Graph Neural Solver for Power Systems

International audienceWe propose a neural network architecture that emulates the behavior of a physics solver that solves electricity differential equations to compute electricity flow in power grids (so-called "load flow"). Load flow computation is a well studied and understood problem, but current methods (based on Newton-Raphson) are slow. With increasing usage expectations of the current infrastructure, it is important to find methods to accelerate computations. One avenue we are pursuing in this paper is to use proxies based on "graph neural networks". In contrast with previous neural network approaches, which could only handle fixed grid topologies, our novel graph-based method, trained on data from power grids of a given size, generalizes to larger or smaller ones. We experimentally demonstrate viability of the method on randomly connected artificial grids of size 30 nodes. We achieve better accuracy than the DC-approximation (a standard benchmark linearizing physical equations) on random power grids whose size range from 10 nodes to 110 nodes, the scale of real-world power grids. Our neural network learns to solve the load flow problem without overfitting to a specific instance of the problem

Predicting flux in Discrete Fracture Networks via Graph Informed Neural Networks

Discrete Fracture Network (DFN) flow simulations are commonly used to determine the outflow in fractured media for critical applications. Here, we extend the formulation of spatial graph neural networks with a new architecture, called Graph-Informed Neural Network (GINN), to speed up the Uncertainty Quantification analyses for DFNs. We show that the GINN model allows better Monte Carlo estimates of the mean and standard deviation of the outflow of a test case DFN

GNN-based physics solver for time-independent PDEs

Physics-based deep learning frameworks have shown to be effective in accurately modeling the dynamics of complex physical systems with generalization capability across problem inputs. However, time-independent problems pose the challenge of requiring long-range exchange of information across the computational domain for obtaining accurate predictions. In the context of graph neural networks (GNNs), this calls for deeper networks, which, in turn, may compromise or slow down the training process. In this work, we present two GNN architectures to overcome this challenge - the Edge Augmented GNN and the Multi-GNN. We show that both these networks perform significantly better (by a factor of 1.5 to 2) than baseline methods when applied to time-independent solid mechanics problems. Furthermore, the proposed architectures generalize well to unseen domains, boundary conditions, and materials. Here, the treatment of variable domains is facilitated by a novel coordinate transformation that enables rotation and translation invariance. By broadening the range of problems that neural operators based on graph neural networks can tackle, this paper provides the groundwork for their application to complex scientific and industrial settings.Comment: 12 pages, 2 figure

Learning Active Constraints to Efficiently Solve Linear Bilevel Problems

Bilevel programming can be used to formulate many engineering and economics problems. However, common reformulations of bilevel problems to mixed-integer linear programs (through the use of Karush-Kuhn-Tucker conditions) make solving such problems hard, which impedes their implementation in real-life. In this paper, we significantly improve solution speed and tractability by introducing decision trees to learn the active constraints of the lower-level problem, while avoiding to introduce binaries and big-M constants. The application of machine learning reduces the online solving time, and becomes particularly beneficial when the same problem has to be solved multiple times. We apply our approach to power systems problems, and especially to the strategic bidding of generators in electricity markets, where generators solve the same problem many times for varying load demand or renewable production. Three methods are developed and applied to the problem of a strategic generator, with a DCOPF in the lower-level. We show that for networks of varying sizes, the computational burden is significantly reduced, while we also manage to find solutions for strategic bidding problems that were previously intractable.Comment: 11 pages, 5 figure

Integration of Data Driven Technologies in Smart Grids for Resilient and Sustainable Smart Cities: A Comprehensive Review

A modern-day society demands resilient, reliable, and smart urban infrastructure for effective and in telligent operations and deployment. However, unexpected, high-impact, and low-probability events such as earthquakes, tsunamis, tornadoes, and hurricanes make the design of such robust infrastructure more complex. As a result of such events, a power system infrastructure can be severely affected, leading to unprecedented events, such as blackouts. Nevertheless, the integration of smart grids into the existing framework of smart cities adds to their resilience. Therefore, designing a resilient and reliable power system network is an inevitable requirement of modern smart city infras tructure. With the deployment of the Internet of Things (IoT), smart cities infrastructures have taken a transformational turn towards introducing technologies that do not only provide ease and comfort to the citizens but are also feasible in terms of sustainability and dependability. This paper presents a holistic view of a resilient and sustainable smart city architecture that utilizes IoT, big data analytics, unmanned aerial vehicles, and smart grids through intelligent integration of renew able energy resources. In addition, the impact of disasters on the power system infrastructure is investigated and different types of optimization techniques that can be used to sustain the power flow in the network during disturbances are compared and analyzed. Furthermore, a comparative review analysis of different data-driven machine learning techniques for sustainable smart cities is performed along with the discussion on open research issues and challenges

Graph-Informed Neural Networks for Regressions on Graph-Structured Data

In this work, we extend the formulation of the spatial-based graph convolutional networks with a new architecture, called the graph-informed neural network (GINN). This new architecture is specifically designed for regression tasks on graph-structured data that are not suitable for the well-known graph neural networks, such as the regression of functions with the domain and codomain defined on two sets of values for the vertices of a graph. In particular, we formulate a new graph-informed (GI) layer that exploits the adjacent matrix of a given graph to define the unit connections in the neural network architecture, describing a new convolution operation for inputs associated with the vertices of the graph. We study the new GINN models with respect to two maximum-flow test problems of stochastic flow networks. GINNs show very good regression abilities and interesting potentialities. Moreover, we conclude by describing a real-world application of the GINNs to a flux regression problem in underground networks of fractures

Power Flow Optimization with Graph Neural Networks

Power flow analysis is an important tool in power engineering for planning and operating power systems. The standard power flow problem consists of a set of non-linear equations, which are traditionally solved using numerical optimization techniques, such as the Newton-Raphson method. However, these methods can become computationally expensive for larger systems, and convergence to the global optimum is usually not guaranteed. In recent years, several methods using Graph Neural Networks (GNNs) have been proposed to speed up the computation of the power flow solutions, without making large sacrifices in terms of accuracy. This class of models can learn localized features that are independent from a global graph structure. Therefore, by representing power systems as graphs these methods can, in principle, generalize to systems of different size and topology. However, most of the current approaches have only been applied to systems with a fixed topology and none of them were trained simultaneously on systems of different topology. Hence, these models are not fully shown to generalize to widely different systems or even to small perturbations of a given system. In this thesis, several supervised GNN models are proposed to solve the power flow problem, using established GNN blocks from the literature. These GNNs are trained on a set of different tasks, where the goal is to study the generalizability to both perturbations and completely different systems, as well as comparing performance to standard Multi-Layered Perceptron (MLP) models. The experimental results show that the GNNs are comparatively successful at generalizing to widely different topologies seen during training, but do not manage to generalize to unseen topologies and are not able to outperform an MLP on slight perturbations of the same energy system. The study presented in this thesis allowed to draw important insights about the applicability of GNN as power flow solvers. In the conclusion, several possible ways for improving the GNN-based solvers are discussed

DC-Approximated Power System Reliability Predictions with Graph Convolutional Neural Networks

The current standard operational strategy within electrical power systems is done following deterministic reliability practices. These practices are deemed to be secure under most operating situations when considering power system security, but as the deterministic practices do not consider the probability and consequences of operation, the operating situation may often become either too strict or not strict enough. This can in periods lead to inefficient operation when regarding the socio-economic aspects. With the continuous integration of renewable energy sources to the electrical power system coupled with the increasing demand for electricity, the power systems have been pushed to operating closer to their stability limit. This poses a challenge for the operation and planning of the power system. Research is therefore being invested into finding more flexible operational strategies which operates according to probabilistic reliability criteria, taking the probability of future events into consideration while also aiming to minimize the expected cost and defining limits for probabilistic reliability indicators. To reliably plan and operate the systems according to a probabilistic reliability criterion, numerical problems such as the Optimal Power Flow (OPF) and the Power Flow (PF) equations are used. These tools are helpful as they are used to determine the optimal way of producing and transporting power. These tools are also used in contingency analyses, where the effect of occurring contingencies is analyzed and evaluated. Due to the non-linearity of the PF equations, the solution is often found through iterative numerical methods such as the Gauss-Seidel method or the Newton-Raphson method. These numerical methods are often computationally expensive, and convergence to the global minimum is not guaranteed either. In recent years, various Machine Learning (ML) models have gathered a lot of attention due to their success in different numerical tasks, particularly Graph Convolutional Networks (GCNs) due to the model’s ability to utilize the topology and learn localized features. As the field of GCN is new, extensive research is being committed to identify the GCNs ability to work on applications such as the electrical power system. This thesis seeks to conduct preliminary experiments where Graph Convolutional Networks (GCN) models are used as a substitution for the numerical DC-OPFs which are used to determine values such as the system load shedding due to contingencies. The GCN models are trained and tested on multiple datasets on both a system- and a node-level, where the goal is to test the models' ability to generalize across perturbations of different system-parameters, such as the system load, the number of induced contingencies and different system topologies. The experiments of the thesis show that the GCNs can predict the load-shedding values across multiple system-parameter perturbations such as the number of induced contingencies, increasing load-variation and a modified system-topology with a high accuracy, without having to be retrained for those specific situations. Though, the further the system-parameters were perturbated, the less accurate the model's predictions became. This reduction in accuracy per system-parameter perturbation was caused by a change in the load-shedding pattern as additional parameters were perturbated, which the models were unable to comprehend. Lastly, this thesis also shows that the GCN models are substantially faster than the numerical methods which they seek to replace

Application of Deep Learning Methods in Monitoring and Optimization of Electric Power Systems

This PhD thesis thoroughly examines the utilization of deep learning techniques as a means to advance the algorithms employed in the monitoring and optimization of electric power systems. The first major contribution of this thesis involves the application of graph neural networks to enhance power system state estimation. The second key aspect of this thesis focuses on utilizing reinforcement learning for dynamic distribution network reconfiguration. The effectiveness of the proposed methods is affirmed through extensive experimentation and simulations.Comment: PhD thesi