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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Optimization of battery swapping infrastructure for e-commerce drone delivery

Drone delivery is widely-researched to alter the current e-commerce delivery convention for providing short delivery lead times. Yet, flight range of drones, constrained by the available battery technology, sets a milestone toward realizing the sole-drone delivery. To tackle with the flight range limitation, locating automated battery swapping machines (ABSM) have been proposed and a few studies modeled the problem. Using the ABSMs, drones can be loaded with fully-charged batteries along the route to a demand location. Here, we introduce a mixed-integer nonlinear program to model the problem. The objective of the program is to optimally select ABSM locations, determine the delivery-mode choices (drone-only, truck-only, and mixed delivery) of demand locations, find drone delivery routes, and approximate the baseline requirements for the number of drones and batteries needed. The program minimizes the overall delivery system costs including: ABSM, delivery, drone ownership, battery inventory, and service congestion. A cutting-plane method is developed to find exact solutions in finite iterations. Computational experiments showed that the method quickly yields the optimal solution to instances with less than 60 ABSM candidates and 20 demand locations. A case study shows that the optimal drone delivery infrastructure can save almost 20% cost compared to the conventional truck-only delivery. Sensitivity analyses were conducted to reveal the impact of key parameters in the decision-making and found that a decrease in the ABSM and drone costs highly affect the system cost.

25 ENERGY STORAGE↗
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 OSTI2021

Convergence of sum-up rounding schemes for cloaking problems governed by the Helmholtz equation

In this work, we consider the problem of designing a cloak for waves described by the Helmholtz equation from an integer programming point of view. The problem can be modeled as a PDE-constrained optimization problem with integer-valued control inputs that are distributed in the computational domain. A first-discretize-then-optimize approach results in a large-scale mixed-integer nonlinear program that is in general intractable because of the large number of integer variables that arise from the discretization of the domain. Instead, we propose an efficient algorithm that is able to approximate the local infima of the underlying nonconvex infinite-dimensional problem arbitrarily close without the need to solve the discretized finite-dimensional integer programs to optimality. We optimize only the continuous relaxations of the approximations for local minima and then apply the sum-up rounding methodology to obtain integer-valued controls. If the solutions of the discretized continuous relaxations converge to a local minimizer of the continuous relaxation, then the resulting discrete-valued control sequence converges weakly \(^*\) in \(L^\infty\) to the same local minimizer. These approximation properties follow under suitable refinements of the involved discretization grids. Our results use familiar concepts arising from the analytical properties of the underlying PDE and complement previous results, derived from a topology optimization point of view.

97 MATHEMATICS AND COMPUTING↗
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 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 OSTI2020

Virtual-Voltage Partition-Based Approach to Optimal Transmission Switching

This article deals with optimal transmission switching (OTS) problems involving binary decisions about network topology and nonconvex power flow constraints. We adopt a semidefinite programming formulation for the optimal power flow (OPF) problem that, however, remains nonconvex due to the presence of discrete variables and bilinear products between the decision variables. To tackle the latter, we introduce a physically inspired, virtual-voltage approximation that leads to provable lower and upper bounds on the solution of the original problem. To deal with the exponential complexity caused by the discrete variables, we introduce a graph partition-based algorithm that breaks the problem into several parallel mixed-integer subproblems of smaller size. Simulations on the IEEE bus test cases demonstrate the high degree of accuracy and affordable computational requirements of our approach.

42 ENGINEERING↗
DOE OSTI2025

Optimizing the design and operation of water networks: Two decomposition approaches

We consider the design and operation of water networks simultaneously. Water network problems can be divided into two categories: the design problem and the operation problem. The design problem involves determining the appropriate pipe sizing and placements of pump stations, while the operation problem involves scheduling pump stations over multiple time periods to account for changes in supply and demand. Our focus is on networks that involve water co-produced with oil and gas. While solving the optimization formulation for such networks, we found that obtaining a primal (feasible) solution is more challenging than obtaining dual bounds using off-the-shelf mixed-integer nonlinear programming solvers. Therefore, we propose two methods to obtain good primal solutions. One method involves a decomposition framework that utilizes a convex reformulation, while the other is based on time decomposition. To test our proposed methods, we conduct computational experiments on a network derived from the PARETO case study.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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 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 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 OSTI2021

Framework for optimization of long-term, multi-period investment planning of integrated urban energy systems

In order to achieve stringent greenhouse gas emission reductions, a transition of our entire energy system from fossil to renewable resources needs to be designed. Such an energy transition brings two main challenges: most renewables generate variable electric energy, yet most demand is currently not electric (carrier mismatch) and does not always manifest at the same time as supply (temporal mismatch). Integrating multiple energy infrastructures can address both challenges by using the synergy between different energy carriers; building on existing infrastructure, while allowing a robust and flexible integration of the new. This paper proposes an optimization framework for long-term, multi-period investment planning of urban energy systems in an integrated manner. We formulate it as a mixed-integer linear program, combining a capacitated facility location with a multi-dimensional, capacitated network design problem. It includes generation and network expansion planning as well as interconnections between networks and storage infrastructure for each energy system. It can incorporate pathway effects like techno-economic developments, policy measures, and weather variations. The intended use is to support urban decision makers with long-term investment planning, though it can be tailored to fit other geographical or temporal scales. We demonstrate the model using two cases based on an average city in The Netherlands, which wants to reduce its CO 2 -emissions with 95% by 2050. In the first case, we include explicit carbon-emission constraints to study the effects of the carrier mismatch. In the second case, we implement interannual weather variations to analyze the temporal mismatch. The results give valuable insights into the energy transition design strategy for urban decision makers. They also show the future potential, as well as the computational challenges of the optimization framework.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Vehicle-to-manufacturing (V2M) system: A novel approach to improve energy demand flexibility for demand response towards sustainable manufacturing

The U.S. manufacturing sector accounts for 77% of the industrial energy consumption, but its participation in demand response (DR) programs is largely lagged behind. The limited flexibility in production scheduling under high capacity utilization and the lack of DR schemes that incorporate energy demand flexibility measures are deemed as major barriers. In this study, a framework of the interactive vehicles-to-manufacturing (V2M) energy sharing system is proposed to improve the energy demand flexibility of the aggregated system and enhance the DR effectiveness for manufacturers. The V2M-based DR scheme aims to reduce the energy cost by load shifting through joint production and energy sharing control, which can eventually promote manufacturing DR implementation even under high capacity utilization requirements and dynamic real-time electricity prices. The V2M system is modeled based on a discrete-Markov chain considering the complex interconnections among various manufacturing resources and multi-directional energy flows among manufacturing facilities, electric vehicles, and the power grid. Based on the system model, a mixed-integer nonlinear programming (MINLP) problem is formulated to identify the optimal DR scheme. The effectiveness of the proposed approach is validated through comparisons with traditional manufacturing DR schemes. Finally, the results show that a 2.1 to 6.5 times energy demand flexibility improvement and an additional 4.7% to 6.9% energy cost reduction can be achieved by the proposed approach.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2018

Evaluating demand response opportunities for power systems resilience using MILP and MINLP Formulations

While peak shaving is commonly used to reduce power costs, chemical process facilities that can reduce power consumption on demand during emergencies (e.g., extreme weather events) bring additional value through improved resilience. For process facilities to effectively negotiate demand response (DR) contracts and make investment decisions regarding flexibility, they need to quantify their additional value to the grid. We present a grid–centric mixed–integer stochastic programming framework to determine the value of DR for improving grid resilience in place of capital investments that can be cost prohibitive for system operators. We formulate problems using both a linear approximation and a nonlinear alternating current power flow model. Our numerical results with both models demonstrate that DR can be used to reduce the capital investment necessary for resilience, increasing the value that chemical process facilities bring through DR. Furthermore, the linearized model often underestimates the amount of DR needed in our case studies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Designing a GIS-based supply chain for producing carinata-based sustainable aviation fuel in Georgia, USA

Carinata is a potential crop for sustainable aviation fuel (SAF) production in the southern USA. However, as a novel crop, the cost-effectiveness and environmental feasibility of carinata feedstock are unknown, and there are questions about the optimal supply chain configuration for carinata-based SAF production. This study aims to design a supply chain model for carinata-based SAF production by optimizing the location of farms and facilities (e.g. storage units, crushing mills, biorefineries) for a minimum transportation cost under a set of supply and demand conditions. An integrated mixed-integer linear programming (MILP) model was combined with geographical information system (GIS) analysis to design a spatially explicit supply chain configuration. The GIS-based network analysis considered all of the counties in Georgia to set the candidate locations of carinata farms and facilities, and determined minimum cost and emission routes between those counties and the airport using existing transportation networks and modes (e.g. road, rail and pipeline). The MILP model determined the final selection of the farms and the number of facilities and their locations over those minimum-cost routes. With this supply chain configuration, the minimum price of SAF was $\$$0.92 L –1 , which is $\$$0.44 higher than conventional aviation fuel (CAF). The associated carbon intensity of SAF was estimated at 940.7 g CO 2 e L –1 , a reduction of 66% relative to the carbon intensity of equivalent CAF. The study found that a carbon tax (or subsidy) of $\$$230.48 t CO 2 e –1 would be needed to overcome the cost differential with CAF and promote carinata-based SAF in Georgia.

09 BIOMASS FUELS↗
DOE OSTI2023

Holistic fleet optimization incorporating system design considerations

The methodology described in this article enables a type of holistic fleet optimization that simultaneously considers the composition and activity of a fleet through time as well as the design of individual systems within the fleet. Often, real-world system design optimization and fleet-level acquisition optimization are treated separately due to the prohibitive scale and complexity of each problem. Importantly, this means that fleet-level schedules are typically limited to the inclusion of predefined system configurations and are blind to a rich spectrum of system design alternatives. Similarly, system design optimization often considers a system in isolation from the fleet and is blind to numerous, complex portfolio-level considerations. In reality, these two problems are highly interconnected. To properly address this system-fleet design interdependence, we present a general method for efficiently incorporating multi-objective system design trade-off information into a mixed-integer linear programming (MILP) fleet-level optimization. This work is motivated by the authors' experience with large-scale DOD acquisition portfolios. However, the methodology is general to any application where the fleet-level problem is a MILP and there exists at least one system having a design trade space in which two or more design objectives are parameters in the fleet-level MILP.

97 MATHEMATICS AND COMPUTING↗