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Results for “Mixed-Integer Linear Program (MILP)”

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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67 records · Page 4
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DOE OSTI2017

Robust optimisation-based microgrid scheduling with islanding constraints

This paper proposes a robust optimization based optimal scheduling model for microgrid operation considering constraints of islanding capability. Our objective is to minimize the total operation cost, including generation cost and spinning reserve cost of local resources as well as purchasing cost of energy from the main grid. In order to ensure the resiliency of a microgrid and improve the reliability of the local electricity supply, the microgrid is required to maintain enough spinning reserve (both up and down) to meet local demand and accommodate local renewable generation when the supply of power from the main grid is interrupted suddenly, i.e., microgrid transitions from grid-connected into islanded mode. Prevailing operational uncertainties in renewable energy resources and load are considered and captured using a robust optimization method. With proper robust level, the solution of the proposed scheduling model ensures successful islanding of the microgrid with minimum load curtailment and guarantees robustness against all possible realizations of the modeled operational uncertainties. Numerical simulations on a microgrid consisting of a wind turbine, a PV panel, a fuel cell, a micro-turbine, a diesel generator and a battery demonstrate the effectiveness of the proposed scheduling model.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2017

Sequential Service Restoration for Unbalanced Distribution Systems and Microgrids

The resilience and reliability of modern power systems are threatened by increasingly severe weather events and cyber-physical security events. An effective restoration methodology is desired to optimally integrate emerging smart grid technologies and pave the way for developing self-healing smart grids. In this paper, a sequential service restoration (SSR) framework is proposed to generate restoration solutions for distribution systems and microgrids in the event of large-scale power outages. The restoration solution contains a sequence of control actions that properly coordinate switches, distributed generators, and switchable loads to form multiple isolated microgrids. The SSR can be applied for three-phase unbalanced distribution systems and microgrids and can adapt to various operation conditions. Mathematical models are introduced for three-phase unbalanced power flow, voltage regulators, transformers, and loads. Furthermore, the SSR problem is formulated as a mixed-integer linear programming model, and its effectiveness is evaluated via the modified IEEE 123 node test feeder.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

A Flexible Operation of Distributed Generation in Distribution Networks With Dynamic Boundaries

Distributed generators performing black start to form isolated microgrids offer a flexible and resilient solution to service restoration in distribution systems. Employing the dynamic microgrid concept, distributed generators can form isolated microgrids by changing their physical boundaries through smart switches and conventional circuit breakers. However, the flexibility of distributed generators has not been thoroughly investigated and utilised in existing works. To address this issue, this letter presents a new model to the reconfiguration formulation in active distribution networks considering different operation modes of distributed generators. Compared with the existing models, this study provides a new formulation supporting different DGs' operation modes and fully making use of their flexibility. Illustrative results on IEEE 34-test systems verify the effectiveness of the proposed model.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

A Multi-Parametric optimization approach for bilevel mixed-integer linear and quadratic programming problems

Optimization problems involving two decision makers at two different decision levels are referred to as bi-level programming problems. Herein, we present novel algorithms for the exact and global solution of two classes of bi-level programming problems, namely (i) bi-level mixed-integer linear programming problems (B-MILP) and (ii) bi-level mixed-integer convex quadratic programming problems (B-MIQP) containing both integer and bounded continuous variables at both optimization levels. Based on multi-parametric programming theory, the main idea is to recast the lower level problem as a multi-parametric programming problem, in which the optimization variables of the upper level problem are considered as bounded parameters for the lower level. The resulting exact multi-parametric mixed-integer linear or quadratic solutions are then substituted into the upper level problem, which can be solved as a set of single-level, independent, deterministic mixed-integer optimization problems. Extensions to problems including right-hand-side uncertainty on both lower and upper levels are also discussed. Finally, computational implementation and studies are presented through test problems.

42 ENGINEERING↗
DOE OSTI2022

A parametric approach to identify synergistic domains of process intensification for reactive separation

Process intensification aims to combine multiple tasks within multi-functional units to drastically improve economic, energy or sustainability metrics of a chemical process. Limited work exists to systematically identify the synergistic domains where intensification outperforms its nonintensified counterpart. In this work, we computationally derive the synergistic domains of a reactive separation system. Specifically, we first postulate general models for both intensified and nonintensified systems. We use these models to generate data to train a ReLU-type artifical neural network (ANN). Further, the trained ReLU-NN model is formulated as a multi-parametric mixed-integer linear program (mp-MILP), and the critical regions of this mp-MILP define the synergistic feasible domains of intensification. We have derived these synergistic domains of vapor–liquid equilibrium (VLE)-based reactive separation for several industrial applications. These synergistic domains enable quick screening of properties that favor intensification.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Dispatch optimization of concentrating solar power with utility-scale photovoltaics

Concentrating solar power (CSP) tower technologies capture thermal radiation from the sun utilizing a field of solar-tracking heliostats. When paired with inexpensive thermal energy storage (TES), CSP technologies can dispatch electricity during peak-market-priced hours, day or night. The cost of utility-scale photovoltaic (PV) systems has dropped significantly in the last decade, resulting in inexpensive energy production during daylight hours. The hybridization of PV and CSP with TES systems has the potential to provide continuous and stable energy production at a lower cost than a PV or CSP system alone. Hybrid systems are gaining popularity in international markets as a means to increase renewable energy portfolios across the world. Typically, CSP-PV hybrid systems have been evaluated using either monthly averages of hourly PV production or scheduling algorithms that neglect the time-of-production value of electricity in the market. To more accurately evaluate a CSP-PV-battery hybrid design, we develop a profit-maximizing mixed-integer linear program ($\mathcal{H}$) that determines a dispatch schedule for the individual sub-systems with a sub-hourly time fidelity. We introduce the mathematical formulation of such a model and show that it is computationally expensive to solve. To improve model tractability and reduce solution times, we offer techniques that: (1) reduce the problem size, (2) tighten the linear programming relaxation of ($\mathcal{H}$) via reformulation and the introduction of cuts, and (3) implement an optimization-based heuristic (that can yield initial feasible solutions for (($\mathcal{H}$) and, at any rate, yields near-optimal solutions). Applying these solution techniques results in a 79% improvement in solve time, on average, for our 48-h instances of (($\mathcal{H}$); corresponding solution times for an annual model run decrease by as much as 93%, where such a run consists of solving 365 instances of (($\mathcal{H}$), retaining only the first 24 h' worth of the solution, and sliding the time window forward 24 h. We present annual system metrics for two locations and two markets that inform design practices for hybrid systems and lay the groundwork for a more exhaustive policy analysis. A comparison of alternative hybrid systems to the CSP-only system reflects that hybrid models can almost double capacity factors while resulting in a 30% improvement related to various economic metrics.

14 SOLAR ENERGY↗
DOE OSTI2025

Mixed-Integer Linear Programming Formulation with Embedded Machine Learning Surrogates for the Design of Chemical Process Families

In previous work, we introduced process family design. The main idea is to design a platform of common elements, and, allowing us to capture additional cost savings, simultaneously design a family of processes, and reducing both engineering and deployment timelines. We formulate this as an optimization problem, specifically a nonlinear generalized disjunctive program (GDP). We have proposed two approaches for reformulating and solving this problem: one based on full-discretization of the design space and one that uses Machine Learning (ML) surrogates to replace the nonlinear process models. Using ML surrogates to predict required system costs and performance indicators allows us to reformulate the nonlinearities in the GDP generate an efficient MILP formulation. In this work, we apply the ML surrogate approach to two case studies. One case study involves designing a family of carbon capture systems to cover a set of different flue gas flow rates and inlet CO 2 concentrations, where we consider the absorber and stripper as common unit module types. The second case study focuses on a water-desalination process, where we design a family of these processes for a variety of salt concentrations and flow rates. In both of these case studies, we demonstrate a scalable optimization approach that enables the design of multiple processes simultaneously, reducing the time-to-market and overall costs by maximizing the cost savings due to both economies of scale and economies of numbers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

PDPTW-DB: MILP-Based Offline Route Planning for PDPTW with Driver Breaks

The Pickup and Delivery Problem with Time Windows (PDPTW) involves optimizing routes for vehicles to meet pickup and delivery requests within specific time constraints, a challenge commonly faced in logistics and transportation. Microtransit, a flexible and demand-responsive service using smaller vehicles within defined zones, can be effectively modeled as a PDPTW. Yet, the need for driver breaks—a key human constraint—is frequently overlooked in PDPTW solutions, despite being necessary for regulatory compliance. This study presents a novel mixed-integer linear programming formulation for the Pickup and Delivery Problem with Time Windows and Driver Breaks (PDPTW-DB). To the best of our knowledge this formulation is the first to consider mandatory periodic driver breaks within optimized Microtransit routes. The proposed model incorporates regulatory compliant break scheduling directly within the vehicle routing optimization framework. By considering driver break requirements as an integral component of the optimization process, rather than as a post-processing step, the model enables the generation of routes that respect hours of service regulations while minimizing operational costs. This integrated approach facilitates the generation of schedules that are operationally efficient and prioritize driver welfare through driver breaks. We work with a public transit agency from the southern USA, and highlight the specific nuances of driver break optimization, and present a Pickup and Delivery Problem with Time Windows formulation for optimizing Microtransit operations and scheduling driver breaks. We validate our approach using real-world data from the transit agency. Our results validate our formulation in producing cost-effective, and regulation-compliant solutions.

Applied Computing, Transportation↗
DOE OSTI2017

An efficient MILP framework for integrating nonlinear process dynamics and control in optimal production scheduling calculations

The emphasis currently placed on enterprise-wide decision making and optimization has led to an increased need for methods of integrating nonlinear process dynamics and control information in scheduling calculations. The inevitable high dimensionality and nonlinearity of first-principles dynamic process models makes incorporating them in scheduling calculations challenging. In this work, we describe a general framework for deriving data-driven surrogate models of the closed-loop process dynamics. Focusing on Hammerstein–Wiener and finite step response (FSR) model forms, we show that these models can be (exactly) linearized and embedded in production scheduling calculations. The resulting scheduling problems are mixed-integer linear programs with a special structure, which we exploit in a novel and efficient solution strategy. A polymerization reactor case study is utilized to demonstrate the merits of this method. Finally, our framework compares favorably to existing approaches that embed dynamics in scheduling calculations, showing considerable reductions in computational effort.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2018

Toward a MILP Modeling Framework for Distribution System Restoration

Large-scale blackouts and extreme weather events in recent decades raise the concern for improving the resilience of electric power infrastructures. Distribution service restoration (DSR), a fundamental application in outage management systems, allows restoration solutions for system operators when power outages happen. As distribution generators (DGs) and remotely controllable devices are increasingly installed in distribution systems, an advanced DSR framework is critical to perform optimally coordinated restoration that can achieve maximal restoration performance. This work introduces a DSR modeling framework, which can generate optimal switching sequences and estimated time of restoration in the presence of remotely controllable switches, manually operated switches, and dispatchable DGs. Two mathematical models, a variable time step model and a fixed time step model, are presented and compared. The proposed models are formulated as a mixed-integer linear programming model, and their effectiveness is evaluated via the IEEE 123 node test feeder.

24 POWER TRANSMISSION AND DISTRIBUTION↗
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 OSTI2020

Dynamic Optimal Dispatch of Energy Systems with Intermittent Renewables and Damage Model

With the increasing penetration of intermittent renewable energy sources into the grid, there is a growing need for process systems-based strategies that integrate dispatchable and variable energy systems for supplying the demand while maintaining grid reliability. The proposed framework corresponds to a dynamic mixed-integer linear programming optimization approach that integrates coal-fired and natural gas-fired power plants, NaS batteries for energy storage, and solar/wind energy to supply the demand. This optimization approach considers an economic goal and constraints to provide power balance while maintaining the overall damage of the natural gas combined cycle (NGCC) power plant drum under a maximum stress as well as avoiding the overheating of the NGCC superheater and reheater. Renewable curtailment levels are also retained at minimum levels. Case studies are analyzed considering different loads and renewable penetration levels. The results show that the demand was met for all cases. Grid flexibility was mostly provided by the NGCC, while the batteries were used sparingly. In addition, considering a CO 2 equivalent analysis, the environmental performance was intrinsically connected to grid flexibility and the level of renewable penetration. Stress analysis results reinforced the necessity for an equipment health-related constraint.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Strengthened MILP formulation for certain gas turbine unit commitment problems

In this study, we derive a strengthened MILP formulation for certain gas turbine unit commitment problems, in which the ramping rates are no smaller than the minimum generation amounts. This type of gas turbines can usually start-up faster and have a larger ramping rate, as compared to the traditional coal-fired power plants. Recently, the number of this type of gas turbines increases significantly due to affordable gas prices and their scheduling flexibilities to accommodate intermittent renewable energy generation. In this study, several new families of strong valid inequalities are developed to help reduce the computational time to solve these types of problems. Meanwhile, the validity and facet-defining proofs are provided for certain inequalities. Finally, numerical experiments on a modified IEEE 118-bus system and the power system data based on recent studies verify the effectiveness of applying our formulation to model and solve this type of gas turbine unit commitment problems, including reducing the computational time to obtain an optimal solution or obtaining a much smaller optimality gap, as compared to the default CPLEX, when the time limit is reached with no optimal solutions obtained.

24 POWER TRANSMISSION AND DISTRIBUTION↗