In this paper, a novel reduced order model based on a convolutional auto-encoder with self-attention (SACAE ROM) is proposed. The proposed model is a non-intrusive reduced order model, which uses a convolutional neural network and a long short-term memory network to extract temporal feature relationships from high-fidelity numerical solutions. The self-attention is introduced into the convolutional neural network to enhance the non-local information perception ability of the convolutional neural network and improve the feature extraction ability of the network. The model adopts a joint construction method, which overcomes the problem of propagating error in each process of the model. The model proposed in this paper has been verified on the problem of the flow around a cylinder. The experimental results indicate that the SACAE ROM has higher robustness and accuracy. Compared with the ROM based on a convolutional auto-encoder, the prediction error of the SACAE ROM is reduced by 42.9%. As with other ROMs based on deep neural networks, the SACAE ROM takes a long time to train. To solve this problem, the transfer and generalization ability of the model is studied in this paper. In the experiment, the flow velocity and spoiler of the flow around the cylinder were changed, and the training time of the transfer model was reduced by about 50% to 60%. This result demonstrates that the problem of too long training time can be solved by transfer learning.

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The main objective of this article is to develop scalable dynamic anomaly detectors with high-fidelity simulators of power systems. On the one hand, models in high-fidelity simulators are typically "intractable" if one opts to describe them in a mathematical formulation in order to apply existing modelbased approaches from the anomaly detection literature. On the other hand, pure data-driven methods developed primarily in the machine learning literature neglect our knowledge about the underlying dynamics of power systems. In this study, we combine tools from these two mainstream approaches to develop a data-assisted model-based diagnosis filter utilizing both the knowledge from a picked abstract model and also the data of simulation results from high-fidelity simulators. The proposed diagnosis filter aims to achieve two desired features: (i) performance robustness with respect to model mismatch; (ii) high scalability. To this end, we propose a tractable (convex) optimization-based reformulation in which decisions are the filter parameters, the model-based information introduces feasible sets, and the data from the simulator forms the objective function to-be-minimized regarding the effect of model mismatch on the filter performance. To validate the theoretical results, we implement the developed diagnosis filter in DIgSILENT PowerFactory to detect false data injection attacks on the Automatic Generation Control measurements in the three-area IEEE 39-bus system.

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Equilibrium analysis has been widely studied as an effective tool to model gaming interactions and predict market results. However, as competition modes are fundamentally changed by the decarbonization and decentralization of power systems, analysis techniques must evolve. This article comprehensively reviews recent developments in modelling methods, practical settings and solution techniques in equilibrium analysis. Firstly, we review equilibrium in the evolving wholesale power markets which feature new entrants, novel trading products and multi-stage clearing. Secondly, the competition modes in the emerging distribution market and distributed resource aggregation are reviewed, and we compare peer-to-peer clearing, cooperative games and Stackelberg games. Furthermore, we summarize the methods to treat various information acquisition degrees, risk preferences and rationalities of market participants. To deal with increasingly complex market settings, this review also covers refined analytical techniques and agent-based models used to compute the equilibrium. Finally, based on this review, this paper summarizes key issues in the gaming and equilibrium analysis in power markets under decarbonization and decentralization.