Grid Nodes Research Articles

Characterization of Qualified Grid Nodes for the Identification of Power Network Oscillations

Characterization of Qualified Grid Nodes for the Identification of Power Network Oscillations

РАЗРАБОТКА МЕТОДИКИ ИДЕНТИФИКАЦИИ И РАЗРЕШЕНИЯ КОНФЛИКТНЫХ СИТУАЦИЙ ПРИ ОПЕРАТИВНОМ ПЛАНИРОВАНИИ ЧЕТЫРЕХМЕРНОЙ ТРАЕКТОРИИ ПОЛЕТА

Conflict detection and resolution is one of the key tasks in ensuring the safety and efficiency of air transport. In Trajectory Based Operation (TBO), aircraft are given greater flexibility in planning trajectories along the route and greater responsibility for self-separation from each other, so the pilot will need assistance to safely and efficiently perform the task of decentralized conflict resolution during the en-route flight. In this work, we develop a method for identifying and resolving conflict situations in cruising phase based on four-dimensional grid nodes (4D-grid) and the A-star shortest path search algorithm (A* for short) to form an optimal four-dimensional trajectory (4D-trajectory) bypass all airspace obstacles. This new approach helps to avoid false warnings about potential conflicts due to the ability to early detect them and accurately determine the distance from aircraft to areas of dangerous proximity (prohibited zones (PZ), zones of bad weather, other aircraft) and then autonomously form a time-spatial trajectory to bypass them. In order to demonstrate the effectiveness of the proposed method, we conduct three experiments in different airspace conditions (with and without the areas of dangerous proximity). The results of the experiments prove that potential dangerous proximities of aircraft in flight are effectively identified and resolved using the proposed methodology.

Algorithmic implementation of an exact three-point difference scheme for a certain class of singular Sturm–Liouville problems

In this article, we present a new algorithmic implementation of exact three-point difference schemes for a certain class of singular Sturm–Liouville problems. We demonstrate that computing the coefficients of the exact scheme at any grid node xj requires solving two auxiliary Cauchy problems for the second-order linear ordinary differential equations: one problem on the interval [xj−1,xj] (forward) and one problem on the interval [xj,xj+1] (backward). We have also proven the coefficient stability theorem for the exact three-point difference scheme.

Toward Data Integrity Attacks Against Distributed Dynamic State Estimation in Smart Grid

With the continuous expansion of the power grid nodes scale, traditional centralized state estimation method shows certain limitations in estimation efficiency and accuracy. Recently, some power grids adopt a distributed state estimation method, in which each partition independently estimates the partial state information by partitioning the entire power system. However, the deviation of the state estimation in certain partition will result in the deviation of the estimation results in the entire power grid system. In this paper, we propose the attack strategy against the distributed state estimation in smart grids from two perspectives, i.e. the attack against local physical measurement value of the power system partition and the attack against the measurement value of coordination center. Moreover, the theoretical analysis of the state estimation deviation caused by the proposed data integrity attack and the propagation processes of proposed attack vectors in measurement calculations are formalized. The effectiveness of the proposed attack strategy is verified in the IEEE-30 bus and IEEE-118 bus systems. Simulation results show that attacking against a certain partition of a distributed system can indirectly affect the state estimation results of other partitions and attacking against the measurement value of coordination center can directly threaten the state estimation results of the entire power grid. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper proposes two attack strategies against the distributed state estimation of power grid from two perspectives, i.e. the attack against local physical measurement value of the power system partition and the attack against the measurement value of coordination center. Most of the previous works fail to formalize the state estimation deviation of both partial and entire state estimation results of power grid after the attacker launches the attack against the distributed state estimation. We formalize the state estimation deviation caused by the proposed data integrity attack and the propagation processes of proposed attack vectors in measurement calculations. The effectiveness of the proposed attack strategy against the state estimation of power grid is verified in the IEEE-30 bus and IEEE-118 bus systems. Simulation results show that attacking against a certain partition of power grid can indirectly cause the deviation in the state estimation results of entire power grid and attacking against the measurement value of the coordination center can directly threaten the state estimation results of the entire power grid. In conclusion, the proposed attack strategies are helpful for the research community to design detection strategies in a targeted manner and can be conveniently applied to the real-world security management system of smart grid.

APPLICATION OF PINN AND THE METHOD OF DIFFERENTIAL CONSTRUCTION OF ADAPTIVE ONE-DIMENSIONAL COMPUTATIONAL GRIDS

This paper presents an approach to constructing adaptive one-dimensional computational grids using the Beltrami equation and Physics-Informed Neural Networks (PINNs). The main focus is on exploring the potential for precise control of grid node density through the control function ω(s), which allows the grid to adapt to the local features of the problem. The Beltrami equation used, being a key component of the method, regulates the distribution of nodes by modifying the function’s derivatives depending on the values of the control function. The effectiveness of this approach is demonstrated through examples involving one and two regions of node clustering. The results showed that the PINN method combined with the Beltrami equation allows for the creation of computational grids with a high degree of adaptation to given conditions, providing detailed modeling in critical regions. This approach has advantages over traditional numerical methods, as integrating physical laws in the grid construction process minimizes numerical errors and improves modeling accuracy. The use of neural networks offers flexibility in model tuning and the ability to account for complex nonlinear dependencies. The discussion of the results highlights the potential of using PINNs for adaptive grid construction in various fields requiring precise and efficient modeling. In conclusion, this study confirms that the combination of the Beltrami equation and PINNs is a powerful tool for adaptive grid construction, opening new possibilities for numerical modeling of complex physical processes.

Temperature prediction model in multiphase flow considering phase transition in the drilling operations

The study considers gas compression properties, gas slippage, back pressure (BP), phase transition (PT), well depth, and differences in gas-liquid physical properties. A new temperature model for multiphase flow is proposed by considering phase transition in the drilling process. The mathematical model of multiphase flow is solved using the finite difference method with annulus mesh division for grid nodes, and a module for multiphase flow calculation and analysis is developed. Numerical results indicate that the temperature varies along the annulus with the variation of gas influx at the bottom of the well. During the process of controlled pressure drilling, as gas slips along the annulus to the wellhead, its volume continuously expands, leading to an increase in the gas content within the annulus, and consequently, an increase in the pressure drop caused by gas slippage. The temperature increases with the increase in BP and decreases in gas influx rate and wellbore diameter. During gas influx, the thermal conductivity coefficient for the gas-drilling mud two phases is significantly weakened, resulting in a considerable change in temperature along the annulus. In the context of MPD, the method of slightly changing the temperature along the annulus by controlling the back pressure is feasible.

Identification of Critical Nodes in Power Grid Based on Improved PageRank Algorithm and Power Flow Transfer Entropy

Identifying critical nodes in the power grid is a crucial aspect of power system security and stability analysis. However, the current methods for identification fall short in fully accounting for the power transfer characteristics between nodes and the consequences of node removal on the security and stability of power grid operation. To enhance the effective and accurate identification of critical nodes in the power grid, a method is proposed. This method is based on improved PageRank algorithm and node-weighted power flow transfer entropy, referred to as IPRA-PFTE. Firstly, based on the power flow and equivalent impedance between nodes, and the introduction of virtual nodes, an improved PageRank algorithm is obtained. Then the node-weighted power flow transfer entropy is derived by considering the uniformity of the transfer power flow distribution in the system following the removal of a node. Finally, the importance of nodes is obtained by combining the improved PageRank algorithm with the node-weighted power flow transfer entropy. The method’s effectiveness and accuracy are validated through simulation using the IEEE 39-bus example and subsequent comparison with existing methods.

Single‐ and multi‐GPU computing on NVIDIA‐ and AMD‐based server platforms for solidification modeling application

SummaryThis work explores the performance of single‐ and multi‐GPU computing on state‐of‐the‐art NVIDIA‐ and AMD‐based server‐class hardware using various programming interfaces to accelerate a real‐world scientific application for solidification modeling based on the phase‐field method. The main computations of this memory‐bound application correspond to 20 stencils computed across grid nodes. We investigate the application's scalability for two basic schemes of organizing computation: without and with hiding data transfers behind computation, combined with using either peer‐to‐peer inter‐GPU data transfers through NVIDIA NVLink and AMD Infinity interconnects or communication over the PCIe and main memory. Among the studied programming interfaces is CUDA, HIP, and OpenMP Accelerator Model. While the first two are designed to write the codes for a specific hardware platform, OpenMP enables code portability between NVIDIA and AMD GPUs. The resulting performance is experimentally assessed on computing platforms containing NVIDIA V100 (up to 8 GPUs) and A100 (one GPU), as well as AMD MI210 (one device) and MI250 (up to 8 logical GPUs).

Gauss-Newton inversion with node-based basis functions: Application to imaging of seabed minerals in an area with rough bathymetry

The Gauss-Newton method has good convergence properties when used for the solution of seismic and electromagnetic inversion problems. One main issue is the high numerical cost. The numerical cost can be reduced if the optimization domain can be decoupled from the simulation domain such that the number of optimization parameters is much smaller than the number of grid nodes required for accurate simulation results. Overparameterization can be avoided. The decoupling can be achieved in a rigorous manner with the use of node-based basis functions. We provide a generic derivation of the method that is easily specialized for seismic and electromagnetic problems. The transformations between the optimization domain and the simulation domain are most effective if both domains can be described by rectilinear grids. A variable seabed depth causes difficulty. We introduce a transform from the true bathymetry to a flat seabed that solves this problem. The method is validated by application to synthetic and real electromagnetic data sets. The real data are acquired at the slow spreading Mohns Ridge located east of Greenland and southwest of Svalbard. We provide a discussion on the interpretation of these data for an inverse scheme using the transverse isotropy with a vertical symmetry axis approximation. We offer some insights on how to interpret inversion results in the case of exploration for marine minerals. The interpretation differs from a hydrocarbon exploration setting owing to the presence of vertical conductors due to the formation water circulation and vertical resistors due to volcanic intrusions.

DEVELOPMENT OF THE CALCULATION PROCEDURE ALGORITHM FOR THE CALCULATION OF LIGHTNING RODS PROTECTION ZONES ACCORDING TO THE INTERNATIONAL STANDARD IEC 62305

A series of publications on the problem of lightning protection in power stations and substations, especially in the conditions of decreasing stability of the functioning of the energy system of Ukraine is continued. In addition, the relevance of the work is substantiated by the increase in thunderstorm activity on the planet as a whole and by the data of the national energy company in Ukraine, which leads to emergency shutdowns on power transmission lines. The system of algorithms for the computational procedure for calculating the protection zones of the system, which consists of numerous rod and cable lightning conductors and protective nets, using the rolling sphere method is developed. It is noted, that the majority of strategic energy facilities in Ukraine have lightning protection systems built according to outdated standards, therefore, their inspection and modernization is necessary taking into account current regulatory documents. A generalized algorithm for constructing a protection zone using the Delaunay algorithm and previously obtained mathematical expressions has been developed, which in turn consists of sub-algorithms: constructing a polygonal grid based on the points of the coordinates of the lightning conductors, finding the areas of contact with the sphere of the vertices of the polygonal grid, constructing a grid of nodes of the analysis points, finding the height coordinates for of each analysis point, construction of the protection surface based on the grid coordinates of the analysis point nodes. The software implementation was carried out and an example of the application of algorithms was shown when calculating the protection of an operating substation with a voltage class of 150 kV. The general features of software implementation in the LiGro software complex are given. The developed software product found its application in the modernization of existing lightning protection systems of operating power facilities of Ukraine with a voltage class of 35-750 kV.

Coupling of smoothed particle hydrodynamics and finite volume method for electrohydrodynamic droplet deformation simulation

In the numerical simulation of droplet electrohydrodynamic deformation, the grid-based method is difficult to handle the large topological deformation of the droplet interface, while the meshless method is challenging in the enforcement of boundary conditions. Therefore, a coupling method of the smoothed particle hydrodynamics (SPH) method and the finite volume method (FVM) is developed in this paper. In the present coupling method, the SPH method is used to solve the governing equations of the two-phase flow, while the FVM is used to solve the governing equations of the electric field. The realization of the coupling method is based on the information transfer between particles and grids. In order to accurately transfer the electric field force of interface grid nodes to SPH particles, a particle splitting interpolation method is developed. The influences of electrical capillary number, electrical conductivity ratio, and permittivity ratio on droplet deformation are studied. The simulation results are in good agreement with the theoretical predictions, and the coupling method can obtain more accurate numerical results than the pure SPH method. The coupling method can provide a reliable way to investigate complex electrohydrodynamic problems.

Congestion Relief Services by Vehicle-to-Grid Enabled Electric Vehicles Considering Battery Degradation

Battery electric vehicles (BEVs) offer substantial potential to enhance the electric grid through bi-directional charging technologies. In essence, BEVs, functioning as portable battery energy storage systems, play a pivotal role in enabling the seamless integration of renewable energy, grid optimization, and ancillary services. This article sets out to explore the value of BEVs equipped with Vehicle-to-Grid (V2G) for grid operators, particularly in the context of alleviating congestion. This valuable service, though not accompanied by direct monetary compensation for users, holds significant promise in minimizing congestion and renewable energy curtailment. This study utilizes the Day-Ahead Locational Marginal Price (LMP) data obtained from various locations within California Independent System Operator (CAISO) to ascertain the financial benefits to BEVs located on either side of congestion at different grid nodes, across various months. Similar analysis is performed on some of the largest solar energy plants in California. Mixed-integer linear programs are used to optimize the charging/discharging decisions for the BEV for maximizing revenue from LMP arbitrage and for minimizing the congestion component of LMP. Additionally, we take into account the impact of battery degradation, quantified as a cost per kilowatt-hour ($/kWh), and integrate this factor into our assessment to understand the evolving discharging behavior of BEVs. The article compares the benefits from the BEVs towards congestion minimization for the two different optimization scenarios, discusses seasonality, and addresses the importance of adequately compensating BEV users and incentivizing them to prioritize congestion relief during specific time intervals.

High-Order Moment-Encoded Kinetic Simulation of Turbulent Flows

Kinetic solvers for incompressible fluid simulation were designed to run efficiently on massively parallel architectures such as GPUs. While these lattice Boltzmann solvers have recently proven much faster and more accurate than the macroscopic Navier-Stokes-based solvers traditionally used in graphics, it systematically comes at the price of a very large memory requirement: a mesoscopic discretization of statistical mechanics requires over an order of magnitude more variables per grid node than most fluid solvers in graphics. In order to open up kinetic simulation to gaming and simulation software packages on commodity hardware, we propose a HighOrder Moment-Encoded Lattice-Boltzmann-Method solver which we coined HOME-LBM, requiring only the storage of a few moments per grid node, with little to no loss of accuracy in the typical simulation scenarios encountered in graphics. We show that our lightweight and lightspeed fluid solver requires three times less memory and runs ten times faster than state-of-the-art kinetic solvers, for a nearly-identical visual output.

Maze Solving Mobile Robot Based on Image Processing and Graph Theory

Advances in the development of collision-free path planning algorithms are the main need not only to solve mazes with robotic systems, but also for their use in modern product transportation or green logistics systems and planning merchandise deliveries inside or outside a factory. This challenge increases as the complexity of the task in its structure also increases. This paper deals with the development of a novel methodology for solving mazes with a mobile robot, using image processing techniques and graph theory. The novelty is that the mobile robot can find the shortest path from a start-point to the end-point into irregular mazes with abundant irregular obstacles, a situation that is not far from reality. Maze information is acquired from an image and depending on the size of the mobile robot, a grid of nodes with the same dimensions of the maze is built. Another contribution of this paper is that the size of the maze can be scaled from 1 m × 1 m to 66 m × 66 m, maintaining the essence of the proposed collision-free path planning methodology. Afterwards, graph theory is used to find the shortest path within the grid of reduced nodes due to the elimination of those nodes absorbed by the irregular obstacles. To avoid the mobile robot to travel through those nodes very close to obstacles and borders, resulting in a collision, each image of the obstacle and border is dilated taking into account the size of the mobile robot. The methodology was validated with two case studies with a mobile robot in different mazes. We emphasize that the maze solution is found in a single computational step, from the maze image as input until the generation of the Path vector. Experimental results show the usefulness of the proposed methodology, which can be used in applications such as intelligent traffic control, military, agriculture and so on.

Assessing flexibility by ramping factor in power systems with high renewable energy proportion

Current flexibility assessment methods (FAMs) have limitations, such as difficulty in evaluating entire grids with static FAMs and challenges in grid planning with interval FAMs. While probability FAMs are commonly used for grid planning, they are unable to provide an analytical mathematical model, leading to slow and complex solutions. To address these issues, this paper proposes a ramping factor-based FAM. This method not only guides flexible planning of the entire grid but also offers simplicity and speed in its application. As the flexibility metric, the ramping factor can evaluate the flexibility of a node or a grid. The ramping factor of a local grid is defined by that of the generalized node in the higher-level grid, and the concept of the generalized node is from electrical grid theory. Building upon this, a mathematical model is developed to optimize the allocation of flexible resources, providing guidance for the planning of these resources in the local grid. The proposed method’s feasibility and effectiveness are verified through a case analysis on an improved IEEE 30-Bus System with high renewable energy proportion, demonstrating its advantages over traditional probability assessment methods.© 2017 Elsevier Inc. All rights reserved.

Spatiotemporal variations in seismic activity in and around the focal region of the 2021 [formula omitted]7.3 and 2022 [formula omitted]7.4 Fukushima-Oki earthquakes, Japan

The spatiotemporal evolution of seismic activity is presented for a broad region surrounding the focal areas of the 2021 M7.3 and 2022 M7.4 Fukushima-Oki earthquakes, which occurred within the subducting slab off the Pacific coast of Fukushima Prefecture, northeastern Japan. This study investigates the spatiotemporal variations in seismic activity during the periods before the 2021 M7.3 earthquake, between the 2021 M7.3 and 2022 M7.4 earthquakes, and after the 2022 M7.4 earthquake using the b-value of the Gutenberg–Richter relation, the aftershock decay rate (p-value), and changes in the seismicity rate (Z-value). The study area is also divided into two depth sections to investigate the depth variations in these seismicity parameters relative to the plate interface. The b-values in the deeper section (intraslab) are generally lower than those in the shallower section (around the plate interface) throughout the entire analysis period, including the hypocentral areas of the M7.3 and M7.4 earthquakes. The aftershock decay rates for the M7.3 and M7.4 earthquakes also show depth-dependent characteristics, with a slower decay rate (p < 1.0) at many grid nodes in the deeper section than in the shallower section. Furthermore, seismic quiescence was noted in the hypocentral area of the M7.3 earthquake about two years before the occurrence of this mainshock. The locations of the M7.3 and M7.4 earthquakes around the down-dip edge of the slip area of the 2011 M9.0 Tohoku earthquake suggests that the variations in seismic activity detected in this study mainly reflect stress increases due to the coseismic slip and postseismic deformation of this great earthquake. The present study suggests that the effect of viscoelastic relaxation is a dominant factor in the deeper section. Furthermore, the variations in seismicity may also reflect heterogeneous structures within the slab.

Comment on: “Insights on the tectonic styles of the Red Sea rift using gravity and magnetic data” by Saada et al. (2021)

Global grids of geophysical data or properties of the Earth are increasingly being used, perhaps because they are easy to access and make calculations on. Where original data are proprietary, researchers can sometimes obtain a form of those data within these grids, albeit at commonly lower resolution. Examples include gravity fields (Balmino et al., 2011; Sandwell et al., 2014), thicknesses of sediment overlying basement (Whittaker et al., 2013; Straume et al., 2019), Earth's topography (Smith and Sandwell, 1997; Becker et al., 2009; Ryan et al., 2009; Weatherall et al., 2015), crustal thickness (Laske et al., 2013), seafloor spreading history (Müller et al., 1997) and magnetic fields (Maus et al., 2009). However, depending on the type of study, when working with such data, we need to know the distribution of the original measurements that were used to compile those grids, hence which grid nodes contain interpolated values and which nodes are close to measurement sites. Ideally, we should be aware of the noise characteristics and resolution of such data also. The term “grid resolution” is commonly used in the literature but is misleading, as it refers to the spacing of nodes in the grid, not the resolution of the contributing data. Resolution can also be affected by processing steps used to create the grid. The article of Saada et al. (2021) describes important calculations and useful observations, though some parts of the study illustrate issues that can be encountered in analysing global grids. Given the increasing use of global grids, we provide this comment to help engender discussion.

Dual-grid mapping method for the advection-diffusion-reaction equation in a heterogeneous medium

Processes described by the advection-diffusion-reaction (ADR) equation often arise in heterogeneous media. Of particular interest is the case of layered or otherwise composite media exhibiting many layers or other intricate geometric complexity. Numerical models for processes in these types of media are generally accompanied by a significant computational cost due to the large number of grid nodes required to capture the detail of the heterogeneous domain. An approach addressing this issue involves obtaining approximate solutions on a coarse grid comprised of a small number of nodes and reconstructing a solution on a fine grid comprising a large number of nodes. In this paper, we discuss a projection-based framework for coarse-to-fine-grid approximation methods, which is used to derive a dual-grid mapping method. We initially utilise an interpolation-based mapping, and then consider a new discretisation-based adaptive mapping defined through the solution of coupled problems on subsets of the fine grid. With our new adaptive dual-grid mapping method, we are able to accurately approximate complex solutions on very coarse grids and reconstruct much finer scale approximations on fine grids. Code implementing the developed methods is provided and also applied to several test cases, where accuracy and significantly reduced computational cost are demonstrated in comparison to a numerical solution applied directly on the fine grid.

Lagrange multiplier imposition of non-conforming essential boundary conditions in implicit material point method

The Material Point Method (MPM) is an established and powerful numerical method particularly useful for simulating large-scale, rapid soil deformations. Therefore, it is often used for the numerical investigation of mass movement hazards such as landslides, debris flows, or avalanches. It combines the benefits of both mesh-free and mesh-based continuum-based discretization techniques by discretizing the physical domain with Lagrangian moving particles carrying the history-dependent variables while the governing equations are solved at the Eulerian background grid, which brings many similarities with commonly used finite element methods. However, due to this hybrid nature, the material boundaries do not usually coincide with the nodes of the computational grid, which complicates the imposition of boundary conditions. Furthermore, the position of the boundary may change at each time step and, moreover, may be defined at arbitrary locations within the computational grid that do not necessarily coincide with the body contour, leading to different interactions between the material and the boundary. To cope with these challenges, this paper presents a novel element-wise formulation to weakly impose non-conforming Dirichlet conditions using Lagrange multipliers. The proposed formulation introduces a constant Lagrange multiplier approximation within the constrained elements in combination with a methodology to eliminate superfluous constraints. Therefore, in combination with simple element-wise interpolation functions classically utilized in MPM (and FEM) to approximate the unknown field, a suitable Lagrange multiplier discretization is obtained. In this way, we obtain a robust, efficient, and user-friendly boundary imposition method for immersed methods specified herein for implicit MPM. Furthermore, the extension to frictionless slip conditions is derived. The proposed methodologies are assessed by comparing the numerical results with both analytical and experimental data to demonstrate their accuracy and wide range of applications.

The method of Haar sums for numerical solution of kinematic Poisson equations system that determine an evolution of a spacecraft position

In the present paper the method for the numerical solution of Poisson kinematic equations system that determine the evolution of the spacecraft position is proposed. The system of Poisson kinematic equations is used to determine the transition matrix from the coordinate system associated with the spacecraft at the selected time t1 to the coordinate system associated with the spacecraft at the current time t2. This matrix is used in the process of solving problems of determining a three-axis orientation of the spacecraft from the readings of the magnetometer using information about its angular velocities. The proposed method is based on replacing the derivatives of the desired functions in the Poisson kinematic equations by partial sums of series in the scaled Haar system. The partial sums of these series are generalized polynomials in the scaled Haar system. Hence these sums are step (piecewise constant) functions. The estimates of the proposed method error are derived, which reveal that in the case of the coefficients of the equations which are functions matching the Lipschitz condition, the absolute error in calculating each of the elements of the transition matrix from one coordinate system to another is the value O(N–1) at N ® ¥, where N is the number of partitions of the segment [t1, t2] when constructing a grid of nodes involved in this method. It is proved that the complexity of constructing an algorithm for approximating the system of Poisson kinematic properties insignificantly exceeds the complexity of solving this system by Euler method, which has the first order of accuracy. The results of numerical experiments are presented, showing that in certain cases the Haar sums method gives an error that is much smaller than the Euler method, and is almost identical to the errors of the Euler – Cauchy and Runge – Kutta methods of the 2nd order, the complexity of which is approximately two times greater than the complexity of the Haar sums method.