TOWARDS PREDICTING DYNAMIC STABILITY OF POWER GRIDS WITH GRAPH NEURAL NETWORKS Anonymous authors Paper under double-blind review

Abstract

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. However, 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 dynamic stability of power grids. We provide new datasets of dynamic stability of synthetic power grids and find that GNNs are surprisingly effective at predicting highly non-linear targets from topological information only. We show that large GNNs trained on our rich dataset outperform GNNs from previous work, as well as several baseline models based on handcrafted features. Furthermore, we use GNNs to demonstrate the accurate identification of particularly vulnerable nodes in power grids, so called troublemakers. Lastly, we find that GNNs trained on small grids generate accurate predictions for on a large synthetic model of the Texan power grid, which illustrates the potential real-world applications of the presented approach.

1. INTRODUCTION

Adaption to and mitigation of climate change jointly influence the future of power grids: 1) Mitigation of climate change requires power grids to be carbon-neutral, with the bulk of power supplied by solar and wind generators. These are more decentralized and as opposed to conventional turbine generators they have no intrinsic ability to respond to power imbalances and frequency deviations. Furthermore, the production of renewables is more volatile. Renewable energies will have to start contributing to the dynamical stability of the system (Milano et al., 2018; Christensen et al., 2020) in the future, requiring a new understanding of the complex synchronisation dynamics of power grids. 2) A higher global mean temperature increases the likelihood as well as the intensity of extreme weather events such as hurricanes or heatwaves (Field et al., 2012; Pörtner et al., 2022) which result in great challenges to power grids. Building sustainable grids as well as increasing the resilience of existing power grids towards novel threats are challenging tasks on their own. Tackling climate change in the power grid sector calls for a solution to both at the same time and requires new methods to investigate aspects of dynamic stability. Power grids are complex networks, consisting of nodes that represent different producers and consumers, as well as edges that represent power lines and power transformers. In contrast to many other networks, the interaction of nodes through the edges is governed by physical equations, the power flow. Their emergent properties can be highly unintuitive. For example, the Braess paradox describes the phenomenon that adding lines to a power grid may reduce its stability ((Witthaut & Timme, 2012; Schäfer et al., 2022) ). Such effects can be non-local, i.e. the parts of the grid with decreased stability might be far away from the added line. Similarly, failures of a line in one part of the network can lead to overloads far away. Our work deals with the challenge of predicting the ability of the grid to dynamically recover after localized faults perturbed the system. Classically, the dynamical actors are connected to the highest voltage level, the transmission grid. Transmission grid operators routinely simulate potential faults in the current state of the power grid, to assess its real time dynamic resilience. The possible faults are called contingencies in this context. Even though such simulations do not explicitly model the lower voltage layers of the grid, they are already compute bound. Hence, not all contingencies of interest can be tested for. As distributed re-newable generation is typically connected at lower grid levels, this problem will become more acute as renewables start playing a larger role in the grids dynamics. Conducting high-fidelity simulations of the whole hierarchy of the power grid and exploring all states will not be feasible (Liemann et al., 2021) . For future power grids, knowledge of how to design robust dynamics is required. This has led to a renewed interdisciplinary interest in understanding the collective dynamics of power grids (Brummitt et al., 2013) , with a particular focus on the robustness of the self-organized synchronization mechanism underpinning the stable power flow (Rohden et al., 2012; Motter et al., 2013; Dörfler et al., 2013) by physicists and control mathematicians Witthaut et al. (2022) . Synchronization refers to the fact that a stable power flow requires all generators to establish a joint frequency. It is self-organized in the sense that this is achieved without further communication or an external signal. To understand which structural features impact the self-organized synchronization mechanism, it has proven fruitful to take a probabilistic view (Menck et al., 2014; Hellmann et al., 2016) . Probabilistic approaches are well established in the context of static power flow analysis (Borkowska, 1974) . In the dynamic context, considering the probability of systemic failure following a random fault effectively averages over the various contingencies. Such probabilities are thus well suited to reveal structural features that enhance the system robustness or vulnerability. This approach has been highly successful in identifying particularly vulnerable grid regions (Menck et al., 2014; Schultz et al., 2014a; Nitzbon et al., 2017) and revealing general mechanisms of desynchronization (Hellmann et al., 2020) . Probabilistic stability assessments recently gained more attention in the engineering community as well (Liu & Zhang, 2017; Liu et al., 2019; Liemann et al., 2021) . Given the need for probabilistic analysis, and the computational cost of explicit simulations, we apply Graph Neural Networks (GNNs) to directly predict probabilistic measures from the system structure. Such GNNs could be used to select critical configurations for which a more detailed assessment should be carried out. Moreover, the analysis of the decision process of ML-models might lead to new unknown relations between dynamical properties and the topology of grids. Such insights may ultimately inform the design and development of power grids. Since datasets of probabilistic stability in power grids of sufficient size do not exist yet, we introduce new datasets, that consist of synthetic models of power grids and statistical results of dynamical simulations. We simulated datasets of increasing complexity to get closer to reality step by step. There are 10,000 small grids, 10,000 medium-sized grids and for evaluation purposes one large grid based on a synthetic Texan power grid model. Related work on power grid property prediction Since power grids have an underlying graph structure, the recent development of graph representation learning (Bronstein et al., 2021; Hamilton, 2020) introduces promising methods to use machine learning in the context of power grids. There is a number of applications using GNNs for different power flow-related tasks (Donon et al., 2019; Kim et al., 2019; Bolz et al., 2019; Retiére et al., 2020; Wang et al., 2020; Owerko et al., 2020; Gama et al., 2020; Misyris et al., 2020; Liu et al., 2021; Bush et al., 2021; Liu et al., 2020; Jhun et al., 2022) and to predict transient dynamics in microgrids (Yu et al., 2022) . In (Nauck et al., 2022) small GNNs are used to predict the dynamic stability on small datasets. The authors demonstrate the general feasibility of the approach, but do not compare to conventional baselines. We add such baselines and introduce datasets that have ten times as many grids. This allows us to train GNNs with much higher capacity to achieve higher predictive power. Our main contributions are: We introduce new datasets of probabilistic dynamic stability of synthetic power grids. The new datasets have 10 times the size of previously published ones and include a Texan power grid model to map the path towards real-world applications. We also observe a relevant new class of nodes in the dataset: So-called troublemakers, at which perturbations are strongly amplified. Such nodes may be dangerous to hardware and the overall grid stability. Their identification constitutes an additional task. We train strong baselines and benchmark models to evaluate the difficulty of all tasks. Our results demonstrate i) that the larger dataset allows to train more powerful GNNs, (ii) which outperform the baselines, and (iii) transfer from the new datasets to a real-sized power grid. The general approach is visualized in Figure 1 .

