## 1 Introduction  
The current bulk power systems require a high level of reliability. To improve the reliability of a power grid, system operators analyze N-1 contingencies, monitor the system margins and develop new technologies such as High Voltage Direct Current (HVDC) and Flexible AC Transmission Systems (FACTS) which have been introduced. Nevertheless, there is the possibility of total and partial blackouts. According to recent blackouts [1, 2], large blackouts can be described as cascading outages, as shown Figure 1. Cascading outages occur sequentially, and they are caused by an initial disturbance. The initial disturbance includes natural disasters, unexpected accidents, misoperation of a facility and imbalanced power systems. It causes sequential trips of facilities such as transmission lines, transformers and generators. Sequential outages are propagated until the system fails to recover due to voltage instability and thermal violations which are alleviated or drop below the operating limits. Eventually, a partial or total blackout occurs. Once the blackouts have occurred, the appropriate system restoration should be performed. Most blackouts are partial and can be restored with the support of neighboring regions [3, 4]. On the other hand, if total blackouts occur, neighboring regions may be not able to assist the system, especially for isolated power systems such as Korean power systems. For isolated systems, a reliable restoration method is more essential than interconnected power systems. When a total blackout  
Figure 1: Typical blackout procedure. occurs in isolated systems, the whole system is usually divided into several subsystems to restore the system as quickly as possible [5], and subsystems are restored in parallel. After the restoration of each subsystem, all subsystems are synchronized. Each subsystem must have at least one black start unit and should be balanced between generation and load [6]. Additionally, each subsystem must satisfy the following reliability criteria: real and reactive power balance, thermal constraints on transmission lines, being sustained over voltages during early restoration, and maintaining a steady state and transient stability during restoration. Figure 2 shows the general black start procedure [7; 8; 9]. First, when a blackout occurs, the status of the power systems is checked through an alarm or communication. In this step, the size and status of the blackout are evaluated. Afterwards, the generators in the systems are identified using their location and capacity and the proximity to the grid. Based on the confirmed information, the sequence of the generators is established [10; 11]. According to the sequence, the generators in the systems are started. While monitoring the power systems and identifying the connectivity of the system, the path for restoration is searched. The transmission lines and transformers on the paths are re-energized, and the load is restored depending on the system balance [12; 13; 14]. During the restoration stage, three limitations are needed to maintain the range: the voltage of the bus, the overload rate of the transmission lines and the frequency of the grid. The restoration sequence of non-black start units, transmission lines, and transformers is different according to the objective function of each system's restoration methodology. Many domestic and foreign studies have been performed, and each Independent System Operator (ISO) has a different restoration methodology [15; 16]. After a complete blackout occurs, the Australian Energy Market Operator (AEMO) in Australia aims to supply power to major generators in 90 minutes and to restore 40% of the system peak load in four hours [17; 18; 19]. The Pennsylvania New Jersey Maryland (PJM) ISO in USA intends to restore 80% of the whole system load in 16 hours and to implement the system restoration with the priority of system stability [20; 21]. The Electric Reliability Council of Texas (ERCOT) ISO in USA aims to restore the whole system within the shortest amount of time [22].