Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Integer programming”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Efficient Topology Design Algorithms for Power Grid Stability

The dynamic response of power grids to small disturbances influences their overall stability. This letter examines the effect of network topology on the linearized time-invariant dynamics of electric power systems. The proposed framework utilizes H 2 -norm based stability metrics to study the optimal placement of lines on existing networks as well as the topology design of new networks. The design task is first posed as an NP-hard mixed-integer nonlinear program (MINLP) that is exactly reformulated as a mixed-integer linear program (MILP) using McCormick linearization. To improve computation time, graph-theoretic properties are exploited to derive valid inequalities (cuts) and tighten bounds on the continuous optimization variables. Moreover, a cutting plane generation procedure is put forth that is able to interject the MILP solver and augment additional constraints to the problem on-the-fly. Finally, the efficacy of our approach in designing optimal grid topologies is demonstrated through numerical tests on the IEEE 39-bus network.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Evaluation of Horizon of Viability Optimization Engine for Sustained Power to Critical Infrastructure: Preprint

In the aftermath of increasingly frequent catastrophic events, a typical scenario is Critical Infrastructure (CI) units being supported by available backup sources with a weak power grid that can be intermittent or absent. Such a scenario is significantly challenging in the sense of reliable supply of power to CI units. In this article, an intelligent optimization scheme termed as Horizon of Viability (HoV) engine is developed to guarantee the viability of a sustained reliable supply of power to the CI units over a time-horizon. The proposed HoV engine generates a cost-optimal portfolio of the locally available generation sources and the loads over a time horizon using a mixed-integer convex programming problem. A Controller hardware-in-the-loop (CHIL) platform is developed to evaluate the control performance of the HoV engine. The experimental results corroborates the efficacy in maintaining the viability of the CI units after a grid interruption event. Further, the proposed HoV optimization scheme performs better compared to existing net-load management schemes in the literature.

disaster resiliency↗
DOE OSTI2025

A Fast Dynamic Internal Predictive Power Scheduling Approach for Power Management in Microgrids: Preprint

This paper presents a Dynamic Internal Predictive Power Scheduling (DIPPS) approach for optimizing power management in microgrids, particularly focusing on external power exchanges among diverse prosumers. DIPPS utilizes a dynamic objective function with a time-varying binary parameter to control the timing of power transfers to the external grid, facilitated by efficient usage of energy storage for surplus renewable power. The microgrid power scheduling problem is modeled as a mixed-integer nonlinear programming (MINLP-PS) and subsequently transformed into a mixed-integer linear programming (MILPPS) optimization through McCormick's relaxation to reduce computational complexity. A predictive window window with 6 data points is solved at an average of 0.92s, a 97.6% improvement over the 38.27s required for the MINLP-PS formulation, implying the numerical feasibility of the DIPPS approach for real-time implementation. Finally, the approach is validated against a static objective using real-world load data across three case studies with different time-varying parameters, demonstrating the ability of DIPPS to optimize power exchanges and efficiently utilize distributed resources while shifting the external power transfers to specified time durations.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Proactive Operations and Investment Planning via Stochastic Optimization to Enhance Power Systems’ Extreme Weather Resilience

We present scalable stochastic optimization approaches for improving power systems’ resilience to extreme weather events. We consider both proactive redispatch and transmission line hardening as alternatives for mitigating expected load shed due to extreme weather, resulting in large-scale stochastic linear programs (LPs) and mixed-integer linear programs (MILPs). We solve these stochastic optimization problems with progressive hedging (PH), a parallel, scenario-based decomposition algorithm. Our computational experiments indicate that our proposed method for enhancing power system resilience can provide high-quality solutions efficiently. With up to 128 scenarios on a 2,000-bus network, the operations (redispatch) and investment (hardening) resilience problems can be solved in approximately 6 min and 2 h of wall-clock time, respectively. Additionally, we solve the investment problems with up to 512 scenarios, demonstrating that the approach scales very well with the number of scenarios. Moreover, the method produces high quality solutions that result in statistically significant reductions in expected load shed. Our proposed approach can be augmented to incorporate a variety of other operational and investment resilience strategies, or a combination of such strategies.

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↗
NASA NTRS1991

RSM 1.0 user's guide: A resupply scheduler using integer optimization

The Resupply Scheduling Model (RSM) is a PC based, fully menu-driven computer program. It uses integer programming techniques to determine an optimum schedule to replace components on or before a fixed replacement period, subject to user defined constraints such as transportation mass and volume limits or available repair crew time. Principal input for RSJ includes properties such as mass and volume and an assembly sequence. Resource constraints are entered for each period corresponding to the component properties. Though written to analyze the electrical power system on the Space Station Freedom, RSM is quite general and can be used to model the resupply of almost any system subject to user defined resource constraints. Presented here is a step by step procedure for preparing the input, performing the analysis, and interpreting the results. Instructions for installing the program and information on the algorithms are given.

Viterna, Larry A.↗
DOE OSTI2021

Joint Topology Identification and State Estimation in Unobservable Distribution Grids

Many distribution system operations (e.g., state estimation, control, fault detection/localization) rely on the assumption that the underlying topology is accurately defined. In general, topology identification is a challenging problem in distribution systems as these systems are unobservable with a very limited number of available measurements. In this paper, we tackle this problem by designing a compressive sensing framework that jointly estimates the systems states and network topology via an integrated mixed integer nonlinear program (MINLP) formulation. Here, two reformulations of the original MINLP problems are investigated. Firstly, in order to remove the nonlinearity in the MINLP formulation, a mixed integer linear programming (MILP) problem that employs auxiliary variables is derived. Furthermore, to achieve a faster solution, convex relaxation of the original formulation is derived. Finally, using a Markovian model for topology changes, prior information about system topology is used to improve topology identification particularly when a limited amount of measurements is available. Simulation results on IEEE 37-bus test feeder and IEEE 123-bus test feeder illustrate the efficiency and scalability of the proposed approaches from both state estimation and topology identification point of view (even with 30% of available data).

42 ENGINEERING↗
DOE OSTI2020

Learning to Solve Large-Scale Security-Constrained Unit Commitment Problems

Security-constrained unit commitment (SCUC) is a fundamental problem in power systems and electricity markets. In practical settings, SCUC is repeatedly solved via mixed-integer linear programming (MIP), sometimes multiple times per day, with only minor changes in input data. In this work, we propose a number of machine learning techniques to effectively extract information from previously solved instances in order to significantly improve the computational performance of MIP solvers when solving similar instances in the future. Based on statistical data, we predict redundant constraints in the formulation, good initial feasible solutions, and affine subspaces where the optimal solution is likely to lie, leading to a significant reduction in problem size. Computational results on a diverse set of realistic and large-scale instances show that using the proposed techniques, SCUC can be solved on average 4.3 times faster with optimality guarantees and 10.2 times faster without optimality guarantees, with no observed reduction in solution quality. Out-of-distribution experiments provide evidence that the method is somewhat robust against data-set shift. Summary of Contribution. The paper describes a novel computational method, based on a combination of mixed-integer linear programming (MILP) and machine learning (ML), to solve a challenging and fundamental optimization problem in the energy sector. The method advances the state-of-the-art, not only for this particular problem, but also, more generally, in solving discrete optimization problems via ML. We expect that the techniques presented can be readily used by practitioners in the energy sector and adapted, by researchers in other fields, to other challenging operations research problems that are solved routinely.

Machine Learning↗
DOE OSTI2025

Planning Amidst Uncertainty: Identifying Core CCS Infrastructure Robust to Storage Uncertainty

Carbon Capture and Storage (CCS) is a critical technology for reducing anthropogenic CO2 emissions, but its large-scale deployment is complicated by uncertainties in geological storage performance. These uncertainties pose significant financial and operational risks, as underperforming storage sites can lead to costly infrastructure modifications, inefficient pipeline routing, and economic shortfalls. To address this challenge, we propose a novel optimization workflow that is based on mixed-integer linear programming and explicitly integrates probabilistic modeling of storage uncertainty into CCS infrastructure design. This workflow generates multiple infrastructure scenarios by sampling storage capacity distributions, optimally solving each scenario using a mixed-integer linear programming model, and aggregating results into a heatmap to identify core infrastructure components that have a low likelihood of underperforming. A risk index parameter is introduced to balance trade-offs between cost, CO2 processing capacity, and risk of underperformance, allowing stakeholders to quantify and mitigate uncertainty in CCS planning. Applying this workflow to a CCS dataset from the US Department of Energy’s Carbon Utilization and Storage Partnership project reveals key insights into infrastructure resilience. Reducing the risk index from 15% to 0% is observed to lead to an 83.7% reduction in CO2 processing capacity and a 77.1% decrease in project profit, quantifying the trade-off between risk tolerance and project performance. Furthermore, our results highlight critical breakpoints, where small adjustments in the risk index produce disproportionate shifts in infrastructure performance, providing actionable guidance for decision-makers. Unlike prior approaches that aimed to cheaply repair underperforming infrastructure, our workflow constructs robust CCS networks from the ground up, ensuring cost-effective infrastructure under storage uncertainty. These findings demonstrate the practical relevance of incorporating uncertainty-aware optimization into CCS planning, equipping decision-makers with a tool to make informed project planning decisions.

Olson, Daniel↗
DOE OSTI2021

The nth-plant scenario for blended feedstock conversion and preprocessing nationwide: biorefineries and depots

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. Defining the future location and supply logistics of conversion plants is imperative to ultimately transform the nation’s renewable biomass resources into cost-competitive, high-performance feedstock for production of biofuels and bioproducts. Since the US has put restrictions on production levels of conventional biofuels from edible resources, the nation needs to plan for the widespread accessibility and development of the cellulosic biofuel scenario. Conventional feedstock supply systems will be unable to handle cellulosic biomass nationwide, making it essential to expand the industry with an advanced feedstock supply system incorporating a distributed network of preprocessing depots and conversion plants, or biorefineries. Current studies are mostly limited to designing supply systems for specific regions of the country. We developed a national database with potential locations for depots and biorefineries to meet the nation’s target demand of cellulosic biofuel. Blended feedstock with switchgrass and corn stover (harvested by either a two- or three-pass method) are considered in a Mixed Integer Linear Programming model to deliver on-spec biomass that considers both, a desired quantity and quality at the biorefinery. A total delivered feedstock cost that is less than $79.07/dt (2016$) is evaluated for years 2022, 2030, and 2040. In 2022, 124 depots and 59 biorefineries could be supplied with 42.8 million dt of corn stover and switchgrass. In 2030 and 2040, the total accessible biomass could increase to 215% and 393% respectively when compared to 2022. However, an $8/dry tons reduction in targeted delivery cost could reduce total accessible biomass by 67%. Kansas, Nebraska, South Dakota and Texas were identified as potential states with a strong biofuel economy given that they had six or more biorefineries located in all scenarios. In some scenarios, Colorado, Alabama, Georgia, Minnesota, Mississippi and South Carolina would greatly benefit from a depot network as these could only deliver to a biorefinery in a nearby state. To elaborate the impact of a nationwide consideration, the findings were compared with existing literature for different US regions. We also present results for biorefinery capacities that are double, triple, and quadruple in size.

09 BIOMASS FUELS↗
DOE OSTI2023

Bi-Level Adaptive Storage Expansion Strategy for Microgrids Using Deep Reinforcement Learning

Battery energy storage (BES) is a versatile resource for the secure and economic operation of microgrids (MGs). Prevailing stochastic optimization-based approaches for BES expansion planning for MGs are computationally complicated. This work proposes a data-driven bi-level multi-period BES expansion planning framework to determine the siting, sizing, and timing of BES installations. The proposed planning framework unifies deep reinforcement learning (DRL) and linear programming, thereby decoupling the determinations for the integer and continuous decision variables in two time scales, respectively. In the upper level, a rainbow DRL agent with quantile regression is trained to provide dynamic planning policies to accommodate stochastic renewable energy resources (RESs), load, and battery price changes efficiently. Further, the lower level computes the optimal operation of MGs with frequency constraints to hedge the islanding contingency. The two levels communicate with one another by exchanging storage configuration and operating expenses in order to accomplish the shared goal of minimizing investment and operation costs. Comparative case studies on an MG are carried out to demonstrate the superiority of the proposed DRL-based solution to the mixed-integer linear programming counterpart on efficiency, scalability, and adaptability.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Solar Field Layout and Aimpoint Strategy Optimization

The existing methods that determine heliostat aiming strategies for concentrating solar power (CSP) central receiver plants typically use heuristics and/or are computationally expensive, and they lack flexibility for different desired flux profiles and receiver geometries. Because of the interaction between layout and aimpoint strategy, considering the former without accounting for the latter may yield solutions with superfluous heliostats that cannot be used efficiently without compromising receiver flux constraints. To that end, we develop a software decision tool that uses innovative optimization methods to both optimize aimpoint strategies and improve candidate layouts for the solar collection field of a CSP central receiver plant. A CSP plant’s effectiveness relies on the optical efficiency of the solar field, which may be limited by losses due to (i) the cosine effect, (ii) atmospheric attenuation, (iii) interference (i.e., shading and blocking) between heliostats, (iv) spillage as a result of heliostat positioning and geometry, and (iv) some heliostats’ inability to direct irradiance to the receiver without damage due to excessive thermal flux. The goal of this work is to obtain optimized aiming strategies and improved solar field layouts that reduce capital cost and increase field optical efficiency and utilization, while meeting the power requirements of a given CSP receiver design. We formulate the aimpoint optimization problem as a mixed-integer linear programming model, which we then decompose into submodels that we solve in parallel. The decomposition subdivides the solar field into sections, and aimpoint strategies for each section are obtained independently of the others. To improve existing layouts, we develop a utilization-weighted efficiency metric that we use to relocate heliostats to sections of the solar field with similar efficiency and higher utilization. Finally, to connect our software to high-fidelity flux models, we develop a Python application programming interface for SolarPILOT, a mature software package that characterizes solar field performance and generates the heliostat layouts and flux maps that serve as input to our models.

14 SOLAR ENERGY↗
DOE OSTI2023

Resilient Distribution System Restoration with Equitable Load Shedding

A methodology is proposed for the improvement of electric distribution system resilience to high-impact, low-probability catastrophic events. An approach for dynamic network reconfiguration and coordination of distributed energy resources is introduced to assist in restoration efforts. The problem is formulated as a mixed-integer linear program that minimizes generation costs, the cost of lost load, and costs associated with equitable load shedding, while respecting operational limits of generation, loads, and the network. Constraints are imposed on binary switching variables to ensure equitable load shedding in emergency situations. Numerical validation of the proposed approach is conducted on an example distribution feeder, and case studies are performed to analyze the impact of various parameters in the optimization problem formulation.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Optimal PMU Restoration for Power System Observability Recovery After Massive Attacks

Cyber-physically resilient power system operation requires rapid recovery of situational awareness after disastrous scenarios such as massive cyber attacks. In this article, the concept of optimal sequential restoration of Phasor Measurement Units is introduced, aiming at rapid recovery of power system observability in post-attack scenarios. Additionally, the observability recovery problem is formulated as a Mixed Integer Linear Programming problem to maximize the cumulative observability level gained over time during the restoration process. Three alternative objective functions-maximizing the number of observable buses, the number of observable branches, and the total amount of observable power flow-are considered. The effectiveness of the proposed optimal strategy is verified by comparing it with heuristic approaches on the IEEE 57-bus system.

24 POWER TRANSMISSION AND DISTRIBUTION↗
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

Optimal Strategies for Hybrid Battery‐Storage Systems Design

As stationary hybrid energy‐storage systems (HESS) for power systems applications have recently drawn interest due to their enhanced performance and decreasing cost, developing systematic approaches for HESS design while considering controls is gaining traction. Herein, a method is presented to optimally design hybrid battery storage by proposing a mathematical modeling framework, formulated as a mixed integer linear programming model. The optimization is capable of handling multiple subsystems of batteries, considering their economic and technological performance. Decisions involve sizing of the batteries, optimal temporal and strategic dispatch to end uses, and energy sources for charging each battery. The applicability of the model is tested on four case studies for three battery chemistries representing distinct objectives: high‐power, high‐energy, and second life. Compared to traditionally designed battery storage with a homogeneous battery, optimally designed hybrid systems can save 12%–26% of system costs, depending on the nature of the dispatch profile. Findings point to design preference toward the second life battery supplemented with some high‐power or high‐energy battery capacity, or both. With the utilized electricity price structure, customers can experience approximately 10%–35% reduction in their bills.

Koleva, Mariya↗
DOE OSTI2021

Switching Device-Cognizant Sequential Distribution System Restoration

This paper presents an optimization framework for sequential reconfiguration using an assortment of switching devices and repair process in distribution system restoration. Compared to existing studies, this paper considers types, capabilities and operational limits of different switching devices, making it applicable in practice. We develop a novel multi-phase method to find the optimal sequential operation of various switching devices and repair faulted areas. We consider circuit breakers, reclosers, sectionalizers, load breaker switches, and fuses. The switching operation problem is decomposed into two mixed-integer linear programming (MILP) subproblems. The first subproblem determines the optimal network topology and estimates the number of steps to reach that topology, while the second subproblem generates a sequence of switching operations to coordinate the switches. For repairing the faults, we design an MILP model that dispatches repair crews to clear faults and replace melted fuses. After clearing a fault, we update the topology of the network by generating a new sequence of switching operations, and the process continues until all faults are cleared. To improve the computational efficiency, a network reduction algorithm is developed to group line sections, such that only switchable sections are present in the reduced network. The proposed method is validated on the IEEE 123-bus and 8500-bus systems.

distribution system↗
DOE OSTI2021

Risk-averse optimization for resilience enhancement of complex engineering systems under uncertainties

With the growth of complexity and extent, large scale interconnected network systems, e.g., transportation networks or infrastructure networks, become more vulnerable to external disturbances. Hence, managing potential disruptive events during the design, operating, and recovery phase of an engineered system and therefore improving the system’s resilience is an important yet challenging task. Here, to ensure system resilience after the occurrence of failure events, this study proposes a mixed-integer linear programming (MILP) based restoration framework using heterogeneous dispatchable agents. The scenario-based stochastic optimization (SO) technique is adopted to deal with the inherent uncertainties imposed on the recovery process from nature. Moreover, different from conventional SO using deterministic equivalent formulations, the CVaR risk measure is implemented for this study because of the temporal sparsity of the decision making in applications such as the recovery from extreme events. The resulting restoration framework involves a large-scale MILP problem and thus an adequate decomposition technique i.e. modified Lagrangian dual decomposition, is also employed to achieve tractable computational complexity. Case study results based on the IEEE 37-bus test feeder demonstrate the benefits of using the proposed framework for resilience improvement as well as the advantages of adopting SO formulations.

42 ENGINEERING↗