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Results for “Mixed 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.

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At least 163 records · Page 9
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DOE OSTI2020

Connected Vehicle-Based Traffic Signal Coordination

This study presents a connected vehicles (CVs)-based traffic signal optimization framework for a coordinated arterial corridor. The signal optimization and coordination problem are first formulated in a centralized scheme as a mixed-integer nonlinear program (MINLP). The optimal phase durations and offsets are solved together by minimizing fuel consumption and travel time considering an individual vehicle’s trajectories. Due to the complexity of the model, we decompose the problem into two levels: an intersection level to optimize phase durations using dynamic programming (DP), and a corridor level to optimize the offsets of all intersections. In order to solve the two-level model, a prediction-based solution technique is developed. The proposed models are tested using traffic simulation under various scenarios. Compared with the traditional actuated signal timing and coordination plan, the signal timing plans generated by solving the MINLP and the two-level model can reasonably improve the signal control performance. When considering varies vehicle types under high demand levels, the proposed two-level model reduced the total system cost by 3.8% comparing to baseline actuated plan. MINLP reduced the system cost by 5.9%. It also suggested that coordination scheme was beneficial to corridors with relatively high demand levels. For intersections with major and minor street, coordination conducted for major street had little impacts on the vehicles at the minor street.

42 ENGINEERING↗
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 OSTI2022

Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment

Nonlinear power flow constraints render a variety of power system optimization problems computationally intractable. Emerging research shows, however, that the nonlinear AC power flow equations can be successfully modeled using neural networks. These neural networks can be exactly transformed into mixed integer linear programs and embedded inside challenging optimization problems, thus replacing nonlinearities that are intractable for many applications with tractable piecewise linear approximations. Such approaches, though, suffer from an explosion of the number of binary variables needed to represent the neural network. Accordingly, this paper develops a technique for training an "optimally compact'' neural network, i.e., one that can represent the power flow equations with a sufficiently high degree of accuracy while still maintaining a tractable number of binary variables. We demonstrate the use of this neural network as an approximator of the nonlinear power flow equations by embedding it in the AC unit commitment problem, transforming the problem from a mixed integer nonlinear program into a more manageable mixed integer linear program. We use the 14-, 57-, and 89-bus networks as test cases and compare the AC-feasibility of commitment decisions resulting from the neural network, DC, and linearized power flow approximations. Our results show that the neural network model outperforms both the DC and linearized power flow approximations when embedded in the unit commitment problem. The neural network formulation most often selects a feasible unit commitment schedule, and furthermore, it only s

AC power flow↗
DOE OSTI2020

Scenario Grouping and Decomposition Algorithms for Chance-Constrained Programs

A lower bound for a finite-scenario-based chance-constrained program is the quantile value corresponding to the sorted optimal objective values of scenario subproblems. This quantile bound can be improved by grouping subsets of scenarios at the expense of solving larger subproblems. The quality of the bound depends on how the scenarios are grouped. In this paper, we formulate a mixed-integer bilevel program that optimally groups scenarios to tighten the quantile bounds. For general chance-constrained programs, we propose a branch-and-cut algorithm to optimize the bilevel program, and for chance-constrained linear programs, a mixed-integer linear-programming reformulation is derived. Here, we also propose several heuristics for grouping similar or dissimilar scenarios. Our computational results demonstrate that optimal grouping bounds are much tighter than heuristic bounds, resulting in smaller root-node gaps and better performance of scenario decomposition for solving chance-constrained 0-1 programs. Also, the optimal grouping bounds can be greatly strengthened using larger group size.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Optimal Network Topology for Node-Breaker Representations With AC Power Flow Constraints

It has been demonstrated that network topology optimization (NTO) may change the topology of power system networks, and consequently, provide additional flexibility to reduce network congestion and violations. Most NTO problems are formulated based on the bus-branch model in which it is challenging to represent a realistic picture of all substation configurations. In this paper, we explore advantages of substation reconfiguration modeling based on node-breaker representations for NTO problem with full nonlinear alternating current power flow. It also proposes a tailored solution algorithm to solve this nonconvex mixed-integer nonlinear programming through the outer approximation method. The proposed solution approach iterates between a mixed-integer linear programming and a nonlinear subproblem. Additional enhancements to further accelerate the iteration process are illustrated. Numerical case studies demonstrate the relative economic and operational impact of optimal network topology with node-breaker representations.

42 ENGINEERING↗
DOE OSTI2017

Generation of feasible integer solutions on a massively parallel computer using the feasibility pump

Here, we present an approach to parallelize generation of feasible mixed integer solutions of mixed integerlinear programs in distributed memory high performance computing environments. This approachcombines a parallel framework with feasibility pump (FP) as the rounding heuristic. It runs multiple FPinstances with different starting solutions concurrently, while allowing them to share information. Ourcomputational results suggest that the improvement resulting from parallelization using our approach is statistically significant.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A centralized-based method to determine the local voltage control strategies of distributed generator operation in active distribution networks

The increasing penetration of distributed generators (DGs) exacerbates the risk of voltage violations in active distribution networks (ADNs). The var capacity provided by DG inverters is a potential solution for voltage regulation. The conventional centralized control strategies limited by computation and communication burdens are difficult to meet the requirement of rapid voltage control. However, the local control strategies based on real-time measurements have a fast response to the frequent fluctuations of DG outputs. The performance of these local controllers depends on the tuning of the control parameters. This paper proposes a centralized-based method to determine the local voltage control strategies for DGs. A centralized parameter tuning model of control curves is built, in which and curves of DG inverters are mathematically formulated based on piecewise linearization. The original mixed-integer nonlinear programming (MINLP) model is converted into an effectively solved mixed-integer second-order cone programming (MISOCP) model using convex relaxation. The potential benefits of DG inverters are explored to regulate both reactive and curtailed active power, based on local voltage measurements. Case studies on a modified PG&E 69-node distribution system are carried out to verify the effectiveness of the proposed method. Results show that power losses of ADNs are significantly reduced and voltage profiles are also improved.

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 OSTI2016

Fuzzy Energy and Reserve Co-optimization With High Penetration of Renewable Energy

In this study, we propose a fuzzy-based energy and reserve co-optimization model with consideration of high penetration of renewable energy. Under the assumption of a fixed uncertainty set of renewables, a two-stage robust model is proposed for clearing energy and reserves in the first stage and checking the feasibility and robustness of re-dispatches in the second stage. Fuzzy sets and their membership functions are introduced into the optimization model to represent the satisfaction degree of the variable uncertainty sets. The lower bound of the uncertainty set is expressed as fuzzy membership functions. The solutions are obtained by transforming the fuzzy mathematical programming formulation into traditional mixed integer linear programming problems.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2019

The allocation of a variable series reactor considering AC constraints and contingencies

The Variable Series Reactors (VSRs) can efficiently control the power flow through the adjustment of the line reactance. When they are appropriately allocated in the power network, the transmission congestion and generation cost can be reduced. Our work proposes a planning model to optimally allocate VSRs considering AC constraints and multi-scenarios including base case and contingencies. The planning model is originally a non-convex large scale mixed integer nonlinear program (MINLP), which is generally intractable. The proposed Benders approach decomposes the MINLP model into a mixed integer linear program (MILP) master problem and a number of nonlinear subproblems. Numerical case studies based on IEEE 118-bus demonstrate the high performance of the proposed approach.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

An MINLP formulation for the optimization of multicomponent distillation configurations

Designing configurations for multicomponent distillation, a ubiquitous process in chemical and petrochemical industries, is often challenging. This is because, as the number of components increases, the number of admissible distillation configurations grows rapidly and these configurations vary substantially in their energy needs. Consequently, if a method could identify a few energy-efficient choices from this large set of alternatives, it would be extremely attractive to process designers. This paper develops here such a method by solving a Mixed Integer Nonlinear Program (MINLP) that is formulated to pick, among the regular-column configurations of Shah and Agrawal (2010b), those configurations that have a low vapor-duty requirement. To compute the minimum vapor-duty requirement for each column within the configuration, we use techniques that rely on the Underwood’s method. The combined difficulty arising from the nonlinearity of Underwood equations and the combinatorial explosion of the choice-set of alternatives poses unmistakable challenges for the branch-and-bound algorithm, the current method of choice to globally solve MINLPs. To address this difficulty, we exploit the structure of Underwood equations and derive valid cuts that expedite the convergence of branch-and-bound by enabling global solvers, such as BARON, infer tighter bounds on Underwood roots. This provides a quick way to identify a few lucrative alternative configurations for separation of a given non-azeotropic mixture. We illustrate the practicality of our approach on a case-study concerning heavy-crude distillation and on various other examples from the literature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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 OSTI2015

Optimization problems in natural gas transportation systems. A state-of-the-art review

Our paper provides a review on the most relevant research works conducted to solve natural gas transportation problems via pipeline systems. The literature reveals three major groups of gas pipeline systems, namely gathering, transmission, and distribution systems. In this work, we aim at presenting a detailed discussion of the efforts made in optimizing natural gas transmission lines.There is certainly a vast amount of research done over the past few years on many decision-making problems in the natural gas industry and, specifically, in pipeline network optimization. In this work, we present a state-of-the-art survey focusing on specific categories that include short-term basis storage (line-packing problems), gas quality satisfaction (pooling problems), and compressor station modeling (fuel cost minimization problems). We also discuss both steady-state and transient optimization models highlighting the modeling aspects and the most relevant solution approaches known to date. Although the literature on natural gas transmission system problems is quite extensive, this is, to the best of our knowledge, the first comprehensive review or survey covering this specific research area on natural gas transmission from an operations research perspective. Furthermore, this paper includes a discussion of the most important and promising research areas in this field. Hence, our paper can serve as a useful tool to gain insight into the evolution of the many real-life applications and most recent advances in solution methodologies arising from this exciting and challenging research area of decision-making problems.

03 NATURAL GAS↗
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 OSTI2019

From graphical to model-based distillation column design: A McCabe-Thiele-inspired mathematical programming approach

We propose a mixed-integer nonlinear programming (MINLP) model for simple and complex distillation column design and optimization. The model is based upon the concepts and equations underpinning the McCabe-Thiele method. Generalizing this method, we introduce material balances at various locations of the column and employ binary variables to determine the optimal number of trays and optimal feed locations. We model the vapor–liquid equilibrium using continuous piecewise linear approximating functions. The model is extended to account for multicomponent mixtures and non-constant-molar overflow. We also discuss how to estimate the minimum number of trays and the minimum reflux ratio.

42 ENGINEERING↗
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 OSTI2019

ADP-Based Home Energy Management System: A Case Study Using Dynamo: Preprint

This paper explores Home Energy Management System (HEMS) algorithms to minimize household cost while maintaining comfort when faced with uncertain weather, and demand. Specifically, we consider a HEMS that optimizes forward looking schedules for a home's heating, ventilation, and air conditioning (HVAC); water heater (WH); and electric vehicle (EV) charging while considering uncertainty in outside temperature, hot water usage, and non-controllable load (NCL). We adopt a Dynamic Programming (DP) formulation and utilize the Dynamic programming for Adaptive Modeling and Optimization (DYNAMO) toolkit to implement DP and approximate dynamic programming (ADP) algorithms. Simulation results under a single tariff plan compare the quality of the solution generated by ADP to that of DP, and show significant improvement in computation time while maintaining acceptable solution accuracy.

24 POWER TRANSMISSION AND DISTRIBUTION↗