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Various supervised machine learning approaches have been used in the past to assess the power system security (also known as reliability). This is typically done by training a classifier on a large number of operating points whose postfault status (stable or unstable) has been determined via time-domain simulations. The output of this training process can be expressed as a security rule that is used online to classify an operating point. A critical, and little-studied aspect of these approaches is the interpretability of the rules produced. The lack of interpretability is a well-known issue of some machine learning approaches, especially when dealing with difficult classification problems. In the case of the security assessment of the power system, which is a complex mission-critical task, interpretability is a key requirement for the adoption and deployment by operators of these approaches. In this paper, for the first time, we explore the tradeoff between predictive accuracy and interpretability in the context of power system security assessment. We begin by demonstrating how decision trees (DTs) can be used to learn data-driven security rules and use the tree depth as a measure for interpretability. We leverage disjunctive programming to formulate novel training methods, capable of learning high-quality DTs while still maintaining interpretability. In particular, we propose two new approaches: 1) optimal classification trees is proposed for training DTs of low-depth and 2) greedy optimization-based tree is proposed for training DTs of intermediate depth, where the increased computational burden is managed by exploiting the nested tree structure. We also demonstrate that the ability to generate high-quality interpretable rules can actually translate to impressive benefits in terms of training requirements. Through case studies on the IEEE 68-bus system, we demonstrate that the proposed methods can produce DTs of higher quality compared to the state-of-the-art approach classification and regression tree approach, also if the DT was trained on a significant smaller database, resulting in computational savings of 80%. Given that generating a large training database is a practical bottleneck in these data-driven approaches, this is a significant breakthrough for real-world application. [ABSTRACT FROM AUTHOR]

Supervised machine learning has been successfully used in the past to infer a system's security boundary by training classifiers (also referred to as security rules) on a large number of simulated operating conditions. Although significant research has been carried out on using classifiers for the detection of critical operating points, using classifiers for the subsequent identification of suitable preventive/corrective control actions remains underdeveloped. This paper focuses on addressing the challenges that arise when utilizing security rules for control purposes. Illustrative examples and case studies are used to show how even very accurate security rules can lead to prohibitively high risk exposure when used to identify optimal control actions. Subsequently, the inherent tradeoff between operating cost and security risk is explored in detail. To optimally navigate this tradeoff, a novel approach is proposed that uses an ensemble learning method (AdaBoost) to infer a probabilistic description of a system's security boundary. Bias in predictions is compensated by the Platt Calibration method. Subsequently, a general-purpose framework for building probabilistic and disjunctive security rules of a system's secure operating domain is developed that can be embedded within classic operation formulations. Through case studies on the IEEE 39-bus system, it is showcased how security rules derived from supervised learning can be efficiently utilized to optimally operate the system under multiple uncertainties while respecting a user-defined balance between cost and risk. This is a fundamental step toward embedding data-driven models within classic optimisation approaches. [ABSTRACT FROM AUTHOR]

• A metric to quantify the impact of topology changes on the accuracy of DSA models. • A construction method for training databases following high-impact topology changes. • Robustness against frequent changes in the network topology. • Study on the IEEE 68-bus system shows improvements in the accuracy up-to 52 %. • Study on the IEEE 68-bus system shows a reduction of up-to 85 % in the training data. Machine learning has been used in the past to construct predictors, also known as classifiers, for dynamic security assessment. Although accurate classifiers can be trained for a single topology, often they do not work for another. However, the power system topology can change frequently during operation due to maintenance and control actions. At one topological configuration, the system may have a different response to a fault than at another as the underlying distribution of power flows can be completely different. Quantifying the impact of changes in the topology on the predictive models' performance is an important step forward to minimize inaccurate predictions and improve their reliability. In this paper, for the first time, a metric for quantifying the impact of a topology change on the accuracy of the classification model is proposed. The key novelty is to first select a subset of power flow features with a physically informed feature selection technique and subsequently compute the metric with a novel convex hull-based analysis. In addition, the approach can advise to effectively constructing new training databases that improve the accuracy of new machines trained after high-impact topology changes. Through a case study using transient stability on the IEEE 68 -bus system, the use of the proposed metric in real-time operation was demonstrated. 17 high-impact topology changes were successfully detected among 42 studied topological changes. The subsequent effective construction of the training database improved the predictive accuracy by around 10 %. An interesting finding is the amount of newly generated data can be reduced by up to 85 % as often the generated data is the barrier for data-driven DSA. The proposed workflow significantly reduces data and trains robust classifiers against topological changes marking a fundamental step forward. [ABSTRACT FROM AUTHOR]

• A novel causality-based feature selection approach for online dynamic security assessment. • A combination between the causality-based feature selection approach and a three-stages workflow for fast, accurate and interpretable security predictions. • Robustness against frequent changes in the probability distributions of the operating conditions. • Case study on the IEEE 68-bus system shows superiority in accuracy, robustness and computational time (e.g., up-to 75% speed-up). • Projections to the French transmission system shows benefits in computational savings of two orders of magnitude. The integration of renewable energy sources increases the operational uncertainty of electric power systems and can lead to more frequent dynamic phenomena. The use of classifiers from machine learning is promising to include dynamics in the security assessment of the power system. The training of these classifiers is typically performed offline on synthetically generated operating conditions (OCs) that are similar to real-time operation. However, the uncertainty in the generated OCs and the classifier's inaccuracy is larger the longer the time between offline and real-time operation. Moving the classifier training closer to real-time operation is an important step forward to reduce inaccurate predictions and improve reliability. In this paper, a novel causality-based feature selection approach for an online dynamic security assessment (DSA) framework is proposed. The key novelty is to use the system's physics to learn the causal structure between the features and then select the features based on this causal structure. The proposed approach results in faster computations, is more robust and more interpretable. Moreover, classifiers can be trained closer to real-time operation which enhances the predictive performance. Through a case study using transient stability on the IEEE 68-bus system, the proposed method reduces computational time by 75% in comparison to state of the art feature selection techniques. The proposed workflow showed superior performance in accuracy and robustness against uncertainty compared to conventional machine learning approaches for DSA. The computational benefit was also projected to a dataset of the French transmission system where the approach has the potential to achieve computational savings of up-to two orders of magnitudes. [ABSTRACT FROM AUTHOR]

• A risk-metric for using machine learning in probabilistic security assessment. • A calibrated training process for accurate probability outputs of machine learning. • A probabilistic balance of machine learning with conventional security assessment. • Robustness against frequent changes in likelihood of contingencies. • Study on French system shows superiority in accuracy, robustness, and 90 % speed-up. Probabilistic security assessment and real-time dynamic security assessments (DSA) are promising to better handle the risks of system operations. The current methodologies of security assessments may require many time-domain simulations for some stability phenomena that are unpractical in real-time. Supervised machine learning is promising to predict DSA as their predictions are immediately available. Classifiers are offline trained on operating conditions and then used in real-time to identify operating conditions that are insecure. However, the predictions of classifiers can be sometimes wrong and hazardous if an alarm is missed for instance. A probabilistic output of the classifier is explored in more detail and proposed for probabilistic security assessment. An ensemble classifier is trained and calibrated offline by using Platt' scaling to provide accurate probability estimates of the output. Imbalances in the training database and a cost-skewness addressing strategy are proposed for considering that missed alarms are significantly worse than false alarms. Subsequently, risk-minimised predictions can be made in real-time operation by applying cost-sensitive learning. Through case studies on a real data-set of the French transmission grid and on the IEEE 6 bus system using static security metrics, it is showcased how the proposed approach reduces inaccurate predictions and risks. The sensitivity on the likelihood of contingency is studied as well as on expected outage costs. Finally, the scalability to several contingencies and operating conditions are showcased. [ABSTRACT FROM AUTHOR]