Engineering Papers⌕ Search

SEARCH · Engineering Papers

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.

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

At least 325 records · Page 18
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 OSTI2019

A Cooperative Multi-Agent Deep Reinforcement Learning Framework for Real-Time Residential Load Scheduling

Internet-of-Things (IoT) enabled monitoring and control capabilities are enabling increasing numbers of household users with controllable loads to actively participate in smart grid energy management. Realizing an efficient real-time energy management system that takes advantage of these developments requires novel techniques for managing the increased complexity of the control action space in resolving multiple challenges such as the uncertainty in energy prices and renewable energy output along with the need to satisy physical grid constraints such as transformer capacity. Addressing these challenges, we develop a multi-household energy management framework for residential units connected to the same transformer and containing DERs such as PV, ESS and controllable loads. The goal of our framework is to schedule controllable household appliances and ESS such that the cost of procuring electricity from the utility over a horizon is minimized while physical grid constraints are satisfied at each scheduling step. Traditional energy management frameworks either perform global optimization to satisfy grid constraints but suffer from high computational complexity (for example Integer Program, Mixed Integer Programming frameworks and centralized reinforcement learning) or perform decentralized real-time energy management without satisfying global grid constraints (for example multi-agent reinforcement learning with no cooperation). In contrast, we propose a cooperative multiagent reinforcement learning (MARL) framework that i) operates in real-time, and ii) performs explicit collaboration to satisfy global grid constraints. The novelty in our framework is two fold. Firstly, our framework trains multiple independent learners (IL) for each household in parallel using historical data and performs real-time inferencing of control actions using the most recent system state. Secondly, our framework contains a low complexity knapsack based cooperation agent which combines the outputs of ILs to minimize cost while satisfying grid constraints. Simulation results show that our cooperative MARL approach achieves significant cost improvement over centralized reinforcement learning and day-ahead planning baselines. Moreover, our approach strictly satisfies physical constraints with no apriori knowledge of system dynamics while the baseline approaches have occasional violations. We also measure the training and inference time by ranging the number of households from 1 to 25. Results show that our cooperative MARL approach scales best among various approaches.

14 SOLAR ENERGY↗
DOE OSTI2019

Coordinated Planning Strategy for Integrated Energy Systems in a District Energy Sector

With the ever-growing integration of diverse distributed energy resources, modern district energy sectors are transitioning into integrated energy systems (IESs), which generally consist of various energy carriers such as electric power, natural gas, and heat. Instead of modeling individual energy carriers, the emergence of IESs requires comprehensive consideration of all involved energy systems in both planning and operation phases. This paper proposes a comprehensive planning strategy for a district energy sector to address the challenges of IES planning considering the coupling of power, gas, and heat systems. The proposed planning model contains an operational module that develops a steady-state optimal multi-energy flow (OMEF) for the IES considered and a multi-stage expansion module that optimizes the investment decisions. To efficiently solve the proposed planning model, which is formulated as a mixed-integer nonlinear programming problem, an improved generalized Benders decomposition algorithm that utilizes dynamic dual multipliers to improve the convergence speed is employed. The effectiveness of the proposed planning model and the feasibility of the improved Benders decomposition algorithm are verified in case studies.

coordinated planning↗
DOE OSTI2023

A Mixed integer linear programming‐based distributed energy management for networked microgrids considering network operational objectives and constraints

Abstract Mixed integer linear programming (MILP)–based distributed energy management for networked microgrids embedded modern distribution systems is proposed. Considering the diverse ownership of microgrids, distributed energy resources (DERs) that interface directly with utilities and responsive loads, an alternating direction method of multipliers–based distributed framework was formulated for the scheduling of networked microgrids embedded modern distribution systems by adjusting nodal price signals iteratively. In addition, to make the formulated optimization problems resolvable through more accessible and popular MILP solvers, different linearisation techniques were employed to transform the nonlinear terms into linear or mixed integer linear formats. The proposed MILP‐based distributed method preserves all participants' autonomy (e.g., microgrids, DERs that interface directly with utilities and responsive loads), while incentivising them to actively participate in the distribution system operation with price signals. The proposed method is validated with results of numerical simulation using a modern distribution system consisting of multiple networked microgrids, DERs that interface directly with utilities, as well as responsive loads.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Spatial-Temporal PV Hosting Capacity Estimation and Evaluation

Evaluating Photovoltaic Hosting Capacity (PVHC) is an essential step in the process of integrating solar energy into power grids, particularly when focusing on the distribution network (DN) as the primary integration target. PVHC needs to be investigated, especially in cases where the grids are unbalanced, and their operational conditions vary spatially and temporally. This motivation prompted us to propose a scalable model tailored to this application. In this paper, we applied linearization to the alternating current optimal power flow (AC-OPF) and solar inverters, transforming the original problem into a mixed-integer linear programming (MILP) problem. Additionally, we accounted for the battery energy storage system (BESS) as a time-coupling factor for calculating PVHC. We then compared the PVHC results between the IEEE-13 bus and SMART-DS San Francisco (SFO) cases and discussed the extent to which BESS can enhance the PVHC of a DN. Furthermore, we designed a web-based graphical visualization for the SFO case, enabling user interaction with raw data and simulation results on a map through a graphical user interface (GUI). In summary, our results and findings provide valuable insights for future three-phase unbalanced AC-OPF PVHC practices and their visualization.

AC-optimal power flow↗
DOE OSTI2024

Distributionally Robust Bilevel Optimization Model for Distribution Network With Demand Response Under Uncertain Renewables Using Wasserstein Metrics

Here, we consider a distribution network integrating demand response (DR) participants in the presence of uncertain renewable suppliers and outdoor temperatures. A bilevel optimization model is proposed to capture the intricate dynamics between price-incentivized DR participants and distribution system operations, including energy procurement and active/reactive power flows. The model is formulated as a distributional robust bilevel optimization using Wasserstein metrics. We show favorable data-driven properties including out-of-sample guarantee and asymptotic consistency. Furthermore, we present a tractable mixed-integer linear programming reformulation and characterize the worst-case distribution. Computational experiments are conducted on a modified 33-bus system. Our findings underscore the efficacy of the pricing strategies derived from the proposed bilevel optimization model. These strategies not only effectively manage DR participants' behavior but also bring equity considerations among households with various characteristics to light. The results contribute to a deeper understanding of the interplay between distribution system operators and DR participants.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2018

Data-Enabled Building Energy Savings (D-E BES)

Building sector energy consumption represents a significant fraction of the overall energy consumption in urban communities. While there has been increasing focus on the development of smart environments to support energy savings in urban commercial buildings, the development of smart environments for the residential sector has been less common. Instead, urban residential energy-saving efforts have focused on improving a building's physical infrastructure, introducing energy-saving appliances, and motivating residents to adopt energy conservation practices. Herein this paper illustrates that creating an affinity between a building resident's thermal preferences and a building apartment's unregulated thermal environment represents an alternative means of generating an energy-efficient environment for multi-family, residential buildings. Two years of 15-min interval summer data, obtained from smart cyber-physical systems installed in 310 apartments across two New York City buildings, is used to develop data-enabled (D-E) models of resident thermal preference and unregulated apartment temperatures. Both of these models use a linear mixed-effects approach. The alignment of optimal resident-apartment pairs is then formulated as an integer-programming problem to explore the building energy saving (BES) potential associated with minimizing the difference between unregulated apartment temperature and the residents' thermal preference based on summer cooling loads. The work shows that the energy saving potential vary with a building's physical characteristics as well as the variation in residents' thermal preferences. The work further demonstrates that both the unregulated temperature and the resident's preferred temperature in a given apartment are not only affected by outside temperature and external relative humidity, but also strongly affected by the apartment's geographic orientation. For the specific buildings considered, up to 28% cooling energy saving is possible with full alignment. The paper provides all building monitoring data as an open source data set.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2022

Stochastic Strategic Participation of Active Distribution Networks With High-Penetration DERs in Wholesale Electricity Markets

With the increasing penetration of distributed energy resources (DERs), traditional distribution networks as load-serving entities in wholesale electricity markets, now evolve towards active distribution networks (ADNs) which can proactively participate in wholesale markets by optimally controlling the DERs in their networks. A stochastic bilevel optimization model is proposed in this paper for the strategic participation of ADNs and DERs to provide energy and grid services in wholesale electricity markets. The bilevel optimization model can capture the interactions between the ADN and the wholesale energy and ancillary service markets, considering the uncertainties of DERs in the ADN. In the upper-level model, the ADN makes optimal decisions on energy and reserve bidding considering the availability, uncertainties, and flexibility of DERs. The joint energy and reserve market-clearing of the independent system operator (ISO) is modeled as the lower-level problem. Using strong duality theory and Karush-Kuhn Tucker (KKT) conditions, the proposed bilevel optimization problem is reformulated as mathematical programming with equilibrium constraints (MPEC) problem and further converted into a computationally-solvable mixed-integer second-order-cone programming (MISOCP) model. The simulation results demonstrate the effectiveness of the model and the interactions between an ADN and wholesale electricity markets.

active distribution network↗
DOE OSTI2021

A two-stage service restoration method for electric power distribution systems

Improving the reliability of power distribution systems is critically important for both utilities and customers. This calls for an efficient service restoration module within a distribution management system to support the implementation of self-healing smart grid networks. Although the emerging smart grid technologies, including distributed generators (DGs) and remote-controlled switches, enhance the self-healing capability and allow faster recovery, they still pose additional complexity to the service restoration problem, especially under cold load pickup (CLPU) conditions. Herein, a novel two-stage restoration framework is proposed to generate a restoration solutions with a sequence of control actions. The first stage generates a restoration plan that supports both the traditional service restoration using feeder reconfiguration and the grid-forming DG-assisted intentional islanding methods. The second stage generates an optimal sequence of switching operations to bring the outaged system quickly to the final restored configuration. The problem is formulated as a mixed-integer linear program that incorporates system connectivity, operating constraints, and the CLPU models. It is demonstrated that on using a multi-feeder test case, the proposed framework is effective in utilizing all available resources to quickly restore the service and generate an optimal sequence of switching actions to be used by the operator to reach the desired optimal configuration.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Physics-Informed Graph Neural Networks for Collaborative Dynamic Reconfiguration and Voltage Regulation in Unbalanced Distribution Systems

Network reconfiguration has long been employed as a strategic approach to minimize power distribution system losses and effectively regulate voltage levels. Tap-changing voltage regulators are also critical for controlling bus voltages, especially in accommodating the increasing integration of distributed energy resources (DERs) with intermittent outputs. This paper introduces novel methodologies to address the challenges of dynamic reconfiguration and optimal tap setting in unbalanced three-phase distribution systems. We propose an approximated mixed-integer quadratically constrained program (MIQCP) to model dynamic reconfiguration, along with a pioneering formulation for voltage regulator (VR) tap-setting based on Special Ordered Set type 1 (SOS1). To mitigate computational complexity, we propose a physics-informed spatial-temporal graph convolutional network (STGCN) with an integrated link classifier. The proposed approach enables efficient solution generation by fixing specific variables in the MIQCP instance and solving the simplified sub-MIP using an MIP solver. Numerical studies demonstrate the superior prediction accuracy of our STGCN model compared to baseline neural network models, resulting in reduced DER curtailment and voltage deviation with shorter computation time.

dynamic reconfiguration↗
DOE OSTI2019

Critical Load Restoration using Distributed Energy Resources for Resilient Power Distribution System

Extreme weather events have a significant impact on the aging and outdated power distribution infrastructures. These high-impact low-probability (HILP) events often result in extended outages and loss of critical services, thus, severely affecting customers' safety. This calls for the need to ensure resilience in distribution networks by quickly restoring the critical services during a disaster. This paper presents an advanced feeder restoration method to restore critical loads using distributed energy resources (DERs). A resilient restoration approach is proposed that jointly maximizes the amount of restored critical loads and optimizes the restoration times by optimally allocating grid's available DER resources. The restoration problem is modeled as a mixed-integer linear program with the objective of maximizing the resilience to post-restoration failures while simultaneously satisfying grid's critical connectivity and operational constraints and ensuring a radial operation for a given open-loop feeder configuration. Simulations are performed to demonstrate the effectiveness of the proposed approach using IEEE 123-node feeder with 5 DERs supplying 11 critical loads and IEEE 906-bus feeder with 3 DERs supplying 17 critical loads. The impacts of DER availability and fuel reserve on restored networks are assessed and it is shown that the proposed approach is successfully able to restore a maximum number of critical loads using available DERs.

resilience, microgrids, reactive power, energy res↗
DOE OSTI2020

An Optimization-Based Planning Tool for On-Demand Mobility Service Operations

Regions worldwide are adopting and exploring low-speed automated electric shuttle (AES) service as an on-demand shared mobility service in dense geofenced urban areas. Building on this concept, the National Renewable Energy Laboratory (NREL) recently developed the Automated Mobility District (AMD) toolkit. The AMD toolkit—comprising of a travel micro-simulation model and an energy estimation model—estimates the mobility and energy impacts of a given shuttle configuration within an AMD. Early-stage AMD deployments need to find optimal operational configurations that include: (a) passenger capacity of an AES, (b) time-dependent routes, and (c) fleet size (AES units) to satisfy the demand for the region. This research extends the AMD toolkit functionality by developing an optimization-based planning module that will assist in the operations of AES units. We developed a constrained mixed-integer program accounting for passenger waiting time, battery range, and passenger capacity of AES units. For scalability, we demonstrated the Tabu search-based solution technique for a real-world network—a proposed AMD deployment in Greenville, South Carolina, USA. Compared to rule-based operations, our developed solution yields higher travel time and energy savings for the network at different demand levels. The sensitivity analyses for waiting time thresholds indicate nonlinearity in the system performance, underscoring the need to meet shared-use mobility user-level expectations. The developed optimization framework can be adapted and extended to accommodate different categories of shared-use on-demand mobility services.

ADVANCED PROPULSION SYSTEMS,ENERGY PLANNING, POLIC↗
DOE OSTI2018

Optimal Black Start Allocation for Power System Restoration

Equipment failures, operator errors, natural disasters and cyber-attacks can and have caused extended blackouts of the electric grid. Even though such events are rare, preparedness for them is critical because extended power outages endanger human lives, compromise national security, or result in economic losses of billions of dollars. Since most of the generating units cannot restart without connecting to an energized grid, the system operator relies on a few units with the ability to start autonomously, called Black Start (BS) units, to restore the power system. Allocating and maintaining these units is costly and can severely impact the restoration security and time. We formulate an optimization problem to optimally allocate BS units in the grid, while simultaneously optimizing over the restoration sequence. We extend existing optimal allocation models by including grid considerations such as active power nodal balance, transmission switching, nodal reactive power support and voltage limits. In order to aid the branch and bound tree that solves the resulting large scale mixed integer program, we propose a randomized heuristic that is executed multiple times in parallel on a high-performance computing environment to find feasible solutions. Here, we proceed to solve the IEEE-39, the IEEE-118, and a simplified WECC system with 225 nodes and 136 generators to near optimality.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Mixed Integer Nonlinear Programming Approaches to Enhance Resiliency and Response Strategies in Critical Infrastructure

Motivation. Critical infrastructures are large, complex engineered systems that must be operated robustly under abnormal conditions resulting from natural hazards or intentional acts. For example, electric power systems must be robust to line faults, water utilities must rapidly mitigate contamination incidents, and computing networks must adapt to adversarial intrusions to protect critical information. Problem. It is difficult for decision-makers within resiliency analysis in critical infrastructure to optimize designs and develop effective response strategies that can account for uncertainties. Facing incomplete information and the sheer scope that a natural hazard or attack vector may incorporate, response can be ineffective without reliable, scalable decision support tools. These problems are intrinsically nonlinear and involve discrete decisions, and unfortunately, existing off-the-shelf mathematical programming methods cannot support optimization-based decision-making of these nonlinear at scale. Method/Approach and Results. This project emphasized development of fundamental optimization strategies that supported real- time mitigation and response for critical infrastructures. In particular, the project developed multi- tree approaches based on piecewise outer-approximations for solution of mixed-integer nonlinear programming (MINLP) problems. These techniques alternate between an MILP or MISOCP relaxation to obtain a lower bound and candidate discrete solutions and an NLP subproblem to obtain upper bounds. Using tailored relaxations based on problem structure, these methods were used to solve several key applications in resilience and response of critical infrastructure. This work resulted in two open-source, copyrighted software packages: CORAMIN (https://github.com/Coramin/Coramin) -- an object-oriented mathematical programming framework that supports tailored multi-tree algorithms for solution of large- scale mixed-integer nonlinear programming; and EGRET (Electrical Grid Research and Engineering Toolkit) (https://github.com/grid- parity-exchange/Egret) -- a declarative mathematical programming framework built upon CORAMIN and Pyomo for formulation and solution of resilience and operations problems in power grid systems. Furthermore, these tools resulted in several important published results, including the following: The first known global optimization approach that could solve the unit-commitment problem with nonlinear power flow constraints on medium-sized test problems; Improved parallel optimization-based bounds tightening and strengthening of relaxations of AC power flow constraints; and, Optimization-based approaches for improved grid resilience and use of demand response to improve grid resilience with reduction in capital requirements. Result Implications. This project developed first-of-a-kind algorithms for decision-making in critical infrastructure resilience operations and planning, as well as a next-generation toolkit for MINLP researchers. These approaches leveraged high-performance computing architectures to solve some of the largest, most challenging nonlinear discrete optimization problems to global optimality, and these successes were captured in open-source software to enable optimization-based decision-making, and efficient solution of MINLP formulations for electric power transmission grids.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2016

Dynamic Multi-Sensor Multi-Mission Optimal Planning Tool

Remote sensing systems have firmly established a role in providing immense value to commercial industry, scientific exploration, and national security. Continued maturation of sensing technology has reduced the cost of deploying highly-capable sensors while at the same time increased reliance on the information these sensors can provide. The demand for time on these sensors is unlikely to diminish. Coordination of next-generation sensor systems, larger constellations of satellites, unmanned aerial vehicles, ground telescopes, etc. is prohibitively complex for existing heuristics-based scheduling techniques. The project was a two-year collaboration spanning multiple Sandia centers and included a partnership with Texas A&M University. We have developed algorithms and software for collection scheduling, remote sensor field-of-view pointing models, and bandwidth-constrained prioritization of sensor data. Our approach followed best practices from the operations research and computational geometry communities. These models provide several advantages over state of the art techniques. In particular, our approach is more flexible compared to heuristics that tightly couple models and solution techniques. First, our mixed-integer linear models afford a rigorous analysis so that sensor planners can quantitatively describe a schedule relative to the best possible. Optimal or near-optimal schedules can be produced with commercial solvers in operational run-times. These models can be modified and extended to incorporate different scheduling and resource constraints and objective function definitions. Further, we have extended these models to proactively schedule sensors under weather and ad hoc collection uncertainty. This approach stands in contrast to existing deterministic schedulers which assume a single future weather or ad hoc collection scenario. The field-of-view pointing algorithm produces a mosaic with the fewest number of images required to fully cover a region of interest. The bandwidth-constrained algorithms find the highest priority information that can be transmitted. All of these are based on mixed-integer linear programs so that, in the future, collection scheduling, field-of-view, and bandwidth prioritization can be combined into a single problem. Experiments conducted using the developed models, commercial solvers, and benchmark datasets have demonstrated that proactively scheduling against uncertainty regularly and significantly outperforms deterministic schedulers.

47 OTHER INSTRUMENTATION↗
DOE OSTI2017

Sustainable network design for multi-purpose pellet processing depots under biomass supply uncertainty

This work develops a two-stage stochastic mixed-integer programming model to manage multi- purpose pellet processing depots under feedstock supply uncertainty. The proposed optimization model would help to minimize cost and to mitigate emissions from the supply chain network. We consider three alternative Biomass Processing and Densi cation Depot (BPDD) technologies; namely, conventional pellet processing, high moisture pellet processing, and ammonia ber expansion. These three technologies pre-process/pre-treat and densify different types of biomass into more highly densi ed intermediate products for different markets in order to improve movability and overall supply network performance in terms of costs and emissions. A hybrid decomposition algorithm was developed that combines sample average approximation with an enhanced Progressive Hedging (PH) algorithm to solve this challenging NP -hard problem. Some heuristics such as Rolling Horizon (RH) heuristic, variable xing technique were later applied to further enhance the PH algorithm. Mississippi and Alabama were selected as a testing ground and ArcGIS was employed to visualize and validate the modeling results. The results of the analysis reveal promising insights that could lead to recommendations to help decision makers achieve a more cost-effective environmentally-friendly supply chain network.

09 BIOMASS FUELS↗
DOE OSTI2020

Mathematical Models for Optimization of Grid-Integrated Energy Storage Systems

Energy storage has been proven to yield positive effects on planning, operation and control of electric grids. It has become a crucial task to properly model the energy storage systems (ESS) under the framework of grid optimization on transmission and distribution networks including microgrids. This paper presents a review on mathematical models and test cases of ESSs used for grid optimization studies, where the network constraints of power systems are included. The existing ESS models are mainly classified into two categories – linear and nonlinear models. The two main categories are further divided into several subcategories respectively; such as mixed-integer linear and convex nonlinear sub-categories. Based on the review and discussions, this paper aims at providing suggestions for choosing proper ESS models for specific grid optimization studies considering the chosen power network model.

24 POWER TRANSMISSION AND DISTRIBUTION↗