## 1 Introduction  
At present, protection schemes play an important role in smart grid operation in terms of security and safety. During the development of a smart power grid, protection scheme reliability has taken priority over verification of whole system security [1]. While reinforcing the systems of protection guarantees grid reliability, the probability of their false function may increase owing to higher complexity [2]. It has been experienced that the hidden failures in the protection devices can lead to cascading outages, which in turn can cause widespread power grid blackouts. A study has been reported by the North American Electric Reliability Council (NERC) in which protective devices are involved in about 75%of main disturbances [3]. Several widespread cascading outages have turned up in recent years, affecting vast customers in the United States. All of these reported blackouts were associated with protection devices' hidden failures due to other system disturbances [4; 5]. Such cases, as mentioned above, create network vulnerable points. In the status quo, the operators have to get a line on the vulnerability of the power system due to the upsurge in the power grid intricacy and continuous development of it [6]. The vulnerability phrase does not have any general determinate description. Suitable ability to tolerate all contingencies, stabilize and recover without passing limits of the system is the commonly accepted description for a power grid, which is named an invulnerable network [7]. In other words, the weaknesses and susceptibility that make damage to the power grid likely are called vulnerability. Several indices and approaches have been introduced in the literature. References [8; 9; 10; 11] propose ranking approaches based on certain performance indices, which consider information as well as active and reactive power, bus voltages of the power grid. Authors in [8] have tried to provide a deep-learning-based effective method in order to model the security-constrained optimal power flow considering the automatic primary response of generation units. This reference has represented the machine learning models' effectiveness at finding feasible solutions. Also assessing the vulnerability of the electrical grid has been investigated in [9; 10; 11]. The vulnerable points in the network can be categorized based on (1) the steady-state vulnerability assessment (SSVA) (2) dynamic vulnerability assessment (DVA) as expressed by the authors of [12]. Authors in [13] have proved that the vulnerability assessment is significant to examine the validation of measures in the electrical grid. It is important to say that having a close look at the uncertainty and contingency effects on the power system operation takes more attention in recent investigations. Hence, references [14; 15] have provided an effective model based on grid operation taking into account the different contingencies in the electrical grid. Authors in [16; 17] have tried getting into a comprehensive survey of uncertainty modeling emerging from renewable sources within a smart grid. The presence of uncertain parameters in the grid causes the emergence of vulnerability challenges facing the electrical power operation, which is proven in [18; 19; 20]. Authors in [18] have proposed a two-stage adaptive robust optimization model to get an immunized solution for vulnerability under uncertain conditions. In this method, some decisions have been made before the uncertainty in the first stage. Then, the defender decision as a second stage is considered after the uncertainty. The reconfiguration of lines in the radial electrical grids can be introduced as an appropriate solution to analyze the vulnerable points under uncertain conditions concerning reference [19]. Authors in [20] have tried to present a mixed OPF-stochastic cascading failure model to assess the uncertainty and vulnerability of a smart grid.