In this paper, the chaotic bat algorithm (CBA) is applied to solve the optimal reactive power dispatch (ORPD) problem taking into account small-scale, medium-scale and large-scale power systems. ORPD plays a key role in the power system operation and control. The ORPD problem is formulated as a mixed integer nonlinear programming problem, comprising both continuous and discrete control variables. The most outstanding benefit of the bat algorithm (BA) is its good convergence for optimal solutions. The BA, however, together with other metaheuristics, often gets stuck into local optima and in order to cope with this shortcoming, the use of the CBA is proposed in this paper. The CBA results from introducing the chaotic sequences into the standard BA to enhance its global search ability. The CBA is utilized to find the optimal settings of generator bus voltages, tap setting transformers and shunt reactive power sources. Three objective functions such as minimization of active power loss, total voltage deviations and voltage stability index are considered in this study. The effectiveness of the CBA technique is demonstrated for standard IEEE 14-bus, IEEE 39 New England bus, IEEE 57-bus, IEEE 118-bus and IEEE 300-bus test systems. The results yielded by the CBA are compared with other algorithms available in the literature. Simulation results reveal the effectiveness and robustness of the CBA for solving the ORPD problem. INDEX TERMS Chaotic bat algorithm, optimal reactive power dispatch, chaotic sequences.

Because of the non-uniformity of the electric power CPS network and the dynamic nature of the risk propagation process, it is difficult to quantify the critical point of a cyber risk explosion. From the perspective of the dependency network, this paper proposes a method for quantitative evaluation of the risk propagation threshold of power CPS networks based on the percolation theory. First, the power CPS network is abstracted as a dual-layered network-directed unweighted graph according to topology correlation and coupling logic, and the asymmetrical balls-into-bins allocation method is used to establish a "one-to-many" and "partially coupled" non-uniform power CPS characterization model. Then, considering the directionality between the cyber layer and the physical layer link, the probability of percolation flow is introduced to establish the propagation dynamic equations for the internal coupling relationship of each layer. Finally, the risk propagation threshold is numerically quantified by defining the survival function of power CPS network nodes, and the validity of the proposed method is verified by the IEEE 30-bus system and 150-node Barabsi-Albert model. 2169-3536 (c) INDEX TERMS Electric power CPS, interdependent network, Percolation probability, Propagation dynamics

The scale of the electric cyber physical system (ECPS) is continuously extending, and the existing cascade failure models ignore both the information flow and power flow transferring characteristics and also lack effective survivability analysis. In this paper, the quantitative evaluation method for cascading failure of ECPS survivability considering optimal load allocation is proposed. Firstly, according to the system topological structure and correlation, the degree-betweenness weighted correlation matrix of ECPS is established by defining the degree function as well as the electric betweenness, and the formal representation of coupled ECPS network model is realized. Secondly, based on the structural connectivity change and risk propagation range of ECPS cascade failure, the survivability evaluation model is designed by taking into account the constraints such as node load capacity limitation, information flow optimal allocation strategy, power flow optimization equation, and system safety operation. Finally, the firefly algorithm with chaotic Lévy flight is proposed to solve the evaluation model efficiently. The case study vividly shows that the evaluation method can effectively quantify the survivability of ECPS and thus enhance the evaluation efficiency of large-scale coupled systems.

In the process of the detection of a false data injection attack (FDIA) in power systems, there are problems of complex data features and low detection accuracy. From the perspective of the correlation and redundancy of the essential characteristics of the attack data, a detection method of the FDIA in smart grids based on cyber-physical genes is proposed. Firstly, the principle and characteristics of the FDIA are analyzed, and the concept of the cyber-physical FDIA gene is defined. Considering the non-functional dependency and nonlinear correlation of cyber-physical data in power systems, the optimal attack gene feature set of the maximum mutual information coefficient is selected. Secondly, an unsupervised pre-training encoder is set to extract the cyber-physical attack gene. Combined with the supervised fine-tuning classifier to train and update the network parameters, the FDIA detection model with stacked autoencoder network is constructed. Finally, a self-adaptive cuckoo search algorithm is designed to optimize the model parameters, and a novel attack detection method is proposed. The analysis of case studies shows that the proposed method can effectively improve the detection accuracy and effect of the FDIA on cyber-physical power systems.