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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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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

A Model Predictive Control Based Generator Start-Up Optimization Strategy for Restoration With Microgrids as Black-Start Resources

Microgrids (MGs) can operate in an islanded mode and serve as black-start resources for power system restoration (PSR). Here, a model predictive control (MPC) based generator start-up optimization strategy for PSR is proposed utilizing MGs as black-start resources. First, the generator start-up sequence (GSUS) optimization is formulated as a mixed integer linear programming. Then, the uncertainties of MG black-start resources (MBSRs) are modeled by discretizing the probability distribution of the forecast errors, and representative scenarios for MBSRs extracted by formulating the probability mass transportation problem. Third, the generator start-up optimization strategy considering MBSRs is proposed utilizing the MPC technique, in which the optimization objective is to maximize the energy capability of the power systems and minimize the load curtailment of the MGs in each looking-ahead interval. Simulations on the IEEE 118 bus system with MGs and Zhejiang provincial power system in China verify that the introduced strategy for PSR can successfully restore the power system and effectively determine the optimal GSUS.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Optimal Membrane Cascade Design for Critical Mineral Recovery Through Logic-based Superstructure Optimization

Critical minerals and rare earth elements play an important role in our climate change initiatives, particularly in applications related with energy storage. Here, we use discrete optimization approaches to design a process for the recovery of Lithium and Cobalt from battery recycling, through membrane separation. Our contribution involves proposing a Generalized Disjunctive Programming (GDP) model for the optimal design of a multistage diafiltration cascade for Li-Co separation. By solving the resulting nonconvex mixed-integer nonlinear program model to global optimality, we investigated scalability and solution quality variations with changes in the number of stages and elements per stage. Results demonstrate the computational tractability of the nonlinear GDP formulation for design of membrane separation processes while opening the door for decom-position strategies for multicomponent separation cascades. Future work aims to extend the GDP formulation to account for stage installation and explore various decomposition techniques to enhance solution efficiency.

Ovalle, Daniel↗
DOE OSTI2019

Joint Fleet Sizing and Charging System Planning for Autonomous Electric Vehicles

This paper studies the joint fleet sizing and charging system planning problem for a company operating a fleet of autonomous electric vehicles (AEVs) for passenger and goods transportation. Most of the relevant published papers focus on intracity scenarios and adopt heuristic approaches, e.g., agent based simulation, which do not guarantee optimality. In contrast, we propose a mixed integer linear programming model for intercity scenarios. This model incorporates comprehensive considerations of 1) limited AEV driving range; 2) optimal AEV routing and relocating operations; 3) time-varying origin-destination transport demands; and 4) differentiated operation cost structure of passenger and goods transportation. The proposed model can be computational expensive when the scale of the transportation network is large. We then exploit the structure of this program to expedite its solution. Numerical experiments are conducted to validate the proposed method. Our experimental results show that AEVs in passenger and goods transportation have remarkable planning and operation differences. We also demonstrate that intelligent routing and relocating operations, charging system and vehicle parameters, e.g., charging power, battery capacity, driving speed etc., can significantly affect the economic efficiency and the planning results of an AEV fleet.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2016

The impact of short-term stochastic variability in solar irradiance on optimal microgrid design

This paper proposes a new methodology to capture the impact of fast moving clouds on utility power demand charges observed in microgrids with photovoltaic (PV) arrays, generators, and electrochemical energy storage. It consists of a statistical approach to introduce sub-hourly events in the hourly economic accounting process. The methodology is implemented in the Distributed Energy Resources Customer Adoption Model (DER-CAM), a state of the art mixed integer linear model used to optimally size DER in decentralized energy systems. Results suggest that previous iterations of DER-CAM could undersize battery capacities. The improved model depicts more accurately the economic value of PV as well as the synergistic benefits of pairing PV with storage.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Optimization of harvest and logistics for multiple lignocellulosic biomass feedstocks in the northeastern United States

A mixed-integer linear programming model was developed to optimize the multiple biomass feedstock supply chains, including feedstock establishment, harvest, storage, transportation, and preprocessing. The model was applied for analyses of multiple biomass feedstocks at county level for 13 states in the northeastern United States. In the base case with a demand of 180,000 dry Mg/year of biomass, the delivered costs ranged from $\$67.90$ to $\$86.97$ per dry Mg with an average of $\$79.58$ /dry Mg. The biomass delivered costs by county were from $\$67.90$ to 150.81 per dry Mg across the northeastern U.S. Considered the entire study area, the delivered cost averaged $\$85.30$ /dry Mg for forest residues, $\$84.47$ /dry Mg for hybrid willow, $\$99.68$ for switchgrass and $\$97.87$ per dry Mg for Miscanthus. Seventy seven out of 387 counties could be able to deliver biomass at $84 per dry Mg or less a target set by US DOE by 2022. A sensitivity analysis was also conducted to evaluate the effects of feedstock availability, feedstock price, moisture content, procurement radius, and facility demand on the delivered cost. Lastly, our results showed that procurement radius, facility capacity, and forest residue availability were the most sensitive factors affecting the biomass delivered costs.

09 BIOMASS FUELS↗
DOE OSTI2024

A multi-objective optimization model for cropland design considering profit, biodiversity, and ecosystem services

More sustainable agricultural methods are needed to alleviate the decreases in biodiversity and ecosystem services that have occurred because of industrial agriculture. One such method is the inclusion of alternative crops into croplands that can support biodiversity, reduce erosion and chemical runoff, and sequester carbon in the soil. However, the question of where such crops should be planted to balance competing economic and environmental objectives remains open. To this end, we develop a mixed-integer quadratically constrained program to optimize the layout of a cropland considering economic, biodiversity, greenhouse gas emissions, and water quality objectives. We include spatially varying fertilization as a decision variable in addition to crop establishment location. We further include the effect of core area and edges between different crops on biodiversity. To demonstrate the applicability of the model, we apply it to an example field, showing how the optimal cropland design changes as a decision-maker prioritizes different objectives and as edges have different impacts on biodiversity.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Advanced Energy Storage Management in Distribution Network

With increasing penetration of distributed generation (DG) in the distribution networks (DN), the secure and optimal operation of DN has become an important concern. In this paper, an iterative mixed integer quadratic constrained quadratic programming model to optimize the operation of a three phase unbalanced distribution system with high penetration of Photovoltaic (PV) panels, DG and energy storage (ES) is developed. The proposed model minimizes not only the operating cost, including fuel cost and purchasing cost, but also voltage deviations and power loss. The optimization model is based on the linearized sensitivity coefficients between state variables (e.g., node voltages) and control variables (e.g., real and reactive power injections of DG and ES). To avoid slow convergence when close to the optimum, a golden search method is introduced to control the step size and accelerate the convergence. The proposed algorithm is demonstrated on modified IEEE 13 nodes test feeders with multiple PV panels, DG and ES. Numerical simulation results validate the proposed algorithm. Various scenarios of system configuration are studied and some critical findings are concluded.

linearization↗
DOE OSTI2022

Microgrid Assisted Design for Remote Areas

In this work, we present a three-stage multiobjective mixed-integer linear programming (MILP) for the optimal expansion planning and operation of isolated multienergy microgrids in remote areas. By selecting the optimal distributed generators (DGs) and energy storage systems (ESSs) mix selection, siting, sizing, and scheduling in the remote microgrid, the proposed model is targeted to minimize the annualized total cost of microgrids while enhancing the performance of the system, i.e., minimizing the voltage deviations and line power loss. To represent the electricity and heat flow between generation resources and various electrical, heating, and cooling loads in the isolated microgrid, linearized power flow, and heat flow constraints are employed in the proposed optimization model. The available capacity of DGs and ESSs are modeled as discrete constants instead of continuous variables for practical purpose. Numerical simulation results on a remote microgrid consisting of DGs, ESSs, and various loads validate the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Dispatch optimization of electric thermal energy storage within System Advisor Model

A stand-alone electric thermal energy storage (ETES) system converts low-value electricity into heat using resistance heating elements. During periods of high-value electricity, an ETES system uses a thermodynamic power cycle to convert stored thermal energy back to electricity. These dispatchable systems derive value from their ability to store energy when prices are low and generate electricity when prices are favorable, i.e., energy arbitrage. Consequently, dispatch optimization of system operations, through maximizing revenue subject to system constraints, is essential to evaluate the economic value of a particular system design. While stand-alone ETES systems offer potential advantages as dispatchable grid storage technologies, there is a lack of a neutral third-party, publicly available, open-source model to evaluate the performance, dispatch, and financial viability of these systems. To address this problem, we have developed a techno-economic model for stand-alone ETES systems, within National Renewable Energy Laboratory's (NREL's) System Advisor Model (SAM). We implement a mixed-integer linear program to determine an ETES optimal operating schedule that maximizes electricity sales less maintenance costs caused by operation and cycling given temporal-varying grid electricity prices. Our contributions include a mixed-integer linear program for energy arbitrage of an ETES system, an ETES performance model through a publicly-available software (i.e., SAM), and an exercise of our model through case studies that compare ETES operational strategies and annual financial metrics. With our dispatch optimization model, we were able to improve revenue by 20% compared to a myopic heuristic while reducing the operational cost of the ETES system through decreases in cycle starts, cycles per day, and heater starts.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Hybrid Imitation Learning for Real-Time Service Restoration in Resilient Distribution Systems

Self-healing capability is a critical factor for a resilient distribution system, which requires intelligent agents to automatically perform service restoration online, including network reconfiguration and reactive power dispatch. Here, the article proposes the imitation learning framework for training such an agent, where the agent will interact with an expert built based on the mixed-integer program to learn its optimal policy, and therefore significantly improve the training efficiency compared with exploration-dominant reinforcement learning (RL) methods. This significantly improved training efficiency makes the training problem under N-k scenarios tractable. A hybrid policy network is proposed to handle tie-line operations and reactive power dispatch simultaneously to further improve the restoration performance. The 33-bus and 119-bus systems with N-k disturbances are employed to conduct the training. The results indicate that the proposed method outperforms traditional RL algorithms such as the deep-Q network.

42 ENGINEERING↗
DOE OSTI2018

Predictively Coordinated Vehicle Acceleration and Lane Selection Using Mixed Integer Programming

Autonomous vehicle technology provides the means to optimize motion planning beyond human capacity. In particular, the problem of navigating multi-lane traffic optimally for trip time, energy efficiency, and collision avoidance presents challenges beyond those of single-lane roadways. For example, the host vehicle must simultaneously track multiple obstacles, the drivable region is non-convex, and automated vehicles must obey social expectations. Furthermore, reactive decision-making may result in becoming stuck in an undesirable traffic position. This paper presents a fundamental approach to these problems using model predictive control with a mixed integer quadratic program at its core. Lateral and longitudinal movements are coordinated to avoid collisions, track a velocity and lane, and minimize acceleration. Vehicle-to-vehicle connectivity provides a preview of surrounding vehicles’ motion. Simulation results show a 79% reduction in congestion-induced travel time and an 80% decrease in congestion-induced fuel consumption compared to a rule-based approach.

Dollar, Robert Austin↗
DOE OSTI2022

Data-Driven Generic Turbines for Distributed Wind Modeling, Optimization, and Economic Studies

As distributed energy resources (DER) become less expensive and more popular, utilities, project developers, and customers have an increasing need to model the performance of existing and proposed DER systems. Distributed wind has been shown to have widespread economic potential but is often represented by a simplified model in - or excluded from - DER modeling tools and studies. There is often no economic imperative to extend models and studies to give full consideration to distributed wind. We present a set of data-driven generic turbines derived from 16 years of annual distributed wind market survey data. The proposed methodology can be used to derive generic turbines from separate or updated data sets. Finally, a mixed-integer linear programming approach to optimal distributed wind project sizing is used to demonstrate the generic turbine models. Combined, these models and methods can reduce barriers to considering distributed wind in modeling tools and studies.

Reiman, Andrew P.↗
DOE OSTI2022

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

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.

25 ENERGY STORAGE↗
DOE OSTI2022

Rolling Optimization of Transmission Network Recovery and Load Restoration Considering Hybrid Wind-Storage System and Cold Load Pickup

A common solution to deal with the stochasticity introduced by fast-ramping wind power integration is to equip wind farms (WFs) with energy storage systems (ESSs) to formulate hybrid WF-ESSs. In addition to leveling off wind power fluctuations during normal operations, a hybrid WF-ESS can be a flexible power source to accumulate the power system restoration. In this paper, we propose a rolling optimization model for transmission network recovery and load restoration considering the contributions of WF-ESSs. The proposed model is formulated as a mixed integer linear programming problem that simultaneously optimizes the amount and location of restorable load blocks as well as the restoration lines. The cold load pickup features of interrupted loads considering the outage duration are modeled in detail. A chance-constrained method is employed to deal with the uncertainty of wind power, and a rolling horizon-based framework is adopted to reduce the influence of forecast error. Case studies are conducted on both New England 39-bus system and part of a provincial power system in China. The results show that the load restoration process can be significantly accelerated by employing the proposed method and contributions of hybrid WF-ESSs to power system restoration are validated.

chance-constrained optimization↗
DOE OSTI2024

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↗
DOE OSTI2023

Phase-based design of CO 2 capture, transport, and storage infrastructure via SimCCS 3.0

The design of optimal infrastructure is essential for the deployment of commercial and large-scale carbon capture and storage (CCS) technology. During the design process, it is important to consider CO 2 capture and storage locations and CO 2 transportation pipelines to minimize the total project cost. SimCCS, first introduced in 2009, is an integrated open-source tool to optimize CCS infrastructure. The core CCS infrastructure design problem in SimCCS is structured as a mixed-integer linear programming problem by selecting the optimal pipeline routes, searching CO 2 source capture and storage locations, and determining the corresponding CO 2 amounts to meet desired capture targets. Multiple important and practical features have been developed to the latest version of SimCCS, SimCCS 3.0 . One of these features is phase-based modeling which enables users to dynamically design the CCS infrastructure. We demonstrate the phased-based modeling capability using two CCS infrastructure optimization case studies. The results from these case studies reveal that the phase-based modeling capability in SimCCS is particularly useful to optimize the dynamic deployment of CCS projects.

54 ENVIRONMENTAL SCIENCES↗