As safety-critical systems, grid cyber-physical systems (GCPSs) are required to ensure the safety of power-related systems. However, in many cases, GCPSs may be subject to uncertain and nondeterministic environmental hazards, as well as the variable quality of devices. They can cause failures and hazards in the whole system and may jeopardize system safety. Thus, it necessitates safety analysis for system safety assurance. This paper proposes an architecture-level safety analysis approach for GCPSs applying the probabilistic model-checking of stochastic games. GCPSs are modeled using Architecture Analysis and Design Language (AADL). Random errors and failures of a GCPS and nondeterministic environment behaviors are explicitly described with AADL annexes. A GCPS AADL model including the environment can be regarded as a game. To transform AADL models to stochastic multi-player games (SMGs) models, model transformation rules are proposed and the completeness and consistency of rules are proved. Property formulae are formulated for formal verification of GCPS SMG models, so that occurrence probabilities of failed states and hazards can be obtained for system-level safety analysis. Finally, a modified IEEE 9-bus system with grid elements that are power management systems is modeled and analyzed using the proposed approach.

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Once an active distribution network of a cyber-physical system is in alert state, it is vulnerable to cross-domain cascading failures. It is necessary to transit the state of an active distribution network of cyber-physical system from an alert state to a normal state using a preventive control policy against cross-domain cascading failures. In fact, it is difficult to construct and analyze a preventive control policy via theoretical analysis methods or physical experimental methods. The theoretical analysis methods may not be accurate due to approximated models, and the physical experimental methods are expensive and time consuming for building prototypes. This paper presents a preventive control policy construction method based on a deep deterministic policy gradient idea (shorted as PCMD) to generate and optimize a preventive control policy with Artificial Intelligence (AI) technologies. It adopts the reinforcement learning technique to make full use of the available historical data to overcome the problems of high cost and low accuracy. Firstly, a preventive control model is designed based on the finite automaton theory, which can guide the data collection and learning policy selection. The control model considers the voltage stability, frequency stability, current overload prevention, and the control cost reduction as a feedback variable, without the specific power flow equations and differential equations. Then, after enough training, a local optimal preventive control policy can be constructed under the comparability condition among a fitted action-value function and a fitted policy function. The constructed preventive control policy contains some control actions to achieve a low cost and in accord with the principle of shortening a cross-domain cascading failures propagation sequence as far as possible. The PCMD is more flexible and closer to reality than the theoretical analysis methods and has a lower cost than the physical experimental methods. To evaluate the performance of the proposed method, an experimental case study, China Electric Power Research-Cyber-Physical System (shorted as CEPR-CPS), which comes from China Electric Power Research Institute, is carried out. The result shows that the effectiveness of preventive control policy construction with the PCMD is better than most current methods, such as the multi-agent method in terms of reducing the number of failure nodes and avoiding the state space explosion.

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Active distribution networks (ADNs) are a typical cyber-physical system (CPS), which consist of two kinds of interdependent sub-networks: power networks (PNs) and communication networks (CNs). The combination of typical characteristics of the ADN includes (1) a large number of distributed generators contained in the PN, (2) load redistribution in both the PN and CN,and (3) strong interdependence between the PN and CN, which makes ADNs vulnerable to cross-domain cascading failures (CCFs). In this paper, we focus on the robustness analysis of the ADN against the CCF. Rather than via the rate of the clusters with size greater than a predefined threshold, we evaluate the robustness of the ADN using the rate of the clusters containing generators after the CCF. Firstly, a synchronous probabilistic model is derived to calculate the proportions of remaining normal operational nodes after the CCF. With this model, the propagation of the CCF in the ADN can be described as recursive equations. Secondly, we analyze the relationship between the proportions of remaining normal operational nodes after the CCF and the distribution of distributed generators, unintentional random initial failure rate, the interdependence between the sub-networks, network topology, and tolerance parameters. Some results are revealed which include (1) the more distributed generators the PN contains, the higher ADN robustness is, (2) the robustness of the ADN is negatively correlated with the unintentional random initial failure rate, (3) the robustness of the ADN can be improved by increasing the average control fan in of each node in the PN and the average power fan in of each node in the CN, (4) the robustness of the ADN with Erdos-Renyi (ER) network topological structure is greater than that with Barabasi-Albert (BA) network topological structure under the same average node degree, and (5) the robustness of the ADN is greater, when the tolerance parameters increase. Lastly, some simulation experiments are conducted and experimental results also demonstrate that the conclusions above are effective to improve the robustness of the ADN against the CCF.Appl. Sci. 2019, 9, 5021 2 of 32 electricity [3]. As shown in Figure 1, the ADN is a large complex network that consists of two interdependent sub-networks: power networks (PNs) and communication networks (CNs) [4]. The PN is composed of the power equipment, such as generators, transmission lines, substations, and loads, etc. The CN is composed of the information equipment, such as sensors, computers, communication lines, data storage, and actuators, etc. All these equipment are interconnected according to a certain topological structure. Some nodes in the PN supply power to the nodes in the CN, meanwhile some nodes in the CN collect information of the nodes in the PN and thus to control the actions of them. In general, the operational process of the ADN includes the physical process and the computational process. The physical process can be described by the continuous change of the PN parameters (e.g....