Search NASA⌕ Search

SEARCH · Search NASA

Results for “Mixed Integer 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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Grid-Aware Charging and Operational Optimization for Mixed-Fleet Public Transit

The rapid growth of urban populations and the increasing need for sustainable transportation solutions have prompted a shift towards electric buses in public transit systems. However, the effective management of mixed fleets consisting of both electric and diesel buses poses significant operational challenges. One major challenge is coping with dynamic electricity pricing, where charging costs vary throughout the day. Transit agencies must optimize charging assignments in response to such dynamism while accounting for secondary considerations such as seating constraints. This paper presents a comprehensive mixed-integer linear programming (MILP) model to address these challenges by jointly optimizing charging schedules and trip assignments for mixed (electric and diesel bus) fleets while considering factors such as dynamic electricity pricing, vehicle capacity, and route constraints. We address the potential computational intractability of the MILP formulation, which can arise even with relatively small fleets, by employing a hierarchical approach tailored to the fleet composition. By using real-world data from the city of Chattanooga, Tennessee, USA, we show that our approach can result in significant savings in the operating costs of the mixed transit fleets.

Sen, Rishav↗
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

Embedding Equality Constraints of Optimization Problems into a Quantum Annealer

Quantum annealers such as D-Wave machines are designed to propose solutions for quadratic unconstrained binary optimization (QUBO) problems by mapping them onto the quantum processing unit, which tries to find a solution by measuring the parameters of a minimum-energy state of the quantum system. While many NP-hard problems can be easily formulated as binary quadratic optimization problems, such formulations almost always contain one or more constraints, which are not allowed in a QUBO. Embedding such constraints as quadratic penalties is the standard approach for addressing this issue, but it has drawbacks such as the introduction of large coefficients and using too many additional qubits. In this paper, we propose an alternative approach for implementing constraints based on a combinatorial design and solving mixed-integer linear programming (MILP) problems in order to find better embeddings of constraints of the type Σ x i = k for binary variables x i . Our approach is scalable to any number of variables and uses a linear number of ancillary variables for a fixed k.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Co-optimized trading of hybrid wind power plant with retired EV batteries in energy and reserve markets under uncertainties

To be competitive in the electricity markets, various technologies have been reported to increase profits of wind farm owners. Combining battery storage system, wind farms can be operated as conventional power plants which promotes the integration of wind power into the power grid. However, high expenses on batteries keep investors away. Retired EV batteries, fortunately, still have enough capacity to be reused and could be obtained at a low price. In this work, a two-stage optimization of a wind energy retired EV battery-storage system is proposed. The economic performance of the proposed system is examined concerning its participation in the frequency containment normal operation reserve (FCR-N) market and the spot market simultaneously. To account uncertainties in the wind farm output, various electricity market prices, and up/down regulation status, a scenario-based stochastic programming method is used. The sizing of the equipment is optimized on top of daily operations of the hybrid system which formulates a mixed-integer linear programming (MILP) problem. Scenarios are generated with the Monte Carlo simulation (MCS) and Roulette Wheel Mechanism (RWM), which are further reduced with the simultaneous backward method (SBM) to increase computational efficiency. A 21 MW wind farm is selected as a case study. Here, the optimization results show that by integrating with a retired EV battery-storage system (RESS) and a bi-directional inverter, the wind farm can increase its profits significantly when forwarding bids in both of the aforementioned electricity markets.

17 WIND ENERGY↗
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

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 OSTI2020

Optimization Framework to Assess the Demand Response Capacity of a Water Distribution System

As large electricity consumers, water distribution system (WDS) pumping stations have the potential to become meaningful participants in demand response (DR) programs. The authors propose an optimization framework for assessing the DR capacity of a WDS and identifying the optimal bidding strategy for maximizing WDS revenue in the DR spot market. The proposed mixed integer linear programming (MILP) model overcomes computational constraints of previous DR optimization models by adopting a preprocessing procedure to minimize the number of binary variables and implementing a convex relaxation technique to linearize the hydraulic equations. The proposed MILP model also explicitly accounts for varying levels of risk tolerance of WDS operators by varying the recovery period over which pumping returns to business-as-usual operation. The optimization framework is implemented on a skeletonized 48-node WDS model that includes 7 pumps, 6 tanks, and 39 pipes. Using a simulated DR event and water consumption profile, the authors derive the optimal DR supply curves (i.e., compensation price versus load curtailment quantity) and revenue potential of the WDS under six scenarios for DR participation.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2019

OPERATIONAL TOPOLOGY ESTIMATION OF THREE PHASE UNBALANCED POWER DISTRIBUTION SYSTEMS WITH OUTAGES

Distribution grid, in general, is constructionally loopy but a radially operated network. Opening and closing of suitable tie-switches allows transition from one radial topology to another. Tie-switches ensure reliability and provide restoration paths when faults (outages) occur. The estimation of the system's current operational topology is a precursor to implementing any optimal control actions (during normal operation) or restorative actions (during outage condition). The existing literature in topology detection suffers with several limitations including: (1) computationally intensive nonlinear formulations that are not scalable for large distribution systems, (2) methods requiring exhaustive search for the correct topology by enumerating the complete topological search space, and (3) approaches requiring large volumes of time-series measurements and are not applicable for estimating continuously changing operational topology. Furthermore, the existing literature on distribution grid topology estimation cannot be extended to estimate the operational topology during outage conditions. For operational topology estimation during outages, our objective is to estimate both energized radial feeder and the outaged sections. Starting with a radial topology, these methods identify outaged feeder sections and hence, are inapplicable when the current radial operational topology is not known. In this work, we present a mathematical programming approach to estimate the operational topology of a three-phase unbalanced power distribution system under both outage and normal operating conditions. The aforementioned limitations of existing literature were countered by modeling the problem as a mixed-integer linear programming (MILP) problem which minimizes the errors in available measurements while satisfying the power flow and structural constraints of the system. Specically, a minimum weighted least absolute value estimator is proposed that uses the instantaneous line flow measurements, historical/ forecasted load data, and ping measurements from a limited set of smart meters and solves an MILP to identify the operational topology based on a linearized three-phase unbalanced power flow model. The proposed approach is tested on IEEE 123-bus feeder and 1069 bus multi-feeder test system and the numerical results prove the applicability of the proposed method to large three phase unbalanced grids with high errors in measurements. It is observed that the approach performs well even at high percentages of measurement errors.

GANDLURU NAGA, ANANDINI↗
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 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 OSTI2023

Bi-Level Adaptive Storage Expansion Strategy for Microgrids Using Deep Reinforcement Learning

Battery energy storage (BES) is a versatile resource for the secure and economic operation of microgrids (MGs). Prevailing stochastic optimization-based approaches for BES expansion planning for MGs are computationally complicated. This work proposes a data-driven bi-level multi-period BES expansion planning framework to determine the siting, sizing, and timing of BES installations. The proposed planning framework unifies deep reinforcement learning (DRL) and linear programming, thereby decoupling the determinations for the integer and continuous decision variables in two time scales, respectively. In the upper level, a rainbow DRL agent with quantile regression is trained to provide dynamic planning policies to accommodate stochastic renewable energy resources (RESs), load, and battery price changes efficiently. Further, the lower level computes the optimal operation of MGs with frequency constraints to hedge the islanding contingency. The two levels communicate with one another by exchanging storage configuration and operating expenses in order to accomplish the shared goal of minimizing investment and operation costs. Comparative case studies on an MG are carried out to demonstrate the superiority of the proposed DRL-based solution to the mixed-integer linear programming counterpart on efficiency, scalability, and adaptability.

24 POWER TRANSMISSION AND DISTRIBUTION↗
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

Uncertainty-Informed Operation Coordination in a Water-Energy Nexus

The widespread deployment of smart heterogeneous technologies and the growing complexity in our modern society calls for effective coordination of the interdependent lifeline networks. In particular, operation coordination of electric power and water infrastructures is urgently needed as the water system is one of the most energy-intensive networks, an interruption in which may quickly evolve into a dramatic societal concern. This paper develops a novel analytic for uncertainty-aware day-ahead operation optimization of the interconnected power and water systems (PaWS). Joint probabilistic constraint (JPC) programming is employed to capture the uncertainties in wind resources and water demand forecasts. The proposed integrated stochastic model is presented as a non-linear non-convex optimization problem, where the non-linear hydraulic constraints in the water network are linearized using piece-wise linearization technique, and the non-convexity is efficiently tackled with a solution methodology to convert the proposed model with JPCs to a tractable mixed-integer linear programming (MILP) formulation that can be quickly solved to optimality. Here, the suggested framework is applied to a 15-node commercial-scale water network jointly operated with a power transmission system using a modified IEEE 57-bus test system. The numerical results demonstrate the of the proposed stochastic framework, resulting in cost reduction (13% on average when compared to the traditional setting) and energy saving of the integrated model under different realizations of uncertain renewable energy sources (RESs) and water demand scenarios. Additionally, the scalability of the proposed model is tested on a modified IEEE 118-bus test system connected to five water networks.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Solving the Unit Commitment Problem: Polyhedral Theory, Symmetry, and Power Flow

In this talk, I will give an overview of mixed integer linear programming (MILP) formulations and extensions thereof which enable the effective solution of the unit commitment problem (UC) when paired with a commercial MILP solver. First, we will place UC in context, stressing the importance of achieving a (near) optimal solution. Then we will discuss the importance of perfect and "good-enough" formulations for individual generators / market participants. Some of these formulations enable symmetry-aware reformulations for identical market participants, which can be critical when symmetry is present. Finally, we will discuss approximations of AC power flow currently used in practice, and the challenges with including these approximations within the UC formulation.

MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Solar Field Layout and Aimpoint Strategy Optimization

The existing methods that determine heliostat aiming strategies for concentrating solar power (CSP) central receiver plants typically use heuristics and/or are computationally expensive, and they lack flexibility for different desired flux profiles and receiver geometries. Because of the interaction between layout and aimpoint strategy, considering the former without accounting for the latter may yield solutions with superfluous heliostats that cannot be used efficiently without compromising receiver flux constraints. To that end, we develop a software decision tool that uses innovative optimization methods to both optimize aimpoint strategies and improve candidate layouts for the solar collection field of a CSP central receiver plant. A CSP plant’s effectiveness relies on the optical efficiency of the solar field, which may be limited by losses due to (i) the cosine effect, (ii) atmospheric attenuation, (iii) interference (i.e., shading and blocking) between heliostats, (iv) spillage as a result of heliostat positioning and geometry, and (iv) some heliostats’ inability to direct irradiance to the receiver without damage due to excessive thermal flux. The goal of this work is to obtain optimized aiming strategies and improved solar field layouts that reduce capital cost and increase field optical efficiency and utilization, while meeting the power requirements of a given CSP receiver design. We formulate the aimpoint optimization problem as a mixed-integer linear programming model, which we then decompose into submodels that we solve in parallel. The decomposition subdivides the solar field into sections, and aimpoint strategies for each section are obtained independently of the others. To improve existing layouts, we develop a utilization-weighted efficiency metric that we use to relocate heliostats to sections of the solar field with similar efficiency and higher utilization. Finally, to connect our software to high-fidelity flux models, we develop a Python application programming interface for SolarPILOT, a mature software package that characterizes solar field performance and generates the heliostat layouts and flux maps that serve as input to our models.

14 SOLAR ENERGY↗
DOE OSTI2020

Environmental and economic optima of solar home systems design: A combined LCA and LCC approach

Here, we compare the economic and environmental optimal design of Solar Home Systems (SHSs) and explore the role of economic incentives (such as tariffs and technology costs) in approximating the two optima. To achieve that, we present a methodology for the environmental and economic evaluation of grid-connected SHSs: user-scale electric systems involving a photovoltaic (PV) power system and a battery energy storage system. The proposed methodology is based on a mixed integer linear programming (MILP) optimization, life cycle assessment and life cycle costing. This methodological framework is applied to a case study involving a typical SHS installation in Italy. The results of the environmental optimal design brought to the evaluation of a 3.25 kW PV assisted by 8.66 kWh of nickel cobalt manganese batteries, whereas the costs of the SHS are minimized by a small PV system (less than 1 kW). Results underline that the environmental optimal configurations rely on battery technologies, which entails a significant cost compared to the grid connection. In contrast, the economic optimal design solutions is less impactful than the grid mix both from an environmental and economic points of view. Thanks to a reduction of batteries and PV costs, the environmental impact of the economic optimal design is expected to decrease in the future.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Decomposing a renewable energy design and dispatch model

We address a mixed-integer linear programming model which selects a cost-minimizing set of available technologies with which to design a renewable energy system and prescribe their associated dispatch decisions. Realistically sized instances of such models pose computational challenges. To this end, we develop a Lagrangian heuristic based on a decomposition methodology which partitions the model into blocks and optimizes these more manageable, smaller subproblems. It also provides a lower bound to assess solution quality. In conclusion, we apply this methodology to the National Renewable Energy Laboratory's Renewable Energy Integration and Optimization (REopt TM ) model to generate near-optimal solutions to realistic instances containing, on average, approximately 300,000 variables and at least as many constraints, with a mean 30% optimality gap improvement using a five-minute solution time limit, compared to directly solving the original monolith.

97 MATHEMATICS AND COMPUTING↗