## 1 Introduction  
In recent decades, many cascading outages on transmission grids have occurred worldwide, causing huge disasters to society [1, 2, 3]. Numerous studies have shown that one of the main factors in triggering cascading outages is the unexpected tripping of backup protection caused by load encroachment (LE), which tends to occur when the power system operates under heavy load and is accompanied by faults. Removing the faulty line will result in a grid-wide redistribution of active power, which may cause overloads in other branches of the transmission grid, called LE [4]. Since the conventional backup protection only acts according to the setting and configuration requirements based on local information, it does not consider the impact of fault removal on the overall grid and cannot distinguish whether the line overload is caused by the fault within the protection range or the LE after the faulty line outside the protection range is removed, so it is easy to cause the unexpected action of backup protection, triggering cascading trips and ultimately causing cascading outages. Therefore, the key to preventing cascading outages is to identify the LE reliably, thus achieving the safe and reliable operation of the whole power grid. The three key problems to be solved are: (1) considering the economy and practical feasibility, explore how to reduce the analysis range of branches that are greatly affected by LE; (2) explore a new method for fast real-time calculation of the active power estimation value (APEV) of each branch after active power redistribution; (3) quickly identify the LEoverload and reliably block the backup protection, laying the foundation for the subsequent load-shedding measures. The WAMS can track the dynamic of the power grid and obtain the dynamic data of the whole grid in real-time [4; 5; 6]. In recent years, many experts have proposed a variety of LE identification methods based on wide-area information, accurately distinguishing the short-circuit fault of the transmission line within the protection range or the LE caused by the removal of the faulty line outside the protection range and effectively prevent the cascading trip accident caused by the unexpected action of the conventional backup protection. The authors of reference [7] use the fault chain theory to simulate the process of successive line outages that occur step by step and lead to LE. The authors of reference [8] propose an intelligent distance relay sensing methodology for the differentiation of LE from fault conditions by analyzing the apparent impedance behavior during a fault and LE. However, the method requires high investment and running costs, can be analyzed to a limited extent, and is difficult to apply in the field. In reference [9], the authors identify faults and LE based on real-time measured voltage and current information. In reference [10], LE and faults are distinguished by calculating the ratio of changes in the phase angle and the voltage magnitude of selected buses, thus supplementing backup protection. The authors of reference [11] perform a decomposition of the momentary power to extract the most valid intrinsic mode function and then identified LE and fault by estimating the energy of this mode and comparing it to an adaptive statistical threshold, but the method relies on the accuracy of the statistical threshold. Based on the fault component complex power, the short-circuit fault and LE are distinguished to avoid cascading trips in reference [12]. The authors of reference [13] define the reliability index as the energy of the critical baseline component with the highest peak value and then identify LE and fault based on the energy index. To prevent backup protection tripping due to LE, the authors of reference [14] propose a corrective scheme based on model predictive control, which sequentially reschedules the loads and the generation, thus avoiding undesired actions of the backup protection. The above research is based on the conventional power grid.