Search NASA⌕ Search

SEARCH · Search NASA

Results for “LINEAR PROGRAMMING”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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

At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Assessing the Optimality of LinDist3Flow for Optimal Tap Selection of Step Voltage Regulators in Unbalanced Distribution Networks: Preprint

The adoption of distributed energy resources such as photovoltaics (PVs) has increased dramatically during the previous decade. The increased penetration of PVs into distribution networks (DNs) can cause voltage fluctuations that have to be mitigated. One of the key utility assets employed to this end are step-voltage regulators (SVRs). It is desirable to include tap selection of SVRs in optimal power flow (OPF) routines, a task that turns out to be challenging because the resultant OPF problem is nonconvex with added complexities stemming from accurate SVR modeling. While several convex relaxations based on semi-definite programming (SDP) have been presented in the literature for optimal tap selection, SDP based schemes do not scale well and are challenging to implement in large-scale planning or operational frameworks. This paper deals with the optimal tap selection (OPTS) problem for wye-connected SVRs using linear approximations of power flow equations. Specifically, the LinDist3Flow model is adopted and the effective SVR ratio is assumed to be continuous–enabling the formulation of a problem called LinDist3Flow-OPTS, which amounts to a linear program. The scalability and optimality gap of LinDist3Flow-OPTS are evaluated with respect to existing SDP-based and nonlinear programming techniques for optimal tap selection in three standard feeders, namely, the IEEE 13-bus, 123-bus, and 8500-node DNs. For all DNs considered, LinDist3Flow-OPTS achieves an optimality gap of approximately 1% or less while significantly lowering the computational burden.

linear approximations↗
DOE OSTI2023

Assessing the Optimality of LinDist3Flow for Optimal Tap Selection of Step Voltage Regulators in Unbalanced Distribution Networks

The adoption of distributed energy resources such as photovoltaics (PVs) has increased dramatically during the previous decade. The increased penetration of PVs into distribution networks (DNs) can cause voltage fluctuations that have to be mitigated. One of the key utility assets employed to this end are step-voltage regulators (SVRs). It is desirable to include tap selection of SVRs in optimal power flow (OPF) routines, a task that turns out to be challenging because the resultant OPF problem is nonconvex with added complexities stemming from accurate SVR modeling. While several convex relaxations based on semi-definite programming (SDP) have been presented in the literature for optimal tap selection, SDP based schemes do not scale well and are challenging to implement in large-scale planning or operational frameworks. This paper deals with the optimal tap selection (OPTS) problem for wye-connected SVRs using linear approximations of power flow equations. Specifically, the LinDist3Flow model is adopted and the effective SVR ratio is assumed to be continuous- enabling the formulation of a problem called LinDist3Flow-OPTS, which amounts to a linear program. The scalability and optimality gap of LinDist3Flow-OPTS are evaluated with respect to existing SDP-based and nonlinear programming techniques for optimal tap selection in three standard feeders, namely, the IEEE 13-bus, 123-bus, and 8500-node DNs. For all DNs considered, LinDist3Flow-OPTS achieves an optimality gap of approximately 1% or less while significantly lowering the computational burden.

linear approximations↗
DOE OSTI2018

Simultaneous Process and Heat Exchanger Network Synthesis Using a Discrete Temperature Grid

We present mixed-integer linear programming models for utility targeting and heat exchanger network synthesis that account for variable stream temperatures and flow rates as well as unclassified streams and thus can be combined with process synthesis optimization models. By projecting temperature information onto a fixed discrete temperature grid, the model remains linear even under variable temperatures and flow rates, leading to a more tractable optimization model. The proposed model is well suited to address problems in the area of process intensification where the close interaction between different phenomena naturally leads to process synthesis problems with unclassified process streams. Several extensions are presented, including nonisothermal mixing as well as phase changes. Moreover, we show how a nonuniform grid can be adopted to reduce the complexity of the model for medium and large-size problems.

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

Linear optimal power flow system and method

An electric power system or power grid is optimized using a computer-implemented tool the represents in computer memory the optimization function and at least one constraint, which the processor operates upon using a linear programming solver algorithm. The constraints are represented in memory as data structures that include both real and reactive power terms, corresponding to at least one of a power flow model and a transmission line model. The transmission line model is represented using a piecewise linear representation. The power flow model may also include for each node in the power system a real power loss term representing transmission line loss allocated to that node.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Linear model decision trees as surrogates in optimization of engineering applications

Machine learning models are promising as surrogates in optimization when replacing difficult to solve equations or black-box type models. This work demonstrates the viability of linear model decision trees as piecewise-linear surrogates in decision-making problems. Linear model decision trees can be represented exactly in mixed-integer linear programming (MILP) and mixed-integer quadratic constrained programming (MIQCP) formulations. Furthermore, they can represent discontinuous functions, bringing advantages over neural networks in some cases. We present several formulations using transformations from Generalized Disjunctive Programming (GDP) formulations and modifications of MILP formulations for gradient boosted decision trees (GBDT). We then compare the computational performance of these different MILP and MIQCP representations in an optimization problem and illustrate their use on engineering applications. Importantly, we observe faster solution times for optimization problems with linear model decision tree surrogates when compared with GBDT surrogates using the Optimization and Machine Learning Toolkit (OMLT).

42 ENGINEERING↗
DOE OSTI2022

Building Load Control Using Distributionally Robust Chance-Constrained Programs with Right-Hand Side Uncertainty and the Risk-Adjustable Variants

Aggregation of heating, ventilation, and air conditioning (HVAC) loads can provide reserves to absorb volatile renewable energy, especially solar photo-voltaic (PV) generation. In this paper, we decide HVAC control schedules under uncertain PV generation, using a distributionally robust chance-constrained (DRCC) building load control model under two typical ambiguity sets: the moment-based and Wasserstein ambiguity sets. We derive mixed integer linear programming (MILP) reformulations for DRCC problems under both sets. Especially, for the Wasserstein ambiguity set, we use the right-hand side (RHS) uncertainty to derive a more compact MILP reformulation than the commonly known MILP reformulations with big-M constants. All the results also apply to general individual chance constraints with RHS uncertainty. Furthermore, we propose an adjustable chance-constrained variant to achieve tradeoff between the operational risk and costs. We derive MILP reformulations under the Wasserstein ambiguity set and second-order conic programming (SOCP) reformulations under the moment-based set. Using real-world data, we conduct computational studies to demonstrate the efficiency of the solution approaches and the effectiveness of the solutions. Summary of Contribution: The problem studied in this paper is motivated by a building load control problem that uses the aggregation of heating, ventilation, and air conditioning (HVAC) loads as flexible reserves to absorb uncertain solar photovoltaic (PV) generation. The problem is formulated as distributionally robust chance-constrained (DRCC) programs with right-hand side (RHS) uncertainty. In addition, we propose a risk-adjustable variant of the DRCC programs, where the risk level, instead of being predetermined, is treated as a decision variable. The paper aims to provide tractable reformulations and solution algorithms for both the (general) DRCC and the (general) adjustable DRCC models with RHS uncertainty.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Optimizing design and dispatch of a renewable energy system with combined heat and power

We embellish a mixed-integer program that prescribes a set of renewable energy, conventional generation, and storage technologies to procure, along with a corresponding dispatch strategy. Specifically, we add combined heat and power to this set. The model minimizes fixed and operational costs less incentives for the use of various technologies, subject to a series of component interoperability and system-wide constraints. The resulting mixed-integer linear program contains hundreds of thousands of variables and constraints. We demonstrate how to efficiently formulate and solve the corresponding instances such that we produce near-optimal solutions in minutes. A previous rendition of the model required hours of solution time for the same instances.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

A stochastic biomass blending problem in decentralized supply chains

Blending biomass materials of different physical or chemical properties provides an opportunity to adjust the quality of the feedstock to meet the specifications of the conversion platform. We propose a model which identifies the right mix of biomass to optimize the performance of the thermochemical conversion process at the mini-mum cost. This is a chance-constraint programming (CCP) model which takes into account the stochastic nature of biomass quality. The proposed CCP model ensures that process requirements, which are impacted by physical and chemical properties of biomass, are met most of the time. We consider two problem settings, a centralized and a decentralized supply chain. We propose a mixed-integer linear program to model the blending problem in the centralized setting and a bilevel program to model the blending problem in the decentralized setting. We use the sample average approximation method to approximate the chance constraints, and propose solution algorithms to solve this approximation. We develop a case study for South Carolina using data provided by the Billion Ton Study. Based on our results, the blends identified consist mainly of pine and softwood residues. The blends identified and the suppliers selected by both models are different. The cost of the centralized supply chain is 2%–6% lower. The implications of these results are twofold. First, these results could lead to improved collaborations in the supply chain. Second, these results provide an estimate of the approximation error from assuming centralized decision making in the supply chain.

09 BIOMASS FUELS↗
DOE OSTI2020

Cost-optimal evaluation of centralized and distributed microgrid topologies considering voltage constraints

Optimal design of hybrid renewable mini-grids requires both economic and power quality considerations. Existing modeling approaches address these considerations via separate or loosely coupled models. Here, we extend REopt—a techno-economic optimization model developed at the National Renewable Energy Laboratory—to consider both within a single model. REopt formulates the design problem as a mixed-integer linear program that solves for a site's optimal technology mix, sizing, and operation to minimize life cycle cost. REopt has traditionally assumed a single node system. In the work presented here, we expand the REopt platform to consider multiple connected nodes with associated voltage constraints. In order to do this, we model power flow using a fixed-point linear approximation method. Additionally, we then use the model to explore design considerations of mini-grids in Sub-Saharan Africa. Specifically, we evaluate under what combinations of transmission line distance and capacity it is technically viable and economically preferable to build multiple isolated mini-grids versus an interconnected, centralized system.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

Design Considerations for GPU-based Mixed Integer Programming on Parallel Computing Platforms

Mixed Integer Programming (MIP) is a powerful abstraction in combinatorial optimization that finds real-life application across many significant sectors. The recent proliferation of graphical processing unit (GPU)-based accelerated computing architectures in large-scale parallel computing or supercomputing presents new opportunities as well as challenges in the advancement of MIP solver technology to effectively use the new accelerated computing platforms and scale to large parallel systems. Here, we recount the conventional processor-based strategies and focus on configurations where the most promising intersection lies between parallel MIP solver approaches and the specific strengths of accelerated parallel platforms. We note that the best potential lies in solving problems whose individual matrix sizes (of the linear program relaxation) fit entirely within one accelerator's memory and whose branch-and-bound (or branch-and-cut) trees cannot be fully contained within a small number of computational nodes. Additionally, we identify ideal features of computational linear algebra support on GPU accelerators that would help advance this direction of scalable parallel solution of MIP problems on GPU-based accelerated computing architectures.

Perumalla, Kalyan↗
DOE OSTI2018

The Ramping Polytope and Cut Generation for the Unit Commitment Problem

We present a perfect formulation for a single generator in the unit commitment problem, inspired by the dynamic programming approach taken by Frangioni and Gentile. This generator can have characteristics such as ramp-up/ramp-down constraints, time-dependent start-up costs, and start-up/shut-down limits. To develop this perfect formulation, we extend the result of Balas on unions of polyhedra to present a framework allowing for flexible combinations of polyhedra using indicator variables. Here, we use this perfect formulation to create a cut-generating linear program, similar in spirit to lift-and-project cuts, and demonstrate computational efficacy of these cuts in a utility-scale unit commitment problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Multistage distributionally robust mixed-integer programming with decision-dependent moment-based ambiguity sets

We study multistage distributionally robust mixed-integer programs under endogenous uncertainty, where the probability distribution of stage-wise uncertainty depends on the decisions made in previous stages. We first consider two ambiguity sets defined by decision-dependent bounds on the first and second moments of uncertain parameters and by mean and covariance matrix that exactly match decision-dependent empirical ones, respectively. For both sets, we show that the subproblem in each stage can be recast as a mixed-integer linear program (MILP). Moreover, we extend the general moment-based ambiguity set in to the multistage decision-dependent setting, and derive mixed-integer semidefinite programming (MISDP) reformulations of stage-wise subproblems. We develop methods for attaining lower and upper bounds of the optimal objective value of the multistage MISDPs, and approximate them using a series of MILPs. We deploy the Stochastic Dual Dynamic integer Programming (SDDiP) method for solving the problem under the three ambiguity sets with risk-neutral or risk-averse objective functions, and conduct numerical studies on multistage facility-location instances having diverse sizes under different parameter and uncertainty settings. Furthermore, our results show that the SDDiP quickly finds optimal solutions for moderate-sized instances under the first two ambiguity sets, and also finds good approximate bounds for the multistage MISDPs derived under the third ambiguity set. We also demonstrate the efficacy of incorporating decision-dependent distributional ambiguity in multistage decision-making processes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A Scalable Approach to Minimize Charging Costs for Electric Bus Fleets

Incorporating battery electric buses into bus fleets faces three primary challenges: a BEB’s extended refuel time, the cost of charging, both by the consumer and the power provider, and large compute demands for planning methods. When BEBs charge, the additional demands on the grid may exceed hardware limitations, so power providers divide a consumer’s energy needs into separate meters even though doing so is expensive for both power providers and consumers. Prior work has developed a number of strategies for computing charge schedules for bus fleets; however, prior work has not worked to reduce costs by aggregating meters. Additionally, because many works use mixed integer linear programs, their compute needs make planning for commercial-sized bus fleets intractable. This work presents a multi-program approach to computing charge plans for electric bus fleets. The proposed method solves a series of subproblems where the solution to the charge problem becomes more refined with each problem, moving closer to the optimal schedule. The results demonstrate how runtimes are reduced by using intermediate subproblems to refine the bus charge solution so that the proposed method can be applied to large bus fleets of 100+ buses. Not only will we demonstrate that runtimes scale linearly with the number of buses but we will also show how the proposed method scales to large bus fleets of over 100 buses while managing the monthly cost of energy.

Mortensen, Daniel (ORCID:0000000276494452)↗
DOE OSTI2022

Two-Stage Optimization Framework for Detecting and Correcting Parameter Cyber-Attacks in Power System State Estimation

One major tool of Energy Management Systems for monitoring the status of the power grid is State Estimation. Since the results of state estimation are used within the energy management system, the security of the state estimation process is most important. The focus research in this area is on detecting False Data Injection attacks on measurements. While this is important, State Estimation also rely on database that are used to describe the relationship between measurements and systems' states. This paper presents a two-stage programming framework to detect and correct attacks in the parameters of the measurement model used by the state estimation process in the Energy Management System. In the first stage, an estimate of the line parameters ratios are obtained. In the second stage, the estimated ratios from stage I are used in a Bi-Level model for obtaining a final estimate of the measurements' model parameters. Hence, the presented framework does not only unify the detection and correction in a single optimization run, but also provide a monitoring scheme for the SE database that is typically considered static. In addition, in the two stages, linear programming framework is preserved. For validation, the IEEE 118 bus system is used for implementation. The results of this paper illustrate the effectiveness of the proposed model for detecting attacks in the database used in the state estimation process.

state estimation, two-stage optimization, cyber-ph↗
DOE OSTI2020

Improving operational flexibility of integrated energy system with uncertain renewable generations considering thermal inertia of buildings

Insufficient flexibility in system operation caused by traditional "heat-set" operating modes of combined heat and power (CHP) units in winter heating periods is a key issue that limits renewable energy consumption. In order to reduce the curtailment of renewable energy resources through improving the operational flexibility, a novel optimal scheduling model based on chance-constrained programming (CCP), aiming at minimizing the lowest generation cost, is proposed for a small-scale integrated energy system (IES) with CHP units, thermal power units, renewable generations and representative auxiliary equipments. In this model, due to the uncertainties of renewable generations including wind turbines and photovoltaic units, the probabilistic spinning reserves are supplied in the form of chance-constrained; from the perspective of user experience, a heating load model is built with consideration of heat comfort and inertia in buildings. To solve the model, a solution approach based on sequence operation theory (SOT) is developed, where the original CCP-based scheduling model is tackled into a solvable mixed-integer linear programming (MILP) formulation by converting a chance constraint into its deterministic equivalence class, and thereby is solved via the CPLEX solver. We report the simulation results on the modified IEEE 30-bus system demonstrate that the presented method manages to improve operational flexibility of the IES with uncertain renewable generations by comprehensively leveraging thermal inertia of buildings and different kinds of auxiliary equipments, which provides a fundamental way for promoting renewable energy consumption.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2017

Generation Expansion Planning With Large Amounts of Wind Power via Decision-Dependent Stochastic Programming

Power generation expansion planning needs to deal with future uncertainties carefully, given that the invested generation assets will be in operation for a long time. Many stochastic programming models have been proposed to tackle this challenge. However, most previous works assume predetermined future uncertainties (i.e., fixed random outcomes with given probabilities). In several recent studies of generation assets' planning (e.g., thermal versus renewable), new findings show that the investment decisions could affect the future uncertainties as well. To this end, this paper proposes a multistage decision-dependent stochastic optimization model for long-term large-scale generation expansion planning, where large amounts of wind power are involved. In the decision-dependent model, the future uncertainties are not only affecting but also affected by the current decisions. In particular, the probability distribution function is determined by not only input parameters but also decision variables. To deal with the nonlinear constraints in our model, a quasi-exact solution approach is then introduced to reformulate the multistage stochastic investment model to a mixed-integer linear programming model. The wind penetration, investment decisions, and the optimality of the decision-dependent model are evaluated in a series of multistage case studies. The results show that the proposed decision-dependent model provides effective optimization solutions for long-term generation expansion planning.

Zhan, Yiduo↗
DOE OSTI2022

Sizing battery energy storage and PV system in an extreme fast charging station considering uncertainties and battery degradation

In this paper, we present mixed integer linear programming (MILP) formulations to obtain optimal sizing for a battery energy storage system (BESS) and solar generation system in an extreme fast charging station (XFCS) to reduce the annualized total cost. The proposed model characterizes a typical year with eight representative scenarios and obtains the optimal energy management for the station and BESS operation to exploit the energy arbitrage for each scenario. Contrasting extant literature, this paper proposes a constant power constant voltage (CPCV) based improved probabilistic approach to model the XFCS charging demand for weekdays and weekends. This paper also accounts for the monthly and annual demand charges based on realistic utility tariffs. Furthermore, BESS life degradation is considered in the model to ensure no replacement is needed during the considered planning horizon. Different from the literature, this paper offers pragmatic MILP formulations to tally BESS charge/discharge cycles using the cumulative charge/discharge energy concept. McCormick relaxations and the Big-M method are utilized to relax the bi-linear terms in the BESS operational constraints. Finally, a robust optimization-based MILP model is proposed and leveraged to account for uncertainties in electricity price, solar generation, and XFCS demand. Case studies were performed to signify the efficacy of the proposed formulations.

24 POWER TRANSMISSION AND DISTRIBUTION↗