SEARCH · Engineering Papers

Results for “DISTRIBUTION”

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 289 records · Page 16

All sources NASA NTRS DOE OSTI

DOE OSTI2023

Establishing metrics to quantify spatial similarity in spherical and red blood cell distributions

As computational power increases and systems with millions of red blood cells can be simulated, it is important to note that varying spatial distributions of cells may affect simulation outcomes. Since a single simulation may not represent the ensemble behavior, many different configurations may need to be sampled to adequately assess the entire collection of potential cell arrangements. In order to determine both the number of distributions needed and which ones to run, we must first establish methods to identify well-generated, randomly placed cell distributions and to quantify distinct cell configurations. We utilize metrics to assess (1) the presence of any underlying structure to the initial cell distribution and (2) similarity between cell configurations. We propose the use of the radial distribution function to identify long-range structure in a cell configuration and apply it to a randomly distributed and structured set of red blood cells. To quantify spatial similarity between two configurations, we make use of the Jaccard index, and characterize sets of red blood cell and sphere initializations. As an extension to our work submitted to the International Conference on Computational Science, we significantly increase our data set size from 72 to 1048 cells, include a similar set of studies using spheres, compare the effects of varying sphere size, and utilize the Jaccard index distribution to probe sets of extremely similar configurations. Our results show that the radial distribution function can be used as a metric to determine long-range structure in both distributions of spheres and RBCs. We determine that the ideal case of spheres within a cube versus bi-concave shaped cells within a cylinder affects the shape of the Jaccard index distributions, as well as the range of Jaccard values, showing that both the shape of particle and the domain may play a role. Furthermore, we also find that the distribution is able to capture very similar configurations through Jaccard index values greater than 95% when appending several nearly identical configurations into the data set.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

On the statistical theory of self-gravitating collisionless dark matter flow: Scale and redshift variation of velocity and density distributions

The statistics of velocity and density fields are crucial for cosmic structure formation and evolution. Here, this paper extends our previous work on the two-point second-order statistics for the velocity field [Phys. Fluids 35, 077105 (2023)] to one-point probability distributions for both density and velocity fields. The scale and redshift variation of density and velocity distributions are studied by a halo-based non-projection approach. First, all particles are divided into halo and out-of-halo particles so that the redshift variation can be studied via generalized kurtosis of distributions for halo and out-of-halo particles, respectively. Second, without projecting particle fields onto a structured grid, the scale variation is analyzed by identifying all particle pairs on different scales $r$. We demonstrate that: (i) Delaunay tessellation can be used to reconstruct the density field. The density correlation, spectrum, and dispersion functions were obtained, modeled, and compared with the N-body simulation; (ii) the velocity distributions are symmetric on both small and large scales and are non-symmetric with a negative skewness on intermediate scales due to the inverse energy cascade on small scales with a constant rate $\varepsilon_u$; (iii) On small scales, the even order moments of pairwise velocity $\Delta u_L$ follow a two-thirds law $\propto{(-\varepsilon_ur)}^{2/3}$, while the odd order moments follow a linear scaling $\langle(\Delta u_L)^{2n+1}\rangle=(2n+1)\langle(\Delta u_L)^{2n}\rangle\langle\Delta u_L\rangle\propto{r}$; (iv) The scale variation of the velocity distributions was studied for longitudinal velocities $u_L$ or $u_L^{'}$, pairwise velocity (velocity difference) $\Delta u_L$=$u_L^{'}$-$u_L$ and velocity sum $\Sigma u_L$=$u^{'}_L$+$u_L$. Fully developed velocity fields are never Gaussian on any scale, despite that they can initially be Gaussian; (v) On small scales, $u_L$ and $\Sigma u_L$ can be modeled by a $X$ distribution to maximize the entropy of the system. The distribution of $\Delta u_L$ can be different; (vi) On large scales, $\Delta u_L$ and $\Sigma u_L$ can be modeled by a logistic or a $X$ distribution, while $u_L$ has a different distribution; (vii) the redshift variation of the velocity distributions follows the evolution of the $X$ distribution involving a shape parameter $\alpha(z)$ decreasing with time.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

The Value of Distributed Wind: A Valuation Framework

While there has been an increase in distributed energy resource (DER) adoption, particularly for solar photovoltaic (PV) DERs, distributed wind deployment is still relatively low. However, distributed wind has significant growth potential for behind-the-meter applications and can provide improved resource diversity and resilience in high-DER grid systems. In order to make optimized decisions about distributed wind deployment, it is important to identify and characterize the value streams of distributed wind in a way that will help policy makers, microgrid developers, utilities, project developers, and others understand the potential value of distributed wind. In our paper, we develop a framework to provide a consistent and comprehensive approach to finding the net benefits of distributed wind to various stakeholders in different scenarios. We do this by considering the main use cases for distributed wind, and then developing a framework which is flexible for these various use cases and the relevant stakeholders while maintaining the same overall structure for analysis. Ongoing work includes applying this framework to valuing two distributed wind power systems, one in a remote village in Alaska and one in a front-of-the-meter deployment in Iowa. Our analysis aims to understand the full value that distributed wind is providing in these systems, including the resilience benefits it is contributing. As a better understanding of distributed wind valuation is gained, it will be easier for stakeholders to make informed decisions in order to have resilient renewable energy systems.

17 WIND ENERGY↗

DOE OSTI2022

Categorizing distributed wind energy installations in the United States to inform research and stakeholder priorities

Abstract Background Distributed wind energy adoption in the United States can contribute to the diverse portfolio of energy technologies needed to achieve ambitious decarbonization goals. However, with limited deployment to date, the current distributed wind market must be better understood; these efforts will support the range of stakeholders who will drive successful deployment. This article first distinguishes three categories of distributed wind from existing literature: (1) behind the meter, (2) intended for explicit local load, and (3) physically distributed. A novel methodology to classify individual wind installations into each of these categories is then presented and applied to two data sets of wind installations in the United States to categorize and illuminate distinct segments in the distributed wind market. Results Physically distributed installations, constituted by small to moderately sized projects serving local loads on distribution systems solely because of their proximity to them, account for the highest amount of capacity but the lowest number of installations out of the three categories. The inverse is true for behind-the-meter installations, which are used to serve on-site loads. Installations intended for explicit local load, which are interconnected on the utility side of the distribution system and intentionally built to provide energy to loads on the same distribution system, rank in the middle for both installed capacity and number of installations. Conclusions Distributed wind energy deployment in the United States is geographically widespread, but the extent to which a single category is developed in each state varies. Policies, wind resources, and broad energy technology trends contribute to these deployment patterns. By identifying the extent to which each category of installations exists, decision-makers are empowered with data necessary to tailor research and development programs and address stakeholder priorities through policy and other means, ultimately supporting future deployment.

17 WIND ENERGY↗

DOE OSTI2021

Standardizing Performance Metrics for Building-Level Electrical Distribution Systems

Building-level electrical distribution systems comprise a myriad of current-carrying equipment, conversion devices, and protection devices that deliver power from the utility or local distributed energy resources to end-use building loads. Electric power has traditionally been generated, transmitted, and distributed in alternating current (AC). However, the last decade has seen a significant increase in the integration of native direct current (DC) equipment that has elevated the importance of DC distribution systems. Numerous studies have comparatively examined the performance of various electrical distribution systems in buildings but have failed to achieve uniform conclusions, primarily because of a lack of consistent and analogous performance evaluation methods. This paper aims to fill this gap by providing a standard set of metrics and measurement boundaries to consistently evaluate the performance of AC, DC, or hybrid AC/DC electrical distribution systems. The efficacy of the proposed approach is evaluated on a representative medium-sized commercial office building model with AC distribution and an equivalent hybrid AC/DC and DC distribution model, wherein the AC distribution model is concluded to be the most efficient. The simulation results show variation in computed metrics with different selected boundaries that verify the effectiveness of the proposed approach in ensuring consistent computation of the performance of building-level electrical distribution systems. This paper provides an initial set of guidelines for building energy system stakeholders to adopt appropriate solutions, thus leading to more efficient energy systems.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2026

Electric Utility Distribution Costs: Scoping Study on Trends, Drivers, and Possible Response Strategies [Slides]

This scoping study synthesizes information that will help stakeholders understand the scope, scale, and drivers of recent increases in investor-owned utility (IOU) expenditures on local distribution power grids, while providing regulators and other decision-makers with potential strategies to keep electricity bills down. The study includes five distinct components. Drawing first on data from FERC Form 1, it summarizes key trends in past and recent IOU distribution costs. Next, through a review of a sample of distribution-system plans, it characterizes material drivers of planned distribution expenditures. Ultimately, regulators must approve cost recovery for IOU expenditures, including those for the distribution system. The study therefore also: examines trends in utility requests and regulatory approvals related to changes in retail rates and return on equity; identifies areas where utility shareholder and customer incentives may be misaligned; and develops a menu of options that state regulators might consider to optimize distribution system expenditures. Some of the key findings include: - IOU distribution spending at a national level has grown by 6%/yr since 2014 in real dollar terms, 4x faster than in the prior 20 years and consisting mostly of capital (not operating) expenditure. - On a per-kWh basis, increases in IOU distribution costs since 2014 represent over 30% of the overall national-average increase in retail electricity rates. - Regional spending growth has ranged from 2-8%/yr, with larger estimated rate impacts in CAISO, then NYISO & ISO-NE, and then the Southeast, MISO & PJM (see figure). - Some utilities are planning for significantly increased distribution system spending. Planned spending on managing the existing system (asset replacement, safety & reliability, and resilience are all important drivers) exceeds that for capacity expansion. - IOU rate increase requests ($18 billion in 2025) and public utility commission (PUC) approval levels (average of 64% of requested amounts from 2021-2025) have recently hit multi-decadal highs. - PUCs in New England and the Southeast have recently approved a greater fraction of rate requests (>75%, on average) than in ther regions, while PUCs in California and the Southeast have generally authorized higher equity returns than in other regions. - Regulators have many tools to tackle potential misalignments between utility and customer interests and, more specifically, to optimize and reduce distribution costs. Shorter-term options include those related to return on equity, capital structure, depreciation, trackers, construction work in progress, and securitization. Longer-term options include performance-based regulation and a wide variety of planning-related requirements. All options embed important tradeoffs.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Preparing Distribution Utilities for the Future - Evolving Customer Consumption in Renewable Rich Grids: A Novel Analytical Framework

The research collaboration between NREL and BYPL focuses on the challenges caused by renewable integration into the power grid at large. Since the challenges and opportunities vary depending on the point of interconnection (distribution or transmission) the research team identified two tracks for research as listed below: 1. Power procurement - This research track focuses on the challenges and opportunities caused by GW scale renewable integration at the transmission level. Specifically, this track focuses on the contribution that utility-scale renewable energy procurement provides to distribution utilities, both from energy and capacity perspectives. In this track of research, utility customers are only considered as traditional (one-directional) consumers of energy. 2. Distributed energy resources - This research track focuses on the challenges and opportunities caused by many small-scale distributed renewable resource integrations at the distribution systems. At the power distribution level, distribution utilities may face not only new solar energy technologies, but also battery energy storage and electric vehicles as well. These three technologies (solar PV, battery energy storage, and electric vehicles) combined, pose unique challenges to distribution utilities. This track focuses on assessing the net-load evolution that distribution utilities observe as these emerging technologies make their way to the grid.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Numerical methods and hypoexponential approximations for gamma distributed delay differential equations

Abstract Gamma distributed delay differential equations (DDEs) arise naturally in many modelling applications. However, appropriate numerical methods for generic gamma distributed DDEs have not previously been implemented. Modellers have therefore resorted to approximating the gamma distribution with an Erlang distribution and using the linear chain technique to derive an equivalent system of ordinary differential equations (ODEs). In this work, we address the lack of appropriate numerical tools for gamma distributed DDEs in two ways. First, we develop a functional continuous Runge–Kutta (FCRK) method to numerically integrate the gamma distributed DDE without resorting to Erlang approximation. We prove the fourth-order convergence of the FCRK method and perform numerical tests to demonstrate the accuracy of the new numerical method. Nevertheless, FCRK methods for infinite delay DDEs are not widely available in existing scientific software packages. As an alternative approach to solving gamma distributed DDEs, we also derive a hypoexponential approximation of the gamma distributed DDE. This hypoexponential approach is a more accurate approximation of the true gamma distributed DDE than the common Erlang approximation but, like the Erlang approximation, can be formulated as a system of ODEs and solved numerically using standard ODE software. Using our FCRK method to provide reference solutions, we show that the common Erlang approximation may produce solutions that are qualitatively different from the underlying gamma distributed DDE. However, the proposed hypoexponential approximations do not have this limitation. Finally, we apply our hypoexponential approximations to perform statistical inference on synthetic epidemiological data to illustrate the utility of the hypoexponential approximation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

An Exact and Near-Exact Distribution Approach to the Behrens–Fisher Problem

The Behrens–Fisher problem occurs when testing the equality of means of two normal distributions without the assumption that the two variances are equal. This paper presents approaches based on the exact and near-exact distributions for the test statistic of the Behrens–Fisher problem, depending on different combinations of even or odd sample sizes. We present the exact distribution when both sample sizes are odd and the near-exact distribution when one or both sample sizes are even. The near-exact distributions are based on a finite mixture of generalized integer gamma (GIG) distributions, used as an approximation to the exact distribution, which consists of an infinite series. The proposed tests, based on the exact and the near-exact distributions, are compared with Welch’s t-test through Monte Carlo simulations, in particular for small and unbalanced sample sizes. The results show that the proposed approaches are competent solutions to the Behrens–Fisher problem, exhibiting precise sizes and better powers than Welch’s approach for those cases. Numerical studies show that the Welch’s t-test tends to be a bit more conservative than the test statistics based on the exact or near-exact distribution, in particular when sample sizes are small and unbalanced, situations in which the proposed exact or near-exact distributions obtain higher powers than Welch’s t-test.

Hong, Serim↗

DOE OSTI2021

Valuing wind as a distributed energy resource: A literature review

As more distributed energy resources are deployed on electric grid systems across the world, it is important to identify, characterize, and quantify the value elements of different types of distributed energy resources so that policymakers, developers, and utilities can make informed energy deployment decisions. This paper focuses on the value of wind energy as a distributed energy resource (i.e., “distributed wind”). Because of a lack of distributed wind-specific valuation studies, in this review we document the current state of distributed energy resource valuation, analyze a wide array of distributed energy resource valuation metastudies, and identify several value elements for which we recommend developing more robust and standardized calculation methodologies for their potential inclusion in distributed wind valuation. These value elements are ancillary services and locational, resilience, reliability, and resource diversity benefits. Furthermore, this work lays the foundation for a future comprehensive framework for distributed wind valuation studies.

17 WIND ENERGY↗

DOE OSTI2022

Performance Evaluation of Peer-to-Peer Distributed Microgrids Coordination for Voltage Regulation

This paper presents the performance evaluation of a peer-to-peer microgrids coordination algorithm for sub-transmission systems. As distributed energy resources (DERs) in distribution system start to show negative impact to the bulk power system, a paradigm shift is needed for transmission planning and operation. Because distribution substations are located far from the sub-transmission system, and it is hard to use traditional centralized control for real-time control and coordination. Thus, distributed control is a natural choice because it requires less communication and central computation. In this paper, each distribution substation is treated as a microgrid, and the peer-to-peer distributed microgrids control is formulated as a real-time optimal power flow problem to reduce the negative impact in sub-transmission systems. A distributed primal-dual optimization algorithm is adopted to solve the problem. Validation of the peer-to-peer algorithm is performed through the simulation of a real-world sub-transmission system composing of many distribution systems with high renewable penetration. Simulation results show that the peer-to-peer algorithm can achieve satisfactory performance (e.g., voltage regulation) in sub-transmission system by coordinating and controlling DERs in distribution systems.

distributed control↗

DOE OSTI2024

Security Constrained Distributed Transaction Model for Multiple Prosumers

Massive access of renewable energy has prompted demand-side distributed resources to participate in regulation and improve flexibility of power systems. With large-scale access of massive, decentralized, and diverse distributed resources, demand-side market members have transformed from traditional “consumers” to “prosumers”. To explore the distributed transaction model of prosumers, in this paper, a multi-prosumer distributed transaction model is proposed, and the Conditional Value-at-Risk (CVaR) theory is applied to quantify potential risks caused by the stochastic characteristics inherited from renewable energy. First, a prosumer model under constraints of the distribution network including photovoltaic units, fuel cells, energy storage system, central air conditioning and flexible loads is established, and a multi-prosumer distributed transaction strategy is proposed to achieve power sharing among multiple prosumers. Second, a prosumer transaction model based on CVaR is constructed to measure risks inherited from the uncertainty of PV output within the prosumer and ensure safety of system operation in extreme PV output scenarios. Then, the alternating direction multiplier method (ADMM) is utilized to solve the constructed model efficiently. Finally, distributed transaction costs of prosumers are distributed fairly based on the generalized Nash equilibrium to maximize social benefits. Simulation results show the multi-prosumer distributed transaction mechanism established under the proposed generalized Nash equilibrium method can encourage power sharing among prosumers, increasing their own income and social benefits. Also, the CVaR can assist decision making of prosumers in weighting the risks and benefits, improving system resilience through energy management of prosumers.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Distributed Wind Controls: A Research Roadmap for Microgrids, Infrastructure Resilience, and Controls Launchpad (MIRACL)

The Microgrids, Infrastructure Resilience, and Advanced Controls Launchpad (MIRACL) project’s controls research area aims to expand the benefits from distributed wind (DW) generation assets beyond solely providing low cost power directly to consumers. To make distributed wind turbines operate more effectively there is a need for more advanced ways to control them, allowing power companies, businesses, and energy consumers to take advantage of the unique characteristics of wind energy. DW can contribute to the safe and secure operation of grid by providing services such as voltage regulation, frequency regulation, spinning reserves, and even black start capabilities. In the larger DER context where much of the research has focused around solar technologies, the inertia available in wind technologies has generally not been considered. For wind turbines to provide these services in an optimal and expanded way, development and demonstration of control methods and communication interfaces within a grid and microgrid framework are required. In this document, NREL led the literature review in collaboration with SNL, of DER controls-focused integration research to establish a baseline for the controls research under the MIRACL project to identify specific control functions to be focused on throughout this project. This literature review focused primarily on the control functions of variable distributed generation, largely pulling from past solar PV and battery controls works, with a specific focus on applicability for distributed wind energy systems. The goal of this document is to identify a research roadmap based on the open literature and past national laboratory works to inform advanced wind turbine and power electronics control functions for four use cases: 1) distributed wind in isolated systems, 2) grid-connected microgrids (wind-hybrid systems and islanded operation), 3) behind-the-meter distributed wind applications in the power distribution systems, and 4) front-of-the-meter distributed wind applications in the power distribution systems.

17 WIND ENERGY↗

DOE OSTI2021

Cost Analysis Framework for Comparing AC and DC Design Alternatives for Building Electrical Distribution Systems

In recent years, in response to the changing nature of building load, direct current (DC) distribution systems for buildings have been proposed as alternatives to traditional alternating current (AC) systems. DC distribution offers a closer match to the types of loads and generation sources found in modern buildings, the majority of which use DC electricity internally either natively or as a power conditioning stage. The proposed benefits of DC distribution compared to AC distribution within buildings include higher efficiency, lower installation cost, lower operating cost, higher reliability, improved communication and control, and simplicity. Most recent DC distribution research has focused on quantifying the efficiency advantage of DC distribution over AC distribution. However, energy savings alone do not guarantee cost savings; a more complete cost accounting is required to establish financial benefit. This report provides a framework for cost analysis and comparison of building electrical distribution systems, including common variants for both AC and DC distribution systems. The framework includes all major cost categories, including up-front costs (capital, installation labor, soft costs) and long-term costs (energy, operations and maintenance).

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Performance Evaluation of Peer-to-Peer Distributed Microgrids Coordination for Voltage Regulation: Preprint

distributed control↗

DOE OSTI2025

Integrated Distribution Planning

The contemporary distribution planning landscape is comprised of an increasing number of factors that require integration into the engineering of the modern electric grid. Expectations for electric utilities to accommodate heightened awareness of stakeholders' interest in things like decarbonization, resilience and equity are growing. As these interests are formed into objectives, many jurisdictions will experience increasing levels of load modifying technologies like DER, building and industrial electrification and electric vehicles which prove not only to challenge the capabilities of the grid; but the processes by which planning for it is traditionally done. Other related factors that strain the conventional distribution planning mold are the swelling amount and sources of data associated with these technologies and the need it creates for improved capabilities in the processes and tools that manage it. As the complexity of the distribution system expands, so will the distribution system's effects on the transmission and generation systems that it is a part of. Forecasting distribution system load and DER are examples of areas where this complexity will manifest, and harmonizing distribution forecasting with transmission and generation forecasting requires higher amounts of intentionality as these typically separate processes become a solitary one. Of course, core activities do not cease as a utility begins to integrate these other factors, and in this webinar we explore specifics of how distribution planning can be expected to evolve as progress towards Integrated Distribution System Planning is made.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Kinetic Landau-fluid closures of non-Maxwellian distributions

New kinetic Landau-fluid closures, based on the cutoff Maxwellian distribution, are derived. A special static case is considered (the frequency ω=0). In the strongly collisional regime, our model reduces to Braginskii's heat flux model, and the transport is local. In the weak collisional regime, our model indicates that the heat flux is non-local and recovers the Hammett–Perkins model while the value of the cutoff velocity approaches to infinity. We compare the thermal transport coefficient χ of Maxwellian, cutoff Maxwellian and super-Gaussian distribution. The results show that the reduction of the high-speed tail particles leads to the corresponding reduction of the thermal transport coefficient χ across the entire range of collisionality, more reduction of the free streaming transport toward the weak collisional regime. In the collisionless limit, χ approaches to zero for the cutoff Maxwellian and the super-Gaussian distribution but remains finite for Maxwellian distribution. χ is complex if the cutoff Maxwellian distribution is asymmetric. The Im(χ) approaches to different convergent values in both collisionless and strongly collisional limit, respectively. It yields an additional streaming heat flux in comparison with the symmetric cutoff Maxwellian distribution. Furthermore, due to the asymmetric distribution, there is a background heat flux q0 though there is no perturbation. Furthermore, the derived Landau-fluid closures are general for fluid moment models, and applicable for the cutoff Maxwellian distribution in an open magnetic field line region, such as the scape-off-layer of Tokamak plasmas, in the thermal quench plasmas during a tokamak disruption, and the super-Gaussian electron distribution function due to inverse bremsstrahlung heating in laser-plasma studies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Modeling and Rapid Prototyping of Integrated Transmission-Distribution OPF Formulations with PowerModelsITD.jl

Conventional electric power systems are composed of different unidirectional power flow stages of generation, transmission, and distribution, managed independently by transmission system and distribution system operators. However, as distribution systems increase in complexity due to the integration of distributed energy resources, coordination between transmission and distribution networks will be imperative for the optimal operation of the power grid. However, coupling models and formulations between transmission and distribution is non-trivial, in particular due to the common practice of modeling transmission systems as single-phase, and distribution systems as multi-conductor phase-unbalanced. To enable the rapid prototyping of power flow formulations, in particular in the modeling of the boundary conditions between these two seemingly incompatible data models, we introduce PowerModelsITD.jl, a free, open-source toolkit written in Julia for integrated transmission-distribution (ITD) optimization that leverages mature optimization libraries from the InfrastructureModels.jl-ecosystem. The primary objective of the proposed framework is to provide baseline implementations of steady-state ITD optimization problems, while providing a common platform for the evaluation of emerging formulations and optimization problems. In this work, we introduce the nonlinear formulations currently supported in PowerModelsITD.jl, which include AC-polar, AC-rectangular, current-voltage, and a linear network transportation model. Results are validated using combinations of IEEE transmission and distribution networks.

24 POWER TRANSMISSION AND DISTRIBUTION↗