Grid Solutions Research Articles

Numerical Study of an Initial-Boundary Value Neumann Problem for a Singularly Perturbed Parabolic Equation

For a singularly perturbed one-dimensional parabolic equation with a perturbation parameter e multiplying the highest-order derivative in the equation, e ∈ (0,1], an initial-boundary value Neumann problem is considered on a segment. In this problem, when the parameter e tends to zero, boundary layers appear in neighborhoods of the lateral boundary. In the paper, convergence of the problem solution and its regular and singular components are studied. It is shown that standard finite difference schemes on uniform grids used to numerically solve this problem do not converge e -uniformly. The error in the grid solution grows unboundedly when the parameter e → 0. The use of a special difference scheme on Shishkin grid which is a piecewise-uniform mesh with respect to x condensing in neighborhoods of boundary layers and a uniform mesh in t , constructed by using monotone grid approximations of the differential problems, allows us to find a numerical solution of this problem convergent in the maximum norm e -uniformly. The results of the numerical experiments confirm the theoretical results.

Computer Difference Scheme for a Singularly Perturbed Reaction- Diffusion Equation in the Presence of Perturbations

In this paper, for a singularly perturbed parabolic reaction-diffusion equation with a perturbation parameter e 2 , e ∈ (0,1], multiplying the highest-order derivative in the equation, an initial-boundary value Dirichlet problem is considered. For this problem, a standard difference scheme constructed by using monotone grid approximations of the differential problem on uniform grids, is studied in the presence of computer perturbations. Perturbations of grid solutions are studied, which are generated by computer perturbations, i.e., the computations on a computer. The conditions imposed on admissible computer perturbations are obtained under which the accuracy of the perturbed computer solution is the same by order as the solution of an unperturbed difference scheme, i.e., a standard scheme in the absence of perturbations. The schemes of this type with controlled computer perturbations belong to computer difference schemes, also named reliable difference schemes.

Profitability of smart grid solutions applied in power grid

The idea of a Smart Grid solution has been developing for years, as complete solution for a power utility, consisting of different advanced technologies aimed at improving of the efficiency of operation. The trend of implementing various smart systems continues, e.g. Energy Management Systems, Grid Automation Systems, Advanced Metering Infrastructure, Smart power equipment, Distributed Energy Resources, Demand Response systems, etc. Futhermore, emerging technologies, such as energy storages, electrical vehicles or distributed generators, become integrated in distribution networks and systems. Nowadays, the idea of a Smart Grid solution becomes more realistic by full integration of all advanced operation technologies (OT) within IT environment, providing the complete digitalization of an Utility (IT/OT integration). The overview of smart grid solutions, estimation of investments, operation costs and possible benefits are presented in this article, with discusison about profitability of such systems.

Practical Experiences in Operationalizing WAMS in the Control Room

The utility industry at large has made significant investments in deployment of production grade Wide Area Monitoring Systems (WAMS) and synchrophasor technology in recent years with now well over 4,000 Phasor Measurement Units (PMUs) globally. In North America alone, the US Smart Grid Investment Grants (SGIG) have resulted in a massive influx of installed Phasor Measurement Unit (PMU) expanding from approximately 200 research-grade units to over 1,700 production-grade devices over the past five years. Some of early real-time PMU applications and visualization being deployed at utility and ISO control rooms worldwide include angular separation, oscillatory stability monitoring, islanding and/or disturbance detection applications. For several years, GE Grid Solutions has been involved in delivery and deployment of WAMS applications around the globe. While the industry-at-large, foresees the promise that synchrophasors and WAMS holds in modernizing the power grid, and shaping the generation Energy Management Systems, there are some common take-always from these early WAMS installations. This paper summarizes some of the common experiences, and what is being done to address the challenges in operationalizing the technology into the control room.

Global Smart Grid Transferability: Insights from Europe, the U.S., and China

The paper tries to address the question of whether the smart grid solution can be transferred internationally, and explore the transferability of the smart grid across countries with three national comparisons: USA, Europe and China. A qualitative content analysis in which data (the academic papers) are coded in preparation for comparison and interpretation is chosen to find the similarities and differences of smart grid development in different national contexts. Trough a comparative analysis of the smart grid development in USA, Europe and China, this paper conducts a transferable framework of smart grid solution with global and local features.

Verification Assessment of Piston Boundary Conditions for Lagrangian Simulation of Compressible Flow Similarity Solutions

This work is concerned with the use of similarity solutions of the compressible flow equations as benchmarks or verification test problems for finite-volume compressible flow simulation software. In practice, this effort can be complicated by the infinite spatial/temporal extent of many candidate solutions or “test problems.” Methods can be devised with the intention of ameliorating this inconsistency with the finite nature of computational simulation; the exact strategy will depend on the code and problem archetypes under investigation. For example, self-similar shock wave propagation can be represented in Lagrangian compressible flow simulations as rigid boundary-driven flow, even if no such “piston” is present in the counterpart mathematical similarity solution. The purpose of this work is to investigate in detail the methodology of representing self-similar shock wave propagation as a piston-driven flow in the context of various test problems featuring simple closed-form solutions of infinite spatial/temporal extent. The closed-form solutions allow for the derivation of similarly closed-form piston boundary conditions (BCs) for use in Lagrangian compressible flow solvers. The consequences of utilizing these BCs (as opposed to directly initializing the self-similar solution in a computational spatial grid) are investigated in terms of common code verification analysis metrics (e.g., shock strength/position errors and global convergence rates).

Two-grid Methods for Finite Volume Element Approximations of Nonlinear Sobolev Equations

ABSTRACTIn this article, two-grid methods are studied for solving nonlinear Sobolev equation using the finite volume element method. The methods are based on one coarse grid space and one fine grid space. The nonsymmetric and nonlinear iterations are only executed on the coarse grid (with grid size H), and the fine grid solution (with grid size h) can be obtained in a single symmetric and linear step. The optimal H1 error estimates are presented for the proposed methods, which show that the two-grid methods achieve optimal approximation as long as the mesh sizes satisfy h = 𝒪(H3|ln H|). As a result, solving such a large class of nonlinear Sobolev equations will not be much more difficult than solving one linearized equation.

A finite element variational multiscale method based on two-grid discretization for the steady incompressible Navier–Stokes equations

By combining the best algorithmic features of two-grid discretization method and a recent variational multiscale method, a two-level finite element variational multiscale method based on two local Gauss integrations for convection dominated incompressible Navier–Stokes equations is proposed and analyzed. In this method, a fully nonlinear Navier–Stokes problem is first solved on a coarse grid, and then a linear problem is solved on a fine grid to correct the coarse grid solution, where the numerical forms of the Navier–Stokes equations both on coarse and fine grids are stabilized by a stabilization term defined by the difference between a consistent and an under-integrated matrix of the velocity gradient. Error bounds of the approximate solution are analyzed. Algorithmic parameter scalings of the method are derived. Numerical tests are also given to verify the theoretical predictions and demonstrate the efficiency and promise of the method.

Progress on the Fabric for Frontier Experiments Project at Fermilab

The FabrIc for Frontier Experiments (FIFE) project is an ambitious, major-impact initiative within the Fermilab Scientific Computing Division designed to lead the computing model for Fermilab experiments. FIFE is a collaborative effort between experimenters and computing professionals to design and develop integrated computing models for experiments of varying needs and infrastructure. The major focus of the FIFE project is the development, deployment, and integration of Open Science Grid solutions for high throughput computing, data management, database access and collaboration within experiment. To accomplish this goal, FIFE has developed workflows that utilize Open Science Grid sites along with dedicated and commercial cloud resources. The FIFE project has made significant progress integrating into experiment computing operations several services including new job submission services, software and reference data distribution through CVMFS repositories, flexible data transfer client, and access to opportunistic resources on the Open Science Grid. The progress with current experiments and plans for expansion with additional projects will be discussed. FIFE has taken a leading role in the definition of the computing model for Fermilab experiments, aided in the design of computing for experiments beyond Fermilab, and will continue to define the future direction of high throughput computing for future physics experiments worldwide.

A spectrally accurate method for overlapping grid solution of incompressible Navier–Stokes equations

An overlapping mesh methodology that is spectrally accurate in space and up to third-order accurate in time is developed for solution of unsteady incompressible flow equations in three-dimensional domains. The ability to decompose a global domain into separate, but overlapping, subdomains eases mesh generation procedures and increases flexibility of modeling flows with complex geometries. The methodology employs implicit spectral element discretization of equations in each subdomain and explicit treatment of subdomain interfaces with spectrally-accurate spatial interpolation and high-order accurate temporal extrapolation, and requires few, if any, iterations, yet maintains the global accuracy and stability of the underlying flow solver. The overlapping mesh methodology is thoroughly validated using two-dimensional and three-dimensional benchmark problems in laminar and turbulent flows. The spatial and temporal convergence is documented and is in agreement with the nominal order of accuracy of the solver. The influence of long integration times, as well as inflow–outflow global boundary conditions on the performance of the overlapping grid solver is assessed. In a turbulent benchmark of fully-developed turbulent pipe flow, the turbulent statistics with the overlapping grids is validated against published available experimental and other computation data. Scaling tests are presented that show near linear strong scaling, even for moderately large processor counts.

Barriers and Solutions to Smart Water Grid Development.

This limited review of smart water grid (SWG) development, challenges, and solutions provides an initial assessment of early attempts at operating SWGs. Though the cost and adoption issues are critical, potential benefits of SWGs such as efficient water conservation and distribution sustain the development of SWGs around the world. The review finds that the keys to success are the new regulations concerning data access and ownership to solve problems of security and privacy; consumer literacy to accept and use SWGs; active private sector involvement to coordinate SWG development; government-funded pilot projects and trial centers; and integration with sustainable water management.

3D conservative cascade semi-Lagrangian transport scheme using reduced latitude–longitude grid (CCS-RG)

The article presents conservative cascade scheme using reduced grid (CCS-RG) - a finite volume semi-Lagrangian (FVSL) algorithm for numerical solution of 3D advection equation on the sphere. The CCS-RG is based on the cascade approach that allows to split 3D advected quantity mass remapping between the Lagrangian and Eulerian grids onto 3 1D remappings. Another feature is using a quasi-uniform spaced reduced latitude-longitude grid on the sphere. The scheme is inherently mass-conservative, monotonic and stable with large time-steps. The CCS-RG performance is tested with the advection cases from the Dynamical Core Model Intercomparison Project test suite. The impact of the reduced grids and two different monotonic filters on the solution is investigated. The comparison with the results obtained by other schemes proves competitive accuracy of CCS-RG. In most cases, the numerical solution obtained with various reduced grids is as accurate as the regular grid solution.

An efficient semi‐implicit subgrid method for free‐surface flows on hierarchical grids

SUMMARYWe present a new modelling strategy for improving the efficiency of computationally intensive flow problems in environmental free‐surface flows. The approach combines a recently developed semi‐implicit subgrid method with a hierarchical grid solution strategy. The method allows the incorporation of high‐resolution data on subgrid scale to obtain a more accurate and efficient hydrodynamic model. The subgrid method improves the efficiency of the hierarchical grid method by providing better solutions on coarse grids. The method is applicable to both steady and unsteady flows, but we particularly focus on river flows with steady boundary conditions. There, the combined hierarchical grid–subgrid method reduces the computational effort to obtain a steady state with factors up to 43. For unsteady models, the method can be used for efficiently generating accurate initial conditions on high‐resolution grids. Additionally, the method provides automatic insight in grid convergence. We demonstrate the efficiency and applicability of the method using a schematic test for the vortex shedding around a circular cylinder and a real‐world river case study. Copyright © 2015 John Wiley & Sons, Ltd.

A Simplified Parallel Two-Level Iterative Method for Simulation of Incompressible Navier-Stokes Equations

AbstractBased on two-grid discretization, a simplified parallel iterative finite element method for the simulation of incompressible Navier-Stokes equations is developed and analyzed. The method is based on a fixed point iteration for the equations on a coarse grid, where a Stokes problem is solved at each iteration. Then, on overlapped local fine grids, corrections are calculated in parallel by solving an Oseen problem in which the fixed convection is given by the coarse grid solution. Error bounds of the approximate solution are derived. Numerical results on examples of known analytical solutions, lid-driven cavity flow and backward-facing step flow are also given to demonstrate the effectiveness of the method.

Distributed Real-Time Demand Response in Multiseller–Multibuyer Smart Distribution Grid

Demand response is a key solution in smart grid to address the ever-increasing peak energy consumption. With multiple utility companies, users will decide from which utility company to buy electricity and how much to buy. Consequently, how to devise distributed real-time demand response in the multiseller–multibuyer environment emerges as a critical problem in future smart grid. In this paper, we focus on the real-time interactions among multiple utility companies and multiple users. We propose a distributed real-time demand response algorithm to determine each user's demand and each utility company's supply simultaneously. By applying dual decomposition, the original problem is firstly decoupled into single-seller–multibuyer subsystems; then, the demand response problem in each subsystem can be distributively solved. The major advantage of this approach is that each utility company and user locally solve subproblems to perform energy allocation, instead of requiring a central controller or any third party. Therefore, privacy is guaranteed because no entity needs to reveal or exchange private information. Numerical results are presented to verify efficiency and effectiveness of the proposed approach.

Ambivalence, designing users and user imaginaries in the European smart grid: Insights from an interdisciplinary demonstration project

The gradual implementation of smart grid solutions is accompanied by an increased concern amongst researchers and policymakers for the role of users in such systems. For smart grids to perform as expected, the role of users in electricity systems must change. One approach to technology-user relationships proposes that the chance of success increases through involving users in the design and development of technologies. This article reports on a research project that set out to involve what was perceived as active and competent users in the design of feedback technologies. We explore how users were imagined in the project, and how the idea of active user participation was shadowed by an ambivalent and paradoxical view of users as knowledge deficient and incompetent. The case illustrates how the boundaries between involving users and by-passing users becomes blurred. Through this, we contribute to the knowledge on how user imaginaries and future expectations influence research and innovation processes, illustrating how traditional models of knowledge deficiency can lead to minimal user engagement.

Improving Large-Eddy Simulation of Neutral Boundary Layer Flow across Grid Interfaces

Abstract Increasing computational power has enabled grid resolutions that support large-eddy simulation (LES) of the atmospheric boundary layer. These simulations often use grid nesting or adaptive mesh refinement to refine the grid in regions of interest. LES generates errors at grid refinement interfaces, such as resolved energy accumulation, that may compromise solution accuracy. In this paper, the authors test the ability of two LES formulations and turbulence closures to mitigate errors associated with the use of LES on nonuniform grids for a half-channel approximation to a neutral atmospheric boundary layer simulation. Idealized simulations are used to examine flow across coarse–fine and fine–coarse interfaces, as would occur in a two-way nested configuration or with block structured adaptive mesh refinement. Specifically, explicit filtering of the advection term and the mixed model are compared to a standard LES formulation with an eddy viscosity model. Errors due to grid interfaces are evaluated by comparison to uniform grid solutions. It is found that explicitly filtering the advection term provides significant benefits, in that it allows both mass and momentum to be conserved across grid refinement interfaces. The mixed model reduces unphysical perturbations generated by wave reflection at the interfaces. These results suggest that the choice of LES formulation and turbulence closure can be used to help control grid refinement interface errors in atmospheric boundary layer simulations.

A Generic Holonic Control Architecture for Heterogeneous Multiscale and Multiobjective Smart Microgrids

Designing the control infrastructure of future “smart” power grids is a challenging task. Future grids will integrate a wide variety of heterogeneous producers and consumers that are unpredictable and operate at various scales. Information and Communication Technology (ICT) solutions will have to control these in order to attain global objectives at the macrolevel, while also considering private interests at the microlevel. This article proposes a generic holonic architecture to help the development of ICT control systems that meet these requirements. We show how this architecture can integrate heterogeneous control designs, including state-of-the-art smart grid solutions. To illustrate the applicability and utility of this generic architecture, we exemplify its use via a concrete proof-of-concept implementation for a holonic controller, which integrates two types of control solutions and manages a multiscale, multiobjective grid simulator in several scenarios. We believe that the proposed contribution is essential for helping to understand, to reason about, and to develop the “smart” side of future power grids .

The Legal Rash Sustainable Energy Action Plan for Sierra Leone (Recommendations to the Minister of Energy and the Government of Sierra Leone)

The UN Sustainable Development Goal 7 on Sustainable Energy is about saving lives and improving energy access. If Sierra Leone must attained this goal by 2030, it would require her to have in the first place a Sustainable Energy for all Policy Agenda and an Action Plan which will help create the enabling environment for huge investments into renewable energy like solar, hydro, wind farms, mini grids, stand alone systems and other off grid solutions from 2015 onwards within the country. These clean sources of energy are the rescue for the future of Sierra Leone’s energy problems and its polluted climate and environment. This LEGAL RASH SUSTAINABLE ENERGY ACTION PLAN for Sierra Leone reflects a significant first step towards realization of sustainable energy for all in the country. If a thorough implementation of its contents are ensured, it will not only help accelerate achievements in the energy sector in Sierra Leone but hopefully will also contribute in the actualization of Goal 7 of the UN Sustainable Development Goals Agenda and the core objectives of the Ecowas Renewable Energy Policy and the SEFA initiative by 2030.

Proactive Management of the Future Grid

The energy management system (EMS) at utility control centers collects real-time measurements to monitor current grid conditions. The EMS is also a suite of analytics that synthesizes these measurements to provide the grid operator with information to identify current problems and potential future problems. With evolving grid influences, such as growth of variable renewable generation resources, distributed generation, microgrids, demand response (DR), and customer engagement programs, managing the grid is becoming more challenging. Concurrently, however, there are nascent new technologies and advances in grid management schemes that will improve the ability to manage the future grid operations. These technologies include new subsecond synchrophasor measurements and analytics, advances in high-performance computing, visualization platforms, digital relays, cloud computing, and so on. Advances in grid management schemes include adding more intelligence at the substation and distribution systems, as well as microgrids and wide-area monitoring systems. One key initiative is to develop a predict-and-mitigate paradigm enabling anticipatory vision and timely decisions to mitigate potential problems before they spread to the rest of the grid. The word “proactive” means “to act now in anticipation of future problems.” Proactive grid management opportunities and solutions are described in this paper.