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.@en

The increasing uncertainty that surrounds electricity system operation renders security assessment a highly challenging task; the range of possible operating states expands, rendering traditional approaches based on heuristic practices and ad hoc analysis obsolete. In turn, machine learning can be used to construct surrogate models approximating the system's security boundary in the region of operation. To this end, past system history can be useful for generating anticipated system states suitable for training. However, inferring the underlying data model, to allow high-density sampling, is problematic due to the large number of variables, their complex marginal probability distributions and the nonlinear dependence structure they exhibit. In this paper, we adopt the C-Vine pair-copula decomposition scheme; clustering and principal component transformation stages are introduced, followed by a truncation to the pairwise dependency modeling, enabling efficient fitting and sampling of large datasets. Using measurements from the French grid, we show that a machine learning training database sampled from the proposed method can produce binary security classifiers with superior predictive capability compared to other approaches.@en

Machine learning techniques have been used in the past using Monte Carlo samples to construct predictors of the dynamic stability of power systems. In this paper we move beyond the task of prediction and propose a comprehensive approach to use predictors, such as Decision Trees (DT), within a standard optimization framework for pre- and post-fault control purposes. In particular, we present a generalizable method for embedding rules derived from DTs in an operation decision-making model. We begin by pointing out the specific challenges entailed when moving from a prediction to a control framework. We proceed with introducing the solution strategy based on generalized disjunctive programming (GDP) as well as a two-step search method for identifying optimal hyper-parameters for balancing cost and control accuracy. We showcase how the proposed approach constructs security proxies that cover multiple contingencies while facing high-dimensional uncertainty with respect to operating conditions with the use of a case study on the IEEE 39-bus system. The method is shown to achieve efficient system control at a marginal increase in system price compared to an oracle model.@en

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.@en

This paper presents a computational platform for dynamic security assessment (DSA) of large electricity grids, developed as part of the iTesla project. It leverages high performance computing to analyze large power systems, with many scenarios and possible contingencies, thus paving the way for pan-European operational stability analysis. The results of the DSA are summarized by decision trees of 11 stability indicators. The platform's workflow and parallel implementation architecture is described in detail, including the way commercial tools are integrated into a plug-in architecture. A case study of the French grid is presented, with over 8000 scenarios and 1980 contingencies. Performance data of the case study (using 10 000 parallel cores) is analyzed, including task timings and data flows. Finally, the generated decision trees are compared with test data to quantify the functional performance of the DSA platform.@en

This paper presents a computational platform for dynamic security assessment (DSA) of large electricity grids, developed as part of the iTesla project. It leverages high performance computing to analyze large power systems, with many scenarios and possible contingencies, thus paving the way for pan-European operational stability analysis. The results of the DSA are summarized by decision trees of 11 stability indicators. The platform's workflow and parallel implementation architecture is described in detail, including the way commercial tools are integrated into a plug-in architecture. A case study of the French grid is presented, with over 8000 scenarios and 1980 contingencies. Performance data of the case study (using 10 000 parallel cores) is analyzed, including task timings and data flows. Finally, the generated decision trees are compared with test data to quantify the functional performance of the DSA platform.@en

This paper presents a computational platform for dynamic security assessment (DSA) of large electricity grids, developed as part of the iTesla project. It leverages high performance computing to analyze large power systems, with many scenarios and possible contingencies, thus paving the way for pan-European operational stability analysis. The results of the DSA are summarized by decision trees of 11 stability indicators. The platform's workflow and parallel implementation architecture is described in detail, including the way commercial tools are integrated into a plug-in architecture. A case study of the French grid is presented, with over 8000 scenarios and 1980 contingencies. Performance data of the case study (using 10 000 parallel cores) is analyzed, including task timings and data flows. Finally, the generated decision trees are compared with test data to quantify the functional performance of the DSA platform.@en

The large-scale integration of intermittent energy sources, the introduction of shiftable load elements and the growing interconnection that characterizes electricity systems worldwide have led to a significant increase of operational uncertainty. The construction of suitable statistical models is a fundamental step towards building Monte Carlo analysis frameworks to be used for exploring the uncertainty state-space and supporting real-time decision-making. The main contribution of the present paper is the development of novel composite modelling approaches that employ dimensionality reduction, clustering and parametric modelling techniques with a particular focus on the use of pair copula construction schemes. Large power system datasets are modelled using different combinations of the aforementioned techniques, and detailed comparisons are drawn on the basis of Kolmogorov-Smirnov tests, multivariate two-sample energy tests and visual data comparisons. The proposed methods are shown to be superior to alternative high-dimensional modelling approaches.@en

The large-scale integration of intermittent energy sources, the introduction of shiftable load elements and the growing interconnection that characterizes electricity systems worldwide have led to a significant increase of operational uncertainty. The construction of suitable statistical models is a fundamental step towards building Monte Carlo analysis frameworks to be used for exploring the uncertainty state-space and supporting real-time decision-making. The main contribution of the present paper is the development of novel composite modelling approaches that employ dimensionality reduction, clustering and parametric modelling techniques with a particular focus on the use of pair copula construction schemes. Large power system datasets are modelled using different combinations of the aforementioned techniques, and detailed comparisons are drawn on the basis of Kolmogorov-Smirnov tests, multivariate two-sample energy tests and visual data comparisons. The proposed methods are shown to be superior to alternative high-dimensional modelling approaches.@en

Supervised machine learning methods were applied to assess the reliability of the power system. Typically, the reliability boundary that defines the operation rules is learned using a training database consisting of a large number of potential operation states. Many of these operation states are historical observations and these are typically all reliable operation states. However, to learn a classifier that can predict unseen operation states requires unreliable operation states as well. Thus, a statistical model is typically fitted to the historical observations, and then, unreliable operation states are sampled from this model. Still, the share of reliable states may be much larger than the portion of unreliable states. This imbalance in the data results in biasing the learning methods toward predicting reliable states with higher accuracy than unreliable states. However, an unreliable operating state involves (per-definition) a risk of failing system operation. Therefore, a higher accuracy is required in predicting unreliable states rather than in reliable states. This paper focuses on accounting for this bias when learning from imbalanced data. To optimally learn operation rules for an imbalanced training database a novel Optimal Classification Tree (OCT) is applied. We modify the OCT approach to address the corresponding bias that is introduced in an imbalanced training database. Our fully Controllable and Optimal Classification Tree (COCT) approach controls directly in the objective function the class weights of each operation state that is used for training. By using a database from the French transmission grid it is showcased how the proposed COCT method results in fewer missed alarms than the standard approach that is used to learn operation rules.@en