Grid Test Cases Research Articles

Sub-grid scale turbulent micro-mixing with infinitely fast chemistry in the context of fire modelling

Combustion modelling with the Eddy Dissipation Model (EDM) requires closure of the mixing time between fuel and oxidizer occurring on a sgs level. Six different models for estimating the micro-mixing times, in the context of fire modelling, are investigated: (1) equal to a constant fraction of the integral time scale (i.e., default EDM approach); (2) allow for this fraction to vary in space and time as a function of the standard deviation of the mixture fraction; (3) use of the geometric mean of the integral time scale and the Kolmogorov time scale; (4) use of the geometric mean of the sub-grid velocity stretching time and the Kolmogorov time scale; (5) calculation of the mixing time scale based on the local variation of the scalar dissipation rate and the mixture fraction variance; (6) use of the minimum of the mixing times for diffusion, sub-grid scale advection and buoyant acceleration. Overall, the performance of all models on fine grids is comparable. However, models 2 and 6 perform better for all the grid sizes and test cases considered. Model 1 predicts the highest temperatures, the performance of models 3 and 4 is similar while the predictions with model 5 are highly grid-dependent.

Reduced Nodal Admittance Matrix Method for Probabilistic GIC Analysis in Power Grids

Efficient probabilistic geomagnetically induced current (GIC) analysis in power grids provides tools for assessing and mitigating small-probability tail risks of geomagnetic disturbances, especially in early warning and real-time scenarios. This letter employs the reduced nodal admittance matrix (RNAM) to speed up GIC calculation based on Kron reduction. Moreover, the proposed RNAM method is used to achieve a more efficient analysis of probabilistic GICs, which considers the uncertainty of the substation grounding resistances. The novel method is compared with the classical algorithms including the nodal admittance matrix method, the Lehtinen-Pirjola method, and the bus admittance matrix method, and its efficiency improvement is illustrated with several power grid test cases.

Fast Newton-Raphson Power Flow Analysis Based on Sparse Techniques and Parallel Processing

Power flow (PF) calculation provides the basis for the steady-state power system analysis and is the backbone of many power system applications ranging from operations to planning. The calculated voltage and power values by PF are essential to determining the system condition and ensuring the security and stability of the grid. The emergence of multicore processors provides an opportunity to accelerate the speed of PF computation and, consequently, improve the performance of applications that run PF within their processes. This paper introduces a fast Newton-Raphson power flow implementation on multicore CPUs by combining sparse matrix techniques, mathematical methods, and parallel processing. Experimental results validate the effectiveness of our approach by finding the power flow solution of a synthetic U.S. grid test case with 82,000 buses in just 1.8 seconds.

A symmetrized and simplified Bernoulli trial collision scheme in direct simulation Monte Carlo

Here, a symmetrized and simplified Bernoulli trials (SSBT) scheme based on the probabilistic approach is introduced to provide less-restricted conditions in choosing selected pairs. Unlike the simplified Bernoulli trials (SBT) method, the SSBT scheme picks the second particle of a selected pair from a whole list of particles with equal probability; it prevents repetitive collisions by introducing a procedure to avoid duplicate colliding pairs. The efficiency of this newly introduced algorithm is investigated in benchmark problems such as a collision frequency test case, Fourier heat transfer, dissociation of simple gas, and hypersonic cylinder flow. Compared with SBT, no time counter (NTC), and nearest neighbor (NN) collision algorithms, the results show that the SSBT method predicts the solutions quite accurately. In the collision frequency test case and Fourier test case, we show that the SSBT scheme could work with few particles per cell (one or even less) if an appropriate space and time discretization is employed. The symmetrized algorithm of the SSBT scheme improves the quality of the selection process, which leads to a smaller sample size in the highly non-equilibrium problem of hypersonic cylinder flow to achieve the same convergence limit at that of the SBT and NN schemes. In addition, the SSBT scheme has inherently a lower separation of free paths in the stagnation point of the cylinder test case compared to the SBT scheme for the same grid test case. These features make SSBT a new, robust model that could be presented as an alternative to state-of-the-art models.

Power Grid Reliability Estimation via Adaptive Importance Sampling

Electricity production currently generates approximately 25% of greenhouse gas emissions in the USA. Thus, increasing the amount of renewable energy is a key step to carbon neutrality. However, integrating a large amount of fluctuating renewable generation is a significant challenge for power grid operating and planning. Grid reliability, i.e., an ability to meet operational constraints under power fluctuations, is probably the most important of them. In this letter, we propose computationally efficient and accurate methods to estimate the probability of line overflow, i.e., reliability constraints violation, under a known distribution of renewable energy generation. To this end, we investigate an importance sampling approach, a flexible extension of Monte-Carlo methods, which adaptively changes the sampling distribution to generate more samples near the reliability boundary. The approach allows to estimate overload probability in real-time based only on a few dozens of random samples, compared to thousands required by the plain Monte-Carlo. Our study focuses on high voltage direct current power transmission grids with linear reliability constraints on power injections and line currents. We propose a novel theoretically justified physics-informed adaptive importance sampling algorithm and compare its performance to state-of-the-art methods on multiple IEEE power grid test cases.

Identification of interdependencies and prediction of fault propagation for cyber–physical systems

Interdependence is an intrinsic feature of cyber–physical systems. Cyber and physical components are tightly integrated with each other, and hence, a trivial impairment in a part of the system may affect several components, leading to a sequence of failures that collapses the entire system. In this paper, we seek to identify the interdependencies among the components of a cyber–physical system using correlation metrics as well as a heuristic causation analysis method. We also demonstrate applicability of neural networks for prediction of imminent failures given the current system state. The proposed prediction tool can help system operators to perform timely preventive actions and mitigate the consequences of accidental failures and malicious attacks. As a case study, we have analyzed two smart grid test cases based on IEEE power bus systems, namely, IEEE-14 and IEEE-57.

Protecting the Grid Against MAD Attacks

Power grids have recently been shown to be vulnerable to MAnipulation of Demand (MAD) attacks using high-wattage IoT devices. In this paper, we introduce two forms of defenses against line failures caused by these attacks: 1) we develop two algorithms named SAFE and IMMUNE for finding efficient operating points for generators during the normal operation of the grid such that no lines are overloaded instantly after any potential MAD attacks, and 2) assuming lines can temporarily tolerate overloads, we develop efficient methods to verify in advance if such overloads can quickly be cleared by changing the operating points of the generators after any attacks. We then define the novel notion of $\alpha D$ -robustness for a grid indicating that line overloads can either be prevented or cleared after any attacks based on the two forms of introduced defenses if an adversary can increase/decrease the demands by at most $\alpha$ fraction. We demonstrate that practical upper and lower bounds on the maximum $\alpha$ for which a grid is $\alpha D$ -robust can be found efficiently in polynomial time. Finally, we evaluate the performance of the developed algorithms and methods on realistic power grid test cases.

Deep Reinforcement Learning for Cybersecurity Assessment of Wind Integrated Power Systems

The integration of renewable energy sources (RES) is rapidly increasing in electric power systems (EPS). While the inclusion of intermittent RES coupled with the wide-scale deployment of communication and sensing devices is important towards a fully smart grid, it has also expanded the cyber-threat landscape, effectively making power systems vulnerable to cyberattacks. This article proposes a cybersecurity assessment approach designed to assess the cyberphysical security of EPS. The work takes into consideration the intermittent generation of RES, vulnerabilities introduced by microprocessor-based electronic information and operational technology (IT/OT) devices, and contingency analysis results. The proposed approach utilizes deep reinforcement learning (DRL) and an adapted Common Vulnerability Scoring System (CVSS) score tailored to assess vulnerabilities in EPS in order to identify the optimal attack transition policy based on $N-2$ contingency results, i.e., the simultaneous failure of two system elements. The effectiveness of the work is validated via numerical and real-time simulation experiments performed on literature-based power grid test cases. The results demonstrate how the proposed method based on deep $Q$ -network ($\text{D}Q\text{N}$ ) performs closely to a graph-search approach in terms of the number of transitions needed to find the optimal attack policy, without the need for full observation of the system. In addition, the experiments present the method's scalability by showcasing the number of transitions needed to find the optimal attack transition policy in a large system such as the Polish 2383 bus test system. The results exhibit how the proposed approach requires one order of magnitude fewer transitions when compared to a random transition policy.

Topology Estimation Using Graphical Models in Multi-Phase Power Distribution Grids

Power distribution grids are structurally operated radially, such that energized lines form a collection of trees with a substation at the root of each tree. The operational topology may change from time to time; however, tracking these changes, even though important for the distribution grid operation and control, is hindered by limited real-time monitoring. This paper develops a learning framework to reconstruct the radial operational structure of the distribution grid from synchronized voltage measurements. To detect operational lines, our learning algorithm uses conditional independence tests for continuous random variables that is applicable to a wide class of probability distributions, and in particular Gaussian, for injections. We validate the algorithm through extensive experiments on ac three-phase IEEE distribution grid test cases.

A Modified IEEE 118-Bus Test Case for Geomagnetic Disturbance Studies–Part I: Model Data

Power grid test cases for geomagnetic disturbance (GMD) studies need particular data that are not provided by the typical IEEE transmission benchmarks. This two-part paper proposes a test case that contains required modeling details for time-domain simulation of a GMD within an electromagnetic transient program (EMT-type). Compared to existing load-flow-based GMD test cases, the proposed test case offers advantages, such as accurate representation of nonlinear transformer magnetization and interaction between the dc geomagnetically-induced currents and transformer saturation, additional var consumption, harmonics, and voltage regulation problems. Part I presents the test case system and parameter data, and Part II provides simulation results to enable software-to-software validation (future work) as a first step toward the establishment of the model as an official GMD benchmark.

Security and Cloud Outsourcing Framework for Economic Dispatch

The computational complexity and problem sizes of power grid applications have increased significantly with the advent of renewable resources and smart grid technologies. The current paradigm of solving these issues consist of in-house high performance computing infrastructures, which have drawbacks of high capital expenditures, maintenance, and limited scalability. Cloud computing is an ideal alternative due to its powerful computational capacity, rapid scalability, and high cost-effectiveness. A major challenge, however, remains in that the highly confidential grid data is susceptible for potential cyberattacks when outsourced to the cloud. In this paper, a security and cloud outsourcing framework is developed for the economic dispatch (ED) linear programming application. The security framework transforms the ED linear program into a confidentiality-preserving linear program, that masks both the data and problem structure, thus enabling secure outsourcing to the cloud. Results show that for large grid test cases the performance gain and costs outperforms the in-house infrastructure.

Direct numerical simulation of particulate flows with an overset grid method

We evaluate an efficient overset grid method for two-dimensional and three-dimensional particulate flows for small numbers of particles at finite Reynolds number. The rigid particles are discretised using moving overset grids overlaid on a Cartesian background grid. This allows for strongly-enforced boundary conditions and local grid refinement at particle surfaces, thereby accurately capturing the viscous boundary layer at modest computational cost. The incompressible Navier–Stokes equations are solved with a fractional-step scheme which is second-order-accurate in space and time, while the fluid–solid coupling is achieved with a partitioned approach including multiple sub-iterations to increase stability for light, rigid bodies. Through a series of benchmark studies we demonstrate the accuracy and efficiency of this approach compared to other boundary conformal and static grid methods in the literature. In particular, we find that fully resolving boundary layers at particle surfaces is crucial to obtain accurate solutions to many common test cases. With our approach we are able to compute accurate solutions using as little as one third the number of grid points as uniform grid computations in the literature. A detailed convergence study shows a 13-fold decrease in CPU time over a uniform grid test case whilst maintaining comparable solution accuracy.

An Anti Mode Mixing EMD Algorithm for Detecting the Characteristics of Low Frequency Oscillations in Power System

The dynamics of modern interconnected power system is characterized by low frequency oscillations (LFOs) which are produced as results of various disturbances such as changes in loads, tripping of lines, faults, and other discrete events. A data-driven empirical mode decomposition (EMD) method is applied to the detection of low frequency oscillation modes from disturbed trajectory with its strong non-stationary signal processing capability, but the mode mixing phenomenon serious impact on the analysis credibility and accuracy of EMD method. In this paper, an anti mode mixing EMD composite algorithm is proposed for detecting the characteristics of LFOs in power system. First, the improved frequency heterodyne method is proposed to increase the spectral distance between adjacent mode components in order to meet the octave resolution requirements. Second, the wavelet singularity detection technology is proposed to determine the adaptive sliding analysis window for each mode, in which there implements the intermittency mixed modes separation and their nonstationary parameters identification. Finally, the analysis result of interconnected grid test case verify that the proposed algorithm can effectively overcome the impact of the mode mixing existed in EMD and improve the characteristics detection accuracy of LFOs characteristics. DOI: http://dx.doi.org/10.11591/telkomnika.v11i8.3134

Generating Statistically Correct Random Topologies for Testing Smart Grid Communication and Control Networks

In order to design an efficient communication scheme and examine the efficiency of any networked control architecture in smart grid applications, we need to characterize statistically its information source, namely the power grid itself. Investigating the statistical properties of power grids has the immediate benefit of providing a natural simulation platform, producing a large number of power grid test cases with realistic topologies, with scalable network size, and with realistic electrical parameter settings. The second benefit is that one can start analyzing the performance of decentralized control algorithms over information networks whose topology matches that of the underlying power network and use network scientific approaches to determine analytically if these architectures would scale well. With these motivations, in this paper we study both the topological and electrical characteristics of power grid networks based on a number of synthetic and real-world power systems. The most interesting discoveries include: the power grid is sparsely connected with obvious <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">small-world</i> properties; its nodal degree distribution can be well fitted by a mixture distribution coming from the sum of a truncated geometric random variable and an irregular discrete random variable; the power grid has very distinctive graph spectral density and its algebraic connectivity scales as a power function of the network size; the line impedance has a heavy-tailed distribution, which can be captured quite accurately by a clipped double Pareto lognormal distribution. Based on the discoveries mentioned above, we propose an algorithm that generates random topology power grids featuring the same topology and electrical characteristics found from the real data.

Dynamic Testing of Wholesale Power Market Designs: An Open-Source Agent-Based Framework

In April 2003 the U.S. Federal Energy Regulatory Commission proposed a complicated market design--the Wholesale Power Market Platform (WPMP)--for common adoption by all US wholesale power markets. Versions of the WPMP have been implemented in New England, New York, the mid-Atlantic states, the Midwest, the Southwest, and California. Strong opposition to the WPMP persists among some industry stakeholders, however, due largely to a perceived lack of adequate performance testing. This study reports on the model development and open-source implementation (in Java) of a computational wholesale power market organized in accordance with core WPMP features and operating over a realistically rendered transmission grid. The traders within this market model are strategic profit-seeking agents whose learning behaviors are based on data from human-subject experiments. Our key experimental focus is the complex interplay among structural conditions, market protocols, and learning behaviors in relation to short-term and longer-term market performance. Findings for a dynamic 5-node transmission grid test case are presented for concrete illustration.

Topology and cascading line outages in power grids

Motivated by the small world network research of Watts & Strogatz, this paper studies relationships between topology and cascading line outages in electric power grids. Cascading line outages are a type of cascading collapse that can occur in power grids when the transmission network is congested. It is characterized by a self-sustaining sequence of line outages followed by grid breakup, which generally leads to widespread blackout. The main findings of this work are twofold: On one hand, the work suggests that topologies with more disorder in their interconnection topology tend to be robust with respect to cascading line outages in the sense of being able to support greater generation and demand levels than more regularly interconnected topologies. On the other hand, the work suggests that topologies with more disorder tend to be more fragile in that should a cascade get started, they tend to break apart after fewer outages than more regularly interconnected topologies. Thus, as has been observed in other complex networks, there appears to be a tradeoff between robustness and fragility. These results were established using synthetically generated power grid topologies and verified using the IEEE 57 bus and 188 bus power grid test cases.