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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A matheuristic for design and dispatch of a utility-connected distributed energy system

Modeling distributed power generation systems often requires complicated mathematical expressions that present challenges for commercial optimization solvers. Here, this paper presents a matheuristic to solve a mixed-integer optimization model that informs decisions regarding the design and dispatch of a utility-connected microgrid. We deploy a genetic algorithm to search the system design space and a linear program to solve the economic dispatch problem. The model is a component of a web tool that requires solutions within a few minutes. Our method yields objective function values within 5% of an exogenously produced optimal in fewer than 30 seconds for 90% of our test cases compared to only 10% of our test cases by a traditional optimization solver in the same amount of time.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Grid Optimization Competition on Synthetic and Industrial Power Systems

This paper summarizes a grid optimization (GO) competition effort in the United States to find the best solution strategies for up to interconnect-scale power system networks with around 32,000 buses. The optimization problem is a mixedinteger, non-convex non-linear problem, (MINLP) and includes discrete variables such as unit commitment and line switching, control settings (transformer taps and phase shifters with impedance correction tables), and bus shunts. The case study includes six actual industry grids as well as 16 realistic synthetic grids created by three different dataset teams. The winners are selected and ranked based on scoring criteria, which consider the solution quality (such as objective functions) within time limits. Nine winner teams are selected from 26 competitor teams. The results achieved by different teams are described and the performance of different algorithms on synthetic grids and actual industry grids are compared and analyzed.

mixed-integer non-linear programming↗
NASA NTRS1985

The role of service areas in the optimization of FSS orbital and frequency assignments

A relationship is derived, on a single-entry interference basis, for the minimum allowable spacing between two satellites as a function of electrical parameters and service-area geometries. For circular beams, universal curves relate the topocentric satellite spacing angle to the service-area separation angle measured at the satellite. The corresponding geocentric spacing depends only weakly on the mean longitude of the two satellites, and this is true also for alliptical antenna beams. As a consequence, if frequency channels are preassigned, the orbital assignment synthesis of a satellite system can be formulated as a mixed-integer programming (MIP) problem or approximated by a linear programming (LP) problem, with the interference protection requirements enforced by constraints while some linear function is optimized. Possible objective-function choices are discussed and explicit formulations are presented for the choice of the sum of the absolute deviations of the orbital locations from some prescribed ideal location set. A test problem is posed consisting of six service areas, each served by one satellite, all using elliptical antenna beams and the same frequency channels. Numerical results are given for the three ideal location prescriptions for both the MIP and LP formulations. The resulting scenarios also satisfy reasonable aggregate interference protection requirements.

Levis, C. A.↗
DOE OSTI2021

Disjunctive linear separation conditions and mixed-integer formulations for aircraft conflict resolution

In this paper, we address the aircraft conflict resolution problem in air traffic control. We introduce new mixed-integer programming formulations for aircraft conflict resolution with speed, heading and altitude control which are based on disjunctive linear separation conditions. We first examine the two-dimensional aircraft conflict resolution problem with speed and heading control represented as continuous decision variables. We show that the proposed disjunctive linear separation conditions are equivalent to the classical nonlinear conditions for aircraft separation. Further, we characterise conflict-free trajectories based on aircraft velocity bounds and propose a simple pre-processing algorithm to identify aircraft pairs which are either always conflict-free, or which cannot be separated using speed and heading control only. We then incorporate altitude control and propose a lexicographic optimisation formulation that aims to minimise the number of flight level changes before resolving outstanding conflicts via two-dimensional velocity control. The proposed mixed-integer programming formulations are nonconvex, and we propose convex relaxations, decomposition methods and constraint generation algorithms to solve the two-dimensional and lexicographic optimisation formulations to guaranteed optimality. Numerical experiments on four types of conflict resolution benchmarking instances are conducted to test the performance of the proposed mixed-integer formulations. Further, the proposed method is compared against two benchmarks based on state-of-the-art approaches for the aircraft conflict resolution problem. Our numerical results show that the proposed method largely outperforms both benchmarks in terms of runtime and is able to solve significantly more instances to global optimality.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1992

Menu-Driven Solver Of Linear-Programming Problems

Program assists inexperienced user in formulating linear-programming problems. A Linear Program Solver (ALPS) computer program is full-featured LP analysis program. Solves plain linear-programming problems as well as more-complicated mixed-integer and pure-integer programs. Also contains efficient technique for solution of purely binary linear-programming problems. Written entirely in IBM's APL2/PC software, Version 1.01. Packed program contains licensed material, property of IBM (copyright 1988, all rights reserved).

Viterna, L. A.↗
DOE OSTI2020

Toward a scalable robust security-constrained optimal power flow using a proximal projection bundle method

Robust security-constrained optimal power flow (rSCOPF) aims to find the worst-case contingencies of alternating current optimal power flow (ACOPF) in power systems. With the rise of GPU architectures on the upcoming supercomputer architectures, optimization algorithms that rely on sparse linear algebra and indefinite linear systems are becoming increasingly hard to solve efficiently (e.g. interior-point method). To address this we revisit a maximin optimization formulation of the rSCOPF and the single-level mixed-integer semidefinite programming (MISDP) reformulation, which is obtained by taking the Lagrangian relaxation of the inner minimization ACOPF problem. In this paper, we focus on the development of a proximal projection bundle method (PPBM) for solving continuous relaxation node subproblems of the MISDP problem, based primarily on the well-known alternating direction method of multipliers. Cutting planes reminiscent of bundle method ideas are also applied in coordination with updates of the proximal parameter. The cutting-plane method can generate a large number of linear inequalities, leading to a large scale but decomposable quadratic programming (QP) subproblem that is amenable to GPUs. We present the numerical results on the IEEE 30, 57, 118, and 300-bus systems by using our PBMM method. We discuss the main computational bottleneck of our method, which is the time taken to solve each iteration of a QP subproblem instance of the PPBM, and how GPU architectures can accelerate this solution process.

bundle method↗
DOE OSTI2025

McCormick envelopes in mixed-integer PDE-constrained optimization

McCormick envelopes are a standard tool for deriving convex relaxations of optimization problems that involve polynomial terms. Such McCormick relaxations provide lower bounds, for example, in branch-and-bound procedures for mixed-integer nonlinear programs but have not gained much attention in PDE-constrained optimization so far. This lack of attention may be due to the distributed nature of such problems, which on the one hand leads to infinitely many linear constraints (generally state constraints that may be difficult to handle) in addition to the state equation for a pointwise formulation of the McCormick envelopes and renders bound-tightening procedures that successively improve the resulting convex relaxations computationally intractable. We analyze McCormick envelopes for a model problem class that is governed by a semilinear PDE involving a bilinearity and integrality constraints. We approximate the nonlinearity and in turn the McCormick envelopes by averaging the involved terms over the cells of a partition of the computational domain on which the PDE is defined. This yields convex relaxations that underestimate the original problem up to an a priori error estimate that depends on the mesh size of the discretization. These approximate McCormick relaxations can be improved by means of an optimization-based bound-tightening procedure. We show that their minimizers converge to minimizers to a limit problem with a pointwise formulation of the McCormick envelopes when driving the mesh size to zero. We provide a computational example, for which we certify all of our imposed assumptions. The results point to both the potential of the methodology and the gaps in the research that need to be closed. Our methodology provides a framework first for obtaining pointwise underestimators for nonconvexities and second for approximating them with finitely many linear inequalities in an infinite-dimensional setting.

Approximations and Expansions↗
DOE OSTI2022

Real-time dispatch optimization for concentrating solar power with thermal energy storage

Concentrating solar power (CSP) plants present a promising path towards utility-scale renewable energy. The power tower, or central receiver, configuration can achieve higher operating temperatures than other forms of CSP, and, like all forms of CSP, naturally pairs with comparatively inexpensive thermal energy storage, which allows CSP plants to dispatch electricity according to market price incentives and outside the hours of solar resource availability. Currently, CSP plants commonly include a steam Rankine power cycle and several heat exchange components to generate high-pressure steam using stored thermal energy. The efficiency of the steam Rankine cycle depends on the temperature of the plant's operating fluid, and so is a main concern of plant operators. However, the variable nature of the solar resource and the conservatism with which the receiver is operated prevent perfect control over the receiver outlet temperature. Therefore, during periods of solar variability, collection occurs at lower-than-design temperature. To support operator decisions in a real-time setting, we develop a revenue-maximizing non-convex mixed-integer, quadradically-constrained program which determines a dispatch schedule with sub-hourly time fidelity and considers temperature-dependent power cycle efficiency. The exact nonlinear formulation proves intractable for real-time decision support. Here we present exact and inexact techniques to improve problem tractability that include a hybrid nonlinear and linear formulation. Our approach admits solutions within approximately 3% of optimality, on average, within a five-minute time limit, demonstrating its usability for decision support in a real-time setting.

14 SOLAR ENERGY↗
DOE OSTI2021

Data-driven optimization of mixed-integer bi-level multi-follower integrated planning and scheduling problems under demand uncertainty

The coordination of interconnected elements across the different layers of the supply chain is essential for all industrial processes and the key to optimal decision-making. Yet, the modeling and optimization of such interdependent systems are still burdensome. Here we address the simultaneous modeling and optimization of medium-term planning and short-term scheduling problems under demand uncertainty using mixed-integer bi-level multi-follower programming and data-driven optimization. Bi-level multi-follower programs model the natural hierarchy between different layers of supply chain management holistically, while scenario analysis and data-driven optimization allow us to retrieve the guaranteed feasible solutions of the integrated formulation under various demand considerations. We address the data-driven optimization of this challenging class of problems using the DOMINO framework, which was initially developed to solve single-leader single-follower bi-level optimization problems to guaranteed feasibility. This framework is extended to solve single-leader multi-follower stochastic formulations and its performance is characterized by well-known single and multi-product process scheduling case studies. Through our data-driven algorithmic approach, we present guaranteed feasible solutions to linear and nonlinear mixed-integer bi-level formulations of simultaneous planning and scheduling problems and further characterize the effects of the scheduling level complexity on the solution performance, which spans over several hundred continuous and binary variables, and thousands of constraints.

42 ENGINEERING↗
NASA NTRS2018

Next Generation Aircraft Design Considering Airline Operations and Economics

Traditional approaches to design and optimization of a new system often use a system-centric objective and do not take into consideration how the operator will use this new system alongside other existing systems. When the new system design is incorporated into the broader group of systems, the performance of the operator-level objective can be sub-optimal due to the unmodeled interaction between the new system and the other systems. Among the few available references that describe attempts to address this disconnect, most follow an MDO (Multidisciplinary Design Optimization)-motivated sequential decomposition approach of first designing a very good system and then providing this system to the operator who, decides the best way to use this new system along with the existing systems. This paper addresses this issue by including aircraft design, airline operations, and revenue management "subspaces"; and presents an approach that could simultaneously solve these subspaces posed as a monolithic optimization problem rather than the traditional approach described above. The monolithic approach makes the problem an expensive Mixed Integer Non-Linear Programming problem, which are extremely difficult to solve. To address the problem, we use a recently developed optimization framework that simultaneously solves the subspaces to capture the "synergy" in the problem that the previous decomposition approaches did not exploit, addresses mixed-integer/discrete type design variables in an efficient manner, and accounts for computationally expensive analysis tools. This approach solves an 11-route airline network problem consisting of 94 decision variables including 33 integer and 61 continuous type variables. Simultaneously solving the subspaces leads to significant improvement in the fleet-level objective of the airline when compared to the previously developed sequential subspace decomposition approach.

Roy, Satadru↗
DOE OSTI2023

Parametric analysis on optimized design of hybrid solar power plants

There is increasing interest in utility-scale solar power plants with storage which can flexibly dispatch renewable energy to the grid. However, plant design possesses many degrees of freedom and non-obvious trade-offs in performance. Software tools can estimate or optimize the performance of a specific plant configuration under market and weather conditions of interest; the associated cost parameters and operating assumptions strongly influence estimates of plant performance and decisions regarding optimal sizing. We employ the National Renewable Energy Laboratory's Hybrid Optimization and Performance Platform, which incorporates optimal dispatch when evaluating plant performance, and investigate the sensitivity to weather and market conditions, operating limitations, and the presence of a capacity-based incentive. We demonstrate changes in plant performance and optimal sizing with respect to these inputs and discuss implications. Here results show that PV-with-battery designs are more profitable under our assumptions, but that designs including a concentrated solar power (CSP) system produce significantly greater annual energy; and that CSP-with-thermal energy storage designs maximizing the benefit-to-cost ratio have an input-dependent linear relationship between the CSP field solar multiple and the hours of storage as the project budget varies.

14 SOLAR ENERGY↗
DOE OSTI2021

Multilane Automated Driving With Optimal Control and Mixed-Integer Programming

Road vehicle lane changes often initiate traffic disturbances and can therefore impact road networks’ energy and time efficiency. Furthermore, unexpected changes in traffic conditions may also render lane changes counterproductive for the lane-changing vehicle. Vehicle-to-vehicle connectivity combined with anticipative control could address these challenges via improved lane change decisions by automated vehicles. In a move toward this objective, receding horizon control cast as a mixed-integer quadratic program is used to plan lane changing and acceleration in a coupled optimization. A long-term pacing module, based on Pontryagin’s minimum principle from optimal control theory, sets terminal and input references for receding horizon control to target a user’s expected travel time. To remove nonlinear vehicle dynamics from the receding horizon controller, lane change commands are passed to a pure pursuit steering module whose response is approximated by a second-order linear model. Here, comparison against a rule-based reactive algorithm in arterial and highway scenarios shows an 8.9%–13.7% reduction in energy consumption and a 5.2%–10.3% reduction in the travel time, along with navigational improvements.

33 ADVANCED PROPULSION SYSTEMS↗
NASA NTRS1981

An optimization model for energy generation and distribution in a dynamic facility

An analytical model is described using linear programming for the optimum generation and distribution of energy demands among competing energy resources and different economic criteria. The model, which will be used as a general engineering tool in the analysis of the Deep Space Network ground facility, considers several essential decisions for better design and operation. The decisions sought for the particular energy application include: the optimum time to build an assembly of elements, inclusion of a storage medium of some type, and the size or capacity of the elements that will minimize the total life-cycle cost over a given number of years. The model, which is structured in multiple time divisions, employ the decomposition principle for large-size matrices, the branch-and-bound method in mixed-integer programming, and the revised simplex technique for efficient and economic computer use.

Lansing, F. L.↗
DOE OSTI2025

A bilevel multistage stochastic self-scheduling model with indivisibilities for trading in the continuous intraday electricity market

In this paper, we study the profit maximization problem of a virtual power plant trading in the continuous intraday electricity market. Our virtual power plant model is compatible with renewable, and thermal assets, covering a range of virtual power plants currently participating in energy markets. We model the trading problem as a bilevel multistage stochastic program. The upper level of the problem accounts for the profit maximization of the virtual power plant with explicit modeling of the technical constraints of the operational status of the thermal power plant including minimum start-up and shut-down times, ramp-up and ramp-down rates, and minimum generation level. The upper level also decides which continuous and indivisible (fill-or-kill) orders are submitted to the market. The lower-level problem accounts for the clearing of the continuous intraday market, i.e., matching of buy and sell orders. Because of the presence of fill-or-kill orders, the lower-level problem is mixed-integer, which prevents its direct conversion to a single-level problem using duality. In order to solve this challenging problem, we develop a convex-hull extended formulation for the lower-level problem, apply duality theory to obtain a single-level stochastic equivalent formulation, and employ McCormick envelopes to turn the problem into a multistage stochastic mixed-integer linear problem, which we solve using the stochastic dual dynamic integer programming algorithm. We conduct numerical experiments and analyze the optimal trading behavior of a virtual power plant trading in an ideal continuous market without arbitrage.

Bilevel multistage stochastic programming problem↗
DOE OSTI2022

Stochastic scheduling of generating units with weekly energy storage: A hybrid decomposition approach

We propose a solution method for the large-scale stochastic unit commitment (SUC) problem with weekly-dispatched energy storage and significant weather-dependent stochastic generating capacity. Weekly storage facilities that mostly charge during weekends and discharge during weekdays require a weekly scheduling of generating units, which result in a large-scale optimization problem. This SUC problem is formulated as a two-stage stochastic model and we use the conditional value-at-risk as a risk measure. Using a Benders framework, the proposed solution method decomposes the problem into a mixed-integer linear master problem and linear and continuous subproblems. The master problem corresponds to the first-stage decisions throughout the week and includes all the commitment (binary) variables and their corresponding constraints. The subproblems correspond to the actual dispatch of the generating units on a weekly basis. Based on the success of column-and-constraint generation algorithms to solve robust optimization problems, we improve the low communication between the master problem and the subproblems in the standard Benders decomposition by adding primal variables and constraints from the subproblems to the master problem, which provides a better approximation of the recourse function. Furthermore, our computational experiments demonstrate the effectiveness of the proposed decomposition method using an instance of the South Carolina synthetic system with 90 generating units under 40 scenarios.

25 ENERGY STORAGE↗
DOE OSTI2021

Encoding Frequency Constraints in Preventive Unit Commitment Using Deep Learning With Region-of-Interest Active Sampling

With the increasing penetration of renewable energy, frequency response and its security are of significant concerns for reliable power system operations. Frequency-constrained unit commitment (FCUC) is proposed to address this challenge. Despite existing efforts in modeling frequency characteristics in unit commitment (UC), current strategies can only handle oversimplified low-order frequency response models and do not consider wide-range operating conditions. This paper presents a generic data-driven framework for FCUC under high renewable penetration. Here, deep neural networks (DNNs) are trained to predict the frequency response using real data or high-fidelity simulation data. Next, the DNN is reformulated as a set of mixed-integer linear constraints to be incorporated into the ordinary UC formulation. In the data generation phase, all possible power injections are considered, and a region-of-interest active sampling is proposed to include power injection samples with frequency nadirs closer to the UFLC threshold, which enhances the accuracy of frequency constraints in FCUC. The proposed FCUC is investigated on the IEEE 39-bus system. Then, a full-order dynamic model simulation using PSS/E verifies the effectiveness of FCUC in frequency-secure generator commitments.

42 ENGINEERING↗
DOE OSTI2026

Relaxations of the steady optimal gas flow problem for a non-Ideal gas

Natural gas ranks second in U.S. primary energy consumption. Because most production sites are remote, gas must be transported through pipeline networks equipped with compressors, valves, and other components. For both economic efficiency and system reliability, it is desirable to operate these networks optimally. The governing physics across pipeline components entails nonlinear, non-convex equality and inequality constraints, and the most general steady-flow operations problem is a Mixed-Integer Nonlinear Program (MINLP).This work focuses on one such steady-flow problem-the Optimal Gas Flow (OGF) for a natural gas pipeline network-which minimizes production cost subject to the steady-flow physics. For day-to-day operations, the ability to quickly compute a globally optimal solution and a strong lower bound for varying demand profiles is crucial. A promising strategy is to build tight relaxations of the OGF’s nonlinear constraints. However, many nonlinearities arising from non-ideal equations of state either lack relaxations or have relaxations that do not scale to realistic network sizes. We address this gap by combining recent advances in polyhedral relaxations for univariate functions to construct tight, computationally efficient relaxations of the OGF with a non-ideal equation of state. These relaxations solve within seconds on a standard laptop. In conclusion, we demonstrate their quality through extensive numerical experiments on very large-scale test networks from the literature and find that the proposed approach proves optimality in 92% of tested instances.

03 NATURAL GAS↗
DOE OSTI2022

Sequential linear integer programming for integer optimal control with total variation regularization

We propose a trust-region method that solves a sequence of linear integer programs to tackle integer optimal control problems regularized with a total variation penalty. The total variation penalty implies that the considered integer control problems admit minimizers. We introduce a local optimality concept for the problem, which arises from the infinite-dimensional perspective. In the case of a one-dimensional domain of the control function, we prove convergence of the iterates produced by our algorithm to points that satisfy first-order stationarity conditions for local optimality. We demonstrate the theoretical findings on a computational example.

97 MATHEMATICS AND COMPUTING↗