Synthetic Power Grids Research Articles

Enhancing power grid resilience to winter storms via generator winterization with equity considerations

We develop two-stage stochastic programming models for generator winterization that enhance power grid resilience while incorporating social equity. The first stage in our models captures the investment decisions for generator winterization, and the second stage captures the operation of a degraded power grid, with the objective of minimizing load shed and social inequity. To incorporate equity into our models, we propose a concept called adverse effect probability that captures the disproportionate effects of power outages on communities with varying vulnerability levels. Grid operations are modeled using DC power flow, and equity is captured through mean or maximum adverse effects experienced by communities. We apply our models to a synthetic Texas power grid, using winter storm scenarios created from the generator outage data from the 2021 Texas winter storm. Our extensive numerical experiments show that more equitable outcomes, in the sense of reducing adverse effects experienced by vulnerable communities during power outages, are achievable with no impact on total load shed through investing in winterization of generators in different locations and capacities.

Generating Synthetic Power Grids Using Exponential Random Graph Models

Synthetic power grids enable real-world energy system simulations and are crucial for algorithm testing, resilience assessment, and policy formulation. We propose a novel method for the generation of synthetic transmission power grids using exponential random graph (ERG) models. Our two main contributions are (1) the formulation of an ERG model tailored specifically for capturing the topological nuances of power grids and (2) a general procedure for estimating the parameters of such a model conditioned on working with connected graphs. From a modeling perspective, we identify edge counts per bus type and k-triangles as crucial topological characteristics for synthetic power-grid generation. From a technical perspective, we develop a rigorous methodology to estimate the parameters of an ERG constrained to the space of connected graphs. The proposed model is flexible, easy to implement, and successfully captures the desired topological properties of power grids. Published by the American Physical Society 2024

Modified Erdős–Rényi Random Graph Model for Generating Synthetic Power Grids

Modified Erdős–Rényi Random Graph Model for Generating Synthetic Power Grids

Transfer Learning for Transient Stability Predictions in Modern Power Systems Under Enduring Topological Changes

The topological configuration of a bulk power grid is often altered by network investment upgrades, forecasted disasters and random faults, as well as planned operator-triggered transmission line maintenance and controlled switching actions. Such topological variations can drastically change the measurement data distribution from phasor measurement units (PMUs), which may in turn compromise the accuracy of the artificial intelligence (AI)-aided monitoring and control applications using the measurements. For instance, data-driven transient stability assessment (TSA) models that were trained with static network topologies may no longer be accurate for monitoring power grid stability as the network topology changes. Not only would the number of possible topology changes be too vast to train all possible scenarios, but also the training process will render computationally intensive. This paper proposes a model-based transfer learning (TL) approach that integrates a convolutional neural network and a long short-term memory network (ConvLSTM), to efficiently train a new stability prediction model that predicts the system operating states (SOSs) and identify critical generators (CGs) in case of instability when the system undergoes enduring topological changes. Numerical analyses on three test cases including the IEEE 39-bus test system, the IEEE 118-bus test system, and the large-scale 2000-bus synthetic power grid in the state of Texas verify the efficiency of the proposed approach and highlight benefits in training time and accuracy, when compared to the state-of-the-art alternatives. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —As the national power grid goes through transitions towards digitalization and modernization with emerging technologies, maintaining its reliability and resiliency against environmental stressors and cyber attacks remains an urgent need. The power system topology is expected to change more frequently, sometimes to accommodate the proliferation of heterogeneous distributed energy resources and tackle their intermittence, sometimes event-driven due to disruptive events (e.g., faults), and sometimes operator-triggered for maintenance activities and responsive control to return the system back to its normal operating condition. This article is motivated by the need for an efficient and computationally-attractive approach for online situational awareness and real-time transient stability monitoring and assessment of the power grid under an enduring topological change, where the main goal is to identify the power system operating states (SOSs) and critical generators (CGs) in case of instability. Instead of training a new model for each topological change, this paper proposes an adaptive power system transient stability assessment (TSA) method that uses transfer learning (TL) which in return reduces the training time yet with less data than a newly-trained model for each topology change scenario.

Toward dynamic stability assessment of power grid topologies using graph neural networks.

To mitigate climate change, the share of renewable energies in power production needs to be increased. Renewables introduce new challenges to power grids regarding the dynamic stability due to decentralization, reduced inertia, and volatility in production. Since dynamic stability simulations are intractable and exceedingly expensive for large grids, graph neural networks (GNNs) are a promising method to reduce the computational effort of analyzing the dynamic stability of power grids. As a testbed for GNN models, we generate new, large datasets of dynamic stability of synthetic power grids and provide them as an open-source resource to the research community. We find that GNNs are surprisingly effective at predicting the highly non-linear targets from topological information only. For the first time, performance that is suitable for practical use cases is achieved. Furthermore, we demonstrate the ability of these models to accurately identify particular vulnerable nodes in power grids, so-called troublemakers. Last, we find that GNNs trained on small grids generate accurate predictions on a large synthetic model of the Texan power grid, which illustrates the potential for real-world applications.

A framework for synthetic power system dynamics.

We present a modular framework for generating synthetic power grids that consider the heterogeneity of real power grid dynamics but remain simple and tractable. This enables the generation of large sets of synthetic grids for a wide range of applications. For the first time, our synthetic model also includes the major drivers of fluctuations on short-time scales and a set of validators that ensure the resulting system dynamics are plausible. The synthetic grids generated are robust and show good synchronization under all evaluated scenarios, as should be expected for realistic power grids. A software package that includes an efficient Julia implementation of the framework is released as a companion to the paper.

From Delaunay triangulation to topological data analysis: generation of more realistic synthetic power grid networks

Abstract Assessing novel methods for increasing power system resilience against cyber-physical hazards requires real power grid data or high-quality synthetic data. However, for security reasons, even basic connection information for real power grid data are not publicly available. We develop a randomised model for generating realistic synthetic power networks based on the Delaunay triangulation and demonstrate that it captures important features of real power networks. To validate our model, we introduce a new metric for network similarity based on topological data analysis. We demonstrate the utility of our approach in application to IEEE test cases and European power networks. We identify the model parameters for two IEEE test cases and two European power grid networks and compare the properties of the generated networks with their corresponding benchmark networks.

Leveraging Power Grid Topology in Machine Learning Assisted Optimal Power Flow

Machine learning assisted optimal power flow (OPF) aims to reduce the computational complexity of these non-linear and non-convex constrained optimization problems by consigning expensive (online) optimization to offline training. The majority of work in this area typically employs fully connected neural networks (FCNN). However, recently convolutional (CNN) and graph (GNN) neural networks have also been investigated, in effort to exploit topological information within the power grid. Although promising results have been obtained, there lacks a systematic comparison between these architectures throughout literature. Accordingly, we introduce a concise framework for generalizing methods for machine learning assisted OPF and assess the performance of a variety of FCNN, CNN and GNN models for two fundamental approaches in this domain: regression (predicting optimal generator set-points) and classification (predicting the active set of constraints). For several synthetic power grids with interconnected utilities, we show that locality properties between feature and target variables are scarce and subsequently demonstrate marginal utility of applying CNN and GNN architectures compared to FCNN for a fixed grid topology. However, with variable topology (for instance, modeling transmission line contingency), GNN models are able to straightforwardly take the change of topological information into account and outperform both FCNN and CNN models.

Power-grid stability predictions using transferable machine learning.

Complex network analyses have provided clues to improve power-grid stability with the help of numerical models. The high computational cost of numerical simulations, however, has inhibited the approach, especially when it deals with the dynamic properties of power grids such as frequency synchronization. In this study, we investigate machine learning techniques to estimate the stability of power-grid synchronization. We test three different machine learning algorithms-random forest, support vector machine, and artificial neural network-training them with two different types of synthetic power grids consisting of homogeneous and heterogeneous input-power distribution, respectively. We find that the three machine learning models better predict the synchronization stability of power-grid nodes when they are trained with the heterogeneous input-power distribution rather than the homogeneous one. With the real-world power grids of Great Britain, Spain, France, and Germany, we also demonstrate that the machine learning algorithms trained on synthetic power grids are transferable to the stability prediction of the real-world power grids, which implies the prospective applicability of machine learning techniques on power-grid studies.

Man‐in‐the‐middle attacks and defence in a power system cyber‐physical testbed

Man-in-The-Middle (MiTM) attacks present numerous threats to a smart grid. In a MiTM attack, an intruder embeds itself within a conversation between two devices to either eavesdrop or impersonate one of the devices, making it appear to be a normal exchange of information. Thus, the intruder can perform false data injection (FDI) and false command injection (FCI) attacks that can compromise power system operations, such as state estimation, economic dispatch, and automatic generation control (AGC). Very few researchers have focused on MiTM methods that are difficult to detect within a smart grid. To address this, we are designing and implementing multi-stage MiTM intrusions in an emulation-based cyber-physical power system testbed against a large-scale synthetic grid model to demonstrate how such attacks can cause physical contingencies such as misguided operation and false measurements. MiTM intrusions create FCI, FDI, and replay attacks in this synthetic power grid. This work enables stakeholders to defend against these stealthy attacks, and we present detection mechanisms that are developed using multiple alerts from intrusion detection systems and network monitoring tools. Our contribution will enable other smart grid security researchers and industry to develop further detection mechanisms for inconspicuous MiTM attacks.

Stochastic properties of the frequency dynamics in real and synthetic power grids

The frequency constitutes a key state variable of electrical power grids. However, as the frequency is subject to several sources of fluctuations, ranging from renewable volatility to demand fluctuations and dispatch, it is strongly dynamic. Yet, the statistical and stochastic properties of the frequency fluctuation dynamics are far from fully understood. Here, we analyse properties of power grid frequency trajectories recorded from different synchronous regions. We highlight the non-Gaussian and still approximately Markovian nature of the frequency statistics. Further, we find that the frequency displays significant fluctuations exactly at the time intervals of regulation and trading, confirming the need of having a regulatory and market design that respects the technical and dynamical constraints in future highly renewable power grids. Finally, employing a recently proposed synthetic model for the frequency dynamics, we combine our statistical and stochastic analysis and analyse in how far dynamically modelled frequency properties match the ones of real trajectories.

Enhanced sensitivity‐based decentralised framework for real‐time transient stability assessment in bulk power grids with renewable energy resources

With the increasing trend in the integration and deployment of distributed energy resources, the real-time assessment of power system transient stability is becoming more and more challenging. This study presents an enhanced sensitivity-based decentralised transient stability assessment scheme, which first virtually decomposes the large-scale power network into several smaller areas. Then, a new sensitivity-based scheme is developed to derive and quantify the kinetic energy-based stability assessment index. This index allows taking into account the effects of both AC generators and power electronic-based generator units. In addition, thanks to the new sensitivity-based scheme, the transient stability can be assessed in a decentralised manner using only the boundary buses in each segmented area, which relaxes the need for massive data availability and transfer across the network and enables its applicability for online applications in large-scale power systems. Simulation results on the 48-machine IEEE 140-bus and 544-machine 2000-bus synthetic power grid test systems demonstrate the efficacy of the proposed method.

AutoSynGrid: A MATLAB-based toolkit for automatic generation of synthetic power grids

In this paper, we introduce a comprehensive MATLAB-based toolkit to automatically generate any number of synthetic power grids featuring the same statistical properties of realistic power grids. The AutoSynGrid toolkit takes into account electric topology, bus type, generation capacities, load settings, generation cost models, and transmission line capacities to generate synthetic cases, providing all necessary data for verity of analysis such as power flow and optimal power flow studies. The toolkit is highly parametrized, providing the flexibility for the user to choose different input options, such as reference system, loading level, generation cost model, and bus type entropy to generate synthetic power grid cases with given network size. In addition, we provide a validation framework for the AutoSynGrid toolkit based on topology metrics, electric parameters, state variables, interdependencies, and scaling properties. It examines the generated synthetic cases by using multiple validation metrics that are observed from realistic power grids to assure that they mitigate the predefined criteria. In addition, to measure the realism of generated synthetic cases the closeness factor is defined. The generated synthetic grids are also examined based on the proposed closeness factor using a number of generated random grids.

A Complex-Network Approach to the Generation of Synthetic Power Transmission Networks

The application of complex-network techniques to the analysis of power grids can provide interesting complementary insights into power studies such as the generation of synthetic power grids. Synthetic power grids are realistic, albeit nonreal, case studies that are topologically consistent with respect to real power networks. As a preliminary step to the generation of synthetic power grids, we use complex-network techniques to analyze several European power networks from a topological point of view. We observe that real topologies are markedly heterogeneous. Then, we present our main contribution: a novel model that generates synthetic spatial power networks that mimics the historical evolution of power systems by taking into account economic and technical factors. The model is articulated in two steps—the first step focused on economic efficiency in which power demand is met and the second one is targeted at increasing network robustness while achieving topological attributes. The resulting synthetic networks are topologically consistent with real power grids. The parametrical nature of the proposed model allows the generation of different instances of consistent power networks, a very interesting feature for grid generation.

Competitive percolation strategies for network recovery

Restoring operation of critical infrastructure systems after catastrophic events is an important issue, inspiring work in multiple fields, including network science, civil engineering, and operations research. We consider the problem of finding the optimal order of repairing elements in power grids and similar infrastructure. Most existing methods either only consider system network structure, potentially ignoring important features, or incorporate component level details leading to complex optimization problems with limited scalability. We aim to narrow the gap between the two approaches. Analyzing realistic recovery strategies, we identify over- and undersupply penalties of commodities as primary contributions to reconstruction cost, and we demonstrate traditional network science methods, which maximize the largest connected component, are cost inefficient. We propose a novel competitive percolation recovery model accounting for node demand and supply, and network structure. Our model well approximates realistic recovery strategies, suppressing growth of the largest connected component through a process analogous to explosive percolation. Using synthetic power grids, we investigate the effect of network characteristics on recovery process efficiency. We learn that high structural redundancy enables reduced total cost and faster recovery, however, requires more information at each recovery step. We also confirm that decentralized supply in networks generally benefits recovery efforts.

A Learning-Based Method for Generating Synthetic Power Grids

Analysis and improvement of power grids resilience and efficiency requires the topologies and geographical coordinates of the real transmission networks. However, due to security reasons, such topologies and particularly the locations of the substations and lines are usually not publicly available. In this work, we thoroughly study the structural properties of the U.S. Western Interconnection grid (WI) and, based on the results, present the network imitating method based on learning (NIMBLE) for generating synthetic spatially embedded networks with similar properties to a given grid. We apply NIMBLE to the WI and show that it can generate networks with similar structural and spatial properties as well the same level of robustness to failures to the WI, without revealing the real locations of the lines and substations. To the best of our knowledge, this is the first attempt to consider the spatial distributions of the buses (nodes) and lines and their importance in generating synthetic grids. Moreover, this is the first time that the power flows and vulnerability against failures are considered in evaluating a synthetic power grid.

Educational Applications of Large Synthetic Power Grids

This paper describes the use of large electric grids in university electric power system courses. Since much actual power system information is not publicly available, the application of public domain synthetic grids developed by the authors is presented including a 2000-bus grid. Discussion of the educational applications utilized in a senior level class are given for power flow analysis and sensitivity, economic dispatch, contingency analysis, optimal power flow (OPF), security-constrained OPF, transient stability, and real-time dynamic operations. In each of these, the application of the large synthetic grids give students insights and experience with cases closer to actual power systems in complexity and size.

Power Flow Convergence and Reactive Power Planning in the Creation of Large Synthetic Grids

To encourage and support innovation, synthetic electric grids are fictional, designed systems that mimic the complexity of actual electric grids but contain no confidential information. Synthetic grid design is driven by the requirement to match wide variety of metrics derived from statistics of actual grids. In order to scale these systems to 10,000 buses or more, robust reactive power planning is needed, accounting for power flow convergence issues. This paper addresses reactive power planning and power flow convergence in the context of large synthetic power grids. The iterative algorithm presented by this paper supplements a synthetic transmission network that has been validated by a dc power flow with a realistic set of voltage control devices to meet a specified voltage profile, even with the constraints of difficult power flow convergence for large systems. The algorithm is illustrated with an example new synthetic 10,000 bus system, geographically situated in the western United States, which is publicly available and useful for a variety of research studies. An analysis is shown validating the synthetic system with actual grid characteristics.

A study of cascading failures in real and synthetic power grid topologies

AbstractUsing the direct current power flow model, we study cascading failures and their spatial and temporal properties in the U.S. Western Interconnection (USWI) power grid. We show that yield (the fraction of demand satisfied after the cascade) has a bimodal distribution typical of a first-order transition. The single line failure leads either to an insignificant power loss or to a cascade which causes a major blackout with yield less than 0.8. The former occurs with high probability if line tolerance α (the ratio of the maximal load a line can carry to its initial load) is greater than 2, while a major blackout occurs with high probability in a broad range of 1 &lt; α &lt; 2. We also show that major blackouts begin with a latent period (with duration proportional to α) during which few lines overload and yield remains high. The existence of the latent period suggests that intervention during early stages of a cascade can significantly reduce the risk of a major blackout. Finally, we introduce the preferential Degree And Distance Attachment model to generate random networks with similar degree, resistance, and flow distributions to the USWI. Moreover, we show that the Degree And Distance Attachment model behaves similarly to the USWI against failures.

Heterogeneity effects in power grid network models.

We have compared the phase synchronization transition of the second-order Kuramoto model on two-dimensional (2D) lattices and on large, synthetic power grid networks, generated from real data. The latter are weighted, hierarchical modular networks. Due to the inertia the synchronization transitions are of first-order type, characterized by fast relaxation and hysteresis by varying the global coupling parameter K. Finite-size scaling analysis shows that there is no real phase transition in the thermodynamic limit, unlike in the mean-field model. The order parameter and its fluctuations depend on the network size without any real singular behavior. In case of power grids the phase synchronization breaks down at lower global couplings, than in case of 2D lattices of the same sizes, but the hysteresis is much narrower or negligible due to the low connectivity of the graphs. The temporal behavior of desynchronization avalanches after a sudden quench to low K values has been followed and duration distributions with power-law tails have been detected. This suggests rare region effects, caused by frozen disorder, resulting in heavy-tailed distributions, even without a self-organization mechanism as a consequence of a catastrophic drop event in the couplings.