This paper presents a model of cascading failures in cyber-physical power systems (CPPSs) based on an improved percolation theory, and then proposes failure mitigation strategies. In this model, the dynamic development of cascading failures is divided into several iteration stages. The power flow in the power grid, along with the data transmission and delay in the cyber layer, is considered in the improved percolation theory. The interaction mechanism between two layers is interpreted as the observability and controllability analysis and data update analysis influencing the node state transformation and security command execution. The resilience indices of the failures reflect the influence of cascading failures on both topological integrity and operational state. The efficacy of the proposed mitigation strategies is validated, including strategies to convert some cyber layer nodes into autonomous nodes and embed unified power flow controller (UPFC) into the physical layer. The results obtained from simulations of cascading failures in a CPPS with increasing initial failure sizes are compared for various scenarios. Dynamic cascading failures can be separated into rapid and slow processes. The interdependencies and gap between the observable and controllable parts of the physical layer with the actual physical network are two fundamental reasons for first-order transition failures. Due to the complexity of the coupled topological and operational relations between the two layers, mitigation strategies should be simultaneously applied in both layers.

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The blackout risks of cascading failures in power systems are notably associated with the failures of transmission lines. Line capacity temporary expansion can reduce blackout risk by decreasing the line failures due to the overloads during the cascading failures. To efficiently quantify the impact of line capacity temporary expansion on blackout risks, we propose a data based state-failure-network method in this paper. The state-failure network, which is formed by the cascading failure data generated by cascading failure simulations, contains the empirical probabilities that correspond to the failure probabilities of lines. Since implementing line capacity temporary expansion to the system can change the failure probabilities of lines and reduce the blackout risk, the empirical probabilities offer the link between line capacity temporary expansion and state-failure network. By updating the values in the state-failure network with changed empirical probabilities, the blackout risk after line capacity temporary expansion is implemented can be efficiently worked out by state-failure network. Thus, the impact of line capacity temporary expansion on blackout risk is quantified by comparing the newly calculated blackout risk with the risk before the line capacity temporary expansion is implemented. The advantage of the proposed method lies in the high accuracy and efficiency of quantifying the impacts of any line capacity temporary expansion schemes once the state-failure network is formed. Case studies verify the accuracy and efficiency of the proposed method.INDEX TERMS Blackout risk, cascading failures, state-failure-network method, line capacity temporary expansion.

The hidden failures generally exist in power systems and could give rise to cascading failures. Identification of hidden failures is challenging due to very low occurrence probabilities. This paper proposes a state-failure-network (SF-network) method to overcome the difficulty. The SF-network is formed by searching the failures and states guided by risk estimation indices, in which only the failures and states contributing to the blackout risks are searched and duplicated searches are avoided. Therefore, sufficient hidden failures can be obtained with acceptable computations. Based on the state and failure value calculations in the SF-network, the hidden failure critical component indices can be obtained to quantify the criticalities of the lines. The proposed SF-network method is superior to common sampling based methods in risk estimation accuracy. Besides, the state and failure value calculations in the SFnetwork used to re-estimate the risks after deployment of measures against hidden failures need shorter time in comparison with other risk re-estimation methods. The IEEE 14-bus and 118-bus systems are used to validate the method.

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