Grid Nodes Research Articles

Efficient State Synchronization in Distributed Electrical Grid Systems Using Conflict-Free Replicated Data Types

Modern electrical grids are evolving towards distributed architectures, necessitating efficient and reliable state synchronization mechanisms to maintain structural and functional consistency. This paper investigates the application of conflict-free replicated data types (CRDTs) for representing and synchronizing the states of distributed electrical grid systems (DEGSs). We present a general structure for DEGSs based on CRDTs, focusing on the Convergent Replicated Data Type (CvRDT) model with delta state propagation to optimize the communication overhead. The Observed Remove Set (ORSet) and Last-Writer-Wins Register (LWW-Register) are utilized to handle concurrent updates and ensure that only the most recent state changes are retained. An actor-based framework, “Vigilant Hawk”, leveraging the Akka toolkit, was developed to simulate the asynchronous and concurrent nature of DEGSs. Each electrical grid node is modelled as an independent actor with isolated state management, facilitating scalability and fault tolerance. Through a series of experiments involving 100 nodes under varying latency degradation coefficients (LDK), we examined the impact of network conditions on the state synchronization efficiency. The simulation results demonstrate that CRDTs effectively maintain consistency and deterministic behavior in DEGSs, even with increased network latency and node disturbances. An effective LDK range was identified (LDK effective = 2 or 4), where the network remains stable without significant delays in state propagation. The linear relationship between the full state distribution time (FSDT) and LDK indicates that the system can scale horizontally without introducing complex communication overhead. The findings affirm that using CRDTs for state synchronization enhances the resilience and operational efficiency of distributed electrical grids. The deterministic and conflict-free properties of CRDTs eliminate the need for complex concurrency control mechanisms, making them suitable for real-time monitoring and control applications. Future work will focus on addressing identified limitations, such as optimizing message routing based on the network topology and incorporating security measures to protect state information in critical infrastructure systems.

Vulnerability analysis of power grid structure based on complex network theory

IntroductionThe key nodes of an intelligent distribution network significantly impact the reliability and stability of the distribution network’s operation. The failure of these key nodes can severely affect the safe operation of the distribution network. Therefore, vulnerability analysis of key nodes is particularly important.MethodsThis article proposes a comprehensive weighting method for evaluating indicators,combining the analytic hierarchy process (AHP) and entropy weighting method, while considering the structure and operational status of the power system grid. Key node structural evaluation indicators, such as node degree, node shrinkage centrality, and electric mediator, are established considering “significance” and “destructiveness.” State indicators are established based on the degree of impact of current, voltage, and load changes on the grid, as well as the uniformity of their distribution, including the improved current distribution entropy, voltage terre entropy, and three-phase state indicators of lost load. Subsequently, based on the AHP and entropy weighting method, a comprehensive weighting method is proposed to assign subjective and objective weights to the comprehensive evaluation indicators, obtaining the comprehensive weights of the indicators. Finally, the gray correlation degree is introduced to improve the ideal solution of the multi-objective decision making method, obtaining the criticality of the grid nodes and then identifying the critical nodes.Results and DiscussionThe example analysis presented in this article shows that the identified critical nodes of the power grid have a high degree of overlap with the identification results of different methods, can better identify edge nodes, and validate the effectiveness of the proposed evaluation indicators and key node identification methods.

A multi-scale path-planning method for large-scale scenes based on a framed scale-elastic grid map

ABSTRACT Environment modeling serves as the foundation for path planning in unmanned systems. Single-scale maps have many nodes and impose large memory requirements; tree-based multi-scale grid maps used for representing large-scale urban scenes have limited aggregation ability in the presence of dimensional anisotropy. This study proposes a novel multi-scale map-construction method based on a scale-elastic discrete grid structure. The method provides more flexible node aggregation in grid-based representations, reducing the number of grid and border-grid nodes while maintaining the same modeling accuracy. Furthermore, a novel multi-scale A* path-planning algorithm that modifies the neighborhood-expansion phase of A* is proposed to reduce the number of algorithm search nodes in framed multi-scale maps while ensuring optimal path planning. The experimental results demonstrate that the proposed map-construction method requires 71.5% fewer grids and 10.8% fewer border grids than framed-octree grid maps in three-dimensional scenarios with the same modeling accuracy. Consequently, memory requirements are smaller, making this method more efficient on devices with limited performance. The multi-scale A* algorithm also improves path-planning efficiency by reducing the number of search nodes. The proposed method is suitable for path planning in large-scale and complex urban scenes.

Modeling of Metal Cutting Processes Within the Material Point Method Using the Johnson–Cook Material Law

ABSTRACTThe material point method represents an alternative approach to simulations, differing from traditional methods like the finite element method (FEM). This technique involves discretizing bodies using material points while solving equations on a separate computational grid where each time step comprises three steps. Initially, the kinematic quantities of the material points are transferred to the grid nodes. Subsequently, computations are carried out on these nodes, with the results then reassigned to the material points, updating their position, velocity, stress as well as deformation state. After each time step, the previous grid is discarded as it does not rely on persistent information. As a result, a new grid is initialized in each time step, avoiding the risk of mesh distortion in the case of huge deformations, a common drawback arising in FEM analyses. This contribution presents simulations of three‐dimensional metal cutting processes utilizing the Johnson–Cook material law to accommodate for plastic strain rates and heat generated by plastic deformations. Additionally, the grid‐shift technique is employed to reduce oscillations and enhance robustness of the simulations.

A wall model for separated flows: embedded learning to improve a posteriori performance

Developing large-eddy simulation (LES) wall models for separated flows is challenging. We propose to leverage the significance of separated flow data, for which existing theories are not applicable, and the existing knowledge of wall-bounded flows (such as the law of the wall) along with embedded learning to address this issue. The proposed so-called features-embedded-learning (FEL) wall model comprises two submodels: one for predicting the wall shear stress and another for calculating the eddy viscosity at the first off-wall grid nodes. We train the former using the wall-resolved LES (WRLES) data of the periodic hill flow and the law of the wall. For the latter, we propose a modified mixing length model, with the model coefficient trained using the ensemble Kalman method. The proposed FEL model is assessed using the separated flows with different flow configurations, grid resolutions and Reynolds numbers. Overall good a posteriori performance is observed for predicting the statistics of the recirculation bubble, wall stresses and turbulence characteristics. The statistics of the modelled subgrid-scale (SGS) stresses at the first off-wall grids are compared with those calculated using the WRLES data. The comparison shows that the amplitude and distribution of the SGS stresses and energy transfer obtained using the proposed model agree better with the reference data when compared with the conventional SGS model.

Measuring-polynomial processing of input data of a computer system

Purpose of research. The purpose of this study is to solve the problem of restoring the external load on the rack– and-beam structural system and to assess the impact on the accuracy of solving the problem of the error of noisy deflections – constructive input data of the computing system.Methods. The main scientific methods used in this study are methods of modeling and identification of boundary conditions, the grid method of regularization of solving inverse incorrect problems. Measurement reduction and approximation methods, methods for evaluating the quality of input data processing, regularization and approximation algorithms using the Lebesgue grid function, and numerical methods are also used.Results. The main result of this work is two theorems about the external load on a rack-and-beam structural system. The existence and uniqueness of the solution is proved. Also, the results are the formulas of Lagrange multipliers in linear Lagrangian approximation and the optimal plan of coordinates of the nodes of the approximation grid for the equation of deflections of the beam of the fourth and fifth degree with Chebyshev alternance. An assessment of the quality of the approximation of the external load on the rack-and-beam structure by the values of the target parameters was carried out.Conclusion. This article proposes a method for restoring the external load on a rack-and-beam structure using the results of solving the inverse Cauchy problem for the equation of deflections of a beam with minimizing the influence of the error of noisy input data.

APPROXIMATION AND SMOOTHING OF A FUNCTION BASED ON GODUNOV REGULARIZATION

A new approach to function approximation is presented, based on S.K. Godunov’s ideas on the regularization of ill-conditioned systems. The proposed method allows for determining function values at nodes of a finer grid from data on a coarser grid while ensuring control over the smoothness of the resulting function. Convergence and smoothness estimates are substantiated, and results from computational experiments illustrate the effectiveness of the proposed method.

The Wideband Oscillatory Localization Method Based on Combining Compressed Sensing and Graph Attention Networks

Due to the increasing integration of new energy sources, the power system now exhibits low inertia, in which the broadband oscillation problem is increasingly significant in the face of the strong coupling of complex and variable power systems, and the current lack of uniform and effective mathematical models and analysis methods. To solve this major problem, a broadband oscillation localization method based on the combination of compressed perception and graph attention network (GAT) is proposed. The method firstly uses the principle of compression perception to compress and transmit the oscillation time series data of the sub-station, reconstructs the compressed signal at the master station and aggregates the grid topology and node characteristic information to effectively reduce the redundancy of the oscillation data; reconstruction error is only 0.031, takes into account the balance of the samples and the effectiveness of the computation, and adopts the multi-attention mechanism and the cross-entropy loss function to improve the performance of the model training. Finally, the offline training and online evaluation model based on the GAT algorithm is constructed, and the accuracy of the model is up to 98.5%; and the results show that the method has a high positioning accuracy and a certain anti-noise ability at the same time.

A slope-based automatic identification and optimization of key time nodes method for adaptive control vector parameterization

Control vector parameterization is a mainstream numerical approach for solving dynamic programming problems. By discretizing the entire time domain into a grid of time nodes, an infinite-dimensional optimal control problem can be transformed into a finite-dimensional static optimization problem. Despite the attractive advantages of high solution accuracy and ease of implementation of control vector parameterization, the rationality of time grid partitioning significantly influences the efficiency of the solution and the approximating accuracy of the optimal control trajectory. In the traditional control vector parameterization method, the time grid is typically set beforehand and remains static in the optimization process, which has a direct impact on how closely the solution result approximates the optimal control trajectory. To address the conflict of accurate approximations and computational time, we propose a slope-based automatic identification and optimization of key time nodes method for adaptive control vector parameterization, which not only optimizes merging and inserting time nodes but also incorporates automatic identification of key time nodes. Through a simulation example, we verify that this improved method can reduce computation time, enhance approximation accuracy, and achieve higher optimization efficiency.

Distribution grid monitoring based on feature propagation using smart plugs

Smart home power hardware makes it possible to collect a large number of measurements from the distribution grid with low latency. However, the measurements are imprecise, and not every node is instrumented. Therefore, the measured data must be corrected and augmented with pseudo-measurements to obtain an accurate and complete picture of the distribution grid. Hence, we present and evaluate a novel method for distribution grid monitoring. This method uses smart plugs as measuring devices and a feature propagation algorithm to generate pseudo-measurements for each grid node. The feature propagation algorithm exploits the homophily of buses in the distribution grid and diffuses known voltage values throughout the grid. This novel approach to deriving pseudo-measurement values is evaluated using a simulation of SimBench benchmark grids and the IEEE 37 bus system. In comparison to the established GINN algorithm, the presented approach generates more accurate voltage pseudo-measurements with less computational effort. This enables frequent updates of the distribution grid monitoring with low latency whenever a measurement occurs.

Evaluation of Spatial and Temporal Distribution of Carbon Emissions in Power Grid Based on Cloud Theory

In order to clearly determine the carbon emission distribution of regions, lines or nodes in the power grid, this paper applies cloud theory to the evaluation of the distribution of carbon emissions in the power grid. Based on the theory of carbon emission flow in the whole life cycle, five indicators that can reflect the spatial and temporal distribution of carbon emissions are constructed from the two dimensions of space and time. Cloud theory is used to establish the standard cloud of the carbon emission distribution level to quantify the randomness and fuzziness of the data to be evaluated. The bilateral constraint cloud theory and data-driven cloud transformation are combined to construct five comprehensive standard clouds of excellent, good, medium, poor and inferior, which are used as the evaluation interval of the evaluation index of carbon emission distribution. The reverse cloud is used to convert multiple sets of data into cloud droplets. Through the similarity measurement algorithm based on cloud model overlap, the comprehensive evaluation level of carbon emission distribution state in the time dimension is determined. Taking the IEEE 39 system as the research object, the spatial and temporal distribution of carbon emissions is evaluated, and the rationality and effectiveness of the proposed model are verified. Finally, the influence of the new energy penetration rate and power supply structure on the carbon emission distribution of the power grid is discussed by using cloud computing. Based on this, the targeted carbon reduction strategies for different types of nodes and the method of measuring the optimal new energy penetration rate are proposed and can provide a decision-making reference for optimizing the carbon emissions of the power grid.

Comparing Two Geostatistical Simulation Algorithms for Modelling the Spatial Uncertainty of Texture in Forest Soils

Uncertainty assessment is an essential part of modeling and mapping the spatial variability of key soil properties, such as texture. The study aimed to compare sequential Gaussian simulation (SGS) and turning bands simulation (TBS) for assessing the uncertainty in unknown values of the textural fractions accounting for their compositional nature. The study area was a forest catchment (1.39 km2) with soils classified as Typic Xerumbrepts and Ultic Haploxeralf. Samples were collected at 135 locations (0.20 m depth) according to a design developed using a spatial simulated annealing algorithm. Isometric log-ratio (ilr) was used to transform the three textural fractions into a two-dimensional real vector of coordinates ilr.1 and ilr.2, then 100 realizations were simulated using SGS and TBS. The realizations obtained by SGS and TBS showed a strong similarity in reproducing the distribution of ilr.1 and ilr.2 with minimal differences in average conditional variances of all grid nodes. The variograms of ilr.1 and ilr.2 coordinates were better reproduced by the realizations obtained by TBS. Similar results in reproducing the texture data statistics by both algorithms of simulation were obtained. The maps of expected values and standard deviations of the three soil textural fractions obtained by SGS and TBS showed no notable visual differences or visual artifacts. The realizations obtained by SGS and TBS showed a strong similarity in reproducing the distribution of isometric log-ratio coordinates (ilr.1 and ilr.2). Overall, their variograms and data were better reproduced by the realizations obtained by TBS.

Exact Solutions and Upscaling for 1D Two‐Phase Flow in Heterogeneous Porous Media

AbstractUpscaling of 1D two‐phase flows in heterogeneous porous media is important in interpretation of laboratory coreflood data, streamline quasi 3D modeling, and numerical reservoir simulation. In 1D heterogeneous media with properties varying along the flow direction, phase permeabilities are coordinate‐dependent. This yields the Buckley‐Leverett equation with coordinate‐dependent fractional flow f = f(s, x), which reflects the heterogeneity. So, an x‐dependency is considered to reflect microscale heterogeneity and averaging over x—upscaling. This work aims to average or upscale the heterogeneous system to obtain the homogenized media with such fractional flow function F(S) that provides the same water‐cut history at the reservoir outlet, x = 1. Thus, F(S) is an equivalent property of the medium. So far, the exact upscaling for 1D micro heterogeneous systems has not been derived. With the x‐dependency of fractional flow, the Riemann invariant is flux f, which yields exact integration of 1D flow problems. The novel exact solutions are derived for flows with continuous saturation profile, transition of shock into continuous wave, transition of continuous wave into shock, and transport in heterogeneous piecewise‐uniform rocks. The exact procedure of upscaling from f = f(s, x) to F(S) is as follows: the inverse function to the upscaled F(S) is equal to the averaged saturation over x of the inverse microscale function s = f −1(f, x). It was found that the Welge's method as applied to heterogeneous cores provides the upscaled F(S). For characteristic finite‐difference scheme, the fluxes for microscale and upscaled‐numerical‐cell systems, coincide in all grid nodes.

Parking problem by oblivious mobile robots in infinite grids

In this paper, the parking problem of a swarm of mobile robots has been studied. The robots are deployed at the nodes of an infinite grid, which has a subset of prefixed nodes marked as parking nodes. A parking node pi has a capacity of ki, which is given as an input and represents the number of robots it is capable of accommodating. As a solution to the parking problem, in the final configuration, robots need to partition themselves into groups so that each parking node contains a number of robots that are equal to the capacity of the node. It is assumed that the number of robots in the initial configuration equals the sum of the capacities of the parking nodes. The robots are assumed to be autonomous, anonymous, homogeneous, identical and oblivious. They operate under an asynchronous scheduler. They do not have any agreement on the coordinate axes, nor do they agree on a common chirality. All the initial configurations for which the problem is unsolvable have been identified. A deterministic distributed algorithm has been proposed for the remaining configurations, ensuring the solvability of the problem.

Optimal Configuration Model for Large Capacity Synchronous Condenser Considering Transient Voltage Stability in Multiple UHV DC Receiving End Grids

In a multi-fed DC environment, the UHV DC recipient grid faces significant challenges related to DC phase shift failure and voltage instability due to the high AC/DC coupling strength and low system inertia level. While the new large-capacity synchronous condensers (SCs) can provide effective transient reactive power support, the associated investment and operation costs are high. Therefore, it is valuable to investigate the optimization of SC configuration at key nodes in the recipient grid in a scientific and rational manner. This study begins by qualitatively and quantitatively analyzing the dynamic characteristics of DC reactive power and induction motors under AC faults. The sub-transient and transient reactive power output model is established to describe the SC output characteristics, elucidating the coupling relationship between the SC’s reactive power output and the DC reactive power demand at different time scales. Subsequently, a critical stabilized voltage index for dynamic loads is defined, and the SC’s reactive power compensation target is quantitatively calculated across different time scales, revealing the impact of transient changes in DC reactive power on the transient voltage stability of the multi-fed DC environment with dynamic load integration. Finally, an optimal configuration model for the large-capacity SC is proposed under the critical stability constraint of dynamic loads to maximize the SC’s reactive power support capability at the lowest economic cost. The proposed model is validated in a multi-fed DC area, demonstrating that the optimal configuration scheme effectively addresses issues related to DC phase shift failures and voltage instability resulting from AC bus voltage drops.

МЕТОД ТА ДОСЛІДЖЕННЯ ТОЧНОСТІ ОБЧИСЛЮВАННЯ МАТЕМАТИЧНОЇ МОДЕЛІ ЕЛЕКТРОГІДРАВЛІЧНОГО ЕФЕКТУ

The mathematical model of the electrohydraulic effect (EHE) is a nonlinear non-stationary system of partial differential equations (PDE), which reflects the motion and contact interaction of two media, gaseous and liquid, under the action of pulsed thermal excitation. Such PDE systems generally do not have analytical solutions and are solved only by numerical methods, which are approximate in nature, i.e. they provide a solution with some error. The peculiarity of the motion of media in the case of EHE is large deformations in the form of flows and vortices. This feature imposes significant restrictions on the choice of the method for solving the PDE model. The widely known Lagrangian finite element method used to solve contact problems, in the case of EHE modeling leads to a pathological change in the shape of the finite elements, and therefore to instability of the calculation process and an unlimited increase in error. In calculation practice, a variant of the finite element method, FEM-ALE, has become widespread. It uses both Lagrangian and Eulerian grids of nodes and a special advection procedure, i.e., transfer by interpolation of the solution from the Lagrangian grid to the Eulerian one, and then vice versa from the Eulerian one to another new Lagrangian grid. Such an additional interpolation procedure, which is used repeatedly in the calculation, leads to additional (in comparison with the Lagrangian FEM) errors. If the causes and kinetics, as well as the methods of error control in the case of the Lagrangian FEM, have been sufficiently studied in the literature, then the kinetics of error development in the simulation of the EGE using the FEM-ALE method has been practically not studied. The article is devoted to the study of the development of errors in the numerical solution in this particular case. An analytical solution of the problem in the asymptotic case for a technological system with a rigid chamber is obtained. This solution is analyzed in comparison with the numerical solution using the FEM-ALE method. Conclusions are made regarding the errors in calculating pressure as the main factor of mechanical impact of EGE on the technological object and technological equipment, as well as errors in calculating deformations of gaseous and liquid media.The scientific novelty consists in the development of a method for determining the accuracy of EHE parameter calculations using the MSE-ALE method. The practical value lies in determining the accuracy of calculating the parameters of the EHE mathematical model, which makes it possible to justify the use of numerical modeling as a method of researching technological processes and systems using EHE

A staggered Lagrangian magnetohydrodynamics method based on subcell Riemann solver

This paper uses a general formalism to derive staggered Lagrangian method for 2D compressible magnetohydrodynamics (MHD) flows. A subcell method is introduced to discretize the MHD system and some Riemann problems over subcells are solved at the cell center and grid node respectively. In these solvers, only the fast-waves in all jumping relations are considered and thus the solution structure is simple. The discrete conservations of mass, momentum and energy are preserved naturally in the proposed numerical method. In order to meet the thermodynamic Gibbs relation in isentropic flows, an adaptive Riemann solver is implemented at the cell center, in which a criterion is proposed to reduce overheating errors in the rarefying problems and maintains the excellent shock-capturing ability simultaneously. It is worth to be noticed that the divergence-free condition is naturally satisfied in the Lagrangian method. Various numerical tests are presented to demonstrate the accuracy and robustness of the algorithm.

Research on Graph Multi-Attention Neural Network for Power System Transient Stability Assessment

Abstract Diagnosing the stability of power grids based on artificial intelligence technology is a research trend. The existing artificial intelligence stability analysis methods rely on a large number of fault case data, while the graph neural network method ignores the correlation characteristics of nodes themselves and the correlation of long-distance nodes. In order to solve the problems, the graph multi-attention neural network (GMANN) was proposed. The self-attention, which characterizes the correlation between different state quantities of a single node, is proposed, firstly. Then, long-distance association attention, which represents the correlation of distant nodes in the power grid, was proposed. The long-distance correlation attention and the adjacent correlation attention in graph attention network are fused to form a global attention that reflects the global importance of the power grid. The channel attention that characterizes the importance of different pooling methods of graph convolutional network is extracted and used to obtain the importance of different convolution operations. Finally, based on the multi-source attention fusion strategy, global attention and channel attention are embedded in the graph attention neural network to form a multi-level evaluation model to achieve power grid stability evaluation efficiently guided by multiple attentions. The proposed GMANN is verified based on simulated fault cases obtained from the 10-machine 39-node system in New England. The results show that the accuracy of the GMANN can reach 97.34%, which is better than other methods. And the missed judgment rate of important indicators is significantly better than other methods.

Fast Spatiotemporal Sequence Graph Convolutional Network-based transient flow prediction around different airfoils

A novel Spatiotemporal Sequence Graph Convolutional Network (ST-SGCN) data-driven model is proposed to predict transient fluid dynamics around airfoils using complex and unstructured flow field data, with the aim of reducing dimensions and expediting predictions. Graph Neural Networks directly interact with the flow field grid, capturing spatiotemporal physical features of grid nodes and their interconnections, while eliminating the need for complex preprocessing steps. The ST-SGCN model integrates a Graph Convolutional Network and a Graph Attention Network with a Deep Recurrent Neural Network that uses a Gate Recurrent Unit as the kernel, adeptly extracting spatial and temporal physical features of the flow field to accurately predict transient flow states. Preliminary airfoil flow experiments demonstrated the model's ability to continuously predict transient flow fields, achieving an average accuracy of 97% for both velocity and pressure field predictions, with a maximum error of approximately 10% in the testing dataset. Further experiments, varying angles of attack, airfoils, and Reynolds numbers, demonstrated the model's generalizability, extensibility, and adaptability, with prediction errors below 5% and a speedup of over 20 times.

Edge Computing Method for False Data Injection Attack Detection in Electromechanical Transient Simulation Grid

Because edge computing is close to the terminal, it has significant advantages of low latency and high-security realtime control and has huge application prospects in the current popular smart grid. Because its edge side is close to the terminal, it can also effectively avoid the risk of information leakage when control instructions or communication data are transmitted to remote cloud center servers over a long distance. However, edge devices have a greater probability of encountering false data injection attacks (FDIAs) from illegal terminals because of their proximity to terminals. The transient electromechanical situation of the smart grid due to FDIAs is analyzed under edge computing. Due to the characteristics that the status values of grid nodes have temporal correlation before and after and spatial correlation between nodes, the Long Short-Term Memory (LSTM) for training time series data is selected to predict the status values of grid nodes in advance. The FDIA detection method is also proposed based on the LSTM network. By calculating the predicted value at each historical moment and the root means square error (RMSE) of the system state estimation at that moment, the detection threshold of the scheme is calculated through the cumulative distribution function of RMSE. Simulation experiments are conducted on the Institute of Electrical and Electronics Engineers (IEEE)-14 node standard system. The detection rate is as high as 99.71%, which verifies the effectiveness of the proposed FDIA detection scheme. This paper studies the security threat of FDIA to the stable power system operation and provides theoretical analysis and practical reference for other power grid security protection strategies.