This paper develops a hierarchical deep learning machine (HDLM) to efficiently achieve both quantitative and qualitative online transient stability prediction (TSP). For the sake of improving its online efficiency, multiple generators' fault-on trajectories as well as the two closest data-points in pre-/post-fault stages are acquired by PMUs to form its raw inputs. An anti-noise graphical transient characterization technique is tactfully designed to transform multiplex trajectories into 2-D images, within which system-wide transients are concisely described. Then, following the divide-and-conquer philosophy, the HDLM trains a two-level convolutional neural network (CNN) based regression model. With stability margin regressions hierarchically refined, it manages to perform reliable and adaptive online TSP almost immediately after fault clearance. Test results on the IEEE 39-bus test system and the real-world Guangdong Power Grid in South China demonstrate the HDLM's superior performances on both stability status and stability margin predictions.

Focusing on fully learning intrinsic spatial and temporal dependencies from smart grids’ complicated transients in a computationally efficient way, this article develops an intelligent machine learning approach for online short-term voltage stability (SVS) assessment. Based on static network information and dynamic system responses, spatial correlations are first comprehensively described from both model-based and data-based viewpoints. Such correlations are further formulated as spatial attention factors, which are leveraged to carefully rectify multiple transient trajectories. Taking the rectified trajectories as inputs, the long short-term memory based deep recurrent neural network (RNN) algorithm is employed to learn sequential SVS features. In this way, the RNN learning procedure is comprehensively guided by both spatial and temporal information, thereby deriving a highly reliable and robust classification model for online SVS assessment. Extensive numerical tests on the Nordic test system and the realistic Guangdong Power Grid in South China illustrate the superior reliability, scalability, and applicability of the proposed approach over existing methods.

To account for the probability distribution information of uncertain scenarios, this letter proposes a novel interval power flow (NIPF) method based on hybrid uncertain sets. Firstly, a NIPF model is established by integrating the hybrid box-ellipsoid sets characterizing uncertainties in interval power flow (IPF), which is solved by the optimizing-scenario method (OSM). Then, a multivariate statistical analysis method (MSAM) and a chance-constrained programming-based method (CCPM) are proposed for determining the optimal radii of the ellipsoid set and side length of the box set under two scenarios, respectively, namely, the normal distributions without correlations and the arbitrary distributions with correlations. Finally, case studies validate the effectiveness and advantage of the proposed method compared with traditional IPF methods based on Monte Carlo simulation, box sets, and ellipsoid sets.

This paper proposes a central limit theorem-based method (CLTM) to overcome the conservatism of interval DC and AC power flow analysis under uncertainty of renewable power generation. Interval DC power flow (IDCPF) models are solved by expressing the bus angle and active transmission power as linear combinations of interval nodal power injections, and then the central limit theorem is applied to obtain high-confidence intervals of DC power flow variables. Interval AC power flow (IACPF) models are solved by first applying the optimizing-scenarios method to acquire more accurate affine arithmetic forms of the power flow variables defined according to linear combinations of nodal power injections, and then high-confidence intervals of AC power flow variables are obtained via the central limit theorem. In addition, a criterion formulation is established to evaluate the errors of interval power flow methods. The results of simulations validate the effectiveness and superiority of the proposed method relative to the performances of previously established methods, including the Monte Carlo simulation, affine arithmetic-based method and optimizing-scenarios method.

The advancing machine learning techniques have been widely applied to data-driven dynamic stability assessment (DSA) in modern smart grids. However, how to extract critical spatial-temporal features from wide-area system stability dynamics still remains an open issue. Emphasizing on short-term voltage stability (SVS) assessment, this paper develops a novel sequential feature learning approach to address this problem in two steps. First, based on visualized voltage contours, it tactfully constructs a comprehensive spatial-temporal sequence model to dynamically characterize multiplex spatial-temporal SVS evolution trends. Second, the time series shapelet classification method is leveraged to subtly extract critical consecutive SVS features in sequential forms, i.e., the multidimensional shapelets (discriminative sub-shapes). Test results on the real-world Hong Kong Power Grid demonstrate the efficacy, adaptability and scalability of the proposed approach for SVS assessment. In addition to the outstanding performances on online DSA, with its favorable interpretability, it is capable of providing intuitive insights into regional SVS patterns from spatial-temporal perspectives.