fit discrete data points or approximate nonlinear functions with continuous functions. Piecewise linear (PWL) functions are a convenient way to achieve this. PWL functions can be modeled in mathematical problems using only linear and integer variables. Moreover, there is a computational benefit in using PWL functions that have the least possible number of segments. This work proposes a novel hierarchical mixed integer linear programming (MILP) formulation that identifies a continuous PWL approximation with minimum number of linear segments for a given target maximum error. The proposed MILP formulation also identifies the solution with the least maximum error among the solutions with minimum number of segments. Then, this work proposes a fast iterative algorithm that identifies non necessarily continuous PWL approximations by solving O(S log N) linear programming (LP) problems, where N is the number of data points and S is the minimum number of segments in the non necessarily continuous case. This work demonstrates that tight bounds for the MILP problem can be derived from these approximations. Next, a fast algorithm is introduced to transform a non necessarily continuous PWL approximation into a continuous one. Finally, the tight bounds and the continuous PWL approximations are used to tighten and warm start the MILP problem. The tightened formulation is shown in experimental results to be more efficient, especially for large data sets, with a solution time that is up to two orders of magnitude less than the existing literature.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

The value of concentrating solar power in ancillary services markets

Ancillary services, such as spinning reserves, can provide grid reliability and contribute to profitability of an energy resource. We exercise an existing dispatch optimization model to estimate the profitability of a concentrating solar power plant by incorporating the sale of spinning reserves in the ancillary service market using the National Renewable Energy Laboratory's System Advisor Model to simulate operations within a 72-h rolling horizon framework. Assuming a price-taker approach with day-ahead energy and spinning reserve prices from both the California Independent System Operator and the Electricity Reliability Council of Texas, we find that selling spinning reserves in addition to electric energy increases plant profitability by up to 7% with perfect knowledge of day-ahead pricing and solar resource availability. Here, this finding suggests that spinning reserve markets provide significant value streams to concentrating solar power plants that can leverage thermal energy storage to offer reliable production in the short-to-medium term.

14 SOLAR ENERGY↗
DOE OSTI2022

North Carolina Water Utility Builds Resilience with Distributed Energy Resources

As the frequency and duration of grid outages increase, backup power systems are becoming more important for ensuring that critical infrastructure continues to provide essential services. Most facilities rely on diesel generators, which may be ineffective during long outages owing to limited fuel supplies and high generator failure rates. Distributed energy resources such as solar, storage, and combined-heat-and-power systems, coupled with on-site biofuel production, offer an alternative source of on-site generation that can provide both cost savings and resilience (i.e., the ability to respond to catastrophic events with longer-term consequences). A mixed-integer linear program minimizes costs and maximizes resilience at a wastewater treatment plant in Wilmington, North Carolina. We find that the plant can reduce life-cycle energy costs by 3.1% through the installation of a hybrid combined-heat-and-power, photovoltaic, and storage system. When paired with existing diesel generators, this system can sustain full load for seven days while saving $664,000 over 25 years and reducing diesel fuel use by 48% compared with the diesel-only solution. This analysis informed a decision by the Cape Fear Public Utility Authority to allocate funds for the implementation of a combined-heat-and-power system at the wastewater treatment plant in fiscal year 2023. Finally, the benefits of deploying hybrid combined-heat-and-power technologies and the utilization of on-site biofuel production extend, on a national scale, to thousands of wastewater treatment facilities and other types of critical infrastructure.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

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↗
DOE OSTI2022

Building Load Control Using Distributionally Robust Chance-Constrained Programs with Right-Hand Side Uncertainty and the Risk-Adjustable Variants

Aggregation of heating, ventilation, and air conditioning (HVAC) loads can provide reserves to absorb volatile renewable energy, especially solar photo-voltaic (PV) generation. In this paper, we decide HVAC control schedules under uncertain PV generation, using a distributionally robust chance-constrained (DRCC) building load control model under two typical ambiguity sets: the moment-based and Wasserstein ambiguity sets. We derive mixed integer linear programming (MILP) reformulations for DRCC problems under both sets. Especially, for the Wasserstein ambiguity set, we use the right-hand side (RHS) uncertainty to derive a more compact MILP reformulation than the commonly known MILP reformulations with big-M constants. All the results also apply to general individual chance constraints with RHS uncertainty. Furthermore, we propose an adjustable chance-constrained variant to achieve tradeoff between the operational risk and costs. We derive MILP reformulations under the Wasserstein ambiguity set and second-order conic programming (SOCP) reformulations under the moment-based set. Using real-world data, we conduct computational studies to demonstrate the efficiency of the solution approaches and the effectiveness of the solutions. Summary of Contribution: The problem studied in this paper is motivated by a building load control problem that uses the aggregation of heating, ventilation, and air conditioning (HVAC) loads as flexible reserves to absorb uncertain solar photovoltaic (PV) generation. The problem is formulated as distributionally robust chance-constrained (DRCC) programs with right-hand side (RHS) uncertainty. In addition, we propose a risk-adjustable variant of the DRCC programs, where the risk level, instead of being predetermined, is treated as a decision variable. The paper aims to provide tractable reformulations and solution algorithms for both the (general) DRCC and the (general) adjustable DRCC models with RHS uncertainty.

97 MATHEMATICS AND COMPUTING↗