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Implementing accurate Distribution System State Estimation (DSSE) faces several challenges, among which the lack of observability and the high density of the distribution system. While data-driven alternatives based on Machine Learning models could be a choice, they suffer in DSSE because of the lack of labeled data. In fact, measurements in the distribution system are often noisy, corrupted, and unavailable. To address these issues, we propose the Deep Statistical Solver for Distribution System State Estimation (DSS$^{2}$), a deep learning model based on graph neural networks (GNNs) that accounts for the network structure of the distribution system and the governing power flow equations of the problem. DSS$^{2}$ is based on GNN and leverages hypergraphs to model the network as a graph into the deep-learning algorithm and to represent the heterogeneous components of the distribution systems. A weakly supervised learning approach is put forth to train the DSS$^{2}$: by enforcing the GNN output into the power flow equations, we force the DSS$^{2}$ to respect the physics of the distribution system. This strategy enables learning from noisy measurements and alleviates the need for ideal labeled data. Extensive experiments with case studies on the IEEE 14-bus, 70-bus, and 179-bus networks showed the DSS$^{2}$ outperforms the conventional Weighted Least Squares algorithm in accuracy, convergence, and computational time while being more robust to noisy, erroneous, and missing measurements. The DSS$^{2}$ achieves a competing, yet lower, performance compared with the supervised models that rely on the unrealistic assumption of having all the true labels.

This paper proposes a method to compute corrective control actions for dynamic security in real-time and quantifies the economic value of corrective control. Lowered inertia requires fast control methods in real-time to correct system operation and maintain system security when equipment fails. However, using corrective control beyond such emergency failure measures does not make fully use of them. The key contribution of this work is the optimal use of corrective control applications in combination with preventive strategies to enhance the network utilisation, reduce the normal operating costs while maintaining adequate security levels. The proposed approach learns a neural network for safety certificates and models the predicted safe dynamic post-fault state as algebraic constraints in an AC optimal power flow (OPF) deciding close to real-time on the optimal corrective control. Considering these safety constraints within the ACOPF can balance simultaneously the system transient stability with the costs for preventive and corrective control. This proposed approach outperforms sub-optimal approaches aiming at sequentially finding the balance. Case studies were based on the IEEE 9-bus system with integrated electrical vehicles and shares of wind power up-to 40% and on the IEEE 39-bus and 118-bus systems. The proposed approach outperforms baseline control approaches in stability, economics, and carbon emissions. One baseline approach was preventive wind curtailment, against which the proposed approach reduced operating costs by up-to 60%, decreased unstable operations by 50% and reduced carbon emissions by 60% in the IEEE 9-bus. In the IEEE 39-bus and 118-bus systems, the approach was promising for larger systems.

Digitalization is one of the key drivers for energy system transformation. The advances in communication technologies and measurement devices render available a large amount of operational data and enable the centralization of such data storage and processing. The greater access to data opens up new opportunities for a more efficient and decentralized management of the energy system. At the distribution level of the energy system, local electricity markets (LEMs) provide new degrees of flexibility by trading and balancing the energy locally and offering ancillary services to the wider transmission and distribution system operators. Maximizing the grid impact from this flexibility calls for novel data analytics and artificial intelligence techniques to enhance the system’s security and reduce the energy costs of local prosumers. At the same time, however, relying on data-based approaches increases the risk of cyberattacks, and robust countermeasures are, therefore, needed as an integral aspect of digitalization efforts. This article discusses the key role of centralized data analytics to fully benefit from the advantages of LEMs in terms of system’s security enhancement and energy costs’ reduction. Data-driven paradigms are investigated that allow for flexibility from decentralized markets, mitigate the physical security risks, and devise defensive strategies shielding the system from cyber threats.

Power systems transport an increasing amount of electricity, and in the future, involve more distributed renewables and dynamic interactions of the equipment. The system response to disturbances must be secure and predictable to avoid power blackouts. The system response can be simulated in the time domain. However, this dynamic security assessment (DSA) is not computationally tractable in real-time. Particularly promising is to train decision trees (DTs) from machine learning as interpretable classifiers to predict whether the system-wide responses to disturbances are secure. In most research, selecting the best DT model focuses on predictive accuracy. However, it is insufficient to focus solely on predictive accuracy. Missed alarms and false alarms have drastically different costs, and as security assessment is a critical task, interpretability is crucial for operators. In this work, the multiple objectives of interpretability, varying costs, and accuracies are considered for DT model selection. We propose a rigorous workflow to select the best classifier. In addition, we present two graphical approaches for visual inspection to illustrate the selection sensitivity to probability and impacts of disturbances. We propose cost curves to inspect selection combining all three objectives for the first time. Case studies on the IEEE 68 bus system and the French system show that the proposed approach allows for better DT-selections, with an 80%increase in interpretability, 5%reduction in expected operating cost, while making almost zero accuracy compromises. The proposed approach scales well with larger systems and can be used for models beyond DTs. Hence, this work provides insights into criteria for model selection in a promising application for methods from artificial intelligence (AI).