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In modern highly interconnected power grids, automatic generation control (AGC) is crucial in maintaining the stability of the power grid. The dependence of the AGC system on the information and communications technology (ICT) system makes it vulnerable to various types of cyber-attacks. Thus, information flow (IF) analysis and anomaly detection became paramount for preventing cyber attackers from driving the cyberphysical power system (CPPS) to instability. In this paper, the ICT network traffic rules in CPPSs are explored and the frequency domain features of the ICT network traffic are extracted, basically for developing a robust learning algorithm that can learn the normal traffic pattern based on the ResNeSt convolutional neural network (CNN). Furthermore, to overcome the problem of insufficient abnormal traffic labeled samples, transfer learning approach is used. In the proposed data-driven-based method the deep learning model is trained by traffic frequency features, which makes our model robust against AGC's parameters uncertainties and modeling nonlinearities.

Distributed stochastic optimization, arising in the crossing and integration of traditional stochastic optimization, distributed computing and storage, and network science, has advantages of high efficiency and a low per-iteration computational complexity in resolving large-scale optimization problems. This paper concentrates on resolving a large-scale convex finite-sum optimization problem in a multi-agent system over unbalanced directed networks. To tackle this problem in an efficient way, a distributed consensus optimization algorithm, adopting the push-sum technique and a distributed loopless stochastic variance-reduced gradient (LSVRG) method with uncoordinated triggered probabilities, is developed and named Push-LSVRG-UP. Each agent under this algorithmic framework performs only local computation and communicates only with its neighbors without leaking their private information. The convergence analysis of Push-LSVRG-UP is relied on analyzing the contraction relationships between four error terms associated with the multi-agent system. Theoretical results provide an explicit feasible range of the constant step-size, a linear convergence rate, and an iteration complexity of Push-LSVRG-UP when achieving the globally optimal solution. It is shown that Push-LSVRG-UP achieves the superior characteristics of accelerated linear convergence, fewer storage costs, and a lower per-iteration computational complexity than most existing works. Meanwhile, the introduction of an uncoordinated probabilistic triggered mechanism allows Push-LSVRG-UP to facilitate the independence and flexibility of agents in computing local batch gradients. In simulations, the practicability and improved performance of Push-LSVRG-UP are manifested via resolving two distributed learning problems based on real-world datasets.

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