SEARCH · Search NASA

Results for “Optimal Allocation”

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.

SourceResearch connectionFrom yearThrough year

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

At least 163 records · Page 9

All sources NASA NTRS DOE OSTI

DOE OSTI2023

2023 Real-time Optimization Workflow Status Update

Nuclear integrated energy systems are composed of a diverse set of energy generation sources and exist in dynamic and competitive electricity markets. With the inclusion of thermal energy storage, nuclear power systems can store heat for future use through various processes, such as water desalination or hydrogen generation. This heat storage can be managed in such a way as to economically optimize its usage. By combining real-time price data from the day-ahead and real-time markets with predictive and intelligent models, the charging and discharging of the thermal energy storage may be determined and optimized. This research details an approach through models and systems for the real-time optimization (RTO) of capacity allocation. Virtual models of the energy system and its physics phenomenon and component interactions provide intelligence to verification and prediction of operations. An optimization framework can use data generated from both a set of physical assets as well as the virtual models to predict future performance and create optimization and control workflows. Data warehouse technologies can be used to combine data across models, optimization workflows, market price data, and sensor data to intuitively store various types of data and provide integrations to physical control systems as well as user visualizations. Put together, these components can create a system for the RTO of nuclear integrated energy systems. Various virtual models and bench-scale physical demonstrations have been successfully performed and verified using this system. Larger scale testbeds that include thermal energy storage systems have been identified as future opportunities. A gap analysis that details the steps necessary to reach a physical demonstration at this scale is provided, along with conclusions on the current effort and future work.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2013

Optimizing geographic allotment of photovoltaic capacity in a distributed generation setting

Explore the source record for details and available documents.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2024

FORCE Update 2024

The Framework for Optimization of Resources and Economics (FORCE) tool suite is the U.S. Department of Energy’s Nuclear Integrated Energy Systems (IES) Program flagship tool suite for technoeconomic IES analysis of IES. This tool suite is useful for analysis designed to evaluate and improve the technoeconomics of energy production systems, particularly for systems including nuclear technology. In this report, we document the development activity for the FORCE tool suite to extend its capabilities as performed during fiscal year 2024. In addition to reliability and accessibility, capability is one of the three standards guiding the development of the FORCE tool suite and the software codes that are its constituent parts. Extending the capabilities of the FORCE tool suite allows analysis both within the IES program as well as industry, university, and laboratory partners to perform analysis with more accuracy, insight, and impactful narrative. Four areas of capability development were the focus of activity this year: economic parameter uncertainty quantification, multiresolution analysis, components-to-optimization workflow automation, and statespace construction workflows for real-time optimal control. In economic parameter uncertainty quantification, the ability of HERON to capture risk due to scenarios (weather and energy demand uncertainty) was expanded to also include uncertainties in financial parameters such as capital cost or operation and maintenance costs. By including these sources of uncertainty, which are sometimes very large compared with scenario uncertainty, HERON is better able to capture the risk posed by investment in various IES technology. Because of this, analysts can also consider the reduction in risks that can be realized by choice of some technologies. In multiresolution analysis, development activity extended on work completed previously. In fiscal year 2023, methods for decomposing time series signals, such as demand, solar and wind availability, and price profiles, were analyzed and down-selected to those most effective at splitting signals into different resolutions. These resolutions allow considering the influence of different energy demand and supply behaviors across different time scales. For example, energy demand might be divided into seasonal, weekly, and hourly profiles. In fiscal year 2024, this preliminary work was extended and implemented within the Risk Analysis Virtual Environment (RAVEN) risk and uncertainty analysis platform, which is used throughout the FORCE framework. This development of the “multi-resolution time series analysis” (MR-TSA) module in RAVEN allows training synthetic history generators on complex time series. These synthetic history generators can then be used in HERON for generating scenarios that represent possible market and weather scenarios that can be analyzed on different time scales. We envision completing this work in the future, implementing multiresolution dispatch optimization strategies that can make the most beneficial use of these stratified time histories. In components-to-optimization workflow development, workflows for translating user inputs of components into algorithms for algebraic optimization were selected and implemented. Similar algorithms within the Holistic Energy Resource Optimization Network (HERON) were separated from the main code base of HERON and gathered with the components-to-optimization workflows in the new Dispatch Optimization Variable Engine (DOVE) software library. This modularization allows FORCE users to analyze dispatch optimization and energy system duty cycles independently of HERON, which previously was a burdensome task. Additionally, these dispatch optimization algorithms, set up in an independent library, can now be used across all software applications within FORCE, especially including the real-time optimal control software Optimization of Real-time Capacity Allocation (ORCA). Allowing FORCE software to share dispatch optimization algorithms within a single library allows for improved software maintenance and reliability. In statespace characterization workflow development, alternative workflows for optimizing dispatch with additional technical accuracy was the focus, particularly to improve the real-time optimization decision making in ORCA. Using algorithms and workflows initially developed for the Feasible Actuator Range Modifier (FARM), workflows for determining the statespace representation of IES were identified and demonstrated. The resulting dispatch optimization required a more robust optimization algorithm than that originally used in HERON (and moved to DOVE), which required adding an alternate workflow to DOVE that can more accurately match the behavior of physical systems using a partial differential equation representation. In conclusion, capability developments in the FORCE tool suite in fiscal year 2024 have improved the ability of the FORCE tool suite to perform

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2015

A model of interaction between anticorruption authority and corruption groups

The paper provides a model of interaction between anticorruption unit and corruption groups. The main policy functions of the anticorruption unit involve reducing corrupt practices in some entities through an optimal approach to resource allocation and effective anticorruption policy. We develop a model based on Markov decision-making process and use Howard’s policy-improvement algorithm for solving an optimal decision strategy. We examine the assumption that corruption groups retaliate against the anticorruption authority to protect themselves. This model was implemented through stochastic game.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Cities Topology - Curbs and Parking

Curbside activity has not traditionally been represented in transportation network modeling in high fidelity. Growing demand for curbside mean that prevailing practices are becoming increasingly untenable. Through outreach to expert practitioners, we established the state-of-practice and needs for quantitative modeling. We proposed a new modeling framework to allow curbspace managers to make optimal decisions about space allocation between legacy and emerging uses. Proposed future work will take the proposed approach and refine it to be suitable for standardized use by practitioners – to facilitate mobility and energy optimization through smart curbside management.

47 OTHER INSTRUMENTATION↗

DOE OSTI2015

A feasibility study: Selection of a personalized radiotherapy fractionation schedule using spatiotemporal optimization

Purpose: To investigate the impact of using spatiotemporal optimization, i.e., intensity-modulated spatial optimization followed by fractionation schedule optimization, to select the patient-specific fractionation schedule that maximizes the tumor biologically equivalent dose (BED) under dose constraints for multiple organs-at-risk (OARs). Methods: Spatiotemporal optimization was applied to a variety of lung tumors in a phantom geometry using a range of tumor sizes and locations. The optimal fractionation schedule for a patient using the linear-quadratic cell survival model depends on the tumor and OAR sensitivity to fraction size (α/β), the effective tumor doubling time (T{sub d}), and the size and location of tumor target relative to one or more OARs (dose distribution). The authors used a spatiotemporal optimization method to identify the optimal number of fractions N that maximizes the 3D tumor BED distribution for 16 lung phantom cases. The selection of the optimal fractionation schedule used equivalent (30-fraction) OAR constraints for the heart (D{sub mean} ≤ 45 Gy), lungs (D{sub mean} ≤ 20 Gy), cord (D{sub max} ≤ 45 Gy), esophagus (D{sub max} ≤ 63 Gy), and unspecified tissues (D{sub 05} ≤ 60 Gy). To assess plan quality, the authors compared the minimum, mean, maximum, and D{sub 95} of tumor BED, as well as the equivalent uniform dose (EUD) for optimized plans to conventional intensity-modulated radiation therapy plans prescribing 60 Gy in 30 fractions. A sensitivity analysis was performed to assess the effects of T{sub d} (3–100 days), tumor lag-time (T{sub k} = 0–10 days), and the size of tumors on optimal fractionation schedule. Results: Using an α/β ratio of 10 Gy, the average values of tumor max, min, mean BED, and D{sub 95} were up to 19%, 21%, 20%, and 19% larger than those from conventional prescription, depending on T{sub d} and T{sub k} used. Tumor EUD was up to 17% larger than the conventional prescription. For fast proliferating tumors with T{sub d} less than 10 days, there was no significant increase in tumor BED but the treatment course could be shortened without a loss in tumor BED. The improvement in the tumor mean BED was more pronounced with smaller tumors (p-value = 0.08). Conclusions: Spatiotemporal optimization of patient plans has the potential to significantly improve local tumor control (larger BED/EUD) of patients with a favorable geometry, such as smaller tumors with larger distances between the tumor target and nearby OAR. In patients with a less favorable geometry and for fast growing tumors, plans optimized using spatiotemporal optimization and conventional (spatial-only) optimization are equivalent (negligible differences in tumor BED/EUD). However, spatiotemporal optimization yields shorter treatment courses than conventional spatial-only optimization. Personalized, spatiotemporal optimization of treatment schedules can increase patient convenience and help with the efficient allocation of clinical resources. Spatiotemporal optimization can also help identify a subset of patients that might benefit from nonconventional (large dose per fraction) treatments that are ineligible for the current practice of stereotactic body radiation therapy.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2026

Optimizing Transportation Networks for E-Waste Reverse Logistics: A Multi-Modal Cost Allocation and Pricing Strategy

The exponential growth of electronic waste (e-waste) poses critical challenges for sustainable reverse logistics and transportation network optimization. This study develops a dual-channel transportation framework for e-waste logistics that integrates dynamic freight pricing, cost allocation mechanisms, and game-theoretic coordination. The model captures interactions between centralized hubs and distributed processing networks, accounting for freight rate elasticity, volume allocation, and capacity constraints. Using Stackelberg game theory and cost-sharing strategies, the framework optimizes transportation efficiency and profit distribution across logistics channels. Numerical simulations show that the dual-channel structure increases centralized hub profit by 226.8% compared to baseline single-channel operations, while boosting total transported volume by 1.2% and nearly doubling freight collector profit under cost-sharing. Scenario analyses across regional infrastructures reveal that network density, policy incentives, and logistics costs shape routing efficiency and profit allocation. These findings suggest that coordinated strategies combining dynamic pricing, targeted infrastructure investment, and strategic cost allocation are needed to design efficient, resilient, and regionally adaptable e-waste transportation systems.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2022

Purple acid phosphatase2 stimulates a futile cycle of lipid synthesis and degradation, and mitigates the negative growth effects of triacylglycerol accumulation in vegetative tissues

Storage lipids (mostly triacylglycerols, TAGs) serve as an important energy and carbon reserve in plants and hyperaccumulation of TAG in vegetative tissues can cause negative effects on plant growth. Purple acid phosphatase2 (PAP2) was shown previously to affect carbon metabolism and boost plant growth. However, the effects of PAP2 on lipid metabolism remain unknown. Here, we demonstrated PAP2 as a factor that can stimulate a futile cycle of fatty acid (FA) synthesis and degradation and mitigate negative growth effects associated with TAG accumulation in vegetative tissues. Constitutive expression of PAP2 in Arabidopsis thaliana enhanced both lipid synthesis and degradation in leaves and led to substantial increase in seed oil yield. Suppressing lipid degradation in a PAP2-overexpressing line by disrupting sugar-dependent1 (SDP1), a predominant TAG lipase, significantly elevated vegetative TAG content and improved plant growth. Diverting FAs from membrane lipids to TAGs in PAP2-overexpressing plants by constitutively expressing phospholipid:diacylglycerol acyltransferase1 (PDAT1) increased TAG contents to up to 6% of dry weight in vegetative tissues without compromising biomass yield. Overall, these results highlight the potential of combining PAP2 with TAG-promoting factors to enhance carbon assimilation, FA synthesis and allocation to TAGs for optimized plant growth and storage lipid accumulation in vegetative tissues.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Optimization of a High Pressure Turbine Blade and Sector-Based Annular Rig Design for Supercritical CO2 Power Cycle Representative Testing

Abstract As part of the ongoing research into the design of hardware for zero emission cycles, a first-stage high-pressure turbine (HPT) blade is optimized for a 300 MWe supercritical CO2 (sCO2) power cycle using the surrogate-assisted genetic algorithm optimizer in Numeca FINE/Design three-dimensional with objectives of increasing efficiency and decreasing heat load to the blade. Supercritical CO2 property tables are constructed from NIST REFPROP data for the condensable gas simulation in FINE/Turbo. A detailed mesh sensitivity study is performed for a baseline design to identify the proper-grid refinement and efficiently allocate resources for the optimization. Seventy design variables are selected for the initial population generation. Self-organizing maps are then used to focus the design variables on the most important ones affecting the objective functions. The optimization results in approximately 3000 three-dimensional Reynolds Averaged Navier Stokes simulations of different blade shapes with increases in efficiency of up to 0.85% and decreases in heat load of 14%. Families of blade shapes are identified for experimental testing in an annular rig at the Purdue Experimental Turbine Aerothermal Laboratory. A design to adapt the annular cascade for testing optimized geometries is introduced, which features eccentric radius sectors allowing for scaled-up geometries of sCO2 optimized blade profiles to be tested at design cycle representative conditions at high Reynolds numbers in dry air. Analysis into the effects of Reynolds number, working fluid, and geometric relations are presented to prove the efficacy of the test method.

Engineering↗

DOE OSTI2018

Optimally configuring a measurement system to detect diversions from a nuclear fuel cycle

The civilian nuclear fuel cycle is an industrial process that produces electrical power from the nuclear fission of uranium. Using a measurement system to accurately account for nuclear material, such as uranium, in a fuel cycle is important because of the possible loss or diversion of this potentially dangerous material. A measurement system is defined by a set of measurement methods, or “devices,” used to account for material flows and inventory values at specific locations in the fuel cycle. Here, we develop a simulation-optimization algorithm and an integer-programming model to find the best, or near-best, resource-limited measurement system with a high degree of confidence. The simulation-optimization algorithm minimizes a weighted sum of false positive and false negative diversion-detection probabilities while accounting for material quantities and measurement errors across a finite, discrete time horizon in hypothetical non-diversion and diversion contexts. In each time period, the estimated cumulative material unaccounted for is compared to a fixed or an optimized threshold value to assess if a “significant amount of material” is lost from a measurement system. The integer-programming model minimizes the population variance of the estimated material loss, i.e., material unaccounted for, in a measurement system. We analyze three potential problems in nuclear fuel cycle measurement systems: (i) given location-dependent device precisions, find the configuration of n devices at n locations ( n = 3) that gives the lowest corresponding objective values using the simulation-optimization algorithm and integer-programming model, (ii) find the location at which improving device precision reduces objective values the most using the simulation-optimization algorithm, and determine the effect of measurement frequency on measurement system configurations and objective values using the simulation-optimization algorithm. We obtain comparable results for each problem at least an order of magnitude faster than existing methods do. Using an optimized, rather than fixed, detection threshold in the simulation-optimization algorithm reduces the weighted sum of false positive and false negative probabilities.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2016

A global scale mechanistic model of photosynthetic capacity (LUNA V1.0)

Abstract. Although plant photosynthetic capacity as determined by the maximum carboxylation rate (i.e., Vc, max25) and the maximum electron transport rate (i.e., Jmax25) at a reference temperature (generally 25 °C) is known to vary considerably in space and time in response to environmental conditions, it is typically parameterized in Earth system models (ESMs) with tabulated values associated with plant functional types. In this study, we have developed a mechanistic model of leaf utilization of nitrogen for assimilation (LUNA) to predict photosynthetic capacity at the global scale under different environmental conditions. We adopt an optimality hypothesis to nitrogen allocation among light capture, electron transport, carboxylation and respiration. The LUNA model is able to reasonably capture the measured spatial and temporal patterns of photosynthetic capacity as it explains ∼ 55 % of the global variation in observed values of Vc, max25 and ∼ 65 % of the variation in the observed values of Jmax25. Model simulations with LUNA under current and future climate conditions demonstrate that modeled values of Vc, max25 are most affected in high-latitude regions under future climates. ESMs that relate the values of Vc, max25 or Jmax25 to plant functional types only are likely to substantially overestimate future global photosynthesis.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Resource distribution under spatiotemporal uncertainty of disease spread: Stochastic versus robust approaches

We consider the problem of optimizing locations of distribution centers (DCs) and plans for distributing resources such as test kits and vaccines, under spatiotemporal uncertainties of disease spread and demand for the resources. We aim to balance the operational cost (including costs of deploying facilities, shipping, and storage) and quality of service (reflected by demand coverage), while ensuring equity and fairness of resource distribution across multiple populations. We compare a sample-based stochastic programming (SP) approach with a distributionally robust optimization (DRO) approach using a moment-based ambiguity set. Numerical studies are conducted on instances of distributing COVID-19 vaccines in the United States and test kits, to compare SP and DRO models with a deterministic formulation using estimated demand and with the current resource distribution plans implemented in the US. We demonstrate the results over distinct phases of the pandemic to estimate the cost and speed of resource distribution depending on scale and coverage, and show the “demand-driven” properties of the SP and DRO solutions. Furthermore, our results further indicate that if the worst-case unmet demand is prioritized, then the DRO approach is preferred despite of its higher overall cost. Nevertheless, the SP approach can provide an intermediate plan under budgetary restrictions without significant compromises in demand coverage.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

An optimization framework for workplace charging strategies

The workplace charging (WPC) has been recently recognized as the most important secondary charging point next to residential charging for plug-in electric vehicles (PEVs). The current WPC practice is spontaneous and grants every PEV a designated charger, which may not be practical or economic when there are a large number of PEVs present at workplace. This study is the first research undertaken that develops an optimization framework for WPC strategies to satisfy all charging demand while explicitly addressing different eligible levels of charging technology and employees’ demographic distributions. The optimization model is to minimize the lifetime cost of equipment, installations, and operations, and is formulated as an integer program. We demonstrate the applicability of the model using numerical examples based on national average data. The results indicate that the proposed optimization model can reduce the total cost of running a WPC system by up to 70% compared to the current practice. The WPC strategies are sensitive to the time windows and installation costs, and dominated by the PEV population size. The WPC has also been identified as an alternative sustainable transportation program to the public transit subsidy programs for both economic and environmental advantages.

Optimization↗

DOE OSTI2022

An Online Approach to Solve the Dynamic Vehicle Routing Problem with Stochastic Trip Requests for Paratransit Services

Many transit agencies operating paratransit and microtransit services have to respond to trip requests that arrive in real-time, which entails solving hard combinatorial and sequential decision-making problems under uncertainty. To avoid decisions that lead to significant inefficiency in the long term, vehicles should be allocated to requests by optimizing a non-myopic utility function or by batching requests together and optimizing a myopic utility function. While the former approach is typically offline, the latter can be performed online. We point out two major issues with such approaches when applied to paratransit services in practice. First, it is difficult to batch paratransit requests together as they are temporally sparse. Second, the environment in which transit agencies operate changes dynamically (e.g., traffic conditions can change over time), causing the estimates that are learned offline to become stale. To address these challenges, we propose a fully online approach to solve the dynamic vehicle routing problem (DVRP) with time windows and stochastic trip requests that is robust to changing environmental dynamics by construction. We focus on scenarios where requests are relatively sparse—our problem is motivated by applications to paratransit services. We formulate DVRP as a Markov decision process and use Monte Carlo tree search to evaluate actions for any given state. Accounting for stochastic requests while optimizing a non-myopic utility function is computationally challenging; indeed, the action space for such a problem is intractably large in practice. To tackle the large action space, we leverage the structure of the problem to design heuristics that can sample promising actions for the tree search. Our experiments using real-world data from our partner agency show that the proposed approach outperforms existing state-of-the-art approaches both in terms of performance and robustness.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Data for Purple Acid Phosphatase2 Stimulates a Futile Cycle of Lipid Synthesis and Degradation, and Mitigates the Negative Growth Effects of Triacylglycerol Accumulation in Vegetative Tissues

Storage lipids (mostly triacylglycerols, TAGs) serve as an important energy and carbon reserve in plants, and hyperaccumulation of TAG in vegetative tissues can have negative effects on plant growth. Purple acid phosphatase2 (PAP2) was previously shown to affect carbon metabolism and boost plant growth. However, the effects of PAP2 on lipid metabolism remain unknown. Here, we demonstrated that PAP2 can stimulate a futile cycle of fatty acid (FA) synthesis and degradation, and mitigate negative growth effects associated with high accumulation of TAG in vegetative tissues. Constitutive expression of PAP2 in Arabidopsis thaliana enhanced both lipid synthesis and degradation in leaves and led to a substantial increase in seed oil yield. Suppressing lipid degradation in a PAP2-overexpressing line by disrupting sugar-dependent1 (SDP1), a predominant TAG lipase, significantly elevated vegetative TAG content and improved plant growth. Diverting FAs from membrane lipids to TAGs in PAP2-overexpressing plants by constitutively expressing phospholipid:diacylglycerol acyltransferase1 (PDAT1) greatly increased TAG content in vegetative tissues without compromising biomass yield. These results highlight the potential of combining PAP2 with TAG-promoting factors to enhance carbon assimilation, FA synthesis and allocation to TAGs for optimized plant growth and storage lipid accumulation in vegetative tissues.

Biomass Analytics↗

DOE OSTI2024

Analysis of the Challenges in Developing Sample-Based Multi-fidelity Estimators for Non-deterministic Models

Multifidelity (MF) uncertainty quantification (UQ) seeks to leverage and fuse information from a collection of models to achieve greater statistical accuracy with respect to a single-fidelity counterpart, while maintaining an efficient use of computational resources. Despite many recent advancements in MF UQ, several challenges remain and these often limit its practical impact in certain application areas. In this manuscript, we focus on the challenges introduced by nondeterministic models to sampling MF UQ estimators. Nondeterministic models produce different responses for the same inputs, which means their outputs are effectively noisy. MF UQ is complicated by this noise since many state-of-the-art approaches rely on statistics, e.g., the correlation among models, to optimally fuse information and allocate computational resources. Here, we demonstrate how the statistics of the quantities of interest, which impact the design, effectiveness, and use of existing MF UQ techniques, change as functions of the noise. With this in hand, we extend the unifying approximate control variate framework to account for nondeterminism, providing for the first time a rigorous means of comparing the effect of nondeterminism on different multifidelity estimators and analyzing their performance with respect to one another. Numerical examples are presented throughout the manuscript to illustrate and discuss the consequences of the presented theoretical results.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

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

24 POWER TRANSMISSION AND DISTRIBUTION↗

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↗