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At least 667 records · Page 37
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Fast yaw optimization for wind plant wake steering using Boolean yaw angles

Abstract. In wind plants, turbines can be yawed into the wind to steer their wakes away from downstream turbines and achieve an overall increase in plant power. Mathematical optimization is typically used to determine the best yaw angles at which to operate the turbines in a plant. In this paper, we present a new heuristic to rapidly determine the yaw angles in a wind plant. In this method, we define the turbine yaw angles as Boolean – either yawed at a predefined angle or nonyawed – as opposed to the typical methods of defining yaw angles as continuous or with fine discretizations. We then optimize which turbines should be yawed with an algorithm that sweeps through the turbines from the most upstream to the most downstream. We demonstrate that our new Boolean optimization method can find turbine yaw angles that perform well compared to a traditionally used gradient-based optimizer for which the yaw angles are defined as continuous. There is less than 0.6 % difference in the optimized power between the two optimization methods for randomly placed turbine layouts and less than a 0.6 % difference in the optimal annual energy production between the two optimization methods for a real wind farm. Additionally, we show that our new method is much more computationally efficient than the traditional method. For plants with nonzero optimal yaw angles, our new method is generally able to solve for the turbine yaw angles 50–150 times faster, and in some extreme cases up to 500 times faster, than the traditional method.

17 WIND ENERGY↗
DOE OSTI2021

The impacts of convex piecewise linear cost formulations on AC optimal power flow

Despite strong connections through shared application areas, research efforts on power market optimization (e.g., unit commitment) and power network optimization (e.g., optimal power flow) remain largely independent. A notable illustration of this is the treatment of power generation cost functions, where nonlinear network optimization has largely used polynomial representations and market optimization has adopted piecewise linear encodings. This work combines state-of-the-art results from both lines of research to understand the best mathematical formulations of the nonlinear AC optimal power flow problem with piecewise linear generation cost functions. An extensive numerical analysis of non-convex models, linear approximations, and convex relaxations across fifty-four realistic test cases illustrates that nonlinear optimization methods are surprisingly sensitive to the mathematical formulation of piecewise linear functions. The results indicate that a poor formulation choice can slow down algorithm performance by a factor of ten, increasing the runtime from seconds to minutes. Furthermore, these results provide valuable insights into the best formulations of nonlinear optimal power flow problems with piecewise linear cost functions, an important step towards building a new generation of energy markets that incorporate the nonlinear AC power flow model.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2017

Deterministic direct aperture optimization using multiphase piecewise constant segmentation

Purpose Direct aperture optimization (DAO) attempts to incorporate machine constraints in the inverse optimization to eliminate the post‐processing steps in fluence map optimization (FMO) that degrade plan quality. Current commercial DAO methods utilize a stochastic or greedy approach to search a small aperture solution space. In this study, we propose a novel deterministic direct aperture optimization that integrates the segmentation of fluence map in the optimization problem using the multiphase piecewise constant Mumford‐Shah formulation. Methods The Mumford‐Shah based direct aperture optimization problem was formulated to include an L2‐norm dose fidelity term to penalize differences between the projected dose and the prescribed dose, an anisotropic total variation term to promote piecewise continuity in the fluence maps, and the multiphase piecewise constant Mumford‐Shah function to partition the fluence into pairwise discrete segments. A proximal‐class, first‐order primal‐dual solver was implemented to solve the large scale optimization problem, and an alternating module strategy was implemented to update fluence and delivery segments. Three patients of varying complexity—one glioblastoma multiforme (GBM) patient, one lung (LNG) patient, and one bilateral head and neck (H&N) patient with 3 PTVs—were selected to test the new DAO method. For each patient, 20 non‐coplanar beams were first selected using column generation, followed by the Mumford‐Shah based DAO (DAO MS ). For comparison, a popular and successful approach to DAO known as simulated annealing—a stochastic approach—was replicated. The simulated annealing DAO (DAO SA ) plans were then created using the same beam angles and maximum number of segments per beam. PTV coverage, PTV homogeneity , and OAR sparing were assessed for each plan. In addition, high dose spillage, defined as the 50% isodose volume divided by the tumor volume, as well as conformity, defined as the van't Riet conformation number, were evaluated. Results DAO MS achieved essentially the same OAR doses compared with the DAO SA plans for the GBM case. The average difference of OAR D max and D mean between the two plans were within 0.05% of the plan prescription dose. The lung case showed slightly improved critical structure sparing using the DAO MS approach, where the average OAR D max and D mean were reduced by 3.67% and 1.08%, respectively, of the prescription dose. The DAO MS plan substantially improved OAR dose sparing for the H&N patient, where the average OAR D max and D mean were reduced by over 10% of the prescription dose. The DAO MS and DAO SA plans were comparable for the GBM and LNG PTV coverage, while the DAO MS plan substantially improved the H&N PTV coverage, increasing D99 by 6.98% of the prescription dose. For the GBM and LNG patients, the DAO MS and DAO SA plans had comparable high dose spillage but slightly worse conformity with the DAO MS approach. For the H&N plan, DAO MS was considerably superior in high dose spillage and conformity to the DAO SA . The deterministic approach is able to solve the DAO problem substantially faster than the simulated annealing approach, with a 9.5‐ to 40‐fold decrease in total solve time, depending on the patient case. Conclusions A novel deterministic direct aperture optimization formulation was developed and evaluated. It combines fluence map optimization and the multiphase piecewise constant Mumford‐Shah segmentation into a unified framework, and the resulting optimization problem can be solved efficiently. Compared to the widely and commercially used simulated annealing DAO approach, it showed comparable dosimetry behavior for simple plans, and substantially improved OAR sparing, PTV coverage, PTV homogeneity, high dose spillage, and conformity for the more complex head and neck plan.

Nguyen, Dan↗
DOE OSTI2014

Progressive construction of a parametric reduced‐order model for PDE‐constrained optimization

Summary An adaptive approach to using reduced‐order models (ROMs) as surrogates in partial differential equations (PDE)‐constrained optimization is introduced that breaks the traditional offline‐online framework of model order reduction. A sequence of optimization problems constrained by a given ROM is defined with the goal of converging to the solution of a given PDE‐constrained optimization problem. For each reduced optimization problem, the constraining ROM is trained from sampling the high‐dimensional model (HDM) at the solution of some of the previous problems in the sequence. The reduced optimization problems are equipped with a nonlinear trust‐region based on a residual error indicator to keep the optimization trajectory in a region of the parameter space where the ROM is accurate. A technique for incorporating sensitivities into a reduced‐order basis is also presented, along with a methodology for computing sensitivities of the ROM that minimizes the distance to the corresponding HDM sensitivity, in a suitable norm. The proposed reduced optimization framework is applied to subsonic aerodynamic shape optimization and shown to reduce the number of queries to the HDM by a factor of 4‐5, compared with the optimization problem solved using only the HDM, with errors in the optimal solution far less than 0.1%. Copyright © 2014 John Wiley & Sons, Ltd.

Zahr, Matthew J.↗
DOE OSTI2017

Co-optimization of CO 2 -EOR and Storage Processes under Geological Uncertainty

This paper presents an integrated numerical framework to co-optimize EOR and CO 2 storage performance in the Farnsworth field unit (FWU), Ochiltree County, Texas. The framework includes a field-scale compositional reservoir flow model, an uncertainty quantification model and a neural network optimization process. The reservoir flow model has been constructed based on the field geophysical, geological, and engineering data. A laboratory fluid analysis was tuned to an equation of state and subsequently used to predict the thermodynamic minimum miscible pressure (MMP). A history match of primary and secondary recovery processes was conducted to estimate the reservoir and multiphase flow parameters as the baseline case for analyzing the effect of recycling produced gas, infill drilling and water alternating gas (WAG) cycles on oil recovery and CO 2 storage. A multi-objective optimization model was defined for maximizing both oil recovery and CO 2 storage. The uncertainty quantification model comprising the Latin Hypercube sampling, Monte Carlo simulation, and sensitivity analysis, was used to study the effects of uncertain variables on the defined objective functions. Uncertain variables such as bottom hole injection pressure, WAG cycle, injection and production group rates, and gas-oil ratio among others were selected. The most significant variables were selected as control variables to be used for the optimization process. A neural network optimization algorithm was utilized to optimize the objective function both with and without geological uncertainty. The vertical permeability anisotropy (Kv/Kh) was selected as one of the uncertain parameters in the optimization process. The simulation results were compared to a scenario baseline case that predicted CO 2 storage of 74%. The results showed an improved approach for optimizing oil recovery and CO 2 storage in the FWU. The optimization process predicted more than 94% of CO 2 storage and most importantly about 28% of incremental oil recovery. The sensitivity analysis reduced the number of control variables to decrease computational time. A risk aversion factor was used to represent results at various confidence levels to assist management in the decision-making process. The defined objective functions were proved to be a robust approach to co-optimize oil recovery and CO 2 storage. The Farnsworth CO 2 project will serve as a benchmark for future CO 2 –EOR or CCUS projects in the Anadarko basin or geologically similar basins throughout the world.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

NEXTorch: A Design and Bayesian Optimization Toolkit for Chemical Sciences and Engineering

Automation and optimization of chemical systems require well-informed decisions on what experiments to run to reduce time, materials, and/or computations. Data-driven active learning algorithms have emerged as valuable tools to solve such tasks. Bayesian optimization, a sequential global optimization approach, is a popular active-learning framework. Past studies have demonstrated its efficiency in solving chemistry and engineering problems. Here we introduce NEXTorch, a library in Python/PyTorch, to facilitate laboratory or computational design using Bayesian optimization. NEXTorch offers fast predictive modeling, flexible optimization loops, visualization capabilities, easy interfacing with legacy software, and multiple types of parameters and data type conversions. It provides GPU acceleration, parallelization, and state-of-the-art Bayesian optimization algorithms and supports both automated an d human-in-the-loop optimization. The comprehensive online documentation introduces Bayesian optimization theory and several examples from catalyst synthesis, reaction condition optimization, parameter estimation, and reactor geometry optimization. NEXTorch is open-source and available on GitHub

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Comparison of tungsten versus molybdenum for double shell capsules using machine learning design optimization

Double shell targets are an alternative ignition platform for inertial confinement fusion. One design consideration for double shell targets is the choice of inner shell material to help trap radiation emitted by the hot fuel to aid ignition. Materials such as molybdenum and tungsten are of interest for the inner shell layer of the targets. While molybdenum has a lower density that could inhibit instability growth and allow for radiography and code benchmarking, tungsten has a higher density that could provide more compression and confinement. These tradeoffs have been explored using optimized designs for each material. Our previous work [Vazirani et al., “Coupling 1D xRAGE simulations with machine learning for graded inner shell design optimization in double shell capsules,” Phys. Plasmas 28, 122709 (2021); Vazirani et al., “Coupling multi-fidelity xRAGE with machine learning for graded inner shell design optimization in double shell capsules,” Phys. Plasmas 30, 062704 (2023); and Vazirani et al., “Bayesian batch optimization for molybdenum versus tungsten inertial confinement fusion double shell target design,” Stat. Anal. Data Min. 17, e11698 (2024)] resulted in a multi-fidelity Bayesian optimization framework to find yield-optimized double shell target geometries. By leveraging simulations of varying fidelities (one-dimensional and two-dimensional) to inform one another, the multi-fidelity optimization was able to optimize a design in the highest fidelity with significantly fewer simulations than would be used in a systematic parameter scan. In this work, we apply the multi-fidelity Bayesian optimization to explore the optimized designs of double shell targets with molybdenum and tungsten inner shells as well as the physics producing the high performing implosions. A physics exploration of all the simulations used in this study shows trends in designs that contribute to high yields, ion temperatures, and fuel areal densities. Comparison of molybdenum and tungsten simulations shows that they can produce similar implosion conditions with different geometries, which would be important to study in experiments. Graded density layers produce varying performances with the two materials but continue to be of interest for future studies along with studies of doped inner shell materials and applied surface roughness.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Evaluating Optimization Strategies for Engine Simulations Using Machine Learning Emulators

This work evaluates different optimization algorithms for computational fluid dynamics (CFD) simulations of engine combustion. Due to the computational expense of CFD simulations, emulators built with machine learning algorithms were used as surrogates for the optimizers. Two types of emulators were used: a Gaussian process (GP) and a weighted variety of machine learning methods called SuperLearner (SL). The emulators were trained using a dataset of 2048 CFD simulations that were run concurrently on a supercomputer. The design of experiments (DOE) for the CFD runs was obtained by perturbing nine input parameters using a Monte-Carlo method. The CFD simulations were of a heavy duty engine running with a low octane gasoline-like fuel at a partially premixed compression ignition mode. Ten optimization algorithms were tested, including types typically used in research applications. Each optimizer was allowed 800 function evaluations and was randomly tested 100 times. The optimizers were evaluated for the median, minimum, and maximum merits obtained in the 100 attempts. Some optimizers required more sequential evaluations, thereby resulting in longer wall clock times to reach an optimum. The best performing optimization methods were particle swarm optimization (PSO), differential evolution (DE), GENOUD (an evolutionary algorithm), and micro-genetic algorithm (GA). These methods found a high median optimum as well as a reasonable minimum optimum of the 100 trials. Moreover, all of these methods were able to operate with less than 100 successive iterations, which reduced the wall clock time required in practice. Two methods were found to be effective but required a much larger number of successive iterations: the DIRECT and MALSCHAINS algorithms. A random search method that completed in a single iteration performed poorly in finding optimum designs but was included to illustrate the limitation of highly concurrent search methods. The last three methods, Nelder–Mead, bound optimization by quadratic approximation (BOBYQA), and constrained optimization by linear approximation (COBYLA), did not perform as well.

Probst, Daniel M.↗
DOE OSTI2014

Beamlet based direct aperture optimization for MERT using a photon MLC

Purpose: A beamlet based direct aperture optimization (DAO) for modulated electron radiotherapy (MERT) using photon multileaf collimator (pMLC) shaped electron fields is developed and investigated. Methods: The Swiss Monte Carlo Plan (SMCP) allows the calculation of dose distributions for pMLC shaped electron beams. SMCP is interfaced with the Eclipse TPS (Varian Medical Systems, Palo Alto, CA) which can thus be included into the inverse treatment planning process for MERT. This process starts with the import of a CT-scan into Eclipse, the contouring of the target and the organs at risk (OARs), and the choice of the initial electron beam directions. For each electron beam, the number of apertures, their energy, and initial shape are defined. Furthermore, the DAO requires dose–volume constraints for the structures contoured. In order to carry out the DAO efficiently, the initial electron beams are divided into a grid of beamlets. For each of those, the dose distribution is precalculated using a modified electron beam model, resulting in a dose list for each beamlet and energy. Then the DAO is carried out, leading to a set of optimal apertures and corresponding weights. These optimal apertures are now converted into pMLC shaped segments and the dose calculation for each segment is performed. For these dose distributions, a weight optimization process is launched in order to minimize the differences between the dose distribution using the optimal apertures and the pMLC segments. Finally, a deliverable dose distribution for the MERT plan is obtained and loaded back into Eclipse for evaluation. For an idealized water phantom geometry, a MERT treatment plan is created and compared to the plan obtained using a previously developed forward planning strategy. Further, MERT treatment plans for three clinical situations (breast, chest wall, and parotid metastasis of a squamous cell skin carcinoma) are created using the developed inverse planning strategy. The MERT plans are compared to clinical standard treatment plans using photon beams and the differences between the optimal and the deliverable dose distributions are determined. Results: For the idealized water phantom geometry, the inversely optimized MERT plan is able to obtain the same PTV coverage, but with an improved OAR sparing compared to the forwardly optimized plan. Regarding the right-sided breast case, the MERT plan is able to reduce the lung volume receiving more than 30% of the prescribed dose and the mean lung dose compared to the standard plan. However, the standard plan leads to a better homogeneity within the CTV. The results for the left-sided thorax wall are similar but also the dose to the heart is reduced comparing MERT to the standard treatment plan. For the parotid case, MERT leads to lower doses for almost all OARs but to a less homogeneous dose distribution for the PTV when compared to a standard plan. For all cases, the weight optimization successfully minimized the differences between the optimal and the deliverable dose distribution. Conclusions: A beamlet based DAO using multiple beam angles is implemented and successfully tested for an idealized water phantom geometry and clinical situations.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Red-QAOA: Efficient Variational Optimization through Circuit Reduction

The Quantum Approximate Optimization Algorithm (QAOA) provides a quantum solution for combinatorial optimization problems. However, the optimal parameter searching process of QAOA is greatly affected by noise, leading to non-optimal solutions. This paper introduces a novel approach to optimize QAOA by exploiting the energy landscape concentration of similar instances via graph reduction, thus addressing the effect of noise. We formalize the notion of similar instances in QAOA and develop a Simulated Annealing-based graph reduction algorithm, called Red-QAOA, to identify the most similar subgraph for efficient parameter optimization. Red-QAOA outperforms state-of-the-art Graph Neural Network (GNN) based graph pooling techniques in performance and demonstrates effectiveness on a diverse set of real-world optimization problems encompassing 3200 graphs. Red-QAOA reduced the node counts and edge counts by 28% and 37%, respectively, while maintaining a low mean square error of 2%. These enable the identification of an optimal parameter set that is closer to the ideal true optimal solution in the presence of noise. By substantially streamlining the search for QAOA parameters, our approach sets the stage for the practical application of quantum algorithms in solving complex optimization problems.

Wang, Meng↗
DOE OSTI2019

Fast, Dynamic, and Scalable Algorithms for Large-Scale Constrained Optimization

Scientists and engineers constantly aim to optimize an objective subject to physical, environmental, and/or resource constraints. The technique of using mathematical models to formulate and find real solutions of such problems is known as mathematical optimization, a process that has become invaluable for design and discovery in numerous scientific fields. This project has focused on the design, analysis, and implementation of high-performance computing algorithms for solving cutting-edge optimization problems. These include problems that involve (1) data uncertainties, such as those in the future supply, demand, and capacity of a given power system, (2) extreme numbers of alternatives, such as in the design of electrical power grids to avoid network vulnerabilities, and (3) real-time decisions, such as in the control of chemical reactors. The key features of the new algorithms are that they are fast, dynamic, and scalable to meet the computational requirements of scientists and researchers working to optimize large-scale, complex systems. The algorithms that have been designed, analyzed, and tested as part of the project can be characterized based on the types of optimization problems they have been designed to solve. Much of the work has focused on algorithms for solving large-scale constrained optimization problems. Contributions have also been made in the design of algorithms for unconstrained optimization, with some specialized methods for solving problems that have inherent nonsmoothness. Contributions have also been made in areas that have grown to prominence in the field over the five-year award period. These include the design of algorithms for solving large-scale stochastic optimization problems, such as those that arise in large-scale machine learning, and in complexity analyses for solving nonconvex problems, which has been a focal point of much recent work in continuous optimization. Overall, the project has supported work that has led to almost 30 articles that have been published or accepted to top journals in the field of mathematical optimization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Impact of K-Optimization on Trap Concentration in (Ag,Cu)(In,Ga)Se 2 Solar Cells

Recent progress has been made in improving efficiency in Cu(In,Ga)Se 2 (CIGS) absorbers with steady increases in peak efficiency. One way this has been achieved is by adding Ag to CIGS (ACIGS) to achieve higher V OC . However, these efficiencies are still well below the Shockley-Queisser efficiency limit, and traps acting as recombination centers and compensating centers are one thing limiting the solar efficiency. Past research in CIGS has shown that alkali treatment can improve the efficiency and metastability problems in CIGS, but less is understood about the role of alkali treatments in ACIGS. Here, we investigate the impact of potassium in ACIGS through its impact on trap incorporation and minority carrier lifetime. The samples in this study were grown in a roll-to-roll coater with Mo, ACIGS, CdS, and ZnO structure. Both cells were grown identically except the second (K-optimized) cell was grown with increased K-doping of the Mo contact and was more Cu-poor near the surface to optimize the K profile. This resulted in an efficiency increase from 16.8% to 18.7% for the K-optimized cell, which was mostly due to a 65 mV V OC increase. The doping profile showed a 2X increase in acceptor concentration of the K-optimized cell (2.5×10 15 cm -3 ) which suggests that the K was better incorporated into the ACIGS after these optimizations. To characterize the traps in these cells, deep level transient and optical spectroscopy were used. The DLOS measurements showed an EV+0.98 eV trap whose concentration was reduced 10X in the K-optimized cell (4×10 14 cm -3 ). This is consistent with previous results from the alkali treatment in CIGS, which also showed a decrease in near-conduction band trap concentration [1], but the reduction was larger than previous studies possibly indicating the combination of K and Cu-poor surface may both have aided in reducing the EV+0.98 eV trap concentration. The other primary trap is the mid-gap trap (EV+0.58 eV), which was quantified using DLTS. Its concentration decreased from 9×10 13 cm -3 to 4×10 13 cm -3 in the K-optimized sample, which is a 2X reduction. Previous studies have shown this trap is likely an efficient recombination center [2], which makes sense because it is near mid-gap. This trap has also been associated with V OC instability and reduction, so reducing this trap concentration is essential to achieve high V OC and cell efficiency. To help confirm this association, time-resolved photoluminescence measurements have shown in this sample set and a previous study that the minority carrier lifetime (19 ns baseline to 56 ns K-optimized) and this EV+0.56 eV trap concentration are inversely proportional, which would be expected for a recombination-limited carrier lifetime. The K optimization of ACIGS results in significantly improved cell efficiency and reduced trap concentrations that correlate with the improved material and electrical properties. We will report on this and the impact of the K optimization on the cell metastability.

14 SOLAR ENERGY↗
DOE OSTI2021

Model-based Design Optimization to Achieve the Performance Goals (16.0 SEER/9.5 HSPF), Developing Heat Pump by Using Low-GWP Refrigerants and 5 mm Diameter Tubes

Usage of low-GWP refrigerants can reduce the Green House Gas (GHG) emission of HVAC systems. Our research in previous milestone report has shown that using heat exchangers with 5 mm diameter tubes instead of 9 mm diameter tubes is a promising solution to meet the performance goals of heat pump using low-GWP refrigerants. In addition, the 5mm tube heat exchangers can lead to lower system refrigerant charge and as a result, reduce environmental impact further. However, shifting to small tube diameters requires in-depth heat exchanger design optimization to adapt to the transition to low-GWP refrigerants. In the 2nd quarter of FY21, we conducted multi-objective optimizations using Particle Swarm Optimization algorithm on a residential 5-ton air source heat pump to investigate the potential system performance improvements and material savings. 4 low-GWP refrigerants, ARM20A, ARM20B, R454A and R454C are investigated in this study. The objectives of the optimization are to minimize the heat pump material cost and to maximize the system performance simultaneously. As a result, the HXs material cost is reduced by up to 77% according to the copper and aluminum material price in current market. Under heating mode operation, the smart 4-way valve guarantees that the optimal low-GWP systems maintain or outperform the heating performance of the R410A baseline system. The model-based design optimization yields 18.3-18.9 SEER and 10.6-11.9 HSPF for optimal systems using different low-GWP refrigerants. The initial performance goals (16.0 SEER/9.5 HSPF) are achieved. Furthermore, up to 50% system refrigerant charge reduction is possible in the optimized low-GWP heat pump system using ARM20B. And 91%-95% predicted life-time direct CO 2 emission reduction is achieved by using the optimal 5mm tube low-GWP heat pumps. The significant material saving, charge reduction and direct CO 2 emission reduction help in reducing the environmental impacts of heat pump systems. The optimal heat exchangers resulting from this research can fit into the original baseline indoor and outdoor fan-coil unit. This can reduce the retrofitting effort by minimizing the change in manufacturing and installation of the heat pumps and guarantee the compatibility with end-users’ house structure. Finally, the new products can be easily accepted by manufacturers and end-users.

42 ENGINEERING↗
DOE OSTI2020

Management of Risk and Uncertainty Through Optimized Co-Operation of Transmission Systems and Microgrids With Responsive Loads (Final Report)

The evolution of the power system to the reliable, efficient and sustainable system of the future will involve development of both demand- and supply-side technology and operations. Ambitious national and state-level goals around the decarbonization of electricity relies on the integration of very high levels of renewable resources, most of which are variable and intermittent. The use of demand response is an ideal approach to counterbalance the intermittency of renewable generation and brings the consumer into the spotlight. Though individual consumers are interconnected at the low-voltage distribution system, these resources are typically modeled as variables at the transmission network level. Demand-side participation cannot be leveraged effectively without explicitly including the distribution system dynamics in the optimization-based wholesale market operations. This project grew from a vision for co-optimized interaction of distribution systems, or microgrids, with the high-voltage transmission system. In this framework, microgrids encompass consumers, distributed renewables and storage. The energy management system of the lower voltage system (distribution or microgrid) can also sell (buy) excess (necessary) energy from the transmission system. Until recently, very little research had been conducted on the co-optimization of these two systems due to computational limitations. However, advances in computational capabilities, and the judicious use of decomposition methods and innovative approximation methods for high-dimension dynamic programming made this goal a viable objective for this project, leading to a fundamental shift in the ability to integrate and fully utilize demand-side resources. To this end, the modeling framework developed introduces a novel co-optimization framework, to include the operations of both the transmission and distribution systems (or microgrids) in operational decision making. This framework was used to analyze renewable and distributed generation along with responsive demand and to compare the capability of co-optimized systems to perform with higher levels of variable renewables. An ideal microgrid is defined as an electric entity capable of operating in both interconnected (with the high-voltage grid) and islanded mode. As such, the microgrid should incorporate generating units (traditional units and intermittent) and if needed, exchange power with the high-voltage grid. The interplay between the microgrid and high-voltage grid motivated the development of the co-optimization approach to ensure efficient performance of the interconnected network. Results show that the use of a bi-level optimization approach is an appropriate structure, capable of co-optimizing a transmission system with multiple distribution systems and microgrids. While increasing the number of connected systems provides increasing flexibility for renewables integration this can also the economic benefits to the low-voltage subsystems with each additional system connected. Comparison of a traditional single-level decision structure with the co-optimization approach illustrates a reduction in overall system cost under co-optimization, while specific cost allocations to transmission and distribution systems are changed.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2015

Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal Control

The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Objective and algorithm considerations when optimizing the number and placement of turbines in a wind power plant

Abstract. Optimizing turbine layout is a challenging problem that has been extensively researched in the literature. However, optimizing the number of turbines within a given boundary has not been studied as extensively and is a difficult problem because it introduces discrete design variables and a discontinuous design space. An essential step in performing wind power plant layout optimization is to define the objective function, or value, that is used to express what is valuable to a wind power plant developer, such as annual energy production, cost of energy, or profit. In this paper, we demonstrate the importance of selecting the appropriate objective function when optimizing a wind power plant in a land-constrained site. We optimized several different wind power plants with different wind resources and boundary sizes. Results show that the optimal number of turbines varies drastically depending on the objective function. For a simple, one-dimensional, land-based scenario, we found that a wind power plant optimized for minimal cost of energy produced just 72 % of the profit compared to the wind power plant optimized for maximum profit, which corresponded to a loss of about USD 2 million each year. This paper also compares the performance of several different optimization algorithms, including a novel repeated-sweep algorithm that we developed. We found that the performance of each algorithm depended on the number of design variables in the problem as well as the objective function.

17 WIND ENERGY↗
DOE OSTI2014

Optimization study of Ultra-long Cycle Fast Reactor core concept

An optimization of an Ultra-long Cycle Fast Reactor (UCFR) design with a power rating of 1000 MW(electric), UCFR-1000, has been performed. Firstly, geometric optimization has been performed in the aspects of core size and core shape in terms of thermal–hydraulic (TH) feedback. Secondly, fuel composition optimization has been performed by adopting pressurized water reactor (PWR) spent fuel (SF) as a blanket material as well as natural uranium (NU). Thirdly, thorium has been loaded in the inner core for the optimization of radial power distribution. Lastly, a small-size UCFR with a power rate of 100 MWe has been developed with optimization of maximum neutron flux and fast neutron fluence limit for a short term deployable nuclear reactor. The equivalent diameter and the height of the optimized UCFR-1000 core are 5.9 and 2.4 m, respectively, while the equivalent diameter and the height of the optimized UCFR-100 core are 4.3 and 1.0 m, respectively. The size of the optimized UCFR-1000 has been enlarged in the radial direction and shortened in the axial direction from those of the initial UCFR design (Tak et al., 2013a) and this modification makes the burning speed of active core movement slower. It has been confirmed for both designs that a full-power operation of 60 years without refueling is feasible with respect to isotopics and criticality by a breed-and-burn strategy. The core performance characteristics of both designs have been evaluated in terms of axial/radial power shapes, neutron flux and nuclide distributions, breeding ratio, reactivity feedback coefficients, control rod worth, etc. By the design optimization study in this paper, the reductions of maximum neutron flux, fast neutron fluence, and axial/radial power peaking have been achieved, which are favorable for the safety of the UCFR.

Breed-and-burn↗
DOE OSTI2018

A deterministic method for PWR loading pattern optimization

A new deterministic approach to core loading optimization is presented. Selection of fuel enrichment and burnable poison (BP) arrangement in a pressurized water reactor (PWR) core are optimally determined subject to power peaking factor (PF) constraints. The deterministic approach is based on the method of Lagrange multipliers and the direct adjoining approach for the inequality power PF constraint. The optimality conditions are derived using calculus of variations resulting in the presence of jump conditions and a linear control Hamiltonian. The optimal control problems are addressed by simultaneously minimizing the Hamiltonian using the gradient method and performing Newton's method in different regions of the core to produce viable solutions for the controls. Without active control of the power profile in PWRs during depletion, our methodology is able to satisfy the power PF constraint at all times by proper loading selection at the beginning of cycle (BOC). This is achieved by promoting the proper burnup path forward in time during the calculation of the forward optimality conditions. Here this information is utilized in the adjoint burnup calculation, which acts to propagate the optimal control path back to the BOC during the calculation of the adjoint optimality conditions. The methodology has been developed into a new code DMCO (Deterministic Multi-Control Optimization) which can produce two-dimensional two-group depletion results in approximately seven minutes per optimization iteration on a personal computer. No application of heuristics is required and the code is capable of finding solutions from initial control distributions. A preliminary case study is presented for the Westinghouse AP600 first cycle fuel loading design which achieved an extended fuel cycle while satisfying power PF constraints.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗