## 1 Introduction  
In the past, due to the limitations of battery power, the lifetimes of sensors used in wireless sensor networks heavily depended on the energy provided by the batteries, which made the stability of the whole network greatly uncertain. Various scholars have put forward a range of studies in attempts to solve the problem of limited battery power, including the use of effective routing protocols [1], efforts to ensure efficient energy consumption [2], and so on. However, the above research did not succeed in solving the problem in a fundamental way. Although the advances they proposed can effectively extend the lifespan of the network, the network will still become unusable in the end when the sensors run out of battery power. In addition, if the sensors in a network rely on solar power provided by the sun, the sensors and the overall efficiency of the network will be affected by various environmental factors. In fact, a number of factors can make a sensor unable to operate effectively for extended periods of time. In order to overcome the power constraints of sensing devices, various discussions relating to the concept of wireless power transmission have been started in recent years [3], and the related studies have provided some solutions to the limited lifetimes of wireless sensor networks. Through chargers, electric power is transmitted to radio-frequency identification (RFID) tags [4], sensing devices [5], and terminal equipment. Due to the convenience and rapid development of wireless charging technology, it has attracted the attentions of both academic scholars and industrial professionals. According to the TechNavio market research analysis and forecast [6], the annual growth rate of the global wireless charging market will be more than 33% in 2020--this shows that this field has great potential. How to improve the survival time of wireless sensor networks using wireless power transmission technology is thus a topic that is currently widely discussed and studied [6; 7]. These new types of networks, which enable the use of wireless charging to prolong the lifespan of the network sensors, are called wireless rechargeable sensor networks (WRSNs). In order to make the sensors within the sensing region maintain stable power, the deployment of the wireless chargers becomes the primary consideration. Due to cost considerations, the number of chargers in the region should be minimized to the greatest extent possible. On the other hand, the amount of power supplied to a sensor has an important influence on the performance of the sensor. Therefore, effectively minimizing the number of wireless chargers used in the deployment while also maximizing the charging ability of the wireless chargers is the goal of this research. Although many studies relating to the deployment of wireless chargers have been published in recent years, these studies did not take into account some important factors. For example, previous research has solved the sensor coverage problem without calculating charging power and without considering the existence of the sink node. To overcome these limitations, this study aims to investigate how to set up X directional chargers in a given area. Previous studies assume a uniform power consumption of the sensor nodes, but this is not the case in a realistic setting. The data sink node collects sensing data from all the sensor nodes, and sensor nodes nearby the sink need to facilitate more data forwarding than sensor nodes far away from the sink, so the power consumption of the nodes close to the sink is larger and the area near the sink is called the hot zone [8]. The sensor nodes in the hot zone run out of battery power more quickly than sensor nodes outside the hot zone. When the sensor nodes in the hot zone run out of battery power, the sensor network fails to work properly and this phenomenon is the famous \"energy hole problem\" [9].