## 1 Introduction  
As one of the most complex industry systems in the history of mankind, the modern interconnected power system has gradually evolved into a large-scale and sophisticated power intermediary, consisting of power stations, substations, transmissions, distributions and utilization. The security and reliability of the whole electric system are always the primary concern of the practitioners. Acting as an invisible carrier, the power grid transmits the power to factories and households. So far, the largest synchronous power grid in the world is the Eastern North America power grid, which is composed of the Eastern American Grid and part of the Canada Grid. With the development of the economy and the growing demand for electricity, the nation-wide power network of China has already been constructed. With the current construction pace, China will have a power grid with the largest scale worldwide. The power systems easily suffer from various external disturbances, such as simultaneous failures of several generators or major transmission lines, human operation errors, control system failures, hidden failures in the protection system and malicious attacks. These disturbances may make the system lose stability and even lead to catastrophic blackout. As the cascaded events evolve, the angle instability, power oscillations and the significant imbalance between the generation and load are very likely to occur, resulting in a widespread voltage collapse and uncontrolled system partitioning [1]. Blackouts have an irretrievably disastrous impact on people's life and social economy. Many previous studies on blackouts or outages in history, such as the 2003 blackout in North America [2], the 2003 blackout in Italy [3] and the 2006 blackout in Europe [4], indicate that proper and active system splitting could have prevented some blackouts from occurring and reduced the losses significantly [5; 6]. When disturbances that can make the power system out of step occur, the control center would automatically and quickly split the interconnected system into several islands by simultaneously tripping the proper transmission lines [7; 8]; the resultant islands can operate independently, must satisfy their internal synchronous requirements and must keep the balance of generation and load. Actually, power system splitting can be considered as the last defense to avoid the occurrence of catastrophic blackouts. The core of system splitting is to maintain a state of operating balance between generation power and load power. Each island has a generation-load difference, which is defined as the absolute value of the difference between the generation power and the load power. This generation-load difference is used to measure the imbalance of the island. The system splitting is a very complicated procedure in the power system. Recently, [PERSON] _et al._[9] presented a new unified framework to answer three critical questions in the system splitting, which are: \"when to separate?\", \"where to separate?\" and \"what to do after separation?\". This unified framework provides a better idea for studying the system splitting, and the proposed methods in [9] can help either perform the system splitting or predict the unintentional separation. The focus of our paper is to answer the \"where\" question. Therefore, we are dedicated to finding optimal splitting strategies quickly and  
To split the system, the control center works as the following three steps. Firstly, it clusters all generators into different coherent groups based on their angle curves. The methods of identifying the coherent generators can be found in [10; 11; 12]. Secondly, it solves a power system islanding problem (PSIP) that aims to partition the system into several different islands while placing the coherent generators in one island and minimizing the generation-load imbalance of all islands. Finally, it checks whether the transmission lines are loaded above their capacity limits, e.g., thermal capacity limits and steady-state stability limits.