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).

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Dynamic Security Assessment (DSA) for the future power system is expected to be increasingly complicated with the higher level penetration of renewable energy sources (RES) and the widespread deployment of power electronic devices, which drive new dynamic phenomena. As a result, the increasing complexity and the severe computational bottleneck in real-time operation encourage researchers to exploit machine learning to extract offline security rules for the online assessment. However, traditional machine learning methods lack in providing information on the confidence of their corresponding predictions. A better understanding of confidence of the prediction is of key importance for Transmission System Operators (TSOs) to use and rely on these machine learning methods. Specifically, from the perspective of topological changes, it is often unclear whether the machine learning model can still be used. Hence, being aware of the confidence of the prediction supports the transition to using machine learning in real-time operation. In this paper, we propose a novel Conditional Bayesian Deep Auto-Encoder (CBDAC) based security assessment framework to compute a confidence metric of the prediction. This informs not only the operator to judge whether the prediction can be trusted, but it also allows for judging whether the model needs updating. A case study based on IEEE 68-bus system demonstrates that CBDAC outperforms the state-of-the-art machine learning-based DSA methods and the models that need updating under different topologies can be effectively identified. Furthermore, the case study verifies that effective updating of the models is possible even with very limited data.

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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.@en

Distribution networks are undergoing fundamental changes at medium voltage level. To support growing planning and control decision-making, the need for large numbers of short-term load forecasts has emerged. Data-driven modelling of medium voltage feeders can be affected by (1) data quality issues, namely, large gross errors and missing observations (2) the presence of structural breaks in the data due to occasional network reconfiguration and load transfers. The present work investigates and reports on the effects of advanced data cleansing techniques on forecast accuracy. A hybrid framework to detect and remove outliers in large datasets is proposed; this automatic procedure combines the Tukey labelling rule and the binary segmentation algorithm to cleanse data more efficiently, it is fast and easy to implement. Various approaches for missing value imputation are investigated, including unconditional mean, Hot Deck via k-nearest neighbour and Kalman smoothing. A combination of the automatic detection/removal of outliers and the imputation methods mentioned above are implemented to cleanse time series of 342 medium-voltage feeders. A nested rolling-origin-validation technique is used to evaluate the feed-forward deep neural network models. The proposed data cleansing framework efficiently removes outliers from the data, and the accuracy of forecasts is improved. It is found that Hot Deck (k-NN) imputation performs best in balancing the bias-variance trade-off for short-term forecasting.@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.

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Transmission expansion planning (TEP) is facing unprecedented challenges with the rise of integrated renewable energy resources (RES), flexible load elements, and the potential electrification of transport and heat sectors. Under this reality, the inadequate information of the stochastic parameters’ behavior may lead to inefficient expansion decisions, especially in the context of very high renewable penetration. This paper proposes a novel data-driven scenario generation framework for the TEP problem to generate unseen but important load and wind power scenarios while capturing inter-spatial dependencies between loads and wind generation units’ output in various locations, using a vine-copula based high-dimensional stochastic variable modeling approach. The superior performance of the proposed model is demonstrated through a case study on a modified IEEE 118-bus system. The expected result of using the expected value problem solution (EEV) and the net benefits of transmission expansion (NBTE) are used as the evaluation metrics to quantitatively illustrate the advantages of the proposed approach. In addition, the case of very high wind penetration is carried out to further highlight the importance of the multivariate stochastic dependence of load and wind power generation. The results demonstrate that the proposed scenario generation method can result in near-optimal investment decisions for the TEP problem that make more net benefits than using limited number of historical data.@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.

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