# Adaptive Energy Balanced Routing Strategy for Wireless Reschargeable Sensor Networks
## 3 Charging Strategy  
In WRSN, the sensor nodes send packets to the sink node hop-by-hop, and some nodes undertake more data transmission tasks and thus consume energy faster. In case of the early death of such nodes, we allocate charging time at different charging points on the basis of the average energy consumption of nearby nodes, and dynamically plan the location of the charging points to reduce the difference of the charging efficiency of nodes, so that those nodes that consume more energy can obtain more energy in the charging stage. Through this way, we achieve the purpose of balancing the network energy and prolonging the node survival time.  
According to Equation (3), the energy that nodes obtain in charging period is positively correlation with charging efficiency and charging time. For the nodes farther away from the charging points, their charging efficiency is lower, so those nodes tend to acquire less energy during the charging cycle. Moreover, the high energy consumption nodes with insufficient charging energy may stay in the low energy state, and then die earlier. Meanwhile, the nodes near the charging points have a high charging efficiency, and they often obtain more energy than average level in each charging cycle, which can easily lead to charging saturation. In order to change the imbalance of charging energy caused by the difference of charging efficiency, the positions of the charging points are changed at the end of each charging cycle, so that the charging efficiency of each node changes in different charging cycles. After several charging cycles, the energy obtained by nodes with the same distance from the charging path will be more balanced, and the charging effect can be improved.  
The sum of charging time at each charging points is fixed, which is recorded as the charge cycle \(T_{c}\). After each charge cycle, the angle formed by a new position of charging point to sink node and the last position of charging point to sink node is \(\theta_{\rm v}\). Here, it should be noted that the charging points turn back to original position after every \(nc\) cycles later. For example, when \(nc=2\), the position before and after turning is shown in Figure 2. And \(\theta_{\rm v}\) can be expressed as:  
\[\theta_{\rm v}=\frac{2\pi}{|s_{\rm v}|\times nc},nc\in\{1,2,3,4,5,\ldots\} \tag{5}\]  
Hence, the charging point \(p_{\rm v}^{u}\) on \(r_{\rm v}\) will rotate to different positions in different charging cycles, and the energy consumptions of the surrounding sensor nodes will be different. Furthermore, we set the charging time of each charging point on the same path \(r_{\rm v}\) to be the same, which is recorded as \(t_{\rm v}\). It satisfies:  
\[\big{|}s_{1}\big{|}t_{1}+\big{|}s_{2}\big{|}t_{2}+\ldots+\big{|}s_{L/2d}\big{|} t_{L/2d}=T_{c} \tag{6}\]  
After that, in order to recharge more energy for those nodes with higher energy consumption in the network, the charging time of them should be extended appropriately. Since the charging time on the same charging path is the same, if the average energy consumption rate of the nodes within the charging range of the charging point on \(r_{\rm v}\) is faster, the charging time \(t_{\rm v}\) should be higher correspondingly. The average energy consumption of all nodes charged by WCV on \(r_{\rm v}\) is recorded as:  
\[aveE_{\rm v}=\sum_{i\in M_{\rm v}}\left(E_{0}-E_{i}\right)/|M_{\rm v}| \tag{7}\]  
where \(E_{0}\) is the initial energy of sensor node, \(E_{i}\) is the residual energy of node \(i\), \(M_{\rm v}\) is the node set charged by the WCV on \(r_{\rm v}\) and \(|M_{\rm v}|\) is the total number of elements in the set \(M_{\rm v}\).  
To ensure that the charging time \(t_{\rm v}\) is positively correlated with the average energy consumption of the sensor nodes, the charging time of the charging points on each path satisfies:  
\[t_{1}/aveE_{1}=t_{2}/aveE_{2}=\ldots=t_{\frac{t_{\rm L}}{\Omega}}/aveE_{\frac{t _{\rm L}}{\Omega}} \tag{8}\]